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This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds,... more... more...
Help your employees flex their mental muscles. This book explains why increasing mental agility leads to heightened innovation and creativity in the workplace.
In Retrain Your Business Brain, restructuring expert and business consultant Donalee Markus, Ph. more... |
MATH 240
Using a calculator
Solving a system of linear equations on a computer or calculator
is surprisingly difficult.
Inverting a matrix or performing certain other matrix operations
can lead to numerical errors that require a lot of theory to understand.
Our department has an entire undergraduate course,
Math 434, Numerical Linear Algebra,
that covers numerical techniques in linear algebra.
We do not have enough time to discuss numerical algorithms in MATH 240,
and if you do not know the relevant theory,
you must be very cautious and skeptical about the answer
when you just press a button on your calculator.
Solving a system of equations
If you have been trained to believe that
a calculator will always give you the correct answer,
you may be in for a shock
if you try to solve a system of equations
by just plugging the coefficients into your calculator and pressing a button.
Even a system of two equations in two unknowns
can present problems for the program used by your calculator.
Here is one example.
We will try to solve this system of equations.
416785x + 415872y = 1
415872x + 414961y = 0
The coefficients in the problem have six significant digits.
Since the TI-85 calculator stores more than twice that many
significant digits internally,
solving the system would seem to present no problem.
Using the equation solver on the TI-85 gives the following "answer".
You can "check" the calculator answer by substituting it
back into the system.
Be sure to use the values stored in the calculator.
Then, to the limits of the calculator's accuracy,
everything checks out,
and, in fact, both solutions appear to be correct.
To find the exact solution,
we can use elementary row operations on the system of equations.
The first goal is to reduce the size of the numbers,
but retain integer values.
Here are the results.
This is not a problem unique to the TI-85.
Using MATLAB on a SUN workstation also gives
an answer that differs substantially from the correct one.
The difficulties are inherent in the problem.
To look at this problem from the geometric point of view,
we could compute the slope of each line.
To 12 decimal point accuracy, we get
416785 ÷ 415872 = -1.00219538704
415872 ÷ 414961 = -1.00219538704
To most calculators, the lines appear to be parallel,
and so there should be no solution at all!
Because the angle between the two lines is very small,
a small change in the coefficients caused by roundoff error
can make a very large difference in the solution.
From a geometric point of view,
shifting the two lines just a little bit
can make a bit difference in the point of intersection.
Inverting a matrix
In the previous problem,
we were able to find an exact inverse for the coefficient matrix.
To illustrate some of the inherent difficulties
in doing Gaussian elimination using floating point arithmetic,
we will look at the row reduction of a standard "badly behaved" matrix.
The matrix given below is called a Hilbert matrix.
It is a well-known example of a matrix that causes problems
for numerical algorithms.
To help understand the problems,
we will do an exact row reduction,
compared to a row reduction done using floating point arithmetic.
To see how the error in the approximations can be compounded,
we will use a highly simplified example,
in which the floating point arithmetic
is carried out with accuracy to only three significant digits.
In the original matrix, labeled (1),
some of the decimal entries are already inaccurate.
In matrix (3), the three digit computation that produces the
3rd entry in row 4 is this:
.837×10-1 - (.904)(.830×10-1)
= .837×10-1 - .750×10-1
= .870×10-2
Comparing this to the correct value of
1 ÷ 120 = .00833 (to 3 digits)
shows that it has only one correct digit.
In matrix (5), the last entry of row 4 is computed as follows:
.837×10-2 - (.690)(.127×10-1)
= .837×10-2 - .876×10-2
= .006×10-2
Because we have to subtract two values that are nearly equal,
the answer has even less accuracy.
The cumulative errors in reducing just 3 rows
produce a value of -.0000600 instead of
(-1) ÷ 4200 = -.000238 (to 3 digits).
The method for defining a Hilbert matrix can be extended to larger sizes,
and the 10 by 10 Hilbert matrix presents substantial problems
for even a very sophisticated numerical algorithm.
You can experiment on your calculator,
by inverting the Hilbert matrices of larger and larger sizes.
REFERENCES
Yves Nievergelt,
Numerical Linear Algebra on the HP-28 or How to Lie With Supercalculators,
American Mathematical Monthly, (1991), 539-544 |
Assessment and LEarning in Knowledge Spaces (ALEKS) is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics they are most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics are also retained.
The Basic Algebra courses will be taught using the software ALEKS. It is possible for students to accelerate through the Basic Algebra sequence by completing the courses early and then following the change of section process. This process starts with printing the Math Emporium Course Section Change Form (See below) and going to see your current Basic Algebra instructor. Have the instructor fill out the top of the form and bring the signed form to the Math Department located in MSB 233. |
An engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them, focusing on interpolation and regression models.
The methods and examples are taken from a wide range of scientific and engineering fields, including chemical engineering, electrical engineering, physics, medicine, and environmental science.
The material is based on several courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested. The required software is provided by way of a freely accessible program library at the University of Milan that provides up-to-date software tools for all the methods described in the book.
Buy Both and Save 25%!
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Interpolation and Regression Models for the Chemical Engineer (US $130.00) |
Learning Goals and Outcomes
Mathematics Learning Goals
At all levels, Georgetown undergraduates gain knowledge of the following through courses in mathematics:
• Fundamental objects, techniques and theorems in the mathematical sciences, including the fields of analysis, algebra, geometry, and discrete mathematics;
• The principles of mathematical reasoning and their use in understanding, analyzing and developing formal arguments;
• The connections between the mathematical sciences and other scientific and humanistic disciplines;
• The main forces driving the evolution of the mathematical sciences and their past relevance and future potential for the broader society.
Mathematics Learning Outcomes
Through active study of this core body of knowledge, Georgetown mathematics students at all levels develop their ability to:
• Make significant progress on typical mathematical problems previously unfamiliar to them, using appropriate techniques and tools;
• Formulate precise and relevant conjectures based on examples and counterexamples, prove or disprove conjectures, and translate between intuitive understandings and formal definitions and proofs;
• Construct, modify and analyze mathematical models of systems encountered in disciplines such as physics, economics or biology, assess the models' accuracy and usefulness, and draw contextual conclusions from them;
• Clearly communicate mathematical ideas in appropriate contexts both orally and in writing to a range of audiences, including the educated general public.
Statistics Learning Goals
At all levels, Georgetown undergraduates gain knowledge of the following through courses in statistics:
• Fundamentals of probability models and theory underlying statistical methods;
• Principles of statistical reasoning and their use in understanding, analyzing, and developing formal arguments;
• The overall process and particular steps in designing studies, collecting and analyzing data, interpreting and presenting results;
• The role of statistics and its applications in other disciplines, e.g. biological sciences, social sciences, and economics.
Statistics Learning Outcomes
Through the statistics courses they take, Georgetown students at all levels will develop their ability to:
• Choose appropriate statistical methods and apply them in various data analysis problems;
• Use various statistical software to perform data analysis;
• Communicate effectively statistical methods and results in appropriate contexts, both orally and in writing;
• Critically assess the strengths and weaknesses of published studies, and evaluate the validity of reported results. |
Algebra I
Grade Level: 8-12 Credit: 1.0 Prerequisite: Math 8
This course presents the basic concepts of algebra. Concepts studied include working with polynomials, solving equations, using formulas, graphing linear equations, solving linear systems, simplifying and solving quadratic expressions and equations, and working with basic functions. Problem solving and real-life applications are emphasized. |
Mathematics
The maths department see mathematics as an engaging and creative activity that develops a student's ability to not only think in an organised and logical way, but also for them to look at imaginative ways to solve problems. As such our emphasis is on students developing transferable skills that are honed using the traditional mathematics content and rigor, but with the students engaging with a more task-led curriculum, that allows them to identify the mathematics required to solve problems and gives them ample opportunity to experiment.
Key Stage 3
We have a two year Key Stage 3 where our aim is to teach the students to develop self-learning skills. This is achieved by giving the students every opportunity to develop thinking skills through themed tasks. The emphasis is not on a correct answer, but on developing a range of strategies to cope with the ever changing world of the 21st century and for these skills to be transferable. We wish to allow the students to continue to improve on their arithmetic, with an emphasis on the development of the "numerate student" who uses a variety of methods of calculation, that depends on the numbers used and the degree of accuracy required. The students also engage with geometry and algebra through tasks where "doing and applying" mathematics is not a separate part, but integral to their success. This will enable them to enter their Key Stage 4 with the skill to pursue a functional approach to their learning.
Key Stage 4
Students are entered at either Higher or Foundation Level GCSE, but the skills initiated at Key Stage 3 are further developed and the aspects of functionality and enquiry are keenly pursued, so that students can transfer their skills to new and more demanding areas of mathematics. We follow a linear course which has two terminal examinations. Students are entered for their final exam when it is appropriate, with their final opportunity to take the examinations at the end of Year 11.
Key Stage 5
We offer both Maths and Further Maths at Key Stage 5.
A Level Maths has four Pure Maths core modules: two in Year 12 and two in Year 13, supported with Statistics in Year 12 and Mechanics in Yearr 13.
If a student opts for Further Maths, this is run in conjunction with the Further Maths support network where the students have a wide choice of modules that they complete online. |
Narberth Cal helped teach some 8th graders at my elementary school some basic algebra concepts. I try to take into consideration what a person is interested in and use that subject to show how algebra is relevant in that subject. I am studying Mathematics at HampshireSet theory is the study of sets, both infinite and finite. Some basic operations of set theory include the union and intersection of sets. Combinatorics studies the way in which discrete structures can be combined or arranged. |
Here we present a few examples of how real benefits are achieved by rigorously applying mathematical programming and optimization on real-world problems.
Optimal Schedules
Optimization is a powerful tool for determining workable schedules that are in accordance with certain requirements. Examples include
Put together a lesson plan taking into account teacher availability and teacher preferences such as morning/afternoon sessions, preferred classes, or days without lessons. At the same time restricted lab availability is taken into account, gaps in teachers' schedules are minimized, and all required subjects are taught for each class.
Create a seminar schedule for multiple locations, topics, and audiences. The requirements to be met are instructor availability in terms of skills/topic coverage, instructor willingness to travel certain distances and to give a certain number of courses, meet customer requirements (offer specific courses within certain time periods in certain regions), and to minimize travel cost.
In a specific implementation we managed to maximize the number of offered training courses for high school teachers across three U.S. states while observing constraints such as travel restrictions, trainer skills and availability, and course demand and frequency. The computed plans do not conflict with business and trainer constraints while the effort to come up with a workable plan was reduced from three days to an hour.
The problem was formulated as a mixed-integer linear program (MILP) and included approx. 75 locations, 100 instructors, 25 time slots, and 20 different courses. Depending on the specific constraints, the resulting schedule contains about 200-250 scheduled courses during the planning period of one quarter.
Optimize utilization of beds in a hospital depending on total number of beds, allocations to certain departments, expected duration of the individual stays in the hospital, required safety quantities, etc. The benefits of optimization include maximized utilization of available beds, minimized waiting time, minimized bottlenecks, and increased visibility into the hospital supply chain.
Other Applications
Apart from optimizing schedules there is an endless list of other applications where using applied mathematics and in particular optimization, greatly improves profitability. Beyond more common areas like route planning, location determination in a logistics network, and commission structures in a multi-level marketing environment, here are examples of successful projects we have done:
Web-based optimal chemical formulation and blending: Upon entering a set of desired chemical and physical properties of the end product on a web page the application computes the optimal chemical formulation in terms of meeting the specifications while minimizing cost and returns the result in the user's web browser. The benefits for sales and marketing include more accurate quotes within significantly shorter response times. |
Special Technology Requirements
Note:
These are course-specific requirements that go above and beyond the Provider Baseline Technical Requirements.
The school or student is responsible for providing:
This class uses Apex Learning online curriculum. Each student will run a system checkup during the Getting Started activity to insure their computer has all the required features and settings; Refer to the Apex Learning System check-up: paper and pencil.
A printer, paper, envelopes and stamps to take and mail the Topic Tests
Description
This first semester of algebra 1 credit retrieval course covers these Washington state standards: solving problems, numbers, expressions, and operations, and characteristics and behaviors of functions. Students begin with a diagnostic assessment on a Washington state standard within the Compass Learning program (CLO) and then based upon those results an individual learning plan is set up for the student. The student works the lessons and then demonstrates mastery of the skills in an assessment that must be passed before moving on to the next standard. Because high school students have unique needs and experiences, CompassLearning ensures that students know where they are while challenging them to grow. Odyssey High School Math focuses on foundational skills to support learners, emphasizes repetition and practice of key skills, reinforces study habits, including note-taking, to sharpen students� comprehension, and covers National Mathematics Advisory Panel�s concepts for success in algebra. |
Functions and Their Graphs. Using Technology: Graphing a Function. The Algebra of Functions. Portfolio. Functions and Mathematical Models. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Summary of Principal Formulas and Terms. Review Exercises.
3. DIFFERENTIATION.
Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Portfolio. Using Technology: Finding the Differential of a Function. Summary of Principal Formulas and Terms. Review Exercises.
4. APPLICATIONS OF THE DERIVATIVE.
Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Function. Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Summary of Principal Terms. Review Exercises.
Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Consumers' Surplus and Producers' Surplus. Summary of Principal Formulas and Terms. Review Exercises.
Functions of Several Variables. Partial Derivatives. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of a Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Summary of Principal Terms. Review Exercises. Answers to Odd-Numbered Exercises.
used - like new 7th Edition. Great condition! Possible minimal highlights Buy from trusted seller! Expedited Shipping may be available for few dollars more! Hardcover. |
ISBN13:978-0201347302 ISBN10: 020134730X This edition has also been released as: ISBN13: 978-0201384086 ISBN10: 0201384086
Summary: This best-selling text emphasizes solid mathematics content, problem-solving skills, and analytical techniques. The seventh edition focuses on the National Council of Teachers of Mathematics (NCTM) Principles and Standards 2000. The text allows for a variety of approaches to teaching, encourages discussion and collaboration among students and with their instructors, allows for the integration of projects into the curriculum, and promotes discovery and active learning...show more. Students using this text will receive solid preparation in mathematics, develop confidence in their math skills and benefit from teaching and learning techniques that really work. For mathematics teachers. ...show less
(Each chapter begins with a ''Preliminary Problem'' and concludes with a ''Hint for Solution to the Preliminary Problem,'' ''Questions from the Classroom,'' ''Chapter Outline,'' ''Chapter Review,'' and a ''Selected Biography.'') (*indicates optional section.)
Integers and the Operations of Addition and Subtraction. Multiplication and Division of Integers. Divisibility. Prime and Composite Numbers. Greatest Common Divisor and Least Common Multiple. *Clock and Modular Arithmetic.
5. Rational Numbers as Fractions.
The Set of Rational Numbers. Addition and Subtraction of Rational Numbers. Multiplication and Division of Rational Numbers. Proportional Reasoning.
Instructor's Edition |
Discrete Mathematics 1st Edition
1441980466
9781441980465
Discrete Mathematics: This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs. «Show less
Discrete Mathematics: This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal... Show more»
Rent Discrete Mathematics 1st Edition today, or search our site for other Gallier |
Understandable and convenient interface:
A flexible work area lets you type in your equations directly. It is as simple as a regular text editor. Annotate, edit and repeat your calculations in the work area. You can also paste your equations into the editor panel.
Example of mathematical expression:
5.44E-4 * (x - 187) + (2 * x) + square(x) + sin(x/deg) + logbaseN(6;2.77)
History of all calculations done during a session can be viewed. Print your work for later use. Comprehensive online help is easily accessed within the program.
2)
Factor Calculator 5.6.2
Calculate the factors of any number with a single click. Small application window allows simultaneous use with Word, Outlook, Excel, etc.. Recommended on The Math Forum @ Drexel (University) for Middle School, High School and College, ages 6+. 99ΒΆ License:Shareware,
$0.99 to buy Size:
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Kids Abacus 2.0 License:Shareware,
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2901KB
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Machinist MathGuru 1.0.90
Solve common trade maths problems in a whiz with Machinist's Math Guru software.
This inexpensive, easy to use utility is designed primarily for students, machinists, toolmakers and CNC programmers. License:Shareware,
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3462KB
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ASCII Art Generator 3.2.4.6
ASCII Art Generator is an amazing graphics art to text art solution, which converts digital pictures into full color text-based images, and makes them eye-catching with a very cool and readable texture, composed of letters and digits. License:Shareware,
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1) Math Game 1.1
Time that children spend on computer games has not been decreasing. In this new age, parents and teachers can find ways to use the entertainment industry to educate and enlighten our youth. License:Shareware,
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FindGraph 2.22
FindGraph is a graphing, curve-fitting, and digitizing tool for engineers, scientists and business. Discover the model that best describes your data. License:Shareware,
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5) Multivariable Calculator - SimplexCalc 4.1.4
SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
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6) Multipurpose Calculator - MultiplexCalc 5.4.4
MultiplexCalc is a multipurpose and comprehensive desktop calculator for Windows. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
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Math Level H: Linear Equations, Inequalities & Graphing
Students will learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs. |
Tutorial 1
Once you have access to an installation of Mathematica, you need to know how to
use it.
Opening the Program
In an on-campus computer lab, go to Start Menu, then Programs, then Wolfram Mathematica. Click
on the icon for Mathematica, named Spikey.
Up will pop an introductory window. On the left hand side of this button is an option to create a new Mathematica notebook or open an old one. The
notebook is where all your interactions with the program will take place.
First steps with Mathematica
Open the file. The file should look like a "Powerpoint" Presentation. If it does not, go to the Format Menu and click on "Format > Screen Environment > SlideShow".
Follow this tutorial step-by-step and discuss the most interesting aspects
with your neighbors.
At the end of the tutorial, you should use the remaining time to explore the power of Mathematica. I suggest looking in the Documentation Center (Help Menu) or at the Wolfram Demonstrations Project. Feel free to explore on your own or with your neighbors. If you are having trouble getting started, here is what I do when I am exploring:
I go to the Documentation Center and type in a command (such as Manipulate)
I do a quick look at the selected examples that are given and see if they are interesting.
If so, I want to see all the examples. So I select the entire notebook (Ctrl-A or Apple-A) and then open all subgroups (Cell Menu: "Grouping > Open All Subgroups").
I play around with the examples, moving sliders, changing variables to see what happens.
If I see a command I do not know, I will search for it in the Documentation Center
At the bottom of the file is a "See Also" section, which tells you similar commands.
Also at the bottom are links to more in depth tutorials, which can be useful sometimes.
Other Items of Note!
In Mathematica, it is important to distinguish between parentheses (), brackets [], and braces {}:
Parentheses (): Used to group mathematical expressions, such as (3+4)/(5+7).
Brackets []: Used when calling functions, such as N[Pi].
Braces {}: Used when making lists, such as {i,1,20}.
If you use the wrong symbols in the wrong places or if you do not have a closing symbol for every opening symbol, Mathematica will
give you an error.
Mathematica is Case-SenSitive (AA is not the same as aA), so
be careful about what you type.
Many of your initial errors will come about because of one of the two above problems.
In Mathematica, there are four types of equals: =, :=, ==, and
===. You need to understand the difference between the first two.
To define a variable to store it in memory, use =. For example, to define z to be 3, write
z=3.
You use == to check for equality. For example, 1-1==0 will
evaluate to True and 1==0 will evaluate to False.
You use := to define your own command. (This is advanced.)
You will likely not use === in this class.
One of the most important things to do is explore. If you are having trouble with a certain function, use the
? command to ask for help. Enter ? Table and the output will be a yellow box
with a quick synopsis of the command. For more detailed information, click the blue >> at the bottom
right of this yellow box. This will open the Documentation Center
which gives examples of using the
command in action, available options for this command,
and anything else you might want to know about the command.
Algebra and Calculus
Mathematica will do everything your calculator can and more.
Use ^ to put something to a power.
pi is Pi, e is E and sqrt(-1) is I.
If you want to see the numerical approximation to a fraction or irrational number, use the function N. For example, to find the decimal represenation of pi, write N[Pi].
Use E^x or Exp[x] to represent the function ex.
To take the derivative of a function, use D and specify the derivative with respect to which
variable. For instance D[x^2 + 3x, x].
To take the integral of a function, use Integrate and specify the integral with respect to
which variable. For instance Integrate[x^2 + 3x, x].
To solve for the roots of ax2+bx+c=0 symbolically, use Solve[a x^2 + b x + c == 0, x].
Notice the double equals sign. (Mathematica is searching for when the expression is True.)
Coefficient[(1 + x)^10, x^3] gives the coefficient of x3 in the expansion
of (1 + x)10. |
idea. The only reason that this book gets 2 stars is because it has a decent answer section.
Reviewed by a reader
We've used this book in our freshman course in Mathematics (Linear Algebra) at University of Copenhagen, Denmark. It's very good as a introduction to Mathematical Proofs too.
Schaum's Outline of Modern Abstract Algebra (Schaum's)
Editorial review
Reviewed by Alex "supermanifold", (MTL)
y, for instance). It's just a matter of scoping them out carefully, and dishing out the money (for photocopies, even).
Reviewed by "torybug", (College Park, Maryland)
ve a few bucks.
Reviewed by "kem2070", (Seattle, WA USA)
y exercises (to test your understanding) have the answers. Some have an answer, some have a partial answer, some have a hint, and some have nothing. This is a little aggravating, but it does not take away from the book.
Reviewed by "pawntep", (BANGKOK, Thailand)
I am an undergrad student in Computer Science. The content in this book is terse and very cohesive. And its cohesiveness is what I like most. Each successive chapter is developed rigorously upon previous chapters. A lot of proofs of most
Algebra for College Students
Editorial review
Intended for a course that blends intermediate and college algebra topics written at an intermediate algebra level, the goal of this text is to provide a sound transition between elementary algebra and more advanced courses in mathematics
Understanding Algebra: Revised
Editorial review
This text features outstanding pedagogy, cumulative exercise sets, end-of-chapter key ideas for review, special boxed features called "Pointers for Better Understanding", annotated worked examples with "concept capsules", and chapter test
Schaum's Outline of Basic Mathematics for Electricity and Electronics (Schaum's)
Editorial review
Elementary Algebra: Structure and Use
Editorial review
This text is intended for a beginning or elementary algebra course offered at both two- and four-year schools. Elementary Algebra Structure and Use is an introductory text for students with either no background in algebra or for those stu
Math for Physics
Reviewed by a reader
Take care that you buy the right edition. I entered the isbn and came up with this book but it ended up being an old edition so I had to get a list of corrections from my professor.
Reviewed by a reader
Well I resented having to buy this book for my physics class during summer. It's not a required book during the fall or spring semesters. Basically this book is a condensation of calculus with physics applications. In addition to being ov
Introduction To Discrete Math
Editorial review
Intended for a one- or two-term discrete math introductory course, Introduction to Discrete Mathematics is designed to fulfill a general education requirement or a prerequisite for computer science courses. Written in an informal and conv
Standard Basic Math and Applied Plant Calculations
Editorial review
Prospective plant operators and engineers are provided with a review of math basics, with emphasis on free-hand calculations and mental-estimating method and are acquainted with typical on-the-job plant problems.
Reviewing Math
Editorial review
For the returning adult to community college or introductory student, this book encourages students to approach math differently. Unusual design includes 3-dimensional stereograms and math playing cards. Answers to problems (on same page)
Pre-Algebra: A Review
Editorial review
PRE-ALGEBRA-A REVIEW is a workbook designed for use in any PreAlgebra course. A student can study typical elementary statistics problems, review geometric perimeter and area applications, perform metric conversions and algebraic translati
Math Activities for Young Children: A Resource Guide for Parents and Teachers (College Custom Series)
Reviewed by a reader
Elementary Algebra Review
Editorial review
This workbook is designed for use in any elementary algebra course or by any student needing to retrace typical elementary algebra problems. Upon completion of these review problems, the student should feel comfortable taking any entrance
Intermediate Algebra, Form A
Editorial review
Revised to accommodate a stronger emphasis on graphing, this second edition introduces graphing and graphing techniques, functional notation, a transitional approach to graphing parabolas, and a formal development of functions. Also new t
Arithmetic and Algebra Again (Schaum's Paperbacks)
Reviewed by a reader
Reviewed by a reader
Mind Over Math: Put Yourself on the Road to Success by Freeing Yourself from Math Anxiety
ssor to teach me the subject. However I have discovered that is not true and that self learning college algebra is better for me. This is one of the most liberating experiences of my life and I am grateful to the authors of this book.
Reviewed by Shari H. Goforth, (Northern California)
This book was recommended to me by a college counselor who has high praise for the authors. If I may paraphrase: The book is eloquently written, the format is very well put together and usable. The authors discuss the aversion to math tha |
Topics from advanced algebra including polynomial,
rational, exponential, logarithmic, and trigonometric functions. This course is
designed to prepare students for MA181 (Calculus I).
Prerequisite:C or better in MA100 and MA102, appropriate
score on mathematics placement test, or consent of department. MA102 may be
taken concurrently during the first half of the semester.
Format: This course is taught in a
lecture/discussion format. Calculator and/or computer exercises may be done in
class. Attendance and participation are expected and will be considered in
grading, especially for "borderline students."
Homework:You will receive a handout with homework assignments
(see attached list) corresponding to each text section covered in the course. It is expected that you will read each
section in the textbook, as it is covered.After completing a section in class, the assigned problems from that
section should be completed before the next class. Class time will be devoted
to discussing challenging problems.There is not enough time to go over every problem.Students should take advantage of office
hours, the MathLearningCenter, and form study groups to
ensure that homework is complete and the topic mastered.
Calculators:A graphing calculator is required for this
course.The course will be taught using
the TI-83 Plus for classroom instruction.Other models are acceptable but will require that the student assume
responsibility for knowing that calculator's capabilities. Students will not be permitted to share calculators during quizzes and
tests. Use of CAS calculators (TI-89, etc.) is not permitted during tests and
quizzes.No electronic devices (cell
phones, etc.) except a dedicated, approved calculator may be used during
quizzes and tests.
V.Grading:
Quizzes:Approximately 10 short, announced quizzes
will be given.
No make up quizzes will be given.
The 2 lowest quiz scores
will be dropped.
Students who arrive late to class will not
be given additionaltime.
Exams:Five (5) one-hour exams and
a comprehensive 2-hour final exam will be given.The lowest one-hour test grade will be
dropped.
No make-up
exams will be given.If you miss more
than one of the one-hour tests, the grade you earn on the final will be used as
the grade on the second missed exam.Any
student who misses more that two exams may be dropped from the course.
All students
must take the final exam 8 – 10 a.m. on May 10, 2005.
Course Grade: You will earn a grade of A (90-100%), B (80-89%), C (70-79%),
D (60-69%), or F (<60%).
Your grade will be based on the following:
Homework:5%
Quizzes:20%
One-hour
tests50%
Final
Exam:25%
Late policy:It is expected that you will be on time for every class. If
circumstances arise that make it impossible to be on time, please do come to class, but try to take a seat near the door to
minimize disruption.
Audit Policy:Students auditing the class are expected to adhere
to attendance and late policy guidelines.Those who do not may be dropped."Audits" may take quizzes and exams, but are not required to do so.
VI.Classroom Policies:
Attendance will be taken at the
beginning of each class. It is expected that all students will attend all
classes except in cases of illness or emergency.Students are responsible for finding out what
they missed.Students missing 4 or more
classes may be dropped.
Academic Honesty:
See the
Student Code of Conduct-"Academic Dishonesty and Misconduct." (Go to MyMC
online.)
Cell phones and
other devices that make noise must be turned off. There will be a
letter-grade deduction for devices that ring, beep, or otherwise disrupt the class
during tests.
Talking during
class that is disruptive and interferes with other students' ability to hear or
concentrate will not be tolerated.Any
student who must be asked to be quiet more than three times, will be required
to meet with the dean and the instructor prior to being readmitted to the
class. Questions are encouraged and there will be many occasions when
students are encouraged to work together during class and discuss mathematics.
Student Code of Conduct is available online through
MyMC.
Computer use that is not directly related to the course is not
permitted.Inappropriate use of the
classroom computers will result in the student being dropped from the course.
Cancellation of class, due to weather, or any other reason, does
not mean we get to cover less material, so, if class is cancelled, please read
through the section that would have been covered and try the homework
problems.This will allow us to cover
that material more quickly during the next class.Any quiz or test scheduled for a day when
class is cancelled will be given
when the class next meets.
MontgomeryCollege does not follow MCPS when it comes to school closings. Please
listen to the radio or TV for College closings, or check the MC web site.
Accommodations:Any student who may need an accommodation due to a disability,
please make an appointment to see me during my office hours, or before or after
class.A letter from Disability Support
Services authorizing your accommodation will be needed as soon as possible.
MathLearningCenter: This is one of the jewels of the
Germantown Campus.
Make it your
home-away-from-home.Located in Room 229
HT, the hours are:
provides problems and guided solutions corresponding
to the text sections covered in this course.
Tutors are available and are eager to help you!Take advantage of them.
Please note that this is a college level course.Tests will include problems that require
students to apply principles and concepts.While some test questions will "look like homework problems," others
will not.It is expected that you will
demonstrate your ability to synthesize skills/concepts covered throughout the
course by applying those skills and concepts to new problems. You can best
prepare yourself for such questions by ensuring that you understand every step
of all problems.Don't skip word
problems!Could you explain every
problem to someone? Could you write a clear, precise explanation of each step?
Successful students are those who come to class, keep up,
do the homework, and ask questions.They
take advantage of office hours, use the MathLearningCenter,
and form study groups. Work to understand the material and take ownership of
the knowledge. I look forward to
working with you this semester. |
Understandable Statistics (Hardcover)
9780618949922
ISBN:
0618949925
Edition: 9 Publisher: Houghton Mifflin Company
Summary: This algebra based text is a thorough yet approachable statistics guide for students. The new edition addresses the growing importance of developing students' critical thinking and statistical literacy skills with the introduction of new features and exercises.
Ships From:Alpharetta, GAShipping:Standard, Expedited, Second Day, Next DayComments: 0618949925 MULTIPLE COPIES AVAILABLE-Very Good Condition-May have writing or highlighting-May ha... [more] 06189499 |
Give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra 1 and developed further in the more advanced Algebra 11. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. 48 pages
Last October, Schoodoodle.com introduced supplemental classroom curriculum books in the form of eBooks into our online store and library. We began with 5,000 eBooks for teachers to download, share and use in their classrooms. The demand has been so great- that we have doubled our selection in just a few months.
We now offer over 10,000 titles for educators to choose from that range in all subject areas. Preview the books for free on the sample links, download immediately, and own forever! Each month- we will be featuring new eBooks for you to use to enhance your classroom curriculum but you can view the entire catalog for a range of categories.
*The enhanced eBooks give you the freedom to copy and paste the content of each page into the format that fits your needs. You can post lessons on your class website, make student copies, extract or rotate pages, and edit the contents of the file.
Why eBooks?
eBooks are less costly than traditional books
eBooks are available instantly.
eBooks take up no physical storage space and minimal electronic storage space.
Shop SchooDoodle.com to buy and access free digital ebook reader pdf downloads for children and schools from our online store and library. We offer over 10,000 electronic book titles to download for elementary school, middle school, and high school students. Preview the books for free on the sample links, download immediately, and own forever!
Each month we will be featuring an educational eBook from our catalog for you to use to enhance your classroom curriculum and offer a free download of the book. We now offer over 10,000 electronic book titles to download for elementary school, middle school, and high school students. Preview the books for free on the sample links, download immediately, and own forever! Since we have added this feature, the demand for this technology has grown substantially.
Why are eBooks the smart choice?
1. eBooks are less costly than traditional books
2. eBooks are available instantly
3. eBooks take up no physical storage space and minimal electronic storage space
Our featured eBook this month is Beginning Algebra (Grades 6-8). This 48 page eBook will help you give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra I and developed further in the more advanced Algebra II. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. We think you will love this eBook so much that we would like to offer it to you for free.
We have a wide selection of other Pre – Algebra, Beginning Algebra, Algebra II etc. so please see all of our Algebra ebooks that are available for download so teachers and parents can access them any time.
For other subjects and grade levels (K-12) see our entire eBook Catalog. We have 10,000 titles for educators to choose from that range in all subject areas. You can preview the books for free on the sample links, download immediately, and own forever! |
This is not a universal recipee for anything, rather a few random points.
1) Make sure your background matches the course expectations. If not, work on it before even thinking of taking an advanced class.
2) Read ahead, not behind. Most teachers will tell you what's coming next and if you come to the class knowing half the story already, you can concentrate on the other half and gain double time for absorbing it.
4) Learn each proof to the level that your professor can wake you up at midnight and you'd be ready to present it right away. Keep in mind that there are millions of theorems but only thousands of proofs, hundreds of proof blocks, and dozens of ideas. Unfortunately, no one has figured out how to transfer the ideas directly yet, so you have to extract them from complicated arguments by yourself.
5) Solve problems, solve problems, and solve problems (not the ones that ask you to do something according to the ready scheme, of course, but the ones that ask you to prove something that is not clear from the beginning). You need to learn how to create simple proofs before you can understand the complex ones. |
Nuffield Advanced Mathematics: Other Resources
In addition to the core text books and the options, the Nuffield Advanced Mathematics project published two other resources for students to support their learning and broaden their appreciation of mathematics Nuffield Advanced Mathematics reader provided articles as background or extensions to topics covered elsewhere in the course. The aim was to encourage students to make further study of the development and applications of the ideas about which they were learning. This was one of the ways by which the course team illustrated how…
The Nuffield Advanced Mathematics Resources file provided supporting material for four types of calculator and for the spreadsheet, Excel.
The program listings in the calculator sections were designed to be transparent and easy to understand. They followed the algorithms in the Nuffield texts as closely as possible, and they used… |
Because of its large command structure and intricate syntax, Mathematica can be difficult to learn. Wolfram's Mathematica manual, while certainly comprehensive, is so large and complex that when trying to learn the software from scratch - or find answers to specific questions - one can be quickly overwhelmed.
A Beginner's Guide to Mathematica offers a simple, step-by-step approach to help math-savvy newcomers build the skills needed to use the software in practice. Concise and easy to use, this book teaches by example and points out potential pitfalls along the way. The presentation starts with simple problems and discusses multiple solution paths, ranging from basic to elegant, to gradually introduce the Mathematica toolkit. More challenging and eventually cutting-edge problems follow. The authors place high value on notebook and file system organization, cross-platform capabilities, and data reading and writing. The text features an array of error messages you will likely encounter and clearly describes how to deal with those situations.
While it is by no means exhaustive, this book offers a non-threatening introduction to Mathematica that will teach you the aspects needed for many practical applications, get you started on performing specific, relatively simple tasks, and enable you to build on this experience and move on to more real-world problems.
"This book is a comprehensive package for knowledge sharing on Mathematics. The language of the book is simple and self-explanatory, this will help the students to grasp the fundamentals of the subject easily. The book follows a to the point approach and lays stress on the understanding of the core concepts. Appropriate number of MCQs are given for each topic that are of great help to the students appearing for competitive and State Board examinations.""
" . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic." --London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking." --SIAM Review "Each chapter discusses a wealth of examples ranging from old standards . . . to novelty . . . each model is developed critically, analyzed critically, and assessed critically." --Mathematical Reviews A Concrete Approach to Mathematical Modelling provides in-depth and systematic coverage of the art and science of mathematical modelling. Dr. Mesterton-Gibbons shows how the modelling process works and includes fascinating examples from virtually every realm of human, machine, natural, and cosmic activity. Various models are found throughout the book, including how to determine how fast cars drive through a tunnel, how many workers industry should employ, the length of a supermarket checkout line, and more. With detailed explanations, exercises, and examples demonstrating real-life applications in diverse fields, this book is the ultimate guide for students and professionals in the social sciences, life sciences, engineering, statistics, economics, politics, business and management sciences, and every other discipline in which mathematical modelling plays a role.
Most texts on nonparametric techniques concentrate on location and linear-linear (correlation) tests, with less emphasis on dispersion effects and linear-quadratic tests. Tests for higher moment effects are virtually ignored. Using a fresh approach, A Contingency Table Approach to Nonparametric Testing unifies and extends the popular, standard tests by linking them to tests based on models for data that can be presented in contingency tables.
This approach unifies popular nonparametric statistical inference and makes the traditional, most commonly performed nonparametric analyses much more complete and informative. It also makes tied data easily handled, and almost exact Monte Carlo p-values can be obtained. With data in contingency tables, one can then calculate a Pearson-type, chi-squared statistic and its components. For univariate data, the initial tests based on these components detect mean differences between treatments. For bivariate data, they detect correlations. This approach leads to tests that detect variance, skewness, and higher moment differences between treatments with univariate data, and higher bivariate moment differences with bivariate data.
Although the methods advanced in this book have their genesis in traditional nonparametrics, incorporating the power of modern computers makes the approach more complete and more valid than previously possible. The authors' unified treatment and readable style make the subject easy to follow and the techniques easily implemented, whether you are a fledgling or a seasoned researcher.
The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB®, Mathematica®, and Maple™, A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field of study. Stressing applications wherever possible, the authors have written this text with the applied math, engineer, or science major in mind. It includes a number of modern topics that are not commonly found in a traditional sophomore-level text. For example, Chapter 2 covers direction fields, phase line techniques, and the Runge-Kutta method; another chapter discusses linear algebraic topics, such as transformations and eigenvalues. Chapter 6 considers linear and nonlinear systems of equations from a dynamical systems viewpoint and uses the linear algebra insights from the previous chapter; it also includes modern applications like epidemiological models. With sufficient problems at the end of each chapter, even the pure math major will be fully challenged. Although traditional in its coverage of basic topics of ODEs, A Course in Ordinary Differential Equations is one of the first texts to provide relevant computer code and instruction in MATLAB, Mathematica, and Maple that will prepare students for further study in their fields. for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include: Contributions from eleven of the world??'s leading figures in time series Shared balance between theory and application Exercise series sets Many real data examples Consistent style and clear, common notation in all contributions 60 helpful graphs and tables Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements: Adopts a generic approach to the subject, and is not application specific In conjunction with a web-based chapter, it integrates code development, theory, and application in one book Provides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources Contains a comprehensive set of homework problems at the end of each chapter Produces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study. Accompanied by a book companion website housing supplementary material that can be found at A First Course in Finite Elements is the ideal practical introductory course for junior and senior undergraduate students from a variety of science and engineering disciplines. The accompanying advanced topics at the end of each chapter also make it suitable for courses at graduate level, as well as for practitioners who need to attain or refresh their knowledge of finite elements through private study.
Although the use of fuzzy control methods has grown nearly to the level of classical control, the true understanding of fuzzy control lags seriously behind. Moreover, most engineers are well versed in either traditional control or in fuzzy control-rarely both. Each has applications for which it is better suited, but without a good understanding of both, engineers cannot make a sound determination of which technique to use for a given situation.
A First Course in Fuzzy and Neural Control is designed to build the foundation needed to make those decisions. It begins with an introduction to standard control theory, then makes a smooth transition to complex problems that require innovative fuzzy, neural, and fuzzy-neural techniques. For each method, the authors clearly answer the questions: What is this new control method? Why is it needed? How is it implemented? Real-world examples, exercises, and ideas for student projects reinforce the concepts presented.
Developed from lecture notes for a highly successful course titled The Fundamentals of Soft Computing, the text is written in the same reader-friendly style as the authors' popular A First Course in Fuzzy Logic text. A First Course in Fuzzy and Neural Control requires only a basic background in mathematics and engineering and does not overwhelm students with unnecessary material but serves to motivate them toward more advanced studies.
The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.Incorporates recent developments in computational probability.Includes a wide range of examples that illustrate the models and make the methods of solution clear.Features an abundance of motivating exercises that help the student learn how to apply the theory.Accessible to anyone with a basic knowledge of probability.A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.
Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra-establishing a clear understanding of basic linear algebra and number, group, and commutative ring theory and progressing to sophisticated discussions on Galois and Sylow theory, the structure of abelian groups, the Jordan canonical form, and linear transformations and their matrix representations.
R is dynamic, to say the least. More precisely, it is organic, with new functionality and add-on packages appearing constantly. And because of its open-source nature and free availability, R is quickly becoming the software of choice for statistical analysis in a variety of fields.
Doing for R what Everitt's other Handbooks have done for S-PLUS, STATA, SPSS, and SAS, A Handbook of Statistical Analyses Using R presents straightforward, self-contained descriptions of how to perform a variety of statistical analyses in the R environment. From simple inference to recursive partitioning and cluster analysis, eminent experts Everitt and Hothorn lead you methodically through the steps, commands, and interpretation of the results, addressing theory and statistical background only when useful or necessary. They begin with an introduction to R, discussing the syntax, general operators, and basic data manipulation while summarizing the most important features. Numerous figures highlight R's strong graphical capabilities and exercises at the end of each chapter reinforce the techniques and concepts presented. All data sets and code used in the book are available as a downloadable package from CRAN, the R online archive.
A Handbook of Statistical Analyses Using R is the perfect guide for newcomers as well as seasoned users of R who want concrete, step-by-step guidance on how to use the software easily and effectively for nearly any statistical analysis.
WILEY-INTERSCIENCE PAPERBACK SERIESFrom the Reviews of History of Probability and Statistics and Their Applications before 1750"This is a marvelous book . . . Anyone with the slightest interest in the history of statistics, or in understanding how modern ideas have developed, will find this an invaluable resource."--Short Book Reviews of ISI
Because of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. Self-contained and largely independent, each topic starts with a problem description and an outline of the solution procedure, followed by its parameter list specification, source code, and a test example that illustrates the usage of the code.
The book begins with a chapter on random graph generation that examines bipartite, regular, connected, Hamilton, and isomorphic graphs as well as spanning, labeled, and unlabeled rooted trees. It then discusses connectivity procedures, followed by a paths and cycles chapter that contains the Chinese postman and traveling salesman problems, Euler and Hamilton cycles, and shortest paths. The author proceeds to describe two test procedures involving planarity and graph isomorphism. Subsequent chapters deal with graph coloring, graph matching, network flow, and packing and covering, including the assignment, bottleneck assignment, quadratic assignment, multiple knapsack, set covering, and set partitioning problems. The final chapters explore linear, integer, and quadratic programming. The appendices provide references that offer further details of the algorithms and include the definitions of many graph theory terms used in the book. |
9780199602124
Free Delivery in U.K
Synopsis: : Maths for Economics
Many years of Teaching led Geoff Renshaw to develop Maths for Economics as a resource which builds your self-confidence in maths by using a gradual learning gradient and constantly reinforcing learning with examples and exercises. Some students embarking on this module feel that they have lost their confidence in maths, or perhaps never had any in the first place. The author has designed the Book so that whether you have a maths A level, GCSE, or perhaps feel that you need to go back over the very basics, Knowledge is built up in small steps, not big jumps. Once you are confident that you have firmly grasped the foundations, this book will help you to make the progression beyond the Mechanical exercises and into the development of a maths tool-kit for the analysis of economic and Business problems. This is a skill which will prove valuable for your degree and for your future employers.
Author Information
Geoff Renshaw, Department of Economics, University of Warwick
Features
* The flexible design of the contents means that this book is suitable if your starting point is maths A level, GCSE, or even if you have forgotten most of the maths you learned in school.
* A gradual learning gradient underpins the text; each concept is explored comprehensively, including numerous examples and exercises at each stage to ensure that you get a really good understanding of it.
* Builds self-confidence in maths through the use of step-by-step examples, progress exercises, hints and rules, encouraging you to develop a 'maths tool-kit' for analysing economics and business problems.
* Any unnecessarily long explanations have been rewritten to make the exposition clearer in the appropriate places.
* Material on matrix algebra, limits, and necessary and sufficient functions has been revised in line with market feedback
* Answers to the progress exercises now appear at the end of the book, rather than online, for ease of use.
Book Information
The Title "Maths for Economics " is written by Geoff Renshaw. This book was published in the year 2011. The ISBN number 0199602123|9780199602124 is assigned to the Paperback version of this title. This book has total of pp. 712 (Pages). The publisher of this title is Oxford University Press. We have about 84121 other great books from this publisher. Maths for Economics is currently Available with us. |
Learning Guide for College Algebra
The Learning Guide begins each chapter with an engaging application and is organized by objective, providing additional examples and exercises for students to work through for greater conceptual understanding and mastery of mathematical topics. The Learning Guide is available as PDFs and customizable Word files in MyMathLab.
It can also be packaged with the textbook and MyMathLab access code.
show more show less
Edition:
6th 2013
Publisher:
Pearson Education
Binding:
Trade Paper
Pages:
272
Size:
8.50" wide x 11.00" long x 0.50 Guide for College Algebra - 9780321840790 at TextbooksRus.com. |
Book summary
This textbook presents statistics conceptually, avoiding the use of maths other than basic arithmetic, and will, therefore, be appropriate for students who find maths exceedingly difficult. The text explains the basic concepts in a very accessible and jargon-free style. It takes students through certain concepts and statistical tests, with diagrams, examples and explanations throughout. [via] |
Program Model C' Pacing Guide
Traditional Model for High School Mathematics
This model features a classic sequence of courses that emphasizes connections across
content strands. Data analysis topics have been added to the familiar high school
mathematics curriculum. Topics
are grouped so that Year 1 focuses on algebra and algebraic reasoning, Year 2 focuses
on geometry, and Year 3 returns to a focus on further algebraic topics leading to
trigonometry and pre-calculus. This sequence works well for many students, is familiar
to teachers and parents, and fits the design of many instructional materials. However,
this does not mean that the status quo is working for all students. Even though
course topics and sequencing may look familiar, effective strategies for presenting
the material must be implemented to make this or any model curriculum successful.
Students must be placed in a course for which they have the prerequisites and have
adequate time and support to fully understand the material. Students must be engaged
with rich problems throughout each course in order to understand the mathematics
fully and develop creative problem solving and reasoning skills. Students must also
be expected to communicate mathematical ideas using formal mathematical language.
Teachers in schools adopting Model C will benefit from professional development
that includes strategies for successfully teaching all students and that familiarizes
teachers with sources of problems to deepen student understanding of mathematical
topics.
This model provides students with the basic mathematical knowledge they will need
for future education and employment. The design offers a progression for the development
of mathematical thinking, with each course presenting the material in a logical,
efficient, and systematic way. Related topics are presented together whenever possible
and learning builds upon previously learned material. Connections between algebraic,
numerical, and geometric representations are made throughout the model to provide
a coherent curricular model.
Model C' is an adaptation of Model C that allows additional time for students who are preparing for postsecondary education in programs that do not include calculus. This adaptation prepares students for OGT requirements by the end of the second year course and meets the Ohio Board of Regents expectations for students to be prepared for a non-remedial college mathematics course by the end of the third year course.
First Year Course
First Year Course Rationale
All students require a rigorous and demanding curriculum in order to develop sound reasoning and strong problem solving skills. The topics covered in Year 1 of this model can provide this rigor. Students progress from their informal middle school experience with number relationships, data analysis, and linear equations to more formal definitions, algebraic reasoning, and graphical representations. With this model, as with any model, different students may require different amounts of time and support to become proficient with the mathematics.
First Year Course Description
The focus of this course is the development of algebraic understanding, reasoning, and skills using mathematical language to express abstract ideas. The Year 1 course has four main themes:
transition from generalized arithmetic to algebra;
data analysis and probability;
linear equations and functions;
nonlinear functions (introduction)
More specifically, students will solve linear equations and inequalities and systems
of equations. They will graph a variety of functions and add the study of probability and statistics to the topics covered in a typical Algebra I course. Appropriate use of technology is encouraged to enhance the study of these topics.
Second Year Course
Second Year Course Rationale
The second year model develops formal logic and reasoning skills through the study of Euclidean geometry. Although geometry is a subject of importance and practical use, the main goal of the course is to develop students' abilities to reason and to present coherent arguments. In addition to this deep involvement with logic and deduction, students discover connections between formal geometry and the algebraic techniques learned earlier, and they learn important practical applications of geometry. With mastery of the Year 1 and Year 2 courses, students will be prepared for further mathematical education and for understanding deeper connections between abstract mathematics and real world situations.
Second Year Course Description
The course begins with polynomial and exponetial functions, with emphasis on quadratics.
The focus of the course is the development of logic and reasoning, along with basic ways to think geometrically. The two foci for the Year 2 course are formal reasoning and applications of geometry (constructions, calculating lengths, areas, and volumes). Geometric constructions should be woven through the course. Appropriate use of technology is encouraged to enhance the study of these topics.
Third Year Course
Third Year Course Rationale
The Third Year course includes content that is critical for all students. The third year continues to build mathematics essential for the workplace and future education, and exposes students to a wide variety of rich mathematics. Algebraic topics are a focus and are developed in relationship to the geometry and mathematical reasoning the students have previously studied.
Third Year Course Description
Prerequisite to this course is working knowledge of key topics from years one and two, including number line and interval notation, solving linear and quadratic equations and inequalities, and absolute value and distance. The thrust of the Year 3 course is to reinforce and extend the algebraic topics from Year 1 and Year 2 courses.
Throughout this course, students should have frequent experiences with numeric, graphical, algebraic, and verbal examples of mathematics. Students should use graphing calculators and other technology as integral parts of the course to enhance the study of these topics.
Fourth Year Course
Fourth Year Course Rationale
With the advent of the core requirements for Ohio, all students must take mathematics inThis course presents a mix of algebraic and geometric topics that will help develop students' algebraic thinking. Throughout this course, students should have frequent experiences with numeric, graphical, algebraic, and verbal examples of mathematics. Mastery of the four courses in this model will provide students with the mathematical and reasoning skills needed to succeed in a rigorous college-level calculus course.
Fourth Year, Option 1, Course Description
The Year 4 course has several focus areas: (1) formal proofs by induction with applications, (2) modeling bivariate data, and (3) trigonometry. By studying these topics, the student will have completed a comprehensive high school curriculum. Students may use graphing calculators and other technology to enhance the study of these topics.
Fourth Year Course, Option 2
Modeling and Quantitative Reasoning
Fourth Year, Option 2, Course Rationale
One purpose of secondary education in the United States has always been preparing
students for their roles as citizens, as well as preparing them for future study
and the workplace. Today numbers and data are critical parts of public and private
decision making. Decisions about health care, finances, science policy, and the
environment are decisions that require citizens to understand information presented
in numerical form, in tables, diagrams, and graphs. Students must develop skills
to analyze complex issues using quantitative tools.
In addition to a textbook, teachers will want to use online resources, newspapers,
and magazines to identify problems that are appropriate for the course. Students
should be encouraged to find issues that can be represented in a quantitative way
and shape them for investigation. Appropriate use of available technology is essential
as students explore quantitative ways of representing and presenting the results
of their investigations.
Fourth Year, Option 2, Course Description
This course prepares students to investigate contemporary issues mathematically
and to apply the mathematics learned in earlier courses to answer questions that
are relevant to their civic and personal lives. The course reinforces student understanding
of:
percent
functions and their graphs
probability and statistics
multiple representations of data and data analysis
This course also introduces functions of two variables and graphs in three dimensions.
The applications in all sections should provide an opportunity for deeper understanding
and extension of the material from earlier courses. This course should also show
the connections between different mathematics topics and between the mathematics
and the areas in which applied. |
"Thank you for providing families with such a high quality, alternative education for their children. I am most appreciative that it allows for a creative approach to educating the young (and not so young) mind."
This course can be taken as a precursor to Algebra I. The course is a combination of a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include prime and composite numbers, fractions and decimals, the order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem, and more. The text Saxon Algebra ½ Homeschool Edition is included.
Consumer Math
This course is designed to enhance understanding of basic, practical math applications. The course focuses on "real life" processes such as budgeting, compound interest, sales tax, small business management, and data processing to teach algebra, geometry, and statistics. The text Glencoe Mathematics Connections Integrated and Applied is included with this course.
For enrolled students only.
This course covers the following skills: evaluation of expressions involving signed numbers, exponents and roots, properties of real numbers, absolute value and equations and inequalities involving absolute value, scientific notation, unit conversions, solution of equations in one unknown and solution of simultaneous equations, the algebra of polynomials and rational expressions, work problems requiring algebra for their solution, graphical solutions of simultaneous equations, the Pythagorean theorem, algebraic proofs, functions and functional notation, solution of quadratic equations via factoring and completing the square, direct and inverse variation, and exponential growth. The text Saxon Algebra I is included with this course.
This course introduces students to the basic theorems of Euclidean plane geometry and their applications, and explores both plane and solid geometric figures. Students learn how to prove theorems by the axiomatic method, and to use these theorems in solving a variety of problems. Students also learn how to accomplish a variety of geometric constructions. The text Mcdougal- Littell Geometry is included with this course.
In this course, students integrate topics from Algebra I and Geometry and begin the study of trigonometry. The course provides opportunities for continued practice of the fundamental concepts of algebra, geometry, and trigonometry to enable students to develop a foundation for the study of Advanced Mathematics. The text Saxon Algebra II is included with this course.
Prerequisite: Geometry and Algebra I.
Advanced Math prepares the student for further study of mathematics at the college level through a presentation of standard pre-calculus topics, including substantial new material on discrete mathematics and data analysis. The text Saxon Advanced Mathematics is included with this course.
Prerequisite: Algebra II.
Calculus treats all the topics normally covered in an Advanced Placement AB-level calculus program, as well as many of the topics required for a BC-level program. The text begins with a thorough review of those mathematical concepts and skills required for calculus. In the early problem sets, students practice setting up word problems they will later encounter as calculus problems. The problem sets contain multiple-choice and conceptually-oriented problems similar to those found on the AP Calculus examination. Whenever possible, students are provided an intuitive introduction to concepts prior to a rigorous examination of them. Proofs are provided for all important theorems. The text Saxon Calculus is included with this course.
Prerequisite: Advanced Math.
This AP Calculus AB course covers topics typically found in a first-year college Calculus I course and explains topics in differential and integral calculus. This course prepares students to succeed in the Advanced Placement (AP) Calculus AB exam and the subsequent courses. Students will learn calculus by actively becoming engaged with the lectures, readings, animations, activities, and resources in the online textbook. In addition to the online textbook, students will be provided with written materials 6 months; students intending to take the AP exam should enroll by early January-calculus with Trigonometry or the equivalent
AP Calculus BC
This AP Calculus BC course covers topics typically found in a first-year college Calculus I and Calculus II course and advances the student's understanding of concepts normally covered in high school Calculus. Major themes include differential and integral calculus. This course prepares students to take the Advanced Placement (AP) Calculus BC exam. The instructor is the guide for this course, but the student is the learner and will learn calculus by actively becoming engaged with the lectures, readings, animations, activities, and resources in the online textbook and written materials provided 9 months; students intending to take the AP exam should enroll by early Octobercalculus with Trigonometry or AP Caluclus AB or equivalent |
An understanding of Mathematics is important in business, commerce and industry. Most employers regard Mathematics as an essential skill for employees to have. In tertiary education, Mathematics is a prerequisite to entry in most of the courses being offered. The following courses provide for the development of these essential skills in preparing students for their future beyond school.
At Kaiapoi High we offer two mathematics courses at Level 2
201 - an Achievement Standards course which has a three hour external exam in November along with up to four internal assessments
202- an Achievement Standards course which has a two hour external exam in November along with up tosix internal assessments |
Graphs and Functions
Graphs and Functions teaches an introduction to using a rectangular (Cartesian) coordinate system, and provides the help necessary to study the basics of graphing functions, including how to plot, identify quadrants and interpret graphs, determine whether a relation is a function and find its domain and range. |
A dynamic new course combining classbook, CD-ROM and online components to offer flexible, time saving and supportive materials. Cambridge Essentials Mathematics Extension 9 Pupil Book is aimed at National Curriculum Levels 6-8. The book gives a map for the pupil and teacher of how to cover all aspects of the topic whilst focussing on delivering exercises with strong progression. The pupil CD-ROM replicates the book page with buttons acting as links to prior knowledge, keywords and explanations. Functional Maths questions are also included.
You can earn a 5% commission by selling Cambridge Essentials Mathematics Extension 9 Pupil's Book with CD-ROM: Year 9 (Cambridge Essentials Mathematics |
What is Algebra II? Algebra II is a college preparatory course designed to get students ready for Pre-Calculus or College Algebra. Throughout the course, we will be building on the student's prior knowledge from Algebra I and Geometry. We explore many different types of functions through algebraic and graphical representations.
To be successful in Algebra II, students need to have good study habits. They will need to take notes, ask good questions, and complete their daily assignments. Don't wait until the last minute to ask for help!
How do I access the Online Book? 1) Click on the book above or the classzone link above. 2) Selct the online book. 3) Create a student account using the activation code you were given in class. 4) Use a login and password you will remember. (I suggest first_last name and your last name for your password.) |
Transforming? There is a step before applying the technique of "completing the square" that is required and that is to come up with the technique of completing the square in the first place. You're not suggesting that the purpose of a course in elementary algebra is to just teach a finite set of techniques to be memorized, understood and used when appropriate, are you? Although I agree that is a subset of the purpose of an algebra class, that still leaves a lot of gaps in between those (finite number of) techniques taught in an algebra class and the only way to fill those gaps is that the student also develop the skill to invent new solutions without prior art. And some techniques, even though they are labeled "techniques" are not algorithmic or formulaic at all, such as substitution of variables or induction. Most students are poor with these because they are just a very high level form and the student must fill in the form with a solution. Call it study, call it practice, call it whatever, but there is a lot of brain work left to do even after you see that a technique works.
Bob Hansen
On Jul 18, 2012, at 3:03 PM, Louis Talman wrote:
> And, in particular, I never thought of learning to complete a square as "studying the solution of quadratic equations". I thought of it, instead, as a way of transforming an expression into an equivalent expression that was more useful in a given context. |
Improve Your Note Taking
Improving Math Skills
When studying for math, we often use exercises, worksheets and sample problems to work through in order to prepare for an upcoming test, exam or review. However, as in most other subjects, note taking and journaling is also very effective and very important to help with the understanding of specific math concepts. Whether you dictate your notes and have them available for audio, or write your notes to review them visually, the strategies and tips here will help you better prepare for math tests and exams. Effective notes will help you to remember important concepts taught in class and they will guide you through various math problems.
Taking Notes
I prefer to use the two column approach in my notes and I also prefer to use pencil. To use the two column approach, your actual notes will be on one side and the examples or theorems/forumulas will be on the other. There is usually more than one method of solving a problem, use your notes to document this. Be sure to include any examples that you believe will help you later. Math is often about making connections as so many concepts are interrelated, be sure to record the connections you make. Areas where you have concerns or believe to be your greatest weakness are also the areas you should emphasize. To emphasize, you may wish to use a highligher and attach a few stickies. Personally, I prefer to date my notes as well, sometimes I include the text pages for handy reference.
Format
I've already mentioned that it is helpful to keep audio notes, however, it is difficult to record examples of exercises in audio. Audio is better when you are reviewing postulates, procedures and formulas. The more you hear the explanations, the greater the chance you will retain the information. However, you may also wish to record your notes on your computer. I have used Microsoft One Note previously and found it quite effective. There is an add-in that allows you to perform calculations and to plot graphs and it contains an extensive collection of mathematical symbols and structures to display expressions and has a pretty good equation gallery. Two others I use are La-Tex, and Math Symbols. Although I like La Tex, it isn't my first choice for taking notes. Math Symbols is great for creating exercises and it allows you to create your equations quickly (newer version has handwriting recognition) but you'll still need another application to integrate it with. A lot of my students prefer One Note because it's where they keep all of their notes. However, everyone is different and you'll need a strategy that works best for you.
Tips for Improving Your Note Taking Skills
Listen carefully to your instructor and jot down the key points about solving problems, proving theorems or using a procedure. Write down everything you think that will help you when you return to this concept later.
Don't get too wordy, keep your notes to the point and simple to understand.
Use logical organization, jumping around from concept to concept will only be confusing. Make sure your examples have key points in your notes.
Explain your reasoning. This component is key, keep it short and sweet but explain the logic behind the application or procedure.
Record alternate methods, as I mentioned earlier, there is usually more than one way to solve a problem, be sure to record the alternative methods.
When taking notes in math, look at your textbook. What do you like about it? What don't you like about it? Think of your notes as a set of cheat notes for you to review. Make them look like a text that you find easy to follow.
In summary, most important of all is to review your notes in a timely way. Make review part of your routine. We are all guilty of cramming before tests and exams but a little review along the way will better equip you to see greater success in math. If journaling works better for you, you may wish to check out some strategies for effective math journaling. |
diving into Algebra, it is a good idea to know how to recognize and work with polynomials. Learn the vocabulary associated with polynomials and how to write and simplify expressions. Includes: practice test, examples, and teacher's guide.
Notes:
Age group: 7th grade - adult.
Downloadable video file.
Title from title screen (viewed on July 15, 2010 |
The School is composed by five set of lectures, designed to introduce young researchers to the more recent advances on geometric and algebraic approaches for integer programming. Each set of lectures will be about six hours long. They will provide the background, introduce the theme, describe the state-of-the-art, and suggest practical exercises. The organizers will try to provide a relaxed atmosphere with enough time for discussion.
Integer programming is a field of optimization with recognized scientific and economical relevance. The usual approach to solve integer programming problems is to use linear programming within a branch-and-bound or branch-and-cut framework, using whenever possible polyhedral results about the set of feasible solutions. Alternative algebraic and geometric approaches have recently emerged that show great promise. In particular, polynomial algorithms for solving integer programs in fixed dimension have recently been developed. This is a hot topic of international research, and the School will be an opportunity to bring up-to-date knowledge to young researchers. |
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Math 2312: Precalculus
As suggested by the catalog description (below), this course focuses on algebra and trigonometry concepts underpinning calculus. Topics include data analysis, functions, graphs, limits, trigonometry, exponential & logarithmic functions, other functions, and math modeling. For detailed information and policies, please the Read the Full Syllabus.
A more rapid treatment of the material in MATH 1314 and MATH 1316, this course is designed for students who wish a review of the above material, or who are very well prepared. Functions, graphs, trigonometry, and analytic geometry.
Class Posts
Instructions for the Final Exam The final exam counts for 25% of your course grade. The exam has 12 exercises (100 points) and must be completed during 8-10:30 on 12/13/11. You may use a calculator with factory-shipped programs, 1 side of a 8.5 by 11 inch page written in your own handwriting, a provided reference sheet,…
The main topic of the second test in precalculus was trigonometry. See the Exam 2 Study Guide for detailed information. Download the Test Math 2312 - Exam 2 - Trigonometry Extra Credit Opportunity You can earn a transformed grade of $(\mbox{original grade})^{0.7}(100)^{0.3}$ by printing a blank copy of the Exam and turning in a full set of…
This is one of two exams while combine to count for 30% of your grade. The exam has 8 exercises for 100 points and must be completed during class on 11/10/11. The exam has two parts – You may only use a writing utensil on Part 1. For Part 2, you will be provided a reference…
This in-class activity is designed to introduce trig identities by defining the complex exponential function according to Euler's Formula. Results in a fairly straight forward proof of the angle sum formulas for sine and cosine. Trigonometry and the Complex Plane (PDF) Trigonometry and the Complex Plane (DOCX)
Available in Two Formats Reference Guide for Basic Trigonometry (DOCX) Reference Guide for Basic Trigonometry (PDF) Used in-class and potentially useful to anyone who may need a refresher on any of the following: Calculating sine, cosine, tangent, cosecant, secant, cotangent for an angle in a right triangle. Calculating sine, cosine, tangent, cosecant, secant, or cotangent…
This activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84. Step 1: Get a TI-84 Graphing Calculator (or similar). Don't have one? If you use Windows, you can download the attached Emulator (ZIP file), extract the Zip folder, and run the Wabbitemu.exe file. Load the…
The following little form produces randomized wave data using javascript. The purpose is to provide example data for someone learning to fit sine and cosine curves to oscillating data. Stop Sitting Around and Go Get You Some Data Press the "Get Data" button to generate some random oscillating data. Then copy and paste into a…
The first precalculus exam was based on functions and graphs. Download the Test and Answer Key Blank Copy of Exam 1 - Functions and Graphs Answer Key - Math 2312 - Exam 1 - Functions and Graphs What's on the Test? The main concepts on the test include reasoning about the following. Challenging topics are…
Exam 1 is scheduled for class time on Tuesday, October 4th. The exam cannot be made up if missed. Review time is set aside for class on Thursday 9/29, and you're encouraged to work on the problems with your mentor. Download the Exam 1 Study Guide |
Pre-Algebra: Word Problems
Find study help on linear applications for pre-algebra. Use the links below to select the specific area of linear applications you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn linear applications for pre-algebra.
Study Guides
Miscellaneous Math Word Problems
This set of practice problems consists of 23 problems dealing with basic math concepts including whole numbers, negative numbers, exponents, and square roots. It will provide a warm-up session before you move on ...
Fractions Word Problems
In order to understand arithmetic in general, it is important to practice and become comfortable with fractions and how they work. The problems in this set help you practice how to perform basic operations with fractions ...
Fractions Word Problems
In order to understand arithmetic in general, it is important to practice and become comfortable with fractions and how they work. The problems in this set help you practice how to perform basic operations with fractionsPercents Word Problems
Percentages have many everyday uses, from figuring out the tip in restaurant to understanding interest rates. This set of practice problems will give you practice in solving word problems that involve percents.
Percents Word Problems
Percentages have many everyday uses, from figuring out the tip in restaurant to understanding interest rates. This set of practice problems will give you practice in solving word problems that involve percents. |
B.3.4 Systems of Linear Equations and Matrices
Solve systems of linear equations, motivated by various application problems. Matrices provide an abstract view of such systems and point to algorithms for solving them. Matrices provide a mathematical system where commutativity fails.
Instructional Days (suggested)
22 - 25 days
Click on subtopics below to see resources from the Ohio Resource Center |
ALGEBRA I
2012-2013
Mrs. Cocco
Room C-8
This course is designed to establish a strong foundation in the language of mathematics. Algebra serves as a prerequisite for all secondary mathematics courses. A spiral approach will be given to solving equations. Students will solve equations involving fractions, decimals, and irrational numbers.
Special emphasis will be placed on real-world applications. Students will thoroughly investigate linear and nonlinear equations, graphs and properties. Emphasis will be placed on practical application involving other disciplines and industry.
In addition, this course introduces the study of polynomials, factoring, and special products. Properties of positive exponents are developed with a brief introduction to negative and rational exponents. Rational expressions are explored and are applied to solving fractional equations. This course concludes with the presentation and application of the quadratic formula.
Text: Algebra 1, McDougal Littell
·You will be issued a book at the beginning of the year
·The book should be COVERED to help you protect it.
·You are also responsible for returning the book at the end of the year in the condition you received it—you pay for any damage you cause.
Preparedness for Class
·You are to use a 3-ring binder for this class so that you can keep your notes, homework and handouts in an orderly fashion.
·DATE ALL MATERIAL!!
·You MUST use PENCIL to do math work.I WILL NOT accept work in PEN!!
·You cannot go to your locker once you are in class (even to pick up homework!)BRING EVERYTHING YOU NEED!!!!
Homework Policy
·Homework will be given every other day, for the most part.(See calendar for actual assignments)It will be checked at the start of each period. Your grade will be based on completeness, not accuracy, so it is better to try than to leave answers blank.However, your work must look like you actually tried!
·There will be NO trips to lockers to retrieve homework.It is your job to remember to bring it with you to class.You will receive a zero even if it's done, but in your locker.
·If you have an unexcused absence, your homework for that day is an automatic 0.
·If you have an excused absence and would like credit for the homework that was due while you were absent, please show it to me when you return to class the next day.
·Upon returning from an excused absence, it is your responsibility to find out the assignment you missed and have it done in a timely manner.
·If you are going to miss class for a field trip or school activity you are to show me any work that is due for that period before you miss it (even if that means coming in before school).And if you miss class for an activity and homework is assigned, it is up to you to find out the assignment as it is still due the next day.
Tests & Quizzes
·Tests will be given either at the end of each chapter or halfway through for long chapters.
·Quizzes will be given approximately once a week (about 2 or 3 sections)
·Partial credit will be given if I can follow your train of thought and your work is correct for what you did
·If you miss a test or quiz you will take a different version than the rest of the class.You have 5 days to make up a missed test or quiz on your own time (NOT IN CLASS!)
·There will be a midterm in January and a final in June.They will be averaged to give you a 5th marking period grade.
·NOTE:If you have completed all of you homework throughout the marking period, I will drop your lowest quiz score.
Grading System
·I will be using a point system for your marking period grade.You and I will both keep a running tally of your grades that we always know where you stand in my class.
·The total amount of points will vary by marking period but the items will always be worth the following:
Test: 100 pointsQuiz: 50 pointsHomework: 10 points
Extra Credit:Extra credit will be available on some quizzes and tests.Also, coming to extra help will count as extra credit.
Extra Help:I am available for extra help most days after school between 2:25 – 2:45 PM. |
"Plateaus" to watch out for - MathOverflow most recent 30 from to watch out forDoubleJay2009-10-25T16:43:39Z2009-10-27T23:14:33Z
<p>I'm a lot earlier in my math education that most of the people on this site. Currently I'm studying computer science, and I'm interested in looking into statistical and optimization applications, as well as theory (yeah, I know that sound broad, but I'm quite early in my education!). Anyways, I want to get deep into the math behind these things - statistics, combinatorics, linear and integer programming, maybe some analysis. Algebra also interests me.</p>
<p>I've found that math studies go okay, but from time to time I have trouble. Understanding delta-epsilon proofs was a big obstacle for calculus back in high school, and more recently generating functions have been giving me serious trouble.</p>
<p>If I pursue a path towards graduate level studies, what sort of things should I watch out for? More generally, since I don't know where I'm going, what concepts did you find hardest to grasp during your undergrad/early graduate studies?</p>
<p>Thanks.</p>
by Wlog for "Plateaus" to watch out forWlog2009-10-25T17:37:06Z2009-10-25T17:37:06Z<p>I have advice, but it is dependent on the size of your university and/or the mathematics department therein.</p>
<p>A large part of my undergraduate process was to tutor others in the class. A good test of your understanding is if you assist someone else in coming to the same understanding. Unfortunately, it may be that your class sizes are <em>epsilon</em>. Thus it will be more difficult to form a study group. Applied Functional Analysis is a topic of great importance for a young computer scientist, especially one who is aspiring for a PhD, but it can be slow to grasp if you are taking it as an independent reading course.</p>
by Scott Morrison for "Plateaus" to watch out forScott Morrison2009-10-25T18:34:40Z2009-10-25T18:34:40Z<p>One general advice about early maths education is to not decide what you like too early!</p>
<p>Keep learning new fields, keep reading books about things you don't know yet. Most mathematicians I know aren't working on problems they would have expected when they arrived in grad school. It takes a surprisingly long time for most people to reach the level of mathematical maturity where they're reading to work on new problems, and until you have an inkling that you're ready for this, don't overspecialise. There's plenty of time for that later!</p>
by Elisha Peterson for "Plateaus" to watch out forElisha Peterson2009-10-27T23:14:33Z2009-10-27T23:14:33Z<p>My gut response is to say there are a limitless supply of these plateaus. There is so much out there that even the best mathematicians are limited in what they can understand well. So in terms of specific concept plateaus, well if you're like most of us you'll probably have lots of them, and that's a good thing.</p>
<p>In terms of concepts, I think what I found tough was often much clearer after I lost an early misconception. E.g. for a long time I thought the Killing form in Lie algebra was using "killing" as a synonym for "erasing"... I tried to build my understanding around that conception and it didn't work very well (Killing is a name). A lot of "simple" mathematical ideas are known by proper names rather than descriptive terms, so as more of these accumulate you have to rely more on memorization than intuition.</p>
<p>Outside of concepts, here's what I found tough:</p>
<ul>
<li><strong>Transition from coursework to research.</strong> Some people are very good at getting the A when the material is put in front of them, and most textbooks are good at giving you the necessary tools to solve the problems they present. I found the transition to more open-ended problems a significant challenge.</li>
<li><strong>Understanding the frontier of a field.</strong> As stated in a previous response, it's tough to get to the frontier of a field. It takes a lot of work, and a lot of time. So graduate school requires a lot of perseverance.</li>
</ul> |
Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continui... read more
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Product Description:
Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. The first five chapters consist of a systematic development of many of the important properties of the real number system, plus detailed treatment of such concepts as mappings, sequences, limits, and continuity. The sixth and final chapter discusses metric spaces and generalizes many of the earlier concepts and results involving arbitrary metric spaces. An index of axioms and key theorems appears at the end of the book, and more than 300 problems amplify and supplement the material within the text. Geared toward students who have taken several semesters of basic calculus, this volume is an ideal prerequisite for mathematics majors preparing for a two-semester course in advanced calculus |
I'm not an extremely mathy person. I can solve basic math problems,
and with some thought I can even solve some complex math problems.
My public high school math education was lacking, and as my oldest
son prepares for algebra next year, he is quickly surpassing my
easily accessed math knowledge. Because of these factors, the Algebra
Survival Guide: A Conversational Handbook for the Thoroughly Befuddled caught
my attention.
The Algebra Survival Guide is a 276-page step-by-step
algebra 1 book. Each black-and-white page covers one algebraic
concept in a question-and-answer format. The question is at the
top of the page, and the answer is at the bottom, along with examples
and a few practice problems. Because each page covers only one
concept, and because there are usually as many words explaining
the concept as numbers, this book is wonderful for those of us
intimidated by math. The pages are visually appealing, with cartoons
and separate text boxes for important information. The Algebra
Survival Guide Workbook includes thousands of practice problems
(with answers), and because it is cross-referenced to the Algebra
Survival Guide, it is easy to locate additional practice
problems.
The Algebra Survival Guide can be used as an algebra
reference book, a resource for explaining difficult concepts, or
a refresher course before taking Algebra 2. The book is only $19.95,
and the workbook is only $9.95, so this is an extremely affordable
course. If you or your students are thoroughly befuddled by algebra,
I would highly recommend the Algebra Survival Guide.
Product review by Courtney Larson, The
Old Schoolhouse® Magazine,
LLC, August 2010 |
Let me explain: one the one hand, linear algebra and calculus are enough to consider a lot of non-trivial problems and describe basic issues in many areas. On the other hand, the various areas of mathematics tend to interact intensely with each other, which is what makes math so cool. So it's going to be difficult to direct you to a specific area, since chances are that a reference that is advanced enough will not be shy about using much more advanced notions (check out the math articles on wikipedia to get an idea of what I mean; even innocuous sounding ones can get pretty intense).
I do want to encourage you to give in to your curiosity: but instead of picking a specific subject, you would be much better off picking up specific references that are written more specifically for your level. There are many of those, look for general math books, e.g. from the AMS and MAA. "Proofs from THE BOOK" might be a bit intense, but roughly at the right level.
Since the various areas of math tend to riff off each other as I mentioned, the last thing you want to do is get specialized too early anyway, so generalist books are better for you now. |
Mathematics of Chance utilizes simple, real-world problems-some of which have only recently been solved-to explain fundamental probability theorems, methods, and statistical reasoning. Jiri Andel begins with a basic introduction to probability theory and its important points before moving on to more specific sections on vital aspects of probability,... more... |
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Tips for Success in Math 3113-3118 Come to class prepared. This means with your homework ready to turn in, prepared to discuss or present the assigned problems, and having read the next section of the text. Note that we will collect homework before
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CombiMap explanationCombiMap is a transform for mapping input features, L dimensional data space, into one dimension (mapping multi-dimensional data to a scalar value). Mathematical representation of this transform has four terms that are:CombiMap
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CVEN 5534: Wastewater Treatment Assignment 1: Due Tuesday, 1/20BACKGROUND In 1905, Pennsylvania passed a law forbidding the discharge of untreated sewage from new sewerage extensions and extensions of existing sewerage systems into streams. The law
AREN 2110: Thermodynamics Midterm 1 Fall 2005_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: Thermodynamics Midterm 1 Fall 2004_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: Thermodynamics Midterm 2 Fall 2005_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: In class exercises 1st Law 1. 7.2 MJ of work is put into a gas at 1 MPa and 150 C while heat is removed at the rate of 1.5 kw. What is the change in internal energy of the gas after one hour? a. 5.7 MJ b. 1.8 MJ c. 8.7 MJ d. 13 MJ 2. One k
FCS Core Learner Outcomes1. Articulate the historical foundation of family and consumer sciences, its evolution over time, its mission, and its integrative focus. 2. Analyze family structures and apply major theoretical perspectives to understand in
Civil EngineeringWhat is Civil Engineering? What can you do as a Civil Engineer? Curriculum at CU "Engineers solve ill-defined problems that have no single "right" answer but many better or worse solutions." Engineering and the Mind's Eye, Fergus
DISCUSSION P APERBOTTLEDWATER:UNDERSTANDING A SOCIAL PHENOMENONCatherine FerrierApril 2001This report, commissioned by WWF, is an independent documentation of research by the author and its contents ultimately the responsibility of the au
DPD Portfolio Evaluation Format Includes the necessary components in the following order (12 points): Cover sheet in outer `pocket' of the binder. Title page (same as cover sheet) Table of Contents Current resumeFCS 4150Professional goals within
AREN 2110 HW #2Fall 20071) What is the difference between gage pressure and absolute pressure? 2) The gage pressure in a liquid at a depth of 3m is read to be 28 kPa. Determine the gage pressure in the same liquid at a depth of 9m. 3) Both a pres3DO PROBLEMS 1 11. EXTRA CREDIT PROBLEMS ARE OPTIONAL Due Thursday, 9/20. 1. If the pressure of a substance is increased during the boiling process, will the temperature also increase or will it r5: Due Thursday, October 11.1. An ideal gas at a given state expands to a fixed final volume first at constant pressure and then at constant temperature. For which case is the work done greater? 2.
AREN 2110: Thermodynamics Fall 2007 Sections 001 and 002 HOMEWORK 6: Due Thursday, October 18 1. The radiator of a steam heating system has a volume of 0.02 m3 is initially filled with 250 C steam at 300 kPa. The valves are closed, and the steam is t
AREN 2110 Thermodynamics Sections 001 and 002 Fall 2007 Homework #7 Due Thursday, October 251. Saturated liquid-vapor mixture of steam at 2 MPa is throttled to a final state of 100 kPa and 120 oC. What is the quality of the influent steam? 2. Durin
AREN 2110 Sections 001 and 002 Fall 2007 Homework # 8: Due Thursday, Nov. 1 1. What are the characteristics of all heat engines? 2. What is the Kelvin Planck expression of the 2nd Law of Thermodynamics? 3. A household refrigerator with a COP of 1.5 r
AREN 2110 Sections 001 and 002 Fall 2007 Homework # 9. Due Thursday, Nov. 151. The entropy of a hot baked potato decreases as it cools. Is this a violation of the increaseof-entropy principle? Explain. 2. When a system process is adiabatic, what ca
AREN 2110 Fall 2007 Sections 001 and 002Homework # 10. Due Thursday, Dec. 61. Consider a steady flow Carnot heat engine cycle with water as the working fluid. The maximum and minimum temperatures are 350 and 60 oC. The quality of the water is 0.89 |
Mathematics
"For the things of this world cannot be made known without a knowledge of mathematics. " – Roger Bacon, philosopher
Bacon also said that, "mathematics is the gate and key to the sciences." At St. George's, we believe the coalescence of math and science is necessary to create highly adept, numerically and scientifically literate students. An intentional and well-planned mathematics and science curriculum prepares St. George's students for an evolving and global world as well as for advanced study in college.
An integrated approach to the curriculum and its emphasis on technology seeks to combine mathematical concepts with concrete matters that are addressed in other areas of academic disciplines. High standards with regard to skill development and conceptual understanding are reinforced through project-based learning that encourages students to apply ideas in real-life settings. Through such integration the mathematical concepts being learned in the specific math classes are reinforced and enriched Students in Math 6—Honors delve deeper into topics than students in Math 6 through examining more applications and critical thinking exercises at a much faster pace The final trimester consists of students reading, analyzing, and writing about classic short stories, while honing their reading comprehension skills. Note: Same as course appearing in English section.
Pre-Algebra 7 prepares students for Algebra I and Geometry slope and y-intercept to graphs and linear expressions. In Pre-Algebra 7, visualization continues with consistent modeling of fractions, percents, mathematical operations, equations, probabilities, and algebraic expressions.
Honors Pre-Algebra prepares students for Algebra I and Geometry at a faster pace and in more depth rate of change, slope, and y-intercept to graphs and linear expressions. In Honors Pre-Algebra, visualization continues with consistent modeling of fractions, percents, mathematical operations, equations, probabilities, and algebraic expressions.
In Accelerated Algebra I, students begin learning how to use graphing calculators.
In Honors Honors Algebra I, students begin learning how to use graphing calculators. Students in Honors Algebra I delve deeper and cover topics more rapidly than students in Accelerated Algebra I Additionally, students are introduced to right triangle trigonometry and their applications in the real world. Honors students should expect a rapid pace and more in-depth coverage.
Algebra II focuses on the study of functions, their graphs, and their properties. Specific functions covered include linear, quadratic, exponential, and logarithmic. However, Algebra II also touches on a wide variety of other topics including, but not limited to, solving higher order equations and inequalities, conics, and polynomial and rational expressions. Students develop a clear understanding of the relationship between algebraic equations and their graphs. All work revolves around the process of solving a problem and the mathematical concepts rather than just "getting the answer." Problem solving through both traditional algebraic methods and graphical methods is an important component of the class.
While Algebra II Honors is a continuation of the concepts learned in Algebra I, this course will introduce the student to some of the theory behind those concepts. Honors Algebra II emphasizes the strong and integral relationship between functions and their graphs. Students will solve problems both algebraically and graphically using pencil and paper as well as a graphing calculator. Students will be asked to think beyond calculations and contemplate the roots and the derivations of the topics. Honors Algebra II is a preparatory course for PreCalculus, Advanced Algebra and Trigonometry, Statistics, and Calculus. To that end, this course covers a variety of topics such as linear and nonlinear functions, relations and systems; exponents and logarithms; conics; rational functions; radical functions. Problem solving strategies as well as how concepts are applied will be emphasized throughout the course.
This course is designed to strengthen students' understanding of concepts taught in Algebra II. Students will focus on a deeper study of functions—analyzing equations, graphs and real-world applications—and the introduction of trigonometry topics needed in advanced mathematics courses. Students will collaborate to construct and share knowledge, building their confidence in mathematics and preparing them for courses in high school and College Algebra or Precalculus at the college level.
This is a functions-based course that both reinforces and broadens concepts taught in Algebra II, and introduces new concepts, preparing students for calculus matrices, series & sequence, analytic geometry and introductory calculus.
This is a functions-based course that both reinforces and broadens concepts taught in Algebra II, and introduces new concepts, preparing the students for AP Calculus BC series & sequence, limits and derivatives. Students should expect more independent work and a faster-paced experience.
This course is divided into three sections, calculus, discrete topics, and statistics. Students will experience the concepts of derivatives and integration through applications in calculus. Discrete mathematics is an umbrella of mathematical topics. Topics include game theory and social theory, which use math to discuss human behavior and its effects. The third component, statistics, will be learned as a tool used in decision making. Students will learn to gather, analyze, interpret and report their findings in a systematic and mathematical manner.
AP Statistics is an introductory, non-calculus based college statistics course that emphasizes understanding and analyzing statistical studies. Students will explore the theory of probability, descriptions of statistical measurements, probability distributions, experimental design and statistical inference. Students will be analyzing samples and understanding populations on an ongoing basis. Graphing calculators are used throughout the course. All students enrolled in this course must take the AP exam in May.
AP Calculus AB is a college-level calculus course that is generally equivalent to a first semester college course: differentiation and integration of polynomial, trigonometric, and exponential functions. Calculators and computers are used to increase and strengthen the students' understanding of the concepts. All students enrolled in this course must take the AP exam in May.
AP Calculus BC is a college-level calculus course that is generally equivalent to the first two semesters of the college Calculus sequence all of the Calculus AB topics as well as additional topics, such as series and polar coordinates. Calculators and computers are used to increase and strengthen the students' understanding of the concepts. All students enrolled in this course must take the AP exam in May. |
Inhaltsangabe
1: Geometry in Regions of a Spaces. Basic Concepts. 2: The Theory of Surfaces. 3: Tensors: The Algebraic Theory. 4: The Differential Calculus of Tensors. 5: The Elements of the Calculus of Variations. 6: The Calculus of Variations in Several Dimensions. |
Mathematics program intended for High School pupils (age 15-17) This Title comprises 20 3 : Analysis, vectors, trigonometry, probabilities… 2.01.002
Mathematics program intended for Middle School pupils (age 12-14) This Title comprises 17 1 : Basic Operations on whole and rational numbers 4.00.005 2 : Developments & applications 4.00.005 can be used for classes or as a homework helper. It has lots .... Free download of RekenTest 4.1 .... Free download of PARI/GP 2.3.4
... is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical ... of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library. YACAS comes with extensive documentation (hundreds of pages) covering the scripting language, the functionality .... Free download of Yacas 1.3.3
A Program for Statistical Analysis and Matrix Algebra MacAnova is a free, open source, interactive ... are analysis of variance and related models, matrix algebra, time series analysis (time and frequency domain), and ... for simple things with only a few commands. 6. It works well with libraries of named data. Free download of MacAnova 5.05.3
AlphaMaths is a totally free program which is user friendly, colorful and easy to use. Note that you MUST have the JRE (Java Runtime Environment) installed for this program to work. The JRE is also totally free. AlphaMaths has a huge variety of worksheets. In addition to the 20+ worksheets included .... Free download of AlphaMaths 1.0 |
short video tutorial deals with the concept of order of operations in mathematics problems and builds on the material covered in earlier lessons.
The narrator reviews the concept, explaining that when a problem contains some combination of addition, subtraction, multiplication or division, the order of operations specifies that the multiplication and division components must be completed first, before carrying out the addition and subtraction work.
He then explains that when the problem contains calculations contained within brackets, the bracketed calculations must be completed first.
The tutorial introduces the mnemonic BEDMAS, which stands for Brackets, Exponents, Division, Multiplication, Addition, and Subtraction, although the instructor points out that exponents will be dealt with only in higher mathematics.
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The order of operations specifies that the multiplication and division components of a math problem must be completed before carrying out the addition and subtraction work. It also specifies that calculations contained within brackets must be completed first.
This video tutorial reinforces that concept by providing three mathematics problems to solve. Each problem is more challenging than the one before.
The problems appear on a computer screen, with the narrator giving step-by-step instructions on how to solve themCitation
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This report examines a set of policies and practices formerly in place in British Columbia that supported access to post-secondary education and upgrading programs for income assistance (IA) recipients, particularly those facing multiple barriers to employment and education. The policies ended in 2002.
Based on interviews with staff who delivered these programs in colleges and institutes during the late 1990s, the authors describe the "best practices" for programs designed to help people with low income improve their educational credentials.
They found that effective programs address the key areas of access, retention, and transition. Other key components include identification of the existence of multiple obstacles to accessing formal education; outreach activities and strong links with community and relevant government agencies; assessment of students' needs and capabilities; financial help with tuition, fees, books, housing, and child care; and support for academic success, including counselling, advocacy, networking, and partnerships with employers.
The authors call on the British Columbia government to change welfare rules so that people receiving income assistance can participate in postsecondary education; restore and increase designated funding to post-secondary institutions to support IA recipients; support colleges and institutes in providing programs and services that offer holistic support to students; and restore tuition-free adult basic education in British Columbia's public post-secondary institutions.
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Phased-in retirement is really a catch phrase that can include special assignments, mentoring, job sharing, and end to shift work, reduced hours and telecommuting. Unfortunately, the tax, pension and paperwork implications of these accommodations pose barriers that can translate into inertia.
In New Brunswick it was the nurses' union that brought phased-in retirement to the bargaining table. Having spent so many years fighting for improved pensions, unions are cautious about sending mixed signals to employers. As our Viewpoints survey found, however, the strongest support for phased-in retirement does in fact come from public sector unions, (48% citing this option as very important in meeting the skill shortage challenge, Viewpoints 2002).
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George and John talked about language and empowerment - giving consumers the information they need to run their lives effectively and safely. They gave examples of baffling communication, and explained why people use complicated language. They discussed some of the myths that surround the term "plain language" and showed how the techniques go beyond just crafting the words. Finally, they used case studies to illustrate the benefits of plain language - efficiency, profitability, precision, and consumer satisfaction.
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This is a report on the National Literacy Secretariat's "Policy Conversation on New Technologies and Literacy." It provides background information about the NLS and an overview of some new technologies. It also explains the policy conversation process, which was intended to obtain information and opinions from the public about whether or not a policy on literacy and technology is needed and if it is, what some of its components might be.
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This set of practice tests is one of the resources for a 40-hour course developed to train people for jobs in water/wastewater treatment facilities.
The document includes tests for material covered in five of the eight course modules: measurement conversions; linear, area and volume calculations; chemical measurements; hydraulics; and wastewater and electricity.
There is also a sample final assessment, covering all the course material. Answers are provided in a separate document. |
cise Calculator Tutorial
The format for the tutorial is different. It is more 'show and tell'. The calculator is a Scientific Programmable Calculator (usually people are concerned and do not like the math or advanced calculators). The idea is to give the problems with how to do, then they can just change the variables (where you put A= 5 - or some number and then all they need to do is change the variables - [the number where A= ??] and it will work the problem. Or see how the calculator is programmed and write their own programs. The easier the calculator is to use, the more chance they will use it (the calculator is FREE).
- How can I change it to make it better (all areas). You can download the calculator and use it (FREE). More examples will be posted as I get time.
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Thank You
falcon
My error. The site is the page Precise Calculator Manual (the link) The Calculator is the link in the banner 'Precise Calculator Download' also there is 'Precise Calculator Examples'. These should make it easier to use and understand. My goal is to make it easy, so anything that needs to be clarified is what I am looking for. I have been programming and setting up calculators (different makes and models) so I miss the concepts or areas that you don't understand because many I take for granted. Mostly using TI calculators and programming in Basic, But many free ones are able to achieve the same results and this is one of the better FREE ones and is easy to program and use (also is better than some expensive ones). I didn't write the calculator program, just trying to help students be able to use it to calculate some advanced math.
-
Thank You
falcon
Good idea! At this stage it's like BASIC with some buttons around.
To make really quick improvements, alter it's syntax:
1. To automatically PRINT raw expressions (i.e. "2+2" line should print "4")
2. To automatically ASK for unknown variables (i.e. "2*X+5" should ask with popup for X value and then print the result).
In general, you should do this as web service for people to calculate online and share common library of macroses.
Check top of page 'Related Articles' "Download Precise Calculator". There you should see many Macros that you can 'copy and paste' to the calculator and run. Then add to your stored Macros. We are adding to the Macros every week, plus we intend to add some line-by-line descriptions for some of the Macros. Make it as easy a possible to use this FREE Programmable Scientific Calculator.
- Thank You
falcon |
Mathematics
To be well informed adults and to have access to desirable jobs, our students require a mathematics education that goes beyond what was needed by students in the past. All students must develop, deepen, and sharpen their skills, their understanding of mathematical concepts and processes, their abilities in problem-solving, reasoning, and communication abilities and hone their ability to make sense of and to solve compelling and complex problems. In order for this to occur, rigorous mathematical content must be organized, taught, and assessed in a problem-solving environment. Students' mathematical knowledge must be connected to the ideas and skills found in all grade levels, as well as to real life situations outside the classroom.
Our goal is to equip each of our students with the ability and preparation to meet the mathematical demands presented by college and careers, and to carry their mathematical thinking and problem-solving into multiple learning situations.
Conceptual Understanding: Making sense of mathematics
Students who understand a concept can:
• identify examples and non-examples
• describe concepts with words, symbols, drawings, tables or models
• provide a definition of a concept
• use the concept in different ways
Expectations for conceptual understanding ask students to demonstrate, describe, represent, connect, and justify.
Procedural Proficiency: Skills, facts, and procedures
Students who demonstrate procedural proficiency can:
• quickly recall basic facts (addition, multiplication, subtraction, and division)
• use standard algorithms – step-by-step mathematical procedures – to produce a correct solution or answer (might also include multiple algorithms)
• use generalized procedures (such as the steps involved in solving an algebraic equation)
• demonstrate fluency with procedures:
o perform the procedure immediately and accurately
o know when to use a particular procedure in a problem or situation
o use the procedure as a tool that can be applied reflexively, and doesn't distract from the task at hand (procedure is stored in long-term memory)
Problem-solving and Processes: reasoning and thinking to apply mathematical content
Students must be able to:
• reason
• solve problems
• communicate theirunderstanding in effective ways
• solve increasingly complex problems from grade to grade
• use increasingly sophisticated language and symbols to communicate their understanding, from grade to grade
Students may substitute a state-approved option for Algebra II, but should check with colleges regarding admission requirements.
PreCalculus
Recommended for College & Career Preparation
12
PreCalculus, AP Statistics, or IB Mathematics
AP Calculus AB, AP Statistics, or IB Mathematics
*A small number of students – generally those in the APP program at the elementary level - will participate in mathematics two years above grade level. Assuming students continue in this pathway, they would take Math 8 in sixth grade and Algebra II in ninth grade, finishing with BC Calculus or IB Mathematics in twelfth grade.
**Beginning in 2010-2011 school year, students enrolled in Algebra I or Geometry will take the state End of Course (EOC) exam for that course, given in June of each year. Students who have taken Algebra I or Geometry prior to 2010-2011 will take a makeup test in that subject, also given in June. |
Algebra Lesson Plans
"Students should understand the concept of slope and be able to calculate the slope of a line given two points on a graph. Students should be able to calculate the slope of a line that is parallel and a line that is perpendicular to a line with a given slope."
"This activity is designed to give students practice in "finding" the correct factors to use when attempting to factor a trinomial. The students are provided with a Tic-Tac sheet to help them discover the relationship or pattern between two numbers. Students then use their discovery to fill in a second Tic Tac sheet. At this point students have uncovered the mystery of how to locate the appropriate factors in a given trinomial. They can now factor any trinomial placed in front of them!" This lesson plan contains all necessary worksheets.
"This lesson will teach students to factor trinomial expressions of the form x2 + bx + c. Students will use algebra tiles to identify the binomial factors and the graphing calculator to verify the result. In addition, students will identify the x-intercepts and y-intercepts of each trinomial function and explore relationships between the trinomial x2 + bx + c and its factored form (x + m)(x + n). "
"This activity uses a series of related arithmetic experiences to prompt students to generalize into more abstract ideas. In particular, students explore arithmetic statements leading to a result that is the factoring pattern for the difference of two squares. A geometric interpretation of the familiar formula is also included."
"This lesson provides students with an introduction to exponential functions. The class first explores the world population since 1650. Students then conduct a simulation in which a population grows at a random yet predictable rate. Both situations are examples of exponential growth."
"This lesson will teach students about several of the rules regarding exponents. It uses a situation from Alice in Wonderland in which Alice's height is doubled or reduced by half depending on what she consumes to introduce negative exponents and the rules for dividing powers."
"This lesson teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil)."
"This lesson teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." |
Synopsis:Stuck On Algebra is a classroom-proven interactive Algebra workstation that keeps students on task doing traditional Algebra in a classic gaming model combining an unbending standard of proficiency with the forgiving and encouraging spirit of "failure without consequence". The result: steady improvement and repeated small successes, the addictive formula of video games without any dilution of the Algebra experience.
Background: SOA is the second generation of a system last sold in the early 90s. More than one educator who used that system in the 90s has sought me out in recent years to ask if it were still available. SOA is available now for beta testing here.
Software In Brief: SOA offers: step-by-step guidance and correction of basic Algebra I problems entered by the student or generated by the application; solved solutions with explanations of generated problems; unassisted exams on a hierarchy of Algebra topics.
Transformations SOA transforms learning mathematics in several important ways:
1. Thanks to step-by-step checking, weak arithmetic skills do not prevent the learner from succeeding with Algebra. Those skills improve as mistakes are caught. The student must work to figure out what they did wrong and correct it. Progress is slower at first, but they are working on Algebra instead of yet another tedious worksheet of arithmetic, so the learner's motivation to persevere is strong.
2. Assistance available in Training Modes lets students of any ability experience the pleasure of solving Algebra puzzles and enjoy math in its own right. They may make more mistakes getting there, but that only increases the satisfaction of finally succeeding and draws them into further study.
3. With SOA correcting all the work, tracking student progress, and offering first-level assistance when students get stuck, the teacher has more time to work with students individually or in small groups.
4. In Mission Mode learners must meet a fixed standard of mastery by passing unassisted, "no second chance" challenges. Missions become available only as prerequisite missions are passed, so the independent learner has a structure they can follow. For any student, Missions draw learners into ever more high-quality practice as they attempt repeatedly to pass the unassisted challenges, encouraged by getting closer each time to succeeding.
Summary The system works for several reasons.
First, Algebra is easy but there is a lot of it and it is cumulative. Algebra requires fluent application of many easy rules, which in turn requires a substantial quantity of high-quality practice to make those rules second-nature. With SOA students get more practice with ever-present feedback and assistance.
Second, Algebra is fun for any student as long as they are given the fighting chance to solve problems on their own. SOA's instant feedback, detailed hints, and solved examples give them that chance.
Third, the stigma of failure is lifted without compromising the standard of proficiency that must be met. The satisfaction of small successes and evidence of steady improvement even as they fail at exams draws learners into further practice and eventual mastery. This is precisely the addictive formula of computer gaming. |
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Mathematics
Mathematics, "The Queen of Sciences" as called by Carl Friedrich Gauss, is the science of number, quantity, and space, either as abstract concepts or as applied to other disciplines (such as physics and engineering).
The distinguished authors of the top-quality books and textbooks listed under Research and Markets' Mathematics category are the world's leading researchers. These publications cover all the key areas in today's research. They are invaluable references, comprehensive and
readily accessible. When available, pre-publication titles are also included, so you can be sure not to miss the latest developments in your research field.
The readership of this category includes both graduate and undergraduate students, as well as researchers and mature mathematics.
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... more
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study
Ordinary Differential Equations presents a thorough discussion of first-order differential...
Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines
Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues...
The 11th edition of Analytic Trigonometry continues to offer readers trigonometric concepts and applications Almost every concept is illustrated by an example followed by a matching problem to encourage...
Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text...
The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent...
Six Sigma methodology is a business management strategy which seeks to improve the quality of process output by identifying and removing the causes of errors and minimizing variability in manufacturing...
Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations...
Practical Text Mining and Statistical Analysis for Non-structured Text Data Applications brings together all the information, tools and methods a professional will need to efficiently use text mining...
Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning...
This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides...
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences
I ntegration is an important function of calculus, and Introduction...
Black's latest outstanding pedagogy of Business Statistics includes the use of extra problems called "Demonstration Problems" to provide additional insight and explanation to working problems, and presents...
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics...
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad. The book's truly discovery-based approach...
An insightful guide to understanding and visualizing multivariate statistics using SAS®, STATA®, and SPSS®
Multivariate Analysis for the Biobehavioral and Social Sciences: A Graphical Approach outlines...
Philosophy of Linguistics investigates the foundational concepts and methods of linguistics, the scientific study of human language. This groundbreaking collection, the most thorough treatment of the...
The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability...
An insightful guide to understanding and visualizing multivariate statistics using SAS, STATA, and SPSS Multivariate Analysis for the Biobehavioral and Social Sciences: A Graphical Approach outlines...
Continuing demand for this book confirms that it remains relevant over 30 years after its first publication. The fundamental explanations are largely unchanged, but in the new introduction to this second...
Statistics in Psychology covers all statistical methods needed in education and research in psychology. This book looks at research questions when planning data sampling, that is to design the intended...
Cynthia Young's 3rd Edition of Trigonometry focuses on revisions and additions including hundreds of new exercises, more opportunities to use technology, and themed modeling projects that help connect...
A complete guide to cutting-edge techniques and best practices for applying covariance analysis methods
The Second Edition of Analysis of Covariance and Alternatives sheds new light on its topic, offering...
Statistical Theories and Methods with Applications to Economics and Business highlights recent advances in statistical theory and methods that benefit econometric practice. It deals with exploratory...
This book is a single-source guide to planning, designing and printing successful projects using the Adobe Creative Suite 5. Packed with real-world design exercises, this revised edition is fully updated...
This book presents recent developments and new trends in Combinatorial Optimization. Combinatorial Optimization is an active research area that has applications in many domains such as communications,...
Focuses on insights, approaches, and techniques that are essential to designing interactive graphics and visualizations
Making Sense of Data III: A Practical Guide to Designing Interactive Data Visualizations...
Praise for the First Edition
"Finally, a book devoted to dynamic programming and written using the language of operations research (OR)! This beautiful book fills a gap in the libraries of OR specialists...
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics
An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical...
Several points of disagreement exist between different modelling traditions as to whether complex models are always better than simpler models, as to how to combine results from different models and...
The ninth edition continues to provide engineers with an accessible resource for learning calculus The book includes carefully worked examples and special problem types that help improve comprehension...
This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish,... |
Summary: Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of...show more mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text. ...show less
Fundemental Definitions of Dimensional Theory The Principal Ideal Theorem and Systems of Parameters Dimension and Codimension One Dimension and Hilbert-Samuel Polynomials The Dimension of Affine Elimination Theory, Generic Freeness, and the Dimension of Fibers Grobner Bases Modules of Differentials |
MBF3C Grade 11 College Course Description
This course enables students to broaden their understanding of mathematics as a problem solving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and
communicate their thinking |
short video tutorial deals with the concept of order of operations in mathematics problems and builds on the material covered in earlier lessons.
The narrator reviews the concept, explaining that when a problem contains some combination of addition, subtraction, multiplication or division, the order of operations specifies that the multiplication and division components must be completed first, before carrying out the addition and subtraction work.
He then explains that when the problem contains calculations contained within brackets, the bracketed calculations must be completed first.
The tutorial introduces the mnemonic BEDMAS, which stands for Brackets, Exponents, Division, Multiplication, Addition, and Subtraction, although the instructor points out that exponents will be dealt with only in higher mathematics.
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Share
The order of operations specifies that the multiplication and division components of a math problem must be completed before carrying out the addition and subtraction work. It also specifies that calculations contained within brackets must be completed first.
This video tutorial reinforces that concept by providing three mathematics problems to solve. Each problem is more challenging than the one before.
The problems appear on a computer screen, with the narrator giving step-by-step instructions on how to solve themCitation
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This report examines a set of policies and practices formerly in place in British Columbia that supported access to post-secondary education and upgrading programs for income assistance (IA) recipients, particularly those facing multiple barriers to employment and education. The policies ended in 2002.
Based on interviews with staff who delivered these programs in colleges and institutes during the late 1990s, the authors describe the "best practices" for programs designed to help people with low income improve their educational credentials.
They found that effective programs address the key areas of access, retention, and transition. Other key components include identification of the existence of multiple obstacles to accessing formal education; outreach activities and strong links with community and relevant government agencies; assessment of students' needs and capabilities; financial help with tuition, fees, books, housing, and child care; and support for academic success, including counselling, advocacy, networking, and partnerships with employers.
The authors call on the British Columbia government to change welfare rules so that people receiving income assistance can participate in postsecondary education; restore and increase designated funding to post-secondary institutions to support IA recipients; support colleges and institutes in providing programs and services that offer holistic support to students; and restore tuition-free adult basic education in British Columbia's public post-secondary institutions.
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Phased-in retirement is really a catch phrase that can include special assignments, mentoring, job sharing, and end to shift work, reduced hours and telecommuting. Unfortunately, the tax, pension and paperwork implications of these accommodations pose barriers that can translate into inertia.
In New Brunswick it was the nurses' union that brought phased-in retirement to the bargaining table. Having spent so many years fighting for improved pensions, unions are cautious about sending mixed signals to employers. As our Viewpoints survey found, however, the strongest support for phased-in retirement does in fact come from public sector unions, (48% citing this option as very important in meeting the skill shortage challenge, Viewpoints 2002).
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George and John talked about language and empowerment - giving consumers the information they need to run their lives effectively and safely. They gave examples of baffling communication, and explained why people use complicated language. They discussed some of the myths that surround the term "plain language" and showed how the techniques go beyond just crafting the words. Finally, they used case studies to illustrate the benefits of plain language - efficiency, profitability, precision, and consumer satisfaction.
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This is a report on the National Literacy Secretariat's "Policy Conversation on New Technologies and Literacy." It provides background information about the NLS and an overview of some new technologies. It also explains the policy conversation process, which was intended to obtain information and opinions from the public about whether or not a policy on literacy and technology is needed and if it is, what some of its components might be.
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This set of practice tests is one of the resources for a 40-hour course developed to train people for jobs in water/wastewater treatment facilities.
The document includes tests for material covered in five of the eight course modules: measurement conversions; linear, area and volume calculations; chemical measurements; hydraulics; and wastewater and electricity.
There is also a sample final assessment, covering all the course material. Answers are provided in a separate document. |
Introductory TechnicalTechnical Mathematics, 5E provides current and practical vocational/technical applications of mathematical concepts for today?s sophisticated trade and technical work environments. Each unit provides a unique learning experience by featuring practical math concepts alongside step-by-step examples and problems drawn from various occupations that illustrate on-the-job applications of math. Enhancements to the Fifth Edition include a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a sec... MOREtion that supplements the basics of working with spreadsheets for graphing. Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math.Enhancements to the fifth edition include improved algebra coverage, a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing. |
components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts. Written in a readable, yet mathematically mature manner appropriate for colleg... MOREe level students, Coburn's Trigonometry uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area. Benefiting from the feedback of hundreds of instructors and students across the country, Trigonometry, Second Edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in trigonometry.
Introduction to Trigonometry
Angle Measure and Special Triangles
Properties of Triangles; Similar Triangles
Mid-Chapter Check
RBC: More on Special Triangles
Trigonometry: A View from the Coordinate Plane
Fundamental Identities and Families of Identities
Summary/Concept Rev, Mixed Rev, Practice Test
Calc Exploration and Discov... MOREery: The Range of Sine, Cosine, and Tangent |
1.Evaluate monomial and polynomial expressions given a value or values for the variable(s)
2.Multiply and divide monomial expressions with a common base, using the properties of exponents
3.Add, subtract, and multiply monomials and polynomials
4.Divide a polynomial by a monomial
5.Find values of variables for which an algebraic fraction is undefined
6.Multiplying Binomials – FOIL
7.Use formulas to calculate volume and surface area of rectangular solids and cylinders.
8.Percent error calculations.
B.Exponents
1.Rules of Exponents
2.Zero Exponent
3.Negative Exponent
4.Scientific Notation
a. Converting to and from scientific notation
b. Products and quotients using scientific notation
(The Variables and Expressions unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A12-A.A.15, A.N.4, A.G.1,, A.A.3, A.G.2, A.CM.5, A.RP.6, A.RP.5)
II.Factoring (3 weeks)
A.Factors
1.GCF
2.Trinomials with a leading coefficient of one (after GCF is factored out)
3.Trinomials with a leading coefficient other than 1
4.Difference of Perfect Squares
B.Algebraic Fractions
1. Finding a value(s) for which an algebraic expression is undefined
2. Simplify fractions with polynomials in the numerator and denominator
3.Add and subtract fractional expressions with monomial or like binomial denominators
4.Multiply and divide algebraic fractions, expressing the result in simplest form
Note: Item 3 will be taught but whether or not it will be tested will be at the discretion of the individual teacher. This item is not listed in the NYS Integrated Algebra curriculum, however we feel by teaching both types of factoring problems together, our students will have a better understanding of the material.
(The Factoring unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A15-A.A.20)
2 . Solve algebraic proportions in one variable which result in a quadratic equation.
3. Understand the relationship between the roots of a quadratic equation and the factors of a quadratic expression.
Note:The introduction of the quadratic formula in this unit of study is optional.
Note:The individual teacher may chose to test multiple times within this unit.Whenever possible, the instructor should stress to students the importance of being able to evaluate all expressions, identify and distinguish between the different types of equations, and know the appropriate/best method for solving the linear or quadratic equation.
(The Linear Equations and Inequalities and Quadratic Equations unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 -A.A.1-A.A.6, A.A.21-A.A. 26, A.N.5, A.CM.11, A.A.8, A.A.26, A.A.27, A.A.41, A.A.28, A.R.8, A.G.4, A.G.5, A.G.8-A.G.10, A.A.11, A.G.1)
** If time allows this item will be discussed in the first semester, otherwise it will be covered in detailed in semester two.
(The Applications and Word Problems unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 -
Embedded with the semester through the use of warm-up problems, applications of the above material, and review sheets are the topics listed below.
V. Mathematical Representations
A. Set Notation and Venn Diagrams
1. Use set-builder/interval notation to illustrate the elements of a set, given the elements in roster form
2. Finding the complement of a set
3. Finding the Intersection and Union of Sets (no more than three sets)
4. Finite Sets and Infinite Sets – use set-builder/interval notation to illustrate the elements of a set, given the elements in roster form -including graphic representation using inequality graphs
5. Empty Set
6. Subsets
7. Overlapping/Intersecting Sets – graphical and algebraic
8.Disjoint Sets
9.Use Venn diagrams to support a logical argument
B.Properties
1. Identify and apply the properties of real numbers
a. Closure
b. Commutative
c. Associative
d. Distributive
e. Identity
f. Inverse
2. Emphasis on examples and counterexamples
3. Absolute Value
a. Definition
b. Using absolute value to evaluate expressions
(The Mathematical Representations unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 -A.A.29-A.A.31, A.RP.11, A.RP.12, A.CM.2, A.CM.3, A.N.1, A.G.4, A.N.6) |
for Economists1 Introduction1.1 Motivation Why do we need to know mathematics in order to learn economics? What is economics? In economics we learn how the economy works in various situations. An economy consists of various people (consu
6 Integration (A.4)6.1 Indenite Integral Consider a continuous function f (x), where f (x) > 0 for all x. Consider the area under the graph of y = f (x) from a certain point a to anotherpoint x and denote it by A(x; a). What is the derivative of A(x;
Denition 36 (p.161). An m m matrix A = (ai j ) is called an upper-triangular matrixif ai j = 0 for i > j. A is called a lower-triangular matrix if ai j = 0 for i < j. A is calleda diagonal matrix if ai j = 0 for i = j.Theorem 56 (Fact 26.11, p.731). Th
Stat 351 Fall 2007Assignment #9This assignment is due at the beginning of class on Friday, November 30, 2007. You must submitsolutions to all problems. As indicated on the course outline, solutions will be graded for bothcontent and clarity of exposit
Statistics 351 (Fall 2007)Review of Linear AlgebraSuppose that A is the symmetric matrix1 1 0A = 1 2 1 .013Determine the eigenvalues and eigenvectors of A.Recall that a real number is an eigenvalue of A if Av = v for some vector v = 0. We callv a
Statistics 351 Midterm #1 October 10, 2007This exam has 4 problems and 6 numbered pages.You have 50 minutes to complete this exam. Please read all instructions carefully, and checkyour answers. Show all work neatly and in order, and clearly indicate yo2 November 16, 2007This exam is worth 50 points.There are 5 problems on 5 numbered pages.You have 50 minutes to complete this exam. Please read all instructions carefully, and checkyour answers. Show all work neatly and in orde
Stat 351 Fall 2007Assignment #1This assignment is due at the beginning of class on Monday, September 10, 2007. You must submitall problems that are marked with an asterix (*).1.* Send me an email to say Hello. If I have never taught you before, tell
Stat 351 Fall 2007Assignment #5This assignment is due at the beginning of class on Friday, October 5, 2007. You must submitsolutions to all problems. As indicated on the course outline, solutions will be graded for bothcontent and clarity of expositio
Stat 351 Fall 2007Assignment #7This assignment is due at the beginning of class on Friday, November 9, 2007. You must submitsolutions to all problems. As indicated on the course outline, solutions will be graded for bothcontent and clarity of expositi
Statistics 351 Midterm #1 October 18, 2006This exam has 4 problems and 5 numbered pages.You have 50 minutes to complete this exam. Please read all instructions carefully, and checkyour answers. Show all work neatly and in order, and clearly indicate yo
Statistics 351 Midterm #2 November 17, 2006This exam is worth 40 points.There are 5 problems on 5 numbered pages. You may attempt all ve and yourfour highest scores will be taken as your mark. You might want to read all vequestions before you begin.Y
Statistics 351 Fall 2006 (Kozdron) Midterm #2 Solutions1. (a) Recall that a square matrix is strictly positive denite if and only if the determinantsof all of its upper block diagonal matrices are strictly positive. Since2 22 3=we see that det( 1 )
Art-labeling Activity: Figure 21.15Part ADrag the appropriate labels to their respective targets.This content requires Adobe Flash Player 10.0.0.0 or newer.ANSWER:ViewCorrectIP: Class I and Class II MHC ProteinsClick on the link or the image below |
Nelson Functions 11 provides 100% coverage of the NEW Ontario curriculum for Grade 11 University (MCR 3U) while preparing students for success in Grade 12 and beyond. Key Features & Benefits include:
• Skills and Concepts Review at the beginning of every chapter
• Multiple solved exam...
Nelson Principles of Mathematics 10 ensures students build a solid foundation of learning so they are prepared for success in senior level courses. The program supports the diverse needs of students (through multiple entry points to help a varying range of learners), and offers extensive supp...
Big Ideas from Dr. Small provides math teachers with what they need to know to teach the curriculum while focusing on the big ideas for each math concept. Each book includes hundreds of practical activities and follow-up questions to use in the classroom. The accompanying Facilitator's Guide ...
The Mathematics Teacher eMentor DVD is a flexible, interactive professional learning resource that brings the expertise of leading Canadian math educator, Dr. Marian Small, to teachers across Canada.
With DVDs for K-3, Grades 4-6, and Grades 7-9, the Mathematics Teacher eMentor provides the full s...
More Good Questions, written specifically for secondary mathematics teachers, presents two powerful and universal strategies that teachers can use to differentiate instruction across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert ... |
Mrs. Paula Smith Algebra 2
This course is mainly a Junior level course. We take the topics learned in Algebra 1 and raise them to the next level. To me, Algebra 2 is all about graphing. First semester, we cover lines and their equations, as well as matrices and exponents. Second semester is more rigorous, as we dive into radicals, exponentials, logarithms, sequences and series. |
Subject: Mathematics (9 - 12) Title: Systems of Linear Inequalities Project Description: The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation. Subject: Mathematics (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of equations.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Thinkfinity Lesson Plans
Subject: Mathematics,Science Title: Shedding the LightAdd Bookmark Description: In this four-lesson unit, from Illuminations, students investigate a mathematical model for the decay of light passing through water. The goal of this investigation is a rich exploration of exponential models in context. Students examine the way light changes as water depth increases, conduct experiments, explore related algebraic functions using an interactive Java applet and analyze the data collected. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
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COMAP periodicals. |
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Description students with the skills and confidence they need in mathematics to succeed in their university courses.
Table of contents
Why this book was written How to use this book Part A - Basic Skills 1. Numbers 2. Algebra 3. Functions and Graphs 4. Differentiation 5. Integration Part B - Additional Topics 6. Optimisation 7. Finance 8. Regression 9. Index Numbers Appendix: Suggestions for Further Study Appendix: Using Computer Programs Solutions to Exercises
Features & benefits
It is designed as a handy reference purchase for interested students and also for lecturers to recommend to students identified as having problems in mathematics.
The book can also be used as a text in mathematics orientation courses for university economics, commerce and business administration students.
It assumes no prior high-level mathematical knowledge on behalf of the student. Only a familiarity with numbers and basic arithmetic is assumed.
Mathematics is becoming increasingly important in economics and business degrees which often excludes those without mathematical skills particularly minority groups. This book hopes to help reverse this trend by showing students that everyone can be successful at maths.
The author is an experienced lecturer familiar with the problems many students face with mathematics. He has written a book that will help retain otherwise good students who may leave economics and business because of a fear of mathematics.
The book includes exercises with solutions.
Author biography
Dr Paul Oslington is a Professor of Economics at Australian Catholic University in Sydney. |
Motivating readers by making maths easier to learn, this work includes complete past exam papers and student-friendly worked solutions which build up to practice questions, for all round exam preparation. It also includes a Live Text CDROM which features fully worked solutions examined step-by-step, and animations for key learning points.
Synopsis:
Edexcel and A Level Modular Mathematics C2 |
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Description
College Algebra and Trigonometry, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today's instructors and students.
New co-author Callie Daniels has experience in all classroom types including traditional, hybrid and online courses, which has driven the new MyMathLab features. For example, MyNotes provide structure for student note-taking, and Interactive Chapter Summaries allow students to quiz themselves in interactive examples on key vocabulary, symbols and concepts. Daniels' experience, coupled with the long-time successful approach of the Lial series, has helped to more tightly integrate the text with online learning than ever before.
Table of contents
R. Review of Basic Concepts
R.1 Sets
R.2 Real Numbers and Their Properties
R.3 Polynomials
R.4 Factoring Polynomials
R.5 Rational Expressions
R.6 Rational Exponents
R.7 Radical Expressions
1. Equations and Inequalities
1.1 Linear Equations
1.2 Applications and Modeling with Linear Equations
1.3 Complex Numbers
1.4 Quadratic Equations
1.5 Applications and Modeling with Quadratic Equations
1.6 Other Types of Equations and Applications
1.7 Inequalities
1.8 Absolute Value Equations and Inequalities
2. Graphs and Functions
2.1 Rectangular Coordinates and Graphs
2.2 Circles
2.3 Functions
2.4 Linear Functions
2.5 Equations of Lines and Linear Models
2.6 Graphs of Basic Functions
2.7 Graphing Techniques
2.8 Function Operations and Composition
3. Polynomial and Rational Functions
3.1 Quadratic Functions and Models
3.2 Synthetic Division
3.3 Zeros of Polynomial Functions
3.4 Polynomial Functions: Graphs, Applications, and Models
3.5 Rational Functions: Graphs, Applications, and Models
3.6 Variation
4. Inverse, Exponential, and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions
4.3 Logarithmic Functions
4.4 Evaluating Logarithms and the Change-of-Base Theorem
4.5 Exponential and Logarithmic Equations
4.6 Applications and Models of Exponential Growth and Decay
5. Trigonometric Functions
5.1 Angles
5.2 Trigonometric Functions
5.3 Evaluating Trigonometric Functions
5.4 Solving Right Triangles
6. The Circular Functions and Their Graphs
6.1 Radian Measure
6.2 The Unit Circle and Circular Functions
6.3 Graphs of the Sine and Cosine Functions
6.4 Translations of the Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Secant, and Cosecant
6.6 Harmonic Motion
7. Trigonometric Identities and Equations
7.1 Fundamental Identities
7.2 Verifying Trigonometric Identities
7.3 Sum and Difference Identities
7.4 Double-Angle and Half-Angle Identities
7.5 Inverse Circular Functions
7.6 Trigonometric Equations
7.7 Equations Involving Inverse Trigonometric Functions
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Vectors, Operation, and the Dot Product
8.4 Applications of Vectors
8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers
8.7 Polar Equations and Graphs
8.8 Parametic Equations, Graphs, and Applications
9. Systems and Matrices
9.1 Systems of Linear Equations
9.2 Matrix Solution of Linear Systems
9.3 Determinant Solution of Linear Systems
9.4 Partial Fractions
9.5 Nonlinear Systems of Equations
9.6 Systems of Inequalities and Linear Programming
9.7 Properties of Matrices
9.8 Matrix Inverses
10. Analytic Geometry
10.1 Parabolas
10.2 Ellipses
10.3 Hyperbolas
10.4 Summary of the Conic Sections
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 The Binomial Theorem
11.5 Mathematical Induction
11.6 Counting Theory
11.7 Basics of Probability
Appendices
Appendix A. Polar Form of Conic Sections
Appendix B. Rotation of Axes
Appendix C. Geometry Formulas
Glossary
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications
Index
Photo Credits
New to this edition
New and Updated Features
The exercise sets offer many new and modified exercises, with updated real life data throughout.
Numbered and Example references within the text are set in the same font as the figure and bold print for the example, helping visual learners identify and connect them.
The "drop down" style is used whenever appropriate to distinguish between simplifying expressions and solving equations.
Explanatory side comments are increased to guide students through the steps of simplifying and solving problems in the examples.
Updates to the MyMathLab Course
MyNotes from new co-author Callie Daniels offer support for student note taking. Interactive chapter summaries allow students to quiz themselves with interactive examples on key vocabulary, symbols, and concepts.
Ready-to-Go MyMathLab courses are pre-built MyMathLab courses that make the start-up time for building your course quick and easy.
Interactive Figures are now available, enabling users to manipulate figures to bring hard-to-convey math concepts to life.
Additional MathXL coverage of key exercises include Summary exercises, Relating Concept exercises, and Chapter Review exercises. Additional MathXL quizzes (without help features) are assignable as homework. These are based on the text's mid-chapter quizzes.
Cumulative assignments follow each chapter test in the homework and test manager, allowing students to synthesize old material throughout the course. These assignments consist of 30 problems each.
Features & benefits
Support for All Classroom Types: a complete suite of instructional materials makes it easier for instructors to prepare for the course, and leads to student success. Updates to MyMathLab® and MathXL® are an integral part of supporting instructors and student success in today's classroom.
Additional MathXL quizzes are assignable as homework. These are based on the text's mid-chapter quizzes.
Cumulative assignments follow each chapter test in the homework and test manager, allowing students to synthesize previous material throughout the course. These assignments consist of 30 problems each.
Support for Learning Concepts: a systematic approach is used to present each topic, and is designed to actively engage students in the learning process. As a result, students develop both the conceptual understanding and the analytical skills necessary for success.
Pointers in the examples provide on-the-spot reminders and warnings about common pitfalls. Examples now offer additional side comments where appropriate in the step-by-step solutions, and there are more section references to previously covered material.
Now Try exercises conclude every example with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. Students are able to immediately apply and reinforce the concepts and skills presented in the examples, while actively engaged in the learning process.
Real-life applications in the examples and exercises draw from fields such as business, pop-culture, sports, life sciences, and environmental studies to show the relevance of algebra to daily life.
Functions are introduced in Chapter 2 and are a unifying theme throughout the text.
Function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
NEW! Animations are available within MyMathLab.
Graphing calculator coverage is optional and may be omitted without loss of continuity. The authors stress that these devices can be useful as an aid to understanding, but that students must master the underlying mathematical concepts first.
Graphing calculator solutions are included for selected examples as appropriate.
Graphing calculator notes and exercises are marked with an icon for easy identification and flexibility.
Cautions and Notes boxes throughout the text give students warnings of common errors and emphasize important ideas.
Looking Ahead to Calculus offers glimpses of how the algebraic topics currently being studied are used in calculus. These notes can be found in the margins of the text in key places.
Connections boxes provide connections to the real world or to other mathematical concepts, historical backgrounds, and thought-provoking questions for writing, class discussion, or group work.
Chapter Openers provide a motivating application topic that is tied to the chapter content, plus a list of sections and any quizzes or summary exercises in the chapter.
Support for Practicing Concepts: the variety of exercise types promotes understanding of the concepts and reduces the opportunity for rote memorization.
25% of the exercises are new in this edition.
Quizzes allow students to periodically check their understanding of the material covered. At least one quiz now appears in each chapter, where appropriate.
Connecting Graphs with Equations problems, by request, provide students with opportunities to write equations for given graphs.
Relating Concepts Exercises help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students and are available in selected exercise sets.
Full solutions to selected exercises are included at the back of the text for exercise numbers that are marked with a green square. There are three to five exercises per section and are chosen because they extend the skills and concepts presented in the examples.
Support for Review and Test Preparation: ample opportunities for review are interspersed within chapters and found at the end of chapters.
Quizzes appear periodically throughout the chapter for students to check their progress. Answers appear in the student answer section at the back of the text. NEW! These are now assignable in MyMathLab.
Summary Exercises offer mixed review, requiring students to decide which methods covered in the chapter should apply to a particular problem. NEW! These are now assignable in MyMathLab.
Chapter Reviews and Test Prep conclude every chapter with the following features:
An extensive Summary, featuring a section-by-section list of Key Terms and New Symbols
A Quick Review of important concepts, presented alongside corresponding Examples
A comprehensive set of Review Exercises
A Chapter Test covering all skills and concepts from the chapter
A glossary of key terms from throughout the text is provided at the back of the book as an additional student study aid.
Author biography
Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.
David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking.
Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a bachelor's degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two master's degrees: one in Applied Mathematics and Statistics from the University of Missouri-Rolla, the second in Adult Education from the University of Missouri- St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students' understanding of mathematics, and creating materials that support classroom teaching and student understanding. |
1: Recording Book (Oxford Maths Zone) R: Big Book: Year R PlanEach of the six books in the Thinking by Numbers series provides clear and practical teaching strategies to help develop children's thinking skills through mathematics. The series focuses on the five main thinking skills outlined by the N
Maths Inspirations: Y3-6/P4-7: New Mastermaths: Evaluation Pack
Editorial review
A new generation of the bestselling junior series Mastermaths, specially created to meet today's classroom needs. Stimulating pupil books provide differentiated practice and consolidation to support the teaching of lessons using the NNS U
Beginning with Numbers: Pack (Oxford Introductory Maths Workbooks)
Editorial review
This pack contains Books 1 and 2 of "Oxford Introductory Maths Workbooks", a series designed to provide young children with a gradual introduction to mathematical ideas, principles and language.
Football Maths
Editorial review
This series was launched with four titles for Key Stage 2 in May 1998. It has now been extended to Key Stage 1. The series of level-by-level fill-in workbooks uses football as the context to get children aged 5-11 doing maths for fun. The
For professional mathematicians and graduate students, especially those working in functional analysis, Dales (pure mathematics, U. of Leeds) explores the relationship between the algebraic and the topological structures both of general
Combinatorial Designs and Tournaments (Oxford Lecture Series in Mathematics and Its Applications, 6)
Editorial review
The mathematics of tournament design are surprisingly subtle, and this book, an extensively revised version of Ellis Horwood's popular Combinatorial Designs: Construction Methods, provides a thorough introduction. It includes a new chapte
theory, and the completeness theorems. Originally published in French as Logique Mathematique in 1993.Book News, Inc.®, Portland, OR
Reviewed by a reader, (Podunk, Iowa)
You'll find this very hard unless you are a competent math major at one of the better universities. Similar to Elliot Mendelson's text, but not quite as good. Good chapter on Boolean algebra as apiece of pure math; Halmos and Givant is ge
The authors provide a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. Their treatment combines elegant algebraic theory with applications to number theory, problems in classical |
GCSE Modules
Important note: These pages contain material that will help you to study for OCR GCSE maths modules. The material is organised in a similar way to the official course textbooks, but this website is not connected to OCR in any way.
The modular syllabus (OCR J562)
You will take three module exams:
Unit A is worth about 25% of your final mark. The exam is one hour long. You are expected to use a calculator in this exam.
Unit B is worth about 25% of your final mark. The exam is one hour long. This is a non-calculator exam.
Unit C is worth about 50% of your final mark. The exam is two hours long for the Higher Tier and 1.5 hours long for the Foundation Tier. You are expected to use a calculator in this exam.
Each module is offered at two tiers:
Higher is for students working at grades A*-D
Foundation is for students working at grades C-G
Modules take place in November, January and June. Your teacher will tell you which exam you are taking next and when it will be.
Revision materials for the modules:
I am planning to have some materials online by September 2011.
I was working on revision materials for the modules, but my school has now subscribed to the very excellent MyMaths.co.uk, which has lots of excellent materials for revision. There are lots of changes planned to GCSE maths in the near future, so I've decided not to spend lots of time making things for this site that will end up getting scrapped! I will be working on some learning resources, watch the news page for more details. |
Representation Standard
for Grades 9–12
Instructional
programs from prekindergarten through grade 12 should enable all students
to—
create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations
to solve problems;
use representations to model and interpret physical, social,
and mathematical phenomena.
If mathematics is the "science of patterns" (Steen 1988), representations are
the means by which those patterns are recorded and analyzed. As students
become mathematically sophisticated, they develop an increasingly large
repertoire of mathematical representations and the knowledge of how to
use them productively. This knowledge includes choosing specific representations
in order to gain particular insights or achieve particular ends.
The importance of representations can be seen in every section of this chapter.
If large or small numbers are expressed in scientific notation, their
magnitudes are easier to compare and they can more readily be used in
computations. Representation is pervasive in algebra. Graphs convey particular
kinds of information visually, whereas symbolic expressions may be easier
to manipulate, analyze, and transform. Mathematical modeling requires
representations, as illustrated in the "drug dosage" problem and in the
"pipe offset" problem. The use of matrices to represent transformations
in the plane illustrates how geometric operations can be represented visually
yet also be amenable to symbolic representation and manipulation in a
way that helps students understand them. The various methods for representing
data sets further demonstrate the centrality of this topic.
p.
360
A wide variety of representations can be seen in the examples in this chapter.
By using various representations for the "counting rectangles" problem
in the "Problem Solving" section, students could find different solutions
and compare them. The use of algebraic symbolism to explain a striking
graphical phenomenon is central to the "string traversing tiles" task
in the "Communication" section. Representations facilitate reasoning and
are the tools of proof: they are used to examine statistical relationships
and to establish the validity of a builder's shortcut. They are at the
core of communication and support the development of understanding in
Marta's and Nancy's work on the "string traversing tiles" problem. Although
at one level the story of Mr. Robinson's class is about connections, at
another level it is about representation: one group of students places
coordinates that "make things eeeasy," the class gains insights from dynamic
representations of geometric objects, and the students produce proofs
in coordinate and Euclidean geometry. A major lesson of that story is
that different representations support different ways of thinking about
and manipulating mathematical objects. An object can be better understood
when viewed through multiple lenses. »
What should representation
look like in grades 9 through 12?
In grades 9–12, students' knowledge and use of representations should
expand in scope and complexity. As they study new content, for example,
students will encounter many new representations for mathematical concepts.
They will need to be able to convert flexibly among these representations.
Much of the power of mathematics comes from being able to view and operate
on objects from different perspectives.
In elementary school, students most often use representations to reason about
objects and actions they can perceive directly. In the middle grades,
students increasingly create and use mathematical representations for
objects that are not perceived directly, such as rational numbers or rates.
By high school, students are working with such increasingly abstract entities
as functions, matrices, and equations. Using various representations of
these objects, students should be able to recognize common mathematical
structures across different contexts. For example, the sum of the first
n odd natural numbers, the areas of square gardens, and the
distance traveled by a vehicle that starts at rest and accelerates at
a constant rate can be represented by functions of the form f(x) = ax2.
The fact that these situations can be represented by the same class of
functions implies that they are alike in some fundamental mathematical
way. Students are ready in high school to see similarity in the underlying
structure of mathematical objects that appear contextually different but
whose representations look quite similar.
p.
361
High school students should be able to create and interpret models of more-complex
phenomena, drawn from a wider range of contexts, by identifying essential
features of a situation and by finding representations that capture mathematical
relationships among those features. They should recognize, for example,
that phenomena with periodic features often are best modeled by trigonometric
functions and that population growth tends to be exponential, or logistic.
They will learn » to describe some real-world
phenomena with iterative and recursive representations.
Consider the graph of the concentration of CO2
in the atmosphere as a function of time and latitude during the period
from 1986 through 1991 (see fig. 7.39) (Sarmiento 1993). Teachers might
use an example such as this to help students understand and interpret
several aspects of representation. Students could discuss the trends in
the change in concentration of CO2 as
a function of time as well as latitude. Doing so would draw on their knowledge
about classes of functions and their ability to interpret three-dimensional
graphs. They should be able to see a roughly linear increase across time,
coupled with a sinusoidal fluctuation with the seasons. Focusing on the
change in the character of the graph as a function of latitude, students
should note that the amplitude of the sinusoidal function lessens from
north to south. Students can test whether the trends they observe in the
graph correspond to recent theoretical work on CO2
concentration in the atmosphere. For example, the author of the article
attributes the sinusoidal fluctuation to seasonal variations in the amount
of photosynthesis taking place in the terrestrial biosphere. Students
could discuss the differences in amplitude across seasons in the Northern
and Southern Hemispheres.
Fig. 7.39. A three-dimensional graph
of the concentration of C02
in the atmosphere as a function of time and latitude (Adapted
from Sarmiento [1993])
Electronic technologies
provide access to problems and methods that until recently were difficult
to explore meaningfully in high school. In order to use the technologies
effectively, students will need to become familiar with the representations
commonly used in technological settings. For example, solving equations
or multiplying matrices using a computer algebra system calls for learning
how to input and interpret information in formats used by the system.
Many software tools that students might use include special icons and
symbols that carry particular meaning or are needed to operate the tool;
students will need to learn about these representations and distinguish
them from the mathematical objects they are manipulating.
What should be the teacher's role in developing representation in grades
9 through 12?
p.
362
An important part of learning mathematics is learning to use the language, conventions,
and representations of mathematics. Teachers should introduce students
to conventional mathematical representations »
and help them use those representations effectively by building
on the students' personal and idiosyncratic representations when necessary.
It is important for teachers to highlight ways in which different representations
of the same objects can convey different information and to emphasize
the importance of selecting representations suited to the particular mathematical
tasks at hand (Yerushalmy and Schwartz 1993; Moschkovich, Schoenfeld,
and Arcavi 1993). For example, tables of values are often useful for quick
reference, but they provide little information about the nature of the
function represented. Consider the table in the "Algebra" section in this
chapter that gives the number of minutes of daylight in Chicago every
other day for the year 2000. The values in the table suggest that the
function is initially increasing and then becomes decreasing. Knowledge
of the context of a graph of those values suggests that the behavior is
actually periodic. Similarly, algebraic and graphical representations
of functions may provide different information. Some global properties
of functions, such as asymptotic behavior or the rate of growth of a function,
are often most readily apparent from graphs. But information about specific
aspects of a function—the exact value of f() or exact values of
x where f(x)has a maximum or a minimum—may best
be determined using an algebraic representation of the function. Suppose
g(x) is given by the equation g(x) = f(x)
+ 1, for all x. The analytic definitions of f(x) and
g(x) may offer the most-effective ways of computing specific
values of f(x) and g(x), but graphing the function
reveals that the "shape" of g(x) is precisely the same as that
of f(x)—that the graph of g(x) is obtained by
translating the graph of f(x) one unit upward.
As in all instruction, what matters is what the student sees, hears, and understands.
Often, students interpret what teachers may consider wonderfully lucid
presentations in ways that are very different from those their teachers
intended (Confrey 1990; Smith, diSessa, and Roschelle 1993). Or they may
invent representations of content that are idiosyncratic and have personal
meaning but do not look at all like conventional mathematical representations
(Confrey, 1991; Hall et al. 1989). Part of the teacher's role
is to help students connect their personal images to more-conventional
representations. One very useful window into students' thinking is student-generated
representations. To illustrate this point, consider the following problem
(adapted from Hughes-Hallett et al. [1994, p. 6]) that might be presented
to a tenth-grade class:
A flight from SeaTac Airport near Seattle, Washington, to LAX Airport
in Los Angeles has to circle LAX several times before being allowed
to land. Plot a graph of the distance of the plane from Seattle against
time from the moment of takeoff until landing.
p.
363
Students could work individually or in pairs to produce distance-versus-time
graphs for this problem, and teachers could ask them to present and defend
those graphs to their classmates. Graphs produced by this class, or perhaps
by students in other classes, could be handed out for careful critique
and comment. When they perform critiques, students get a considerable
amount of practice in communicating mathematics as well as in constructing
and improving on representations, and the teacher gets information that
can be helpful in assessment. One representation of the flight that a
student might produce is shown in figure 7.40. »
Fig. 7.40. A representation that
a student might produce of an airplane's distance from
its take-off point against the time from takeoff to landing
This representation indicates a number of interesting and not uncommon misunderstandings,
in which literal features of the story (the plane flying at constant height
or circling around the airport) are converted inappropriately into features
of the graph (Dugdale 1993; Leinhardt, Zaslavsky, and Stein 1990).
Representations of this type can provoke interesting classroom conversations,
revealing what the students really understand about graphing. This revelation
puts the teacher in a better position to move the class toward a more nearly
accurate representation, as sketched in figure 7.41.
Fig. 7.41. A more nearly accurate
representation of the airplane's distance from its take-off
point against the time from takeoff to landing
Mathematics is one of humankind's greatest cultural achievements. It is
the "language of science," providing a means by which the world around us
can be represented and understood. The mathematical representations that
high school students learn afford them the opportunity to understand the
power and beauty of mathematics and equip them to use representations in
their personal lives, in the workplace, and in further study. |
Teaching Conic Sections
Teaching Conic Sections
So I currently teach a precalc class and new this year we are required to teach conic section.
We cover parabolas, circles, ellipses, and hyperbolas. Since I haven't taught this before, I was wondering if anyone has suggestions on how to teach it? The book we use has a bunch of formulas, but I'm looking for a way to teach it to my students without using all the formulas so they don't have to memorize a bunch of formulas before their exam. What has worked for others?
You should be able to design good lessons directly based on the book sections. As long as you use a Pre-Calculus book you will have rich enough information available.
Be sure to demonstrate the conic sections using a realistic three-dimensional model. Also use the definitions of each conic section and the distance formula to derive the equation for each conic section, and include the analytical cartesian graph for each.
You are right on-target about not just giving a bunch of formulas. The demonstration and the derivations are important for learning and understanding.
Teaching Conic Sections
As a student who struggled through conic sections, I found that by exploring how they were really just variations of the of the same things cemented my understanding of the topic. So if I were in your shoes I would try to show the similarities and differences of the different sections. Specifically between the hyperbola and parabola and the circle and ellipse.
As someone who not long ago learnt Conic Sections, I found the derivations of the formula much easier than remembering them. It was good to see the formulas at first but I much preferred the derivations.
As above said, use a 3D model as well. The 2D drawing didn't really do it justice for me.
I was definitely going to derive the formulas using the distance formula and talk about applications. I wouldn't scratch formulas altogether, but our book has like 8 different formulas, which isn't fair to give all of them to my students if I don't give them on an exam.
Something one of my physics professors said to our class is recalled to me by this thread. He said students of today are so used to tv games, comics, etc. rather than playing with things with their hands, that they can't visualize 3d objects anymore. He was of course exaggerating. I think it quite odd if a student can't visualize what's going on with conic sections, so yes a model would be quite good. Maybe you could get someone to cut it at all the right angles.
Also, the old books on geometry, particularly solid geometry, should be good with conic sections, so maybe go down to the library and have a look at them.
Ah yes, I have a fun experiment using that! You should certainly teach that!
Here it goes: Dandelin was a Belgian, and some people decided to celebrate him. So what they did was the following. They made an ice-cream cone, they put a small biscuit in there (they made it like an ellipse so it would fit inside the cone). And they they put a ball of ice-cream in the cone. Then they would sell it to people.I always tought that it was very clever, and it was quite the financial succes too!did they then discover another, smaller, ice-cream (just like discovering another layer of chocolates when you finish the first layer!), which touched the other focus on the other side of the biscuit? |
... MOREcommonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way. The8.2 Solving a System of Equations in Two Variables by the Substitution Method
8.3 Solving a System of Equations in Two Variables by the Addition Method
How Am I Doing? Sections 8.1—8.3
8.4 Review of Methods for Solving Systems of Equations
8.5 Solving Word Problems Using Systems of Equations
Use Math to Save Money
Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach
9. Radicals
9.1 Square Roots
9.2 Simplifying Radical Expressions
9.3 Adding and Subtracting Radical Expressions
9.4 Multiplying Radical Expressions
How Am I Doing? Sections 9.1—9.4
9.5 Dividing Radical Expressions
9.6 The Pythagorean Theorem and Radical Equations
9.7 Word Problems Involving Radicals: Direct and Inverse Variation
Use Math to Save Money
Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
10. Quadratic Equations
10.1 Introduction to Quadratic Equations
10.2 Using the Square Root Property and Completing the Square to Find Solutions
10.3 Using the Quadratic Formula to Find Solutions
How Am I Doing? Sections 10.1—10.3
10.4 Graphing Quadratic Equations
10.5 Formulas and Applied Problems
Use Math to Save Money
Chapter 10 Organizer
Chapter 10 Review Problems
How Am I Doing? Chapter 10 Test
Math Coach
Practice Final Examination
Appendix A. Table of Square Roots
Appendix B. Metric Measurement and Conversion of Units
Appendix C. Interpreting Data from Tables, Charts, and Graphs
Appendix D. The Point–Slope Form of a Line
Solutions to Practice Problems
Answers to Selected Exercises
Glossary
Subject Index
Photo Credits
Index of Applications (Available in MyMathLab) |
Print Resources
What can I do with a Math Major?
Essays from 101 people using their math in different ways.
"Most of the writers in this volume use the mathematical sciences on a daily basis in their work; others rely on the general problem-solving skills acquired in their mathematics courses as they deal with complex issues." p. 1
Two Major Themes
These authors liked math so studied it, even when they were not sure what they would do with it for a career.
They found a satisfying career, made possible by their math skills.
"I chose a degree in mathematics for two reasons: I was good at it, and I enjoyed it. I figured that was all I needed to find a job which was both challenging and fun. Although I wasn't aware of the multitude of career opportunities at the time, I knew that the sound logic skills one hones while obtaining a degree in math would be useful in doing just about anything. How can you go wrong learning skills that can be applied to any type of problem in any job?"
"I thoroughly enjoy the career I've chosen, and I have no question that I wouldn't be here if I had not started my training with a degree in mathematics." p. 140"
My training in mathematics provided me with the invaluable ability to apply logic, reason, and careful quantitative, as well as qualitative, analysis to my work. These thought processes along with good written and oral communications skills are desirable and applicable to almost any field."
"Remember--a calculating mind is a good mind!" p.21
"Studying mathematics gives you the tools to analyze problems and think logically, which helps in whatever profession you choose. People have great respect for a degree in mathematics." p.195
"Mathematics is a vast field, populated with thousands of job titles you have never heard before." p. 45.
"Applications, problem solving, and reasoning are some of the elements that bind most math jobs." p. xii.
Communication to relate the results of using these skills to people who want answers to their problems, but lack these skills to solve the problems.
Essays from women about how they use their math training.
"In today's competitive world, a good education is a necessity. By combining that education with a strong background in math and logic, you are ready for any career." p. vii
"One of the most important things a technical education can do is teach students how to learn what they will need to know when they change from one field to another." p. 106
Mathematical Scientists at Work (booklet)
Image not available.
Essays from 20 people about their jobs.
"Mathematicians have the best jobs! Mathematicians have virtually an unlimited number of career opportunities!" p. 1 |
Merrill, Carole
8th Grade Math/Algebra
Math at the 8th grade level includes state objectives one through six. Objective one concerns numbers, objective wo concerns patterns and algebraic thinking, objective three covers geometry, objective four is about measurement, objective five concerns statistical analysis and probability, and objective six covers critical thinking and problem solving strategies. Students are refining skills using ratios and proportions, pattern recognition, making predictions, and some fundamental skills that will prepare them for Algebra and geometry.
Algebra is the study of patterns and making predictions. Patterns can be found in linear, quadratic and exponential forms. Students look at, and make predictions about these patterns in graphs, tables, equations and apply them problems in business, the sciences and every day living.
This year, in both 8th grade math and in AlgebraI, we are using C-scope for our curriculum. |
Quick Links
English-Spanish Editions for California Math
California is a uniquely diverse state, with over half of K-12 students from a Spanish-speaking background and over 25% categorized as ELL.
At CGP Education we're proud to engage these students and we've gone the extra mile to ensure they're equipped to succeed in Math.
We offer English-Spanish editions of our Student Textbooks, Homework Books and Skills Review / Reteaching Resources CD-ROMs.
Each of these products shows a high quality Spanish translation directly underneath the English so that students are immersed in
English whilst they still have the Spanish support they need.
Homework Book
Skills Review and Reteaching CD-ROM
These handy intervention tools include straightforward explanations and practice exercises in both Spanish and English.
They cover material from the previous two grades making Math accessible for students who have missed previous tuition. English-Spanish Edition Skills Review CD-ROM Sample |
In this limits worksheet, students apply L'Hopital's rule to solve four limits problems. They solve a total of eleven short answer problems. The final seven problems ask students to find the asymptotes of functions.
In this limiting reagent and percent yield worksheet, students fill in 6 blanks with terms related to limiting reagents and percent yield. They determine if 6 statements are true or false, they match 5 terms with their definitions and they solve 2 problems related to percent yield and limiting reagents.
Students examine the importance of limiting power in governments. In this government lesson, students investigate the importance of placing limits on government by looking at the US Constitution. They look at ways that being an active citizen benefits the common good and study the definition of philanthropy.
In this limits and continuity test, learners solve 8 multiple choice questions. They define the words limits and continuity. Students determine the limits of 8 functions. Learners find the value for a constant in one function, and prove one function is continuous at x=0. 4 questions require students to graph functions. There are 25 questions in all (plus one extra credit question).
In this infinite limit instructional activity, students compute horizontal and vertical asymptotes. They use trigonometric functions to find the limits of functions and compare results. This two-page instructional activity contains examples and explanations and fourteen problems.
In this successive approximations activity, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page activity contains explanations, examples, and approximately ten problems. |
Take the Parent Guide with You!
Math Lab
The goal of the Math Lab is to offer the highest quality service to students requiring assistance in lower-level mathematics classes up to and including differential equations.
We promote an atmosphere that is conducive to learning, which makes the lab an ideal place for those wanting to work on a homework assignment or study for an upcoming exam.
We also have solution manuals for many of the courses with which we assist. Past results have shown that regular attendance of the Math Lab can make a difference in gaining a higher grade, so we strongly recommend that students take advantage of the resources available. |
ENEE 759F: Mathematical Foundations for Computer Systems
Course Goals:
Mathematical modeling, design, analysis, and proof techniques related to
computer systems.
Probability, logic, combinatorics, set theory, and graph theory, as they
pertain to the design and performance of computer systems.
Techniques for the design and analysis of algorithms and data structures.
Study of efficient algorithms from areas such as graph theory and networks.
Translation from mathematical theory to actual programming.
Understanding of the inherent complexity of problems: polynomial time,
NP-completeness and approximation algorithms.
The course emphasizes mathematical rigor. |
Lesson 4 Updated
Hey everyone, I've updated Lesson 4 finally. It now covers section 2.1 and the exercises are all from that section. It's the same homework that used to be for lesson 3.
Also, I got a little behind on looking through everyone's homeworks for lesson 2. There was a lot of great work there and I'll try to leave a comment for everyone soon.
In the mean time, if you have completed lesson 2's homework then feel free to browse through other people's submissions and point out things that are good or could be improved on. It's a great way to learn the material even more in depth. |
PUMP Algebra Curriculum Home Page
This page is very out of date and is currently being modified. In the
meantime, please go to Carnegie Learning to learn
more about currently available cognitive tutors for mathematics and
writing.
Who are we?
The PUMP(Pittsburgh Urban Mathematics Project)
Algebra Project is a collaboration between the ACT
Research Group and the PACT
Center at Carnegie Mellon University, and a group of teachers
in the Pittsburgh Public Schools. It is an attempt to make high school
Algebra accessible to all students through the use of situational curriculum
materials and an intelligent computer based tutoring system.
The high school tutor and course materials are now called "Cognitive
Tutor Algebra" and are being marketed by the PACT Center's spin-off
company, Carnegie
Learning. The PACT Center is currently developing tutors for
Middle School math.
The development of Algebra throughout the curriculum is based on the
students' own informal knowledge of mathematics and on problem situations.
Modelling situations such as the Nintendo Problem, shown above, students
begin to construct intuitive understandings of and connections between
multiple representations of functions. From the beginning of the course
students are asked to make the connections between the various representations
and to construct each representation based on their understanding of the
problem situation.
A mere listing of topics covered does not adequately provide the necessary
framework for the curriculum. Consequently, we use a matrix which attempts
to show the development of the curriculum in a more meaningful way; however,
a three dimensional framework showing the multiple representations as the
core which expands from the first quadrant with simple direct variation
to mx+b to all four quadrants to systems to data analysis to quadratics
would probably be more appropriate.
Currently students work in their regular classrooms three days a week on
the curriculum. The other two class periods are spent in the computer lab
working on the computer tutors. (See the PAT
tutor). The classroom curriculum is reproduced for each student on
loose-leaf notebook paper with space for them to write their responses
on the actual workbook. ALL answers must be written in complete sentences.
Homework is also reproduced on loose-leaf. TI-81 scientific calculators
are provided by the school for use in the classroom. Each student can be
issued a scientific calculator to use on homework.
The U.S. Shirts
Problem is a sample three day lesson module from the first quarter
of the classroom curriculum. Teachers are encouraged to read over the problem
situation at the beginning of the period and then give the students time
to work in cooperative groups to solve the problem. Groups are given overlays
to describe the problem and asked to present their results to the rest
of the class.
Learning in Cooperative Groups
The PUMP project is committed not only to providing the opportunity
for all students to enroll in Algebra, but also to providing the students
with the human and technological support to enable them to be successful
in Algebra. This support includes the computer tutors, the support of the
Chapter One reading specialist, after school tutoring, Family Algebra Nights,
the inclusion of Special Education students and teachers, support for the
teachers including summer workshops and on-going help, and new assessment
strategies.
Family Algebra Night
Student assessment is a major area of emphasis. The first
semester final exam and the year
end final exam from the1993-94 school year are presented to the new
students at the beginning of the school year along with level 4 student
responses in order to clearly communicate our expectations to the students.
Students are assessed on their performance on group tasks in the classroom,
individual on demand performance tasks, portfolios, and their work on the
computer tutors, as well as on more the traditional homework and tests.
At the end of each grading period students are given an individual on-demand
performance task similar to the situations that they have worked on in
the classroom. Each of these requires the student to do a mathematical
analysis of a situation and to produce a writen report based on their analysis.
At the end of the first and third grading periods, these tasks are graded
by the individual teachers; but at the end of each semester these tasks
are graded using the New
Standards Type Grading Conference Model. |
5. Trigonometry (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Concept of a function, sine and cosine functions, tables
and graphs, other trigonometric functions, identities and equations. Trigonometric
functions of angles, solution of triangles. (See Duplication of Courses.)
6. Precalculus (4)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Basic algebraic properties of real numbers; linear and quadratic
equations and inequalities; functions and graphs; polynomials; exponential
and logarithmic functions; analytic trigonometry and functions; conics;
sequences, and series.
11. Elementary Statistics (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Illustration of statistical concepts: elementary probability
models, sampling, descriptive measures, confidence intervals, testing hypotheses,
chi-square, nonparametric methods, regression. It is recommended that students
with credit in Math 72 or 75 take Math 101.
41. Number Systems (3)
Not open to mathematics majors. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C or better
in a college-taught intermediate algebra course. Designed for elementary
credential candidates. Development of rational number system and its subsystems
from the informal point of view; sets, relations and operations, equivalence
classes; definitions of number systems and operations; algorithms for operations;
prime numbers, divisibility tests; ratios.
43. Elementary Problem Solving (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. The purpose of this course is to develop problem solving
skills using elementary mathematics.
45. What Is Mathematics? (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Intended primarily for liberal arts students. Topics: mathematics
and social science, mathematics of shape and growth, statistics, mathematics
of management science and mathematics of computers.
51. Elements of Modern Mathematics (3)
Prerequisite: passing score on the Entry Level Mathematics (ELM) Exam and
intermediate algebra. Logic, set theory, vectors and matrices, linear programming,
permutations and combinations, probability, Markov chains, applications
to business and social sciences.
70. Mathematis for Life Sciences (4)
No credit if taken after Math 72 or 75; one unit of credit if taken after
Math 71. Prerequisite: Students must take the ELM exam; students who do
not pass the exam must record a grade of C or better in a college-taught
intermediate algebra course. Functions and graphs, limits, derivatives,
antiderivatives, differential equations, and partial derivatives with applications
in the Life Sciences.
71. Elementary Mathematical Analysis I (3)
No credit if taken after Math 70, 72, or 75. Prerequisite: Students must
take the ELM exam; students who do not pass the exam must record a grade
of C or better in a college-taught intermediate algebra course. Review of
algebra, real numbers, inequalities, function, graph, finite induction,
limit, differentiation of algebraic functions and applications to extrema,
mean value theorem, I'Hôpital's rule.
75. Mathematical Analysis I (4)
No credit if taken after Math 72; 2 units of credit if taken after Math
71; 3 units of credit if taken after Math 70. Prerequisite: Students must
take the ELM exam. Additionally,beginning in the fall of 1994, a passing
score on the Precalculus Diagnostic Test or a grade of C or better in Math
6 will be required prior to registration. Inequalities, functions, graphs,
limits, continuity, derivatives, antiderivatives, the definite integral
and applications.
143. History of Mathematics (4)
Prerequisite: Math 72 or 75. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry, and calculus
from ancient times through modern times. Theorems with historical significance
will be studied as they relate to the development of modern mathematics.
145. Problem Solving (3)
Prerequisite: at least ine 100-200 series mathematics course. A study of
formulation of problems into mathematical form; analysis of methods of attack
such as specialization, generalization, analogy, induction, recursion, etc.
applied to a variety of non-routine problems. Topics will be handled through
student presentation.
161. Principles of Geometry (3)
Prerequisite: Math 77. The classical elliptic, parabolic, and hyperbolic
geometries developed on a framework of incidence, order and separation,
congruence; coordinatization. Theory of parallels for parabolic and hyperbolic
geometries. Selected topics of modern Euclidean geometry.
165. Differential Geometry (3)
Prerequisite: Math 77. Study of geometry in Euclidean space by means of
calculus, including theory of curves and surfaces, curvature, theory of
surfaces, and intrinsic geometry on a surface.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical research
in field of student's interest.
298. Research Project in Mathematics (3)
Prerequisite: graduate standing. Independent investigation of advanced character
as the culminating requirement for the master's degree. Approved for SP
grading. |
Lab Math 9
This course is structure to reinforce Core Curriculum Content Standards in numerical operations, data analysis, geometric reasoning, and algebra in preparation for the HSPA and SAT.
Preparedness for Class
·Please use a 3-ring binder for this class so that you can keep your notes and handouts in an orderly fashion.
·You MUST use PENCIL to do math work.I WILL NOT accept work in PEN!!
Tests & Quizzes
·Tests will be given either at the end of each concept.You will get the whole period to complete and check over a test.
·Quizzes will be given approximately once a week and will take half a period.
·Quizzes will be open notebook!
·Partial credit will be given if I can follow your train of thought and your work is correct for what you did
·If you miss a test or quiz, excused or unexcused, you will make it up upon your return.However, you will take a different version than the rest of the class.You have 5 days to make up a missed test or quiz on your own time (NOT IN CLASS!)
·There will be a midterm in January and a final in June.They will be averaged to give you a 5th marking period grade.
Projects
·We will be doing a number of different projects throughout the year.Each one will have a different point value.That information will be given with the directions for the project.
Homework
·There is (usually) no homework in this class!!(I reserve the right to give homework, if necessary)
Grading System
·I will be using a point system for your marking period grade.You and I will both keep a running tally of your grades that we always know where you stand in my class.
·The total amount of points will vary by marking period but the items will always be worth the following:
Test: 100 pointsQuiz: 50 pointsClasswork: 20 points
Extra Credit:Extra credit will be available on tests.Also, coming to extra help will count as extra credit.
Extra Help:I am available for extra help most days after school between 2:25 – 2:45 PM
Contact Information
Phone: 732-222-9300 x3890 (voicemail)Email: [email protected]
School Rules:Review school handbook for school rules.
Ways to be successful:
1.Be on time2. Never laugh at a classmate
3.Raise hand to ask or answer questions4. Watch your language
Please sign below acknowledging that you have read and are aware of the information on the syllabus. |
Information
Parents did you know you can go to the parent portal and set up email notifications for when your students receive a grade for an assignment, quiz or test? You can also receive your student's progress report online. Here's how to do it:
1.Once you sign in to the system with your user name and password look for the left hand side menu/listing.
2.Under the left hand menu bar, select e-mail notification
3.When that window opens, click change my notifications. This will allow you to set up the type of notifications you would like to receive so that you know when your student needs some additional support. You may select the range of scores from which you would like to receive notifications for as well as select when you would like to receive a progress report for your student (monthly, weekly, or daily)
4.Then Click SAVE
Because the Algebra grades can fluctuate so much at any given time, I would like to suggest that you set this notification process up so that you are always aware of how well your student is doing in the class
Katie O'Brien
Welcome to Pre AP Algebra I!
The overarching goal of Holt Algebra I is to help students develop mathematical knowledge, understanding, and skills, as well as awareness and appreciation of the rich connections among mathematical strands and between mathematics and other disciplines.
In accordance with the district's self directed learning initiative, most of the homework assignments will consist of students completing problems from the day's lesson (answers are in the back of the book), reading the next section to be covered, taking notes and defining key terms/ vocabulary from the section, answering at least one "Check It Out" problem under each example highlighted in the section and answering one, two or all of the "Think and Discuss" questions from the section.
Students have HOMEWORK every night and it is posted on the board everyday. Students are expected to copy the homework assignment in their agendas. Student success is directly correlated to students continued dedication to completing and checking homework. Please check that your student has COMPLETED the homework assignment each night or before they arrive at school the next day. |
Welcome to Calculus! This semester will be a
challenging one for you, but hopefully, with my suggestions, you will be able
to successfully get through this class!
In order to succeed, you will have to know some
things even before you walk into your Calculus classroom on the first
day. First off, sit towards the front. If you do this, you will be
forced to pay attention. Secondly, make sure you get to know the people
that sit around you. If you are outgoing, strive to know the majority of
the people in the class. This will make class time more enjoyable for you
but will also help you with your grades. If you have trouble with
something, you will have a peer to ask for help out of class. Lastly,
when your professor gives you the syllabus for the semester, start right
away! Start to do some of the assigned problems. If they don't make
any sense to you, at least read the material you will be going over in class
the next day thouroughly.
There have been many things that I have discovered
over the course of the semester that could be of value to you. First,
always keep up with your assignments. Have your assignment done so that
you can follow along when your professor lectures about the topic. Some
of the assigned problems will be difficult and you will not be able to
understand them. When this comes up, make sure that you ask
questions. The best way is to ask questions while in class. If
class time runs out, do not just forget about the problems you had on the
assignment, go in and ask your professor during his/her office hours. In
addition to doing your assignments, take your own notes from the book.
This will help you to understand topics covered in lecture better. For
me, this technique really worked. Once I began to take my own notes in addition
to the notes I took from my professor's lecture, I did a lot better, especially
on my weekly quizzes. Lastly, everyone messes up sometimes. If you
get a bad grade on a quiz or an exam, make sure you know all the mistakes you
made and why. Chances are, you will see problems that you had trouble
with on comprehensive tests. Learn from your mistakes, and you will do
better the next time you have the opportunity.
I hope some of my suggestions help you during your
semester in Calculus. Good luck! |
Friday, March 25, 2011
UPSC SCRA Exam Mathematics Syllabus of Examination Paper III
UNION PUBLIC SERVICE COMMISSION (UPSC)
UPSC Special Class Railway Apprentices (SCRA) Examination
Syllabus of Examination
Paper-III
MATHEMATICS
1. Algebra :
Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal set and Power set, Venn diagrams and simple applications. Cartesian product of two sets, relation and mapping — examples, Binary operation on a set — examples.
Representation of real numbers on a line. Complex numbers: Modulus, Argument, Algebraic operations on complex numbers. Cube roots of unity. Binary system of numbers, Conversion of a decimal number to a binary number and viceversa. Arithmetic, Geometric and Harmonic progressions. Summation of series involving A.P., G.P., and H.P.. Quadratic equations with real co-efficients. Quadratic expressions: extreme values. Permutation and Combination, Binomial theorem and its applications.
Matrices and Determinants: Types of matrices, equality, matrix addition and scalar multiplication - properties. Matrix multiplication — non-commutative and distributive property over addition. Transpose of a matrix, Determinant of a matrix. Minors and Co-factors. Properties of determinants. Singular and non-singular matrices. Adjoint and Inverse of a square-matrix, Solution of a system of linear equations in two and three variables- elimination method, Cramers rule and Matrix inversion method (Matrices with m rows and n columns where m, n < to 3 are to be considered).
Idea of a Group, Order of a Group, Abelian group. Identitiy and inverse elements- Illustration by simple examples.
Rectangular Cartesian. Coordinate system, distance between two points, equation of a straight line in various forms, angle between two lines, distance of a point from a line. Transformation of axes. Pair of straight lines, general equation of second degree in x and y — condition to represent a pair of straight lines, point of intersection, angle between two lines. Equation of a circle in standard and in general form, equations of tangent and normal at a point, orthogonality of two cricles. Standard equations of parabola, ellipse and hyperbola — parametric equations, equations of tangent and normal at a point in both cartesian and parametric forms.
4. Differential Calculus:
Concept of a real valued function — domain, range and graph. Composite functions, one to one, onto and inverse functions, algebra of real functions, examples of polynomial, rational, trigonometric, exponential and logarithmic functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative - applications. Derivative of sum, product and quotient of functions derivative of a function with respect to another function, derivative of a composite function, chain rule. Second order derivatives. Rolle's theorem (statement only), increasing and decreasing functions. Application of derivatives in problems of maxima, minima, greatest and least values of a function.
Differential equations : Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equation of various types - examples. Solution of second order homogeneous differential equation with constant co-efficients.
6. Vectors and its applications :
Magnitude and direction of a vector, equal vectors, unit vector, zero vector, vectors in two and three dimensions, position vector. Multiplication of a vector by a scalar, sum and difference of two vectors, Parallelogram law and triangle law of addition. Multiplication of vectors —scalar product or dot product of two vectors, perpendicularity, commutative and distributive properties. Vector product or cross product of two vectors. Scalar and vector triple products. Equations of a line, plane and sphere in vector form - simple problems. Area of a triangle, parallelogram and problems of plane geometry and trigonometry using vector methods. Work done by a force and moment of a force.
Each candidate will be interviewed by a Board who will have before them a record of his career both academic and extramural. They will be asked questions on matters of general interest. Special attention will be paid to assessing their potential qualities of leadership, initiative and intellectual curiosity, tact and other social qualities, mental and physical energy, power of practical application and integrity of character.
About SCRA
Special Class Railway Apprentices' (SCRA) refers to a handful of candidates that are selected by the Union Public Service Commission India, after a rigorous selection process, to the undergraduate program in Mechanical Engineering at the Indian Railways Institute of Mechanical and Electrical Engineering. This programme was started in 1927 and is one of the oldest in India.
The exam is in two parts.
Part I consists of a written examination carrying a maximum of 600 marks in basic academic subjects, such as English, science and mathematics. A personality test is given to those who qualified on the written exam.
The training is conducted at the IRIMEE and the students stay at the Jamalpur Gymkhana. The selected candidates undergo a four-year rigorous training programme in Mechanical Engineering, for which IRIMEE has signed a Memorandum of Understanding with BIT, Mesra, Ranchi. The semester system of BIT, Mesra is followed, with workshop training sessions during the holidays at BIT, Mesra. |
Topics vary from year to year. Topic for Fall: Eigenvalues of random matrices. How many are real? Why are the spacings so important? Subject covers the mathematics and applications in physics, engineering, computation, and computer science. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers. |
What is CHEATS FOR MATH?
WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by-step solution. Covers arithmetic, algebra, geometry, calculus and statistics.
But I just can't seem to get math at all. I am currently in the 10th grade, and I want to know are there any sites into which you plug in an equation and it ouputs an answer? ... were can i find a website to cheat on math homework?
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How to Cheat On a Math Test. Math can be hard. If you get overwhelmed and decide to turn to cheating, this may work for you. Write a program the day before the test. Make sure it has all of your notes. (Or, you can put them in the Y=...
This is a site Accompanying the book 'cryptography, the mathematics of secret codes'. It teaches kids cryptography with games and cipher tools. It also provides a secret message board for kids to send secrect messages to each other.
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Cheat Sheet Everyday Math For Dummies. Everyday math comes in handy when you're dealing with finances like credit cards and mortgages, and even helps when you're trying to figure out how much to leave for a tip.
The official First In Math site: the foremost online math resource for grades K to 8 and beyond! The First In Math® Online Program is a proven curriculum supplement that solidifies basic mathematics skills, and can significantly improve test scores.
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Math Learning Issues
"How can I ..."
Simulation
Simulation software can be particularly
powerful for students. Complex
mathematical concepts can be
understood easily when a visual
simulation is used, instead of the concept
simply being explained in a textbook.
Simulations that are paired with other
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understanding of what the representation
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Trigonometric Derivatives
In this lecture you will cover Trigonometric Derivatives with Professor Switkes. You will start off by learning the Six Basic Trigonometric Functions as well as their Patterns. This lecture is finished off with six fully worked out video examples.
This content requires Javascript to be available and enabled in your browser.
You can use the
derivative formulas for
and
to derive the derivative formulas for the other trigonometric
functions.
Trigonometric Derivatives
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
Rectilinear Motion for High School and College Students introduces and explains the rectilinear motion. In 4 LIVE online classes, the teacher will help you master the concepts of rectilinear motion like Distance, displacement, speed, uniform speed, velocity, uniform velocity, and acceleration. By the end of this course, you will be able to apply the equations of accelerated motion along a straight line to solve numerical problems. You will also be able to interpret distance-time, displacement-time, velocity-time and acceleration-time graphs. This course will be conducted by Prof. S.C. Benjamin, a teacher with 29 years experience in teaching Physics at High School and College level.
Why should you enroll in this course:
Unlike most online courses where you see the tutorials/ videos at your end, this is an interactive course where you are free to ask questions as many times as you want.
The instructor has guaranteed 100% student satisfaction in this course.
This is a comprehensive course and will cover all the important concepts which come under Rectilinear Motion
With 29 years experience in teaching Physics to his students, S.C. Benjamin is a teacher with strong foundations in Physics. He has taught students in High School, IGCSE, K-12, O - Level, A - Level, and IB Physics. S.C. Benjamin holds a M.SC degree in Physics. This course is prepared to cover the basic concepts which come under One Dimensional Motion.
Testimonial
A very helpfull class where I could learn a lot of physics and also revise what I have done in the past. I was also able to futher understand the concepts better and improve in what I already knew. |
Book Description: A plain-English guide to the basics of trigFrom sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English, offering lots of easy-to-grasp example problems, and adding a dash of humor and fun. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.Mary Jane Sterling (Peoria, IL) has taught mathematics at Bradley University in Peoria for more than 20 years. She is also the author of the highly successful Algebra For Dummies (0-7645-5325-9). |
Authors
Why a liberal arts mathematics book with a quantitative literacy focus?
How do you engage students with the study of math? Crauder, Evans, Johnson, and Noell have found the answer: Help them become intelligent consumers of the quantitative data to which they are exposed every day—in the news, on TV, and on the Internet.
In an age of record credit card debt, opinion polls, and questionable statistics, too few students have mastered the basic mathematical concepts required to think about and evaluate data. Quantitative Literacy: Thinking Between the Lines develops the idea of rates of change as a key concept in helping students make good personal, financial, and political decisions.
The goal of Quantitative Literacy is a more informed generation of college students who think critically about the data provided to them, the images shown to them, the facts presented to them, and the offers made to them. Quantitative Literacy shows students the mathematics that matters to them: their bank account, their medical tests, their daily news feed. It also develops their mathematical thinking, helping them to understand the difference between truthful and misleading mathematical reporting.
It's All in the Examples…
After taking your course and working with Quantitative Literacy, students will be equipped to think about and answer all of the following questions:
Will the Atkins Diet really help me lose weight?
How do I use logic to get the best results from a Google search?
Is the local carpet store trying to fool me into thinking their prices are lower because they quote price by the square foot instead of the square yard?
How far can I go on this tank of gas?
How do I interpret the results of my medical tests?
How can businesspeople and politicians use graphs and charts to mislead me?
Will inflation affect my savings and the age at which I can retire?
How do I avoid getting tricked by a Ponzi scheme?
I want to buy a new car in two years. How much do I need to save each month to achieve my goal? How much car can I really afford?
Why are games of chance so financially risky?
Does the golden rectangle explain the beauty of some paintings and architecture?
LearningCurve A research-based breakthrough in adaptive quizzing available in MathPortal. For more productive classtime and better grades. Simple to assign and simple to use. See for yourself. |
Matrix Calculator Pro is a professional windows software which can calculate matrix with real numbers and complex numbers. The complex number support for Polar format. Complex and Polar format can be... |
Each chapter of this complement to any course in discrete mathematics examines an application to business, computer science, the sciences, or the social sciences. Students work these chapter-length models using basic concepts of combinatorics, graphs, recursion, relations, logic, probability, and finite state machines. [via]
Artificial Intelligence is a somewhat dated introduction to the subject. If you are looking for an introduction to core topics in artificial intelligence (AI), such as logic, knowledge representation, and search, this book has something to offer. However, if you want to learn about some of the newer areas of AI, such as genetic algorithms, neural networks, and intelligent agents, you will wish to select a different text.'Throughout my young days at school and just afterwards a number of things happened to me that I have never forgotten'. "Boy" is a funny, insightful and at times grotesque glimpse into the early life of Roald Dahl, one of the world's favourite authors. We discover his experiences of the English public school system, the idyllic paradise of summer holidays in Norway, the pleasures (and pains) of the sweetshop, and how it is that he avoided being a Boazer. This is the unadulterated childhood - sad and funny, macabre and delightful - that inspired our most-loved children's writer. [via]
discrete mathematics and its applications, sixth edition", is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 600 [via]
More editions of Discrete Mathematics and Its Applications: And Its Applications:
Disc&from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. [via]
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Electric Circuits, Seventh Edition features a redesigned art program, a new four-color format, and 75% new or revised problems throughout. In the midst of these changes, the book retains the goals that have made it a best-seller: 1) To build an understanding of concepts and ideas explicitly in terms of previous learning; 2) To emphasize the relationship between conceptual understanding and problem solving approaches; 3) To provide readers with a strong foundation of engineering practices. Chapter topics include Circuit Variables; Circuit Elements; Simple Resistive Circuits; Techniques of Circuit Analysis; The Operational Amplifier; Inductors, Capacitors, and Mutual Inductance; Response of First-Order RL and RC Circuits; Natural and Step Responses of RLC Circuits; Sinusoidal Steady-State Analysis; and more. For anyone interested in circuit analysis.More than 30 years before it was made into a movie, Harriet the Spy was a groundbreaking book: its unflinchingly honest portrayal of childhood problems and emotions changed children's literature forever. Happily, neither Fitzhugh's style has dated nor her themes become obsolete, and it is still recognized as one of the finest children's novels around. The fascinating story centres around an intensely curious and intelligent girl, Harriet lovable heroine, is one of literature's most unforgettable characters. (Ages 8 to 12)Not all whites in South Africa are outright racists. Some, like Bam and Maureen Smales in Nadine Gordimer's thrilling and powerful novel July's People, are sensitive to the plights of blacks during the apartheid state. So imagine their quandary when the blacks stage a full-scale revolution that sends the Smaleses scampering into isolation. The premise of the book is expertly crafted; it speaks much about the confusing state of affairs of South Africa and serves as the backbone for a terrific adventure. [via]100 [via]
More editions of Looking for Information: A Survey of Research on Information Seeking, Needs, and Behavior:Revisions of previous books by the authors on macroeconomics and microeconomics. They have been updated to reflect the latest developments in economics. They feature a fully integrated global perspective and a new design and art programme. [via]
Dornbusch, Fischer, and Startz has been a long-standing, leading intermediate macroeconomic theory text since its introduction in 1978. This revision retains most of the text's traditional features, including a middle-of-the-road approach and very current research, while updating and simplifying the exposition. [Praised by readers for its usefulness, this book covers the entire area of mechanical behavior of materials from a practical engineering viewpoint, providing a single-source introductory analysis with specific coverage on materials testing, yield criteria, stress-based fatigue, fracture mechanics, crack growth, strain-based fatigue, and creep. Explains test methods and the principles behind them, and explores engineering methods for predicting strength and life, with real-date worked examples. Completely updates discussions on fracture mechanics, stress-based fatigue, and creep, and adds three new appendices; one that reviews useful topics from elementary mechanics of materials, one that considers statistical variation in materials properties, and a third that aids in locating materials property information in the tables found in various chapters. Updated end-of-chapter references lead to sources of materials data and to more detailed information. For the mechanical engineer, materials engineer, aeronautical engineer, structural engineer, design engineer, or test engineer. [via]
More editions of Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue:
It was a preference for cricket over schoolwork that united Mike and Psmith in their reluctance to attend their new school, Sedleigh. The school insists that its attendees be keen, but it is sorely unprepared for boys of such foresight and resources as Mike and Psmith who have decided to devote their energies exclusively to raggingContains Don Quixote, in Samuel Putnam's acclaimed translation, substantially complete, with editorial summaries of the omitted passages; two 'Exemplary Novels, 'Rinconete and Cortadillo' and 'Man of Glass'; and 'Foot in the Stirrup,' Cervantes's extraordinary farewell to life from The Troubles of Persiles and Sigismunda************ExIt would seem that 14-year-old Mia Thermopolis ("five foot nine inches tall, with no visible breasts, feet the size of snowshoes") has the kind of life every Manhattan teenager could only dream of: She is, in her spare time, the princess of the European country of Genovia. Alas, the Royal Privilege is more like a Predicament. Not only does she have to endure daily princess lessons from her critical Grandmère ("It isn't as if I'm going to show up at the castle and start hurling olives at the ladies-in-waiting"), but her new stepfather is also her algebra teacher, her mother is pregnant and vomiting, she doesn't like her boyfriend very much, and she's convinced the real love of her life--her best friend's older brother--thinks of her as a kid.
Written in diary form like Louise Rennison's award-winning Angus, Thongs, and Full-Frontal Snogging, Meg Cabot's endearing and often hilarious novel Princess in Love--third in the series after The Princess Diaries and Princess in the Spotlight--is sure to appeal to teen readers who will be able to relate to Mia--a young woman who would like people to know that "behind this mutant facade beats the heart of a person who is striving, just like everybody else in this world, to find self-actualization." (Ages 12 and older) --Karin SnelsonNarnia ... where giants wreak havoc ... where evil weaves a spell ... where enchantment rules.Through dangers untold and caverns deep and dark, a noble band of friends are sent to rescue a prince held captive. But their mission to Underland brings them face-to-face with an evil more beautiful and more deadly than they ever expected say background babble of brand-name consumerism. Then a lethal black chemical cloud floats over their lives, an "airborne toxic event" unleashed by an industrial accident. The menacing cloud is a more urgent and visible version of the "white noise" engulfing the Gladney family--radio transmissions, sirens, microwaves, ultrasonic appliances, and TV murmerings--pulsing with life, yet heralding the danger of death. [via] |
Practical application of principles of mathematics to various phases of business, common and decimal fractions, cash and trade discounts, simple and compound interest, bank discount, and cost of credit. Elective credit only. 3 hours |
Lessons for Algebra I - Linear equations
Summary: This is an iMovie which is designed to help students and viewers to understand how to derive linear equations from few given points by calculating slopes and y-intercepts of straight lines. Then post their responses to given problems for further feedback.
Links
Example links
Contex
This project is designed as an open educational source so that anyone learning online may may have access to the lessons. Traditional classroom students who miss classes and independent learners may have access to this project's lectures.
Objective
These lesson learners are able to develop linear equations from few given points by calculating slopes and y-intercepts.
Project Rationale/Purpose
The purpose of this project is to provide students who have missed classes a chance to catch up, to assist independent learners who might be in preparations of GED exams, and other online learners who wwould like to increase their math general knowledge. Additionally, this project is to support English Language Learners (ELL) who have difficulties keeping up with live lecture pace (Merryfield, 2003).
Why This project Was Put On YouTube?
YouTube is an interesting media that attracts a huge number of Internet surfers. It was created in 2005; however, it had the third largest Internet traffic behind Google and Yahoo in 2009. Thefefore, it is an ideal means for distance learning (Bonk, 2009).
Why Asynchronous Communication Was Chosen?
Asynchronous lectures are ideal in distance learn because they convenient for busy individuals who cannot afford to attend regular classes. In addition, they can access these lectures as many times as they like (Harism, 2000). Also asynchronous lectures are convenient for ELL because they cannot keep up with fast paced lectures, and they decode every word they hear in the lecture. At the time they complete processing the first few sentences of the lecture, the speaker may finish the speech or start talking about new materials (Merryfield, 2003). Many postsecondary and K-12 school institutions that implemented online courses and studies found that students learning online modestly perform better than students learning in classrooms (Means et al., 2010).
References:
Bonk, C. J. (2009). The world is open: How web technology is revolutionizing education. San Francisco, California: Jossey-Bass.
Harasim, L. (2000). Shift happens: online education as a new paradigm in learning. The Internet and Higher Education, 3(1-2), 41-61 |
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This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the "paper and pencil" presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics. |
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