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If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
First principle: Understand the problem
"Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to prompt each student with appropriate questions, depending on the situation, such as:
What are you asked to find or show?
Can you restate the problem in your own words?
Can you think of a picture or a diagram that might help you understand the problem?
Is there enough information to enable you to find a solution?
Do you understand all the words used in stating the problem?
Do you need to ask a question to get the answer?
The teacher is to select the question with the appropriate level of difficulty for each student to ascertain if each student understands at their own level, moving up or down the list to prompt each student, until each one can respond with something constructive.
Second principle: Devise a plan
Pólya mentions that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:
Guess and check
Make an orderly list
Eliminate possibilities
Use symmetry
Consider special cases
Use direct reasoning
Solve an equation
Also suggested:
Look for a pattern
Draw a picture
Solve a simpler problem
Use a model
Work backward
Use a formula
Be creative
Use your head/noggin
Third principle: Carry out the plan
This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled; this is how mathematics is done, even by professionals.
Fourth principle: Review/extend
Pólya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.
The book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example:
The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., n men digging m ditches) problems.
The book has achieved "classic" status because of its considerable influence (see the next section).
Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya's work.
From Yahoo Answers
Question:I am searching the WWW but I can't find what I need. I need a site that breaks down how to slove this arithmetic reasoning problems found on the Officer Aptitude Rating exam given by the navy to Qualify for OCS. I'm math eliterate!!!!!
Answers:Well, I was unable to find a site as well. I do have a suggestion.... In doing research, I came across the description of the math portion of the exam....
"The math skills assessed by the ASTB subtests include arithmetic and algebra, with some geometry. The assessments include both equations and word problems. Some items require solving for variables, others are time and distance problems, and some require the estimation of simple probabilities. Skills assessed include basic arithmetic operations, solving for variables, fractions, roots, exponents, and the calculation of angles, areas, and perimeters of geometric shapes."
Given each of these topics, maybe will be a good place to start, looking under algebra and geometry primarily. From browsing the site, it looks like it provides enough information necessary to help you learn the steps needed to work most problems on the exam.
Hope this was of some help to you. Best wishes on your exam.
Question:I've been trying to convince my parents to let me do online high school and they just wont give in! I have solid reasons as to why I want to study at home and I'm wondering why they're so stubborn about it.
If you were a parent, would you think that these are good reasons to let your child do online schooling?
- I'm originally from California but my family moved to Switzerland. The school system is so different here and they focus on shoving French down my throat before any other subject. I've studied at the public school here for a year and counting, and they teach me things that I already know. I don't feel like I'm up-to-par with the things the kids my age are studying back in the US. For example: Before I left, I was in the 8th grade and in Algebra. I actually felt challenged in all of my classes. When I got here, the teacher was teaching our class how to add fractions.
- I also don't want to end up like my brother, who was told that he can't go to "college" (the high school here) if he doesn't perfect his French by June. My brother is supposed to be in his senior year of high school in the US, yet they won't even let him start the first year of "college" here because he can't speak French. I feel like I'm cracking under the pressure to learn this language and not have to repeat grades.
- I'm harassed at school on a daily basis to the point where I can't even go through the same hallways anymore. I've changed my routes to all my classes just to avoid being bullied. I feel THAT threatened at school. Because of the bullying, I constantly feel stressed and scared. I can't defend myself either because I still have a ton of French to learn and I'll end up looking like even more of an idiot.
I'm being reasonable, right? It's not like I want to do online schooling just to sit at home and rot. I feel like it's the best thing to do if I want to stay sane. The only problem is that my mom is extremely old-fashioned and thinks that anything out of the ordinary should be shunned by society! She doesn't realize how bad of an influence public school has on me because I'm so good at controlling myself at home.
Answers:You can easily compare info about these schools in this site - schools.iblogger.org
Question:how does it benefit us to know other peoples learning styles?
Answers:Numero Uno: If I know your preferred way of learning, then I can adjust my training/teaching in such a way to make it easier for you to learn
Question:Scientists can now determine the complete DNA sequences of organisms, including humans. Now that this milestone has been reached, is there a reason to continue to learning about Mendel, alleles, and inheritance patterns.
Answers:Just because you have a few million base pairs of code doesn't mean you have a clue about how the genes are regulated and interact in order to fashion an organism. When you selectively breed and make crosses you can study the interactions of combinations of alleles.
Basic introduction to mendelian genetics shows you a maximum of three or four gene interactions with no linkage but an organism is the cascading series of interactions of thousands of genes.
Looking at restricted breeding experiments can give insight in how the the allelic combinations respond. This is done to link a variation in phenotype with actual genotypes. This often how specific desirable alleles that influence predisposition to disease resistance are found.
More Reasons NOT to Believe in God - 2 :More Reasons NOT to Believe in God: Reason #2: Arrogance To quote douglas adams: Space... is big. Really big. You just won't believe how vastly hugely mindboggingly big it is... -We, are just one species of many on this tiny planet. -There are 9 planets, (give of take pluto) orbiting this average star we call the sun. -there are over 200 billion stars in our average galaxy we call the milky way. -traveling at 186000 miles per second it would take 100000 years to travel from one side of our galaxy to the other. -There are hundreds of BILLIONS of galaxies in the universe. -the Universe existed 9.1 billion years before earth was ever even formed. -The earth existed for almost 1 billion years before primitive life even began to emerge -microbes didn't even exist on land until 2.7 billion years ago. -245 million years ago the earth was populated by giant dinosaurs and prehistoric beasts (Dinosaurs lived on earth for 180 million years, homosapiens have lived on Earth for less than 1 million years) -over the course of 2.5 million years our primate species evolved from the genus: homo into the homosapiens we are now. -for hundreds of thousands of years mankind told stories and developed folklore. only recently, within the past ten thousand years have we learned to sustain our culture through written language. And to be certain, based on nothing but personal intuition, that in this TINY TINY TINY fragment of a blink in time, on this TINY TINY spec of dust we call home, and out of ... |
Tabula Bookmark
Publisher Description
Tabula is a new software program for math instruction that joins the conveniences of a presentation program with the tools specific to teaching geometry. Tabula also excels at modeling math concepts with geometry.
A novel set of manipulation and transformation tools facilitates and extends activities that use paper, scissors, straight edge, and other hands-on items. Students can use Tabula to apply concepts in projects involving tiling patterns, tessellation, perspective drawing, and more. Tabula can be used in 5th grade through high school geometry.
Soft-Files is not responsible for the content of "Tabula" software description. We encourage you to determine whether this product or your intended use is legal. We do not encourage or condone the use of any software in violation of applicable laws. |
Mathematics for electronics engineer
Mathematics for electronics engineer
Hello all,
I am currently working on modelling organic FETs. I would like to know if there exists any book that can help me in modelling i.e. I have a curve and I need a method or approach as to how this can be represented using an eqn. Also I need some literature recommendation for approximations (Taylor's expansion etc. ) to dilute complex eqns to simpler ones.
You aren't making it clear what "this" refers to. You say that you doing modelling. A model for a physical situation can be a complicated representation that contains many equations and algorithms. Or it could be one equation fit to some empirical data.
Exactly what sort of model are you dealing with? In the math section, there might be a shortage of experts on Field Effect Transistors, so don't assume your readers know about them. As to "organic" FETs, I don't know what those are.
Hello Tashi,
Thank you for your reply. My task is to develop a empirical model that is simple and closely mimics the current (Ids) behaviour of the transistor. Organic field effect transistors (FET) are a kind of MOSFET but with an organic semiconductor. The current output when plotted looks like that of a silicon MOSFET but with more non-linearities. My task is to use the same model eqns of a silicon MOSFET and supplement with appropriate equations to model the non-linearitites present in organic FET. I have read something similar in few semiconductor modeling books, where the author uses a funtion [sqrt(Vds + Const) - sqrt(Vds)] to model the short channel effect (a kind of non-linearity) in the case of silicon MOSFET. I can visualize when the function is a simple sqrt, square, exp etc. But it gets hard, when there is superposition of 2 or more functions.
Moreover, we have come across hundreds of mathematical functions. But only a handful of this is required to model the real world systems emphirically. Is there any book that explains in detail the mathematical (emphirical) modeling of real world systems in a systematic way. |
MAS170 Practical Calculus
In this course we learn how to define and evaluate derivatives and
integrals for functions which depend on more than one variable,
with an emphasis on functions of two variables, for which the main
ideas already appear. We also think about what it means to
approach a limit or to add up a sum with infinitely many terms,
but throughout the emphasis is on explicit examples and getting
answers.
Differential equation for continuous compound interest. Solution by
inspection and by separation of variables. Radioactive decay,
half-life. Newton's law of cooling. Other examples of separable
equations.
4. Partial derivatives (4 lectures)
Functions of two variables, their graphs, level curves and tangent
planes. Partial derivatives, their graphical interpretation and
evaluation. Jacobians, higher derivatives. Increments, the Chain Rule
and its applications, including to Laplace's equation.
5. Double integrals (5 lectures)
Review of the Fundamental Theorem of Calculus. Two-dimensional
integrals as volumes under graphs, their evaluation by double
integration, in either order. Change of variables, including to polar
coordinates. ∫−∞∞ e−[1/2]x2 dx.
6. Infinite series (5 lectures)
Infinite series of positive terms. Basic examples including
geometric
and harmonic series. Sum as a limit of partial sums. Numerical and
graphical illustration. Absolute convergence. Manipulating Maclaurin
series. Finding the radius of convergence. |
Introductory Technical Mathematics, 6th Edition
ISBN10: 1-111-54200-7
ISBN13: 978-1-111-54200-9
AUTHORS: Peterson/Smith
With an emphasis on real-world math applications, the Sixth Edition of INTRODUCTORY TECHNICAL MATHEMATICS is essential for anyone considering a career in today's sophisticated trade and technical work environments. Practical, straightforward, and easy to understand, this hands-on text helps you build a solid understanding of math concepts through step-by-step examples and problems drawn from various occupations. Updated to include the most current information in the field, the sixth edition includes expanded coverage of topics such as estimation usage, spreadsheets, and energy-efficient electrical applications |
I've always wanted to learn grade 9 algebra in indian books, it seems like there's a lot that can be done with it that I can't do otherwise. I've browsed the internet for some good learning resources, and checked the local library for some books, but all the information seems to be targeted at people who already understand the subject. Is there any tool that can help new people as well?
Can you be a bit more clear about grade 9 algebra in indian books ? I possibly could help you if I knew some more . A proper computer program can help you solve your problem instead of paying big bucks for a math tutor. I have tried many algebra program and guarantee that Algebrator is the best program that I have come across . This Algebrator will solve any math problem that you enter and it also explains every step of the solution – you can exactly write it down as your homework assignment. However, this Algebrator should also help you to learn math rather than only use it to copy answers.
Algebrator is a fabulous software. All I had to do with my problems with graphing parabolas, powers and linear equations was to just type in the problems; click the 'solve' and presto, the result just popped out step-by-step in an effortless manner. I have used this to problems in Algebra 2, Basic Math and Algebra 1. I would for sure say that this is just the solution for you.
absolute values, y-intercept and linear inequalities were a nightmare for me until I found Algebrator, which is truly the best algebra program that I have come across. I have used it through many algebra classes – Algebra 1, Intermediate algebra and College Algebra. Just typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my math homework would be ready. I really recommend the program. |
Business Mathematics Brief, CourseSmart eTextbook, 12th Edition
Description
For shorter courses in business math or the mathematics of business.
This concise text teaches business math with a strong focus on current issues, real companies, and realistic business scenarios. It places essential business math concepts in context, teaching through highly relevant examples. Each chapter begins with an actual company case study that is carried through with examples and exercises. Two realistic cases conclude each chapter, helping students integrate key concepts with real business math challenges. Data and graphs are incorporated throughout. New coverage in this edition includes: the global financial crisis and globalization; personal debt and savings; and inventory tracking. More examples are provided, and this edition has been edited for greater clarity and simplicity.
Table of Contents
1. Whole Numbers and Decimals
2. Fractions and Mixed Numbers
3. Percent
4. Equations and Formulas
5. Bank Services
6. Payroll
7. Mathematics of Buying
8. Mathematics of Selling
9. Simple Interest
10. Compound Interest and Inflation
11. Annuities, Stocks, and Bonds
12. Business and Consumer Loans
13. Taxes and Insurance
Appendix A. The Metric System
Appendix B. Basic Scientific Calculators
Appendix C. Financial Calculators
Answers to Selected Exercises |
Grading Policies
Your grade will be based off of tests, homework, notes, and class participation. The following scale is what I will use to figure your score.
100 – 90% = A
89 – 80% = B
79 – 70% = C
69 -60% = D
59 – 0% = F
Course Grade/Points Possible
Your grade will be based off of points you have earned from notes, homework, tests, and class participation.
You semester test will be worth 10% of you semester grade.
Class Requirements
1. TEXTBOOKS
**THESE BOOKS ARE EXPENSIVE. IF YOU DAMAGE OR LOSE IT YOU
WILL PAY FOR IT.**
2. CALCULATORS
• You will be issued a TI-83 calculator to be used for the class. YOU WILL BE RESPONSIBLE FOR THE CARE OF THIS CALCULATOR AND WILL HAVE TO REIMBURSE THE SCHOOL FOR DAMAGES.
3. HOMEWORK POLICIES
• Homework must be turned in on the day it is due. I will not accept any late work.
• In the event that you are absent, it is YOUR responsibility to find out what assignments or other work you missed. You need to talk to me or ask a classmate what you missed.
• All work must be done in pencil. I will not accept any work done in any other media.
4. Tests/Quizzes
• There will be quizzes throughout each unit, a test at the end of every unit, and there will be a semester final. The test/quizzes will be based on notes taken in class, homework, and activities done in class.
Class Procedures
1. GENERAL CLASS RULES
• DO NOT interfere with the teacher's right to teach.
• DO NOT interfere with the right of other students to learn.
• RESPECT the room and the equipment in it.
• Keep your hand & feet to yourself.
2. Come to class PREPARED each day. You will not be allowed to go back to your locker to get book, paper, pencil, etc. after the bell has rang. |
Course Content and Outcome Guide for ALC 63
Date:
02-OCT-2012
Posted by:
Heiko Spoddeck
Course Number:
ALC 63
Course Title:
Basic Math Skills Lab
Credit Hours:
3
Lecture hours:
0
Lecture/Lab hours:
0
Lab hours:
90
Special Fee:
$36
Course Description
In conjunction with the instructor, students choose a limited number of topics in Basic Math (MTH 20) and/or Introductory Algebra (MTH 60 and 65) to review over the course of one term. Instruction and evaluation are self-guided. Students must spend a minimum of 90 hours in the lab. Completion of this course does not meet prerequisite requirements for other math courses.
7.3Classify points by quadrant or as points on an axis; identify the origin
7.4Label and scale axes on all graphs
7.5Interpret graphs in the context of an application
7.6Create a table of values from an equation
7.7Plot points from a table
8.0INTRODUCTION TO FUNCTION NOTATION
8.1Determine whether a given relation presented in graphical form represents a function
8.2Evaluate functions using function notation from a set, graph or formula
8.3Interpret function notation in a practical setting
8.4Identify ordered pairs from function notation
9.0LINEAR EQUATIONS IN TWO VARIABLES
9.1Identify a linear equation in two variables
9.2Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
9.3Find ordered pairs that satisfy a linear equation written in standard or slope-intercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs
9.4Find the intercepts given a linear equation; express the intercepts as ordered pairs
9.5Graph the line using intercepts and check with a third point
9.6Find the slope of a line from a graph and from two points
9.7Given the graph of a line identify the slope as positive, negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope
9.8Graph a line with a known point and slope
9.9Manipulate a linear equation into slope-intercept form; identify the slope and the vertical-intercept given a linear equation and graph the line using the slope and vertical-intercept and check with a third point
9.10Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
9.11Given the equation of two lines, classify them as parallel, perpendicular, or neither
9.12Find the equation of a line using slope-intercept form
9.13Find the equation of a line using point-slope form
10.0APPLICATIONS OF LINEAR EQUATIONS IN TWO VARIABLES
10.1Interpret intercepts and other points in the context of an application
10.2Write and interpret a slope as a rate of change
10.3Create and graph a linear model based on data and make predictions based upon the model
10.4Create tables and graphs that fully communicate the context of an application problem
11.0LINEAR INEQUALITIES IN TWO VARIABLES
11.1Identify a linear inequality in two variables
11.2Graph the solution set to a linear inequality in two variables
11.3Model application problems using an inequality in two variables
Introductory Algebra II
THEMES:
1.Functions 2.Graphical understanding
3.Algebraic manipulation
4.Number sense
5.Problem solving
6.Applications, formulas, and modeling
7.Critical thinking
8.Effective communication
SKILLS:
1.0SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
1.1Solve and check systems of equations graphically and using the substitution and addition methods
1.2Create and solve real-world models involving systems of linear equations in two variables
1.2.1Properly define variables; include units in variable definitions
1.2.2Apply dimensional analysis while solving problems
1.2.3State contextual conclusions using complete sentences
1.2.4Use estimation to determine reasonableness of solution
2.0WORKING WITH ALGEBRAIC EXPRESSIONS
2.1Apply the rules for integer exponents
2.2Work in scientific notation and demonstrate understanding of the magnitude of the quantities involved |
The
course develops fundamental geometric tools of mathematical analysis,
in particular integration theory, and is a preparation for further
geometry/topology courses. The central statement is the famous Stokes
theorem, a classical version of which appeared for the first time
as an examination problem in Cambridge in 1854. Various manifestations
of the general Stokes theorem are associated with the names of Newton,
Leibniz, Ostrogradski, Gauss, Green. This theorem, both in its
infinitesimal and global forms, relates integral over a boundary of a
surface or of a solid domain ("circulation" or "flux") with a natural
differential operator, known in particular cases as "curl" or
"divergence". The prototype and the simplest case of the Stokes theorem
is the Newton-Leibniz formula linking the difference of the values of f
on endpoints of a segment with the integral of df . The
standard modern language for these topics is differential forms
and the exterior derivative. Differential forms are used
everywhere from pure mathematics to engineering. We give an
introduction to the theory of forms, as well as a simplifying treatment
for the traditional technique of operations with vector fields in the
Euclidean three-space. |
Download Mathematics: introduction to units of time
Mathematics: introduction to units of time is an educational software. It is very basic but helpful software that will help every mathematics and physics student. This program is focused to help students get hold of time and its units in a better way. This program will help students to learn the units of time in effective manner without getting confused. It has some unique automatically generated questions that will assist students in learning the units. These questions will test the student's knowledge and if they are not able to solve them then they can learn it using this program within no time. |
For discrete mathematics, I would recommend Van Lint-Wilson's "A Course in Combinatorics" as a good introductory text. It consists of 38 (in my edition) chapters that give (often largely self-contained) introductions to various areas of the field. Although it doesn't go nearly as in depth as, say, Stanley's "Enumerative Combinatorics" or a text focused solely on graph theory, I found it excellent for giving a broad overview and indicating to me where I wanted to explore deeper.
My one caveat would be that some chapters require background in either linear algebra or basic group theory, though those are easily skippable due to the structure of the book. |
The ASC offers three math classes to help
prepare students for their college level math courses.
Placement in these courses is based on COMPASS, ACT and/or
SAT scores and advisor recommendations. Credits for these courses DO NOT apply toward
graduation requirements nor do they fulfill Academic
Foundations requirements. However, the credits do count
towards enrollment status for financial aid.
This course begins with a brief review of elementary
algebraic concepts and then covers more advanced factoring,
operations on rational expressions and radical expressions,
quadratic equations, the rectangular coordinate system, and
exponential and logarithmic functions.
Who should take this course?
Students with the following placement scores: COMPASS: 26-75 Pre-Algebra
and
0-15 Algebra
Students with the following placement
scores: COMPASS: 76-100 Pre-Algebra
16-26 Algebra SAT: up to 489 ACT: up to 14
Students with the following placement scores: COMPASS: 27-50 Algebra SAT: 490-530 ACT: 15-21
Course
Materials
There is no text required for this
course this semester. All materials will be provided to
students free of charge. |
Description
of Major:
Mathematics is offered as a major and minor at JMU.
The department offers a program of study in the mathematical
sciences which meets the needs of a wide variety of
students and make a continuing contribution to the advancement of mathematical
knowledge and dissemination. The program provides opportunities for in-depth study which
lead to careers as mathematicians and statisticians in industry and government, mathematics
teachers; and to further study in graduate school. The
first two years of introductory mathematics focus on
differential and integral calculus. The studies of the
last two years are devoted primarily to basic material
in the fields of analysis, algebra, geometry, computing
and statistics. The two parts of the program are distinguished
by methods of presentation, as well as by content. The
first two years lead gradually to appreciation of definitions
and proofs, and to precision in mathematical language.
The latter two years anchor basic mathematical concepts,
results and methods, and increase the knowledge of applications.
The program is committed to promoting mathematics as
an art of human endeavor as well as a fundamental method
of inquiry into the sciences and a vast array of other
disciplines. In addition to the concentrations listed
above, the department also offers a minor in Statistics.
Students seeking teacher licensure are encouraged to
consult with the appropriate program in the College
of Education.
Tell
me more about this field of study.
Mathematics is the study of such objects as numbers,
operations, space configurations, mappings, and abstract
structures. Those studying mathematics develop skills
to manipulate these objects and analyze the relationships
between them. Much of the knowledge and effort of a
mathematician is devoted to formulating and analyzing
models, which can be used to make predictions. A mathematical
model is a set of equations whose solution can be used
to predict the behavior of the phenomenon being modeled.
The 5-day forecast that we see on the 11:00 news is
prepared using output from a weather model. The predictions
we see in the news concerning the growth of the economy
are based on various mathematical models. The performance
and reliability of communication networks are often
predicted using a network model. The predictions produced
by mathematical models vary in quality. Sometimes they
are right on target and sometimes they are meaningless.
Certain models can be calibrated by running an experiment.
For example, a fully instrumented building can be burned
down and the results compared to the output from a fire
model. When used as part of a design process, a well-constructed
mathematical model can often produce enormous cost savings.
Tell
me more about specializations in this field.
Mathematicians specialize in a wide variety of areas
such as algebra, geometry, analysis, probability and
statistics, mathematics education, and applied mathematics.
The college graduate with a bachelor's degree in mathematics
or actuarial science can qualify for a broad range of
highly paid positions in a variety of industries. In
private industry, companies in the computer, communications,
and energy field employ many mathematicians. Students
interested in government work will find that almost
every bureau and branch of the federal government employs
mathematicians in some capacity. Mathematicians, statisticians,
operations researchers, and actuaries work in the Department
of Health and Human Services, the General Accounting
Office, the Office of Management and Budget, and the
National Institute of Standards. The Department of Energy,
the Department of Defense, the National Aeronautics
and Space Administration, and the National Security
Agency also employs many mathematicians. Many mathematicians
are attracted to teaching and research opportunities
at primary, college and university settings. In most
four-year colleges and universities, the Ph.D. is necessary
for full faculty status. Many mathematicians with a
bachelor's or master's degree teach at the K-12 level.
Major Research Laboratories like IBM, ATT, Bell, and
Research Institutes support purely scientific research
positions. Many other job titles apply to mathematicians
who have specialized in an applied branch of mathematics.
Actuaries assemble and analyze statistics to calculate
probabilities, and thereby set rates, in the insurance
industry. Operations Research Analysts apply scientific
methods and mathematical principles to organizational
problems. Statisticians design, carry out, and interpret
the numerical results of surveys and experiments. All
of these careers begin with an education in mathematics,
and a curiosity about the use of mathematics to solve
problems.
CHARACTERISTICS
OF SUCCESSFUL STUDENTS
Those students who are able to think independently and
creatively and are not afraid of hard work are the most
successful in mathematics.
CAREERS
Recently, JobsRated.com ranked Mathematician as the best job in America, with Actuary and Statistician at second and third, based on salary, work conditions, and other factors. Many graduates choose typical career paths associated
with this major. However, some graduates choose nontraditional career fieldsThere are a number of "hands on" experiences
available to students in mathematics, especially through
the Center for Mathematical Modeling and the Office
of Statistical Services, both housed in the Department
of Mathematics and Statistics. Students intending to teach complete
an "internship" through the student teaching
experience, required in the senior year for those who
seek teaching licensure. Students also gain experience
and/or exposure to the field of mathematics through
involvement in the Mathematics Club, Pi Mu Epsilon (Mathematics
Honor Society), and the student chapter of the American
Mathematical Society. Come to Career and Academic Planning, located in Wilson 301, to learn more about identifying internships relating to mathematics. |
Humble Precalculus
...Student are taught how to set of and solve elementary word problems. Algebra 2 basically introduces the notion of a function, and it extends this notion to a variety of different types of functions. We see polynomial, exponential, logarithmic functons and more. |
... read more
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A Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961Invitation to Geometry by Z. A. Melzak Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.A Modern View of Geometry by Leonard M. Blumenthal Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.
Geometry, Relativity and the Fourth Dimension by Rudolf Rucker Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
Product Description:
the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Reprint of the Prentice-Hall, Englewood Cliffs, New Jersey, 1965 |
0199205353
9780199205356
The Chemistry Maths Book: The Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a clear, straightforward approach, the book develops ideas in a logical, coherent way, allowing students progressively to build a thorough working understanding of the subject.Topics are organized into three parts: algebra, calculus, differential equations, and expansions in series; vectors, determinants and matrices; and numerical analysis and statistics. The extensive use of examples illustrates every important concept and method in the text, and are used to demonstrate applications of the mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter, are an essential element of the development of the subject, and have been designed to give students a working understanding of the material in the text.Online Resource Centre:The Online Resource Centre features the following resources for registered adopters of the text:- Figures from the book in electronic format, ready to download- Full worked solutions to all end of chapter exercises «Show less
The Chemistry Maths Book: The Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a... Show more»
Rent The Chemistry Maths Book 2nd Edition today, or search our site for other Heather |
Registration Fee: $275 per person ($350 for registrations received after June 10,2013)
Undergraduate Sustainability Experiences in Mathematics (USE Math) projects are sustainability-focused, technology-enabled, single class-period projects, offering students authentic quantitative experiences within the context of sustainability The USE Math on Campus workshop will explore the relationship between sustainability and introductory-level mathematics on college campuses through active use of existing projects, sharing of ideas, and development of new USE Math projects. Prior to the workshop, participants will be introduced to a collection of sustainability-motivated mathematics materials and will be encouraged to identify the role (and meaning) of sustainability on their campus. At the workshop we will initially focus on incorporating existing modules to fit specific campus needs. Working groups, based on sustainability and course interests, will develop new modules to incorporate into their classrooms. Following classroom implementation, participants will share in-class USE Math experiences with the group to develop engaging modules to share broadly on a public website.
Questions about PREP? Contact Olga Dixon at 202-319-8498 or [email protected]. |
Classification
Reviews (1)
A link to a website which has numerous PowerPoints covering a wide range of algebraic topics. The PowerPoints provide simple step-by-step instructions on how to answer questions which provides a good revision tool for students. |
Text: College Algebra: Concepts and Models by Larson, Hostetler, and Hodgins, Heath Publishing (2nd ed) 1996. Sections covered P1 to P7, 1.1 to 1.7, 2.1 to 2.5, 3.1 to 3.7, 4.1 to 4.5, 5.1 to 5.5, 6.1 to 6.4, 8.1 to 8.8 . Tentative
Homework schedule is given on the back page.
Teaching Style Usually a chapter including the chapter quiz will be covered in less than two weeks. Teaching is done in a hands-on style that consists of daily homework assignment and solving problems, and discussing concepts. The word is "DOING mathematics. Quiz is given in every class. Students are required to have a notebook where all their work ( homework assignment and glasswork) is done and they are credited for 10% of the grade for this. Calculators are only used as a tool and students will find one like TI 85 very useful. Midterm test is given around 6th week and is done on an individual basis. Final comprehensive examination will cover Chapter 3 to the end of the material covered.
Attendance will be taken at the beginning of each class. Arriving late disturbs everybody in the class. All students are expected to come to all classes on time. Any excused absences should be informed preferably in advance or e-mailed. There is a 2% of the grade reserved for punctuality in attending classes, turning in assignments on time, and constructive participation. |
PRIZM is revolutionary among graphing calculators with features that enhance users' understanding of mathematics. |
Investigating student learning and building the concept of inverse function
by Dandola-DePaolo, Andrea, Ed.D., RUTGERS THE STATE UNIVERSITY OF NEW JERSEY - NEW BRUNSWICK, 2011, 439 pages; 3499196
Abstract:
The concept of function is one of the most important ideas in the learning of mathematics (Dubinsky & Harel, 1992). Yet it is considered by many researchers to be the least understood by high-school and college students (Breidenbach, Dubinsky, Hawks, & Nichols, 1992; Sfard, 1992). Reforming early mathematics curricula in algebra, therefore, is justified. To this end, the National Council of Teachers of Mathematics (2000) called for a longitudinal view of algebra, from elementary to advanced mathematics education. As a strand in the Rutgers-Kenilworth longitudinal study in 1993, Robert B. Davis introduced early algebra ideas to eleven-year-old students during the sixth grade. Research prior to Davis' intervention with the students showed how they built their understanding of linear, quadratic, and exponential functions (Spang, 2009; Giordano, 2008; Mayansky, 2007). Building on Davis' approach to early algebra and the learning of function, Emily Dann designed a study to determine whether these students, now seventh graders, could extend their understanding to the concept of inverse function.
The present study analyzes videotaped work of seventh-grade students who were engaged in a series of activities that Dann had devised. The Guess-My-Rule activities, as they were called, were conducted over three consecutive days. Using the model that Powell, Francisco, and Maher (2003) described for analyzing videotaped data, this study examines in detail the students' work as they collaborated in small groups to develop rules for function and inverse; the study also investigates the obstacles students had experienced.
This research demonstrates that seventh-graders understood the idea of function by writing rules, symbolically, to describe the relationships of quantities. Understanding function as action, they progressed to the process concept when creating their own function tables and corresponding rules. Using inverse operations, students wrote inverse rules; however, due to difficulties with integer and fraction arithmetic, they needed to adjust their initial attempts in order to be successful.
This study maintains that having facility with function and inverse function concepts will permit students to learn the subject matter, to communicate ideas and solutions, and to interconnect mathematical ideas. In the process of exploring these related concepts, students will be encouraged to think independently and to devise original strategies in their work with function and inverse.
The results demonstrate to researchers and educators how students build the concepts of function and of inverse function through group work in a specific environment. Seventh-grade students can engage in activities, similar to those described above, that are essential to the study of algebra |
MA240 DISCRETE MATHEMATICS (4 cr.)
COURSE DESCRIPTION
This course covers the mathematical foundations of computer science. The goal
is to make students comfortable with formal systems, data structures, abstract
models, and analysis of problems and algorithms, so that they can apply these
intellectual tools in later CS courses.
Learn, and become comfortable with, the range of discrete mathematical
structures that are fundamental to the further study and application of
computation. Acquire the conceptual tools for modeling real-world
situations as abstract problems amenable to computational solution. |
Personal tools
Sections
Calculators
Calculators don't normally fit people's ideas of educational computing, but the need to calculate numerical tables for navigation, tides and gunnery was a major driving force for the invention of algorithms and computers, and thus calculators hold a special place in the historical development of computing at its most mathematical and its teaching |
Teaching Textbooks™ is a math curriculum based on 3 easy steps: watch the lesson, do the problems, and watch a tutor explain the ones you missed. Teaching Textbooks™ were designed specifically for independent learners (they focus on teaching/explanations). From the website: A Teaching Textbook™, with its approximately 700 pages of text and 120 – 160 |
This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced undergraduates and graduate students will find this a nice entry point to differential geometry.
In order to study the global properties of curves and surfaces, it is necessary to have more sophisticated tools than are usually found in textbooks on the topic. In particular, students must have a firm grasp on certain topological theories. Indeed, this monograph treats the Gauss-Bonnet theorem and discusses the Euler characteristic. The authors also cover Alexandrov's theorem on embedded compact surfaces in \(\mathbb{R}^3\) with constant mean curvature. The last chapter addresses the global geometry of curves, including periodic space curves and the four-vertices theorem for plane curves that are not necessarily convex.
Besides being an introduction to the lively subject of curves and surfaces, this book can also be used as an entry to a wider study of differential geometry. It is suitable as the text for a first-year graduate course or an advanced undergraduate course.
This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Readership
Undergraduate students, graduate students, and research mathematicians interested in the geometry of curves and surfaces.
Reviews
"With its readable style and the completeness of its exposition, this would be a very good candidate for an introductory graduate course in differential geometry or for self-study." |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
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How to Program? - Part 1 Part 1: Problem Solving Analyze a problem Decide what steps need to be taken to solve it. Take into consideration any special circumstances. Plan a sequence of actions that must take place in a specified order Solve the
AgendaIAT 201:Workshop D102/103Week 5TA: Daniel [email protected] Business items Review: Requirements for the next assignment Team Activity: Task analysis Team Activity: Volere templateBusiness1. Most of you have done so already, but for t
You are only allowed to read this if you are standing on your head and you have tried all four parts! 11a. [6, 4] and R = 5. 11b. (7, 1) and R = 4. 11c. [2 1/8, 2 + 1/8) and R = 1/8. 11d. The series only converges when x = 1/2, so R = 0.11. Find t
Math 114 Calculus II Spring 2009 Exam II Scores Each exam grade is listed by code name and score before curving. If you cannot nd your code name, it means it was too easy for me to break and I am instead posting your grade by the last two digits of y
Math 114 Calculus II Spring 2009 Each exam grade is listed by code name and score before curving. If you did not list a code name, I am instead posting your exam grade by the last two digits of your student ID. Final Exam Results: High: 97 Low: 28 Av
MATH and PIZZATangents to Four Unit Spheres:An Introduction to Enumerative Algebraic GeometrySpeakersDavid CoxWilliam J. Walker Professor of Mathematics at Amherst College Sponsored by Department of Mathematics University of KentuckyDate: Thu
Fall 2007 Name(printed neatly): Quiz Grade:Math 131-501Quiz 9Fri, 9/Nov/20071. In the study of markets, economists dene consumers willingness and ability to spend as the maximum amount that consumers are willing and able to spend for a specic
ENVS 680 Doing a Summer Internship You can do your actual internship during the summer and take the internship course, ENVS 680, the following fall. However, you need to do certain homework assignments for the internship course during the summer. You
EE 143 Optical Lithography Lecture, A.R. Neureuther, Sp 2006Ver: 02/01/2009OPC Scatterbars or Assist FeaturesMain Feature The isolated main pattern now acts somewhat more like a periodic line and space pattern which has a higher quality image es
Topics Covered Final Exam ReviewLast Lecture R&G - All Chapters Covered First half of the course (see midterm review) you are responsible for it; final will lean towards material covered since then. SQL (covered before and after midterm) Impleme |
Mrs. Holeman
8th grade math
Go to Online Textbook page to access the textbook.
Tutoring is available daily from 7:50 - 8:10 a.m. on Tuesday and Thursday and Wednesday afternoons from 3:35- 4:00. Other times by appointment. Students wishing to attend morning tutorials must have a note from a parent to get into the building.
Week of May 13-17
Unit Focus:Functions - Algebra Unit
Day
Activities
Homework
Monday
BINGO! solving equations Given Comic Book Project
finish problems
Comic Book Project due May 24 for test grade
Tuesday
The Birthday Gift - linear equations
finish worksheet
Comic Book Project due May 24 for test grade
Wednesday
Spending Money - linear equations
finish worksheet
Comic Book Project due May 24 for test grade
Thursday
writing linear equations to solve
and work on comic book
finish worksheet and
Comic Book Project due May 24 for test grade
Friday
Guess My Functions
finish and
Comic Book Project due May 24 for test grade
Week of May 20-24
Unit Focus: Scaling Pictures and Review
Day
Activities
Homework
Monday
Reflect and Apply - functions
Start scaling pictures
work on comic book project due Friday
Tuesday
Scaling picture
work on comic book project due Friday
Wednesday
Review/ finish picture/comic book
worksheet
Thursday
Review/comic book
worksheet
Friday
Review - turn in comic book
review sheet
*All attempts to stay on this posted schedule will be made, but assignments may change. This is a working document. Thank you for understanding.* |
This is a decision that should be made by students and their parents. It should be based on a realistic view of the student's skills and aspirations.
How many units of mathematics should you study?
This will usually be 2 to 8.
Which units of mathematics should you study?
It is recommended that students should choose a "Pathway" in VCE mathematics. Suggested Pathways are shown below.
Accelerated Mathematics Yr 10
What is this unitUnitsSemester 1: Acceleration Mathematics
Real and Complex Number Systems
Matrices
Sequences and Series
Variation
Semester 2: Acceleration Mathematics
Non-linear Graphs
Trigonometric Ratios
Non linear Relations and Equations
Data
What type of things will I do?
Work with numbers and surds
Substitute, Transpose and Solve Equations
Plot and sketch graphs
Use technology to help with learning
Application of Matrices
Display and Summaries data
Correlations and Regression of data
Applications of Sequences and Series such as financial arithmetic
Minimization in problems of time and distance
What can this lead to?
Specialist Mathematics 3 and 4
Mathematical Methods (CAS) 3 and 4
Further Mathematics 3 and 4
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Accelerated Mathematics
Year 11
Further Mathematics (3 and 4)
Year 12
Mathematical Methods CAS
Specialist Mathematics
Why choose this study?
Choose this study if you are interested in learning about:
Numbers
Uses of Data
Interpreting Graphs
Matrices
CAS
Foundation Mathematics Units 1-2
What's it all UnitsUnit 1: Foundation Mathematics
Space and Shape
Patterns in Number
Handling Data
Measurement and Design
Unit 2: Foundation Mathematics
Pattern and Number
Space and Shape
Measurement and Design
Handling Data
What type of things will I do?
Two dimensional plans
Diagrams incorporating scales
Practical problems involving decimals, fractions and percentages
Formulas and their use
Reading roads maps, time tables, flowcharts
Metric measurement problems
Recording and analyzing instrument readings
Ordering and weighing food items
Interpreting financial information
What can this lead to?
VCAL
VET
Apprenticeships
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Pathway 1 Mathematics
Year 11
Foundation Mathematics
Year 12
VCAL and VET
Why choose this study?
Choose this study if you are interested in learning about:
Numbers
Uses of Data
Interpreting Graphs
Finance
General Mathematics (Further) Units 1-2
What's it all about?
This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the needs and aspirations of a wide range of students Further Mathematics Units 3 and 4. A Computer Algebra System (CAS) will be used by students to assist them in their learning and understanding.
Assessment for satisfactory completion of Units 1 and 2 is by tests, analysis tasks, and students work during the year.
What will I learn?
Unit 1: General Mathematics (Further)
Number Theory
Number Patterns and Applications
Relations in Linear Equations
Linear Graphs
Unit 2: General Mathematics (Further)
Represent and Interpret types of Data
Describe and use Networks
Matrices and their Applications
What type of things will I do?
Work with schedules, time zones
Applications of Sequences and Series such as financial arithmetic
Formulate Equations
Plot and sketch graphs
Display and Summarise data
Correlations and Regression of data
Minimisation in problems of time and distance
Eulerian Paths and Circuits
Use a Computer Algebra System
What can this lead to?
Further Mathematics 3 and 4
VCAL
VET
Apprenticeships
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Pathway 1 Mathematics
Year 11
General Mathematics (Futher)
Year 12
Futher Mathematics
Why choose this study?
Choose this study if you are interested in learning about:
Numbers
Uses of Data
Interpreting Graphs
Matrices
CAS
General Mathematics (Methods) Units 1-2
What's it all about?
This course is designed for students intending to do tertiary studies that will involve complex and/or specialized mathematical calculations and skills. Students selecting these units should be able to manipulate algebraic expressions and solve equations. These skills are further developed in this course Mathematical Methods (CAS) and/or Specialist Maths Units 3 and 4. A Computer Algebra System will be used by students to assist them in their learning and understanding.
Assessment for satisfactory completion of Units 1 and 2 is by tests, analysis tasks, and student's work during the year.
What will I learn?
Unit 1: General Mathematics (Methods)
Matrices
Number Systems
2D and 3D Geometry
Linear Graphs and Relations
Unit 2: General Mathematics (Methods)
Trigonometry
Non-Linear Graphs and Relations
Co-ordinate Geometry
Vectors
What type of things will I do?
Work with numbers and surds
Substitute, Transpose and Solve Equations
Apply geometry to applications
Plot and sketch graphs
Use trig ratios, pythagoras and geometry to solve problems
Use technology to help with learning
Application of Matrices
What can this lead to?
Specialist Mathematics 3 and 4
Mathematical Methods(CAS) 3 and 4
Further Mathematics 3 and 4
VET
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Pathway 2 Mathematics
Year 11
General Mathematics (Methods)
Mathematical Methods
Year 12
Mathematical Methods(CAS)
Specialist Mathematics
Further Mathematics
Why choose this study?
Choose this study if you are interested in learning about:
Numbers
Applications of Geometry
Interpreting Graphs
Matrices
CAS
Further Mathematics Units 3-4
What's it all about?
This course is designed for those students whose employment and/or further study aspirations do not require heavily algebra based mathematical skills.
Students will develop their mathematical knowledge and skills to be able to investigate, analyse and solve problems. They will be required to communicate mathematical ideas clearly and concisely.
A Computer Algebra System will be used by students to assist them in their learning and understanding.
Assessment is by satisfactory completion of three outcomes, judged by the student's results in Student Assessed Coursework (SACS).
What will I learn?
Unit 3: Further Mathematics
Networks and Decision Mathematics
Statistics
Unit 4: Further Mathematics
Number Patterns and Applications
Matrices
What type of things will I do?
Use statistical techniques
Model relationships between data
Matrix representation and arithmetic
Predicting ahead in situations involving number patterns
Correlations and Regression of data
Minimisation in problems of time and distance
Features of networks and their applications
Use a Computer Algebra System
What can this lead to?
Tertiary Education
Apprenticeship
General Employment
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Pathway 1 Mathematics
Year 11
General Mathematics (Further)
General Mathematics (Methods)
Year 12
Further Mathematics
Why choose this study?
Choose this study if you are interested in learning about:
Numbers
Uses of Data
Interpreting Graphs
Matrices
Networks
Mathematical Methods (CAS) Units 1-4
What's it all about?
Mathematical Methods consists of study in the areas of 'Co-ordinate Geometry', 'Trigonometric Functions', 'Calculus', 'Algebra', and 'Statistics and Probability'.
There are no prerequisites for entry to Mathematical Methods (CAS) Units 1 and 2. However, students attempting Mathematical Methods (CAS) are expected to have a sound background in number, algebra, function, and probability. Students wanting to do Mathematical Methods (CAS) Units 3 and 4 should have completed Mathematical Methods (CAS) Units 1 and 2 and General Mathematics (Methods) Units 1 and 2.
The appropriate use of CAS technology to support and develop the teaching and learning of mathematics, and in related assessments, is to be incorporated throughout the course.
Assessment is by satisfactory completion of three outcomes, judged by the student's results in Student Assessed Coursework (SACS) and exams.
What will I learn?
Unit 1: Maths Methods(CAS)
Functions and Graphs
Algebra
Probability
Rates of Change
Unit 2: Maths Methods(CAS)
Functions and Graphs
Algebra
Probability
Calculus
Unit 3: Maths Methods(CAS)
Functions and Graphs
Differential Calculus
Unit 4: Maths Methods(CAS)
Integral Calculus
Probability
What type of things will I do?
Problem solving
Substitute, Transpose and Solve Equations
Apply geometry to applications
Plot and sketch graphs
Calculate and Interpret Probabilities
Apply Algebra, Logarithmic and Trigonometric properties
Use CAS to assist with learning
What can this lead to?
Tertiary Education
Apprenticeship
General Employment
Possible Pathways @ TLSC
Year
Studies Offered
Year 10
Pathway 2 Mathematics
Acceleration Mathematics
Year 11
General Mathematics (Methods)
Mathematics Methods (CAS)
Year 12
Mathematics Methods (CAS)
Specialist Mathematics
Why choose this study?
Choose this study if you are interested in learning about:
Calculus
Geometry
Functions
Probability
CAS
Specialist Mathematical Units 3-4
What's it all about?
Specialist Mathematics consists of the following areas of study: 'Functions, relations and graphs' 'Algebra', 'Calculus', 'Vectors' and 'Mechanics'. Students are expected to be able to apply techniques, routines and processes, involving rational, real and complex arithmetic, algebraic manipulation, diagrams and geometric constructions, solving equations, graph sketching, differentiation and integration related to the areas of study, as applicable, both with and without the use of technology.
Enrolment in Specialist Mathematics Units 3 and 4 assumes a current enrolment in Mathematical Methods (CAS) Units 3 and 4.
Assessment is by satisfactory completion of three outcomes, judged by the student's results in Student Assessed Coursework (SACS). |
Research, consultation and experience have helped us select math materials excellent for their organization and presentation of college prep coursework. These texts provide step-by-step instruction and plenty of practice exercises along with periodic reviews and tests.
Star Academics Mathematics Courses
Fundamentals of Mathematics (grade 6 – 7)Pre-Algebra (grade 8)Algebra 1 (grade 9)Algebra 2 (grade 10 – 11)It is essential that parents consistently score math assignments. If parents are not personally able to provide this academic support, we recommend purchasing optional materials and/or obtaining private instruction. Parents should also ensure that students read and complete the practice problems before attempting the exercises. |
Number Properties Guide provides a comprehensive analysis of the properties and rules of integers tested on the GRE to help you learn, practice, and master everything from prime products to perfect squares.
Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the GRE tests a given topic and how you can respond accurately and quickly. The Guide contains 150+ questions: \"Check Your Skills\" questions in the chapters that test your understanding as you go and \"In-Action\" problems of increasing difficulty, all with detailed answer explanations.
Purchase of this book includes one year of access to 6 of Manhattan GRE\'s online practice exams. |
Subject overview
Why mathematics?
Mathematics is core to most modern-day science, technology and business. When you turn on a computer or use a mobile phone, you are using sophisticated technology that mathematics has played a fundamental role in developing. Unravelling the human genome or modelling the financial markets relies on mathematics.
As well as playing a major role in the physical and life sciences, and in such disciplines as economics and psychology, mathematics has its own attraction and beauty. Mathematics is flourishing: more research has been published in the last 20 years than in the previous 200, and celebrated mathematical problems that had defeated strenuous attempts to settle them have recently been solved.
The breadth and relevance of mathematics leads to a wide choice of potential careers. Employers value the numeracy, clarity of thought and capacity for logical argument that the study of mathematics develops, so a degree in mathematics will give you great flexibility in career choice.
Why mathematics at Sussex?
Mathematics at Sussex was ranked in the top 20 in the UK in The Sunday Times University Guide 2012.
In the 2008 Research Assessment Exercise (RAE) 90 per cent of our mathematics research and 97 per cent of our mathematics publications were rated as recognised internationally or higher, and 50 per cent of our research and 64 per cent of our publications were rated as internationally excellent or higher.
The Department awards prizes for the best student results each year, including £1,000 for the best final-year student.
In 2011, US careers website Jobs ratedranked mathematician to be the second most popular job out of the 200 considered.
You will find that our Department is a warm, supportive and enjoyable place to study, with staff who have a genuine concern for their students.
Our teaching is informed by current research and understanding and we update our courses to reflect the latest developments in the field of mathematics.
MMath or BSc?
The MMath courses are aimed at students who have a strong interest in pursuing a deeper study of mathematics and who wish to use it extensively in careers where advanced mathematical skills are important, such as mathematical modelling in finance or industry, advanced-level teaching or postgraduate research.
Applicants unsure about whether to do an MMath or a BSc are strongly advised to opt initially for the MMath course. If your eventual A level grades meet the offer level for a BSc but not an MMath we will automatically offer you a place on the BSc course. Students on the MMath course can opt to transfer to the BSc at the end of the second year.
Why economics?
Addressing many of the world's problems and issues requires an understanding of economics. Why are some countries so rich and others so poor? Should Microsoft be broken up? Should the private sector be involved in providing health and education? Could environmental taxes help reduce global warming? What is the future of the euro?
Economics provides a framework for thinking about such issues in depth, allowing you to get to the heart of complex, topical problems. The methods of economics can be applied to a wide range of questions and will prove useful to you in your future career. In addition, the study of economics teaches you a variety of practical skills, including the ability to use and evaluate evidence (often statistical) in order to arrive at sound conclusions.
Why economics at Sussex?
In the 2008 Research Assessment Exercise (RAE) 100 per cent of our economics research was rated as recognised internationally or higher, and 60 per cent rated as internationally excellent or higher.
We emphasise the practical application of economics to the analysis of contemporary social and economic problems.
We have strong links to the major national and international economic institutions such as the European Commission, the World Bank and the Department for International Development.
The Department has strong research clusters in labour markets and in development economics, and is one of Europe's leading centres for research on issues of international trade.
We offer you the chance to conduct an economics research project supervised by a faculty member.
Programme content
This degree exploits the strong relationship between mathematical modelling and economics. Alongside the mathematics core modules, you study the principles of economic analysis and its policy applications at both the macro (economy-wide) and the micro (individual/ company) levels. The economics element provides an opportunity to acquire practical skills and to apply mathematical methods.
As well as the core mathematics modules in Years 1 and 2, you will spend 25 per cent of your time studying economics modules. In the third year, you take a combination of mathematics and economics options.
On the MMath course, you carry out a project in the fourth year and choose from a range of more advanced mathematical modules recognise that new students have a range of mathematical backgrounds and that the transition from A level to university-level study can be challenging, so we have designed our first-term modules to ease this. Although university modes of teaching place more emphasis on independent learning, you will have access to a wide range of support from tutors.
Teaching and learning is by a combination of lectures, workshops, lab sessions and independent study. All modules are supported by small-group teaching in which you can discuss topics raised in lectures. We emphasise the 'doing' of mathematics as it cannot be passively learnt. Our workshops are designed to support the solution of exercises and problems.
Most modules consist of regular lectures, supported by classes for smaller groups. You receive regular feedback on your work from your tutor. If you need further help, all tutors and lecturers have weekly office hours when you can drop in for advice, individually or in groups. Most of the lecture notes, problem sheets and background material are available on the Department's website.
Upon arrival at Sussex you will be assigned an academic advisor for the period of your study. They also operate office hours and in the first year they will see you weekly. This will help you settle in quickly and offers a great opportunity to work through any academic problemsexcellent training in problem-solving skills
understanding of the structures and techniques of mathematics, including methods of proof and logical arguments
written and oral communication skills
organisational and time-management skills
an ability to make effective use of information and to evaluate numerical data
IT skills and computer literacy through computational and mathematical projects
you will learn to manage your personal professional career development in preparation for further study, or the world of work.
Core content
Year 1
You take modules on topics such as calculus • introduction to pure mathematics • geometry • analysis • mathematical modelling • linear algebra • numerical analysis. You also work on a project on mathematics in everyday life.
Year 2
You take modules on topics such as calculus of several variables • an introduction to probability • further analysis • group theory • probability and statistics • differential equations • complex analysis • further numerical analysis core ideas and analytical techniques are presented in lectures and supplemented by classes or workshops where you can test your understanding and explore the issues in more depth. These provide the opportunity for student interaction, an essential part of the learning process at Sussex. The more quantitative skills, such as using statistical software, are taught in computer workshops. On the dissertation module in the final year, you receive one-to-one supervision as you investigate your chosen research topic in depth.
Formal assessment is by a range of methods including unseen exams and coursework. In addition there are regular assignments, which allow you to monitor your progress. In the first year, you have regular meetings with your academic advisor to discuss your academic progress and to receive feedback on your assignments and understanding of the principles of economics
the skills to abstract the essential features of a problem and use the framework of economics to analyse it
the ability to evaluate and conduct your own empirical research
the confidence to communicate economic ideas and concepts to a wider audience
a range of transferable skills, applicable to a wide variety of occupations.
Core content
Year 1
You are introduced to the principles of economics and their application to a range of practical and topical issues. The aim is not to look at economic theory in isolation but to learn how it is used to analyse real issues. You also take a mathematics module, giving you some of the tools you need to understand contemporary economics.
Year 2
You develop your understanding of economics principles through the study of more advanced topics such as trade and risk. You also take a statistics module and learn how to analyse and interpret data. In addition, there are more applied modules, allowing you to see how the subject deals with empirical issues. There are opportunities for small research projects, including a group project.
Year 3
You have the opportunity to choose from a range of options such as labour or development economics. These modules go into the relevant issues in greater depth, giving you a high level of expertise. There is the opportunity to do a sustained piece of research on a chosen topic. You can also take more advanced quantitative modules – useful if you wish to do postgraduate work.
Geometry
15 credits
Autumn teaching, Year 1
Topics include: vectors in two and three dimensions. Vector algebra: addition, scalar product, vector product, including triple products. Applications in two- and three-dimensional geometry: points, lines, planes, geometrical theorems. Area and volume. Linear dependence and determinants. Polar co-ordinates in two and three dimensions. Definitions of a group and a field. Polynomials. Complex numbers, Argand plane, De Moivre's theorem. Matrices: addition, multiplication, inverses. Transformations in R^2 and R^3: isometries. Analytical geometry: classification and properties of conics.
Introduction to Economics
15 credits
Autumn teaching, Year 1
This course provides an introduction to the fundamental principles of economics. The first half of the course deals with microeconomic issues including the behaviour of individuals and firms, their interaction in markets and the role of government. The second half of the course is devoted to macroeconomics and examines the determinants of aggregate economic variables, such as national income, inflation, and the balance of payments, and the relationships between them. This course also provides students with a basic introduction to mathematical economics, covering solving linear equations, differential calculus, and discounting.
Microeconomics 1
15 credits
Spring teaching, Year 1
This module develops consumer and producer theory, examining such topics as consumer surplus, labour supply, production and costs of the firm, alternative market structures and factor markets. It explores the application of these concepts to public policy, making use of real-world examples to illustrate the usefulness of the theory.
Numerical Analysis 1
15 credits
Spring teaching, Year 1
This module covers topics such as:
Introduction to Computing with MATLAB
Basic arithmetic and vectors, M-File Functions, For Loops, If and else, While statements
Analysis 2
15 credits
Autumn teaching, Year 2
Topics covered: power series, radius of convergence; Taylor series and Taylor's formula; applications and examples; upper and lower sums; the Riemann integral; basic properties of the Riemann integral; primitive; fundamental theorem of calculus; integration by parts and change of variable; applications and examples. Pointwise and uniform convergence of sequences and series of functions: interchange of differentiation or integration and limit for sequences and series; differentiation and integration of power series term by term; applications and examples. Metric spaces and normed linear spaces: inner products; Cauchy sequences, convergence and completeness; the Euclidean space R^n; introduction to general topology; applications and examples.
First order PDEs: Method of characteristics for semilinear and quasilinear equations, initial boundary value problems.
Macroeconomics 1
15 credits
Spring teaching, Year 2
This module introduces core short-run and medium-run macroeconomics.
First you will consider what determines demand for goods and services in the short run. You will be introduced to financial markets, and outline the links between financial markets and demand for goods. The Keynesian ISLM model encapsulates these linkages. Second, you will turn to medium-term supply. You will bring together the market for labour and the price-setting decisions of firms in order to build an understanding of how inflation and unemployment are determined. Finally, you will look at supply and the ISLM together to produce a full medium-term macroeconomic model.
Microeconomics 2
15 credits
Autumn teaching, Year 2
This module develops the economics principles learned in Microeconomics 1. Alternative market structures such as oligopoly and monopolistic competition are studied and comparisons drawn with perfect competition and monopoly. Decision-making under uncertainty and over multiple time periods is introduced, relaxing some of the restrictive assumptions made in the level 1 module. The knowledge gained is applied to such issues as investment in human capital (eg education), saving and investment decisions, insurance and criminal deterrence.
Distribution theory: Chebychev's inequality, weak law of large numbers, distribution of sums of random variables, t,\chi^2 and F distributions;
Confidence intervals;
Statistical tests including z- and t-tests, \chi^2 tests;
Linear regression;
Nonparametric methods;
Random number generation;
Introduction to stochastic processes.
Macroeconomics 2
15 credits
Autumn teaching, Year 3
This module is concerned with two main topics. 'The long run' is an introduction to how economies grow, gradually raising the standard of living, decade by decade. Once we have the basic analysis in place, we can begin to explain why there are such huge disparities in living standards around the world. 'Expectations' is a deepening of the behavioural background to modelling, saving and investment decisions, emphasising the intrinsically forward-looking nature of saving and investment decisions and analysing the financial markets which coordinate these decisions.
Advanced Macroeconomics
15 credits
Spring teaching, Year 3
The module completes the macroeconomics sequence, starting with a consideration of the policy implications of rational expectations. The macroeconomy is then opened up to international trade and capital movements: the operation of monetary and fiscal policies and the international transmission of disturbances under fixed and flexible exchange rates are contrasted, and the issues bearing on the choice of exchange-rate regime are explored. The major macroeconomic problems of hyperinflation, persistent unemployment and exchange-rate crises are examined. The module concludes by drawing together the implications of the analysis for the design and operation of macroeconomic policy.
Advanced Microeconomics
15 credits
Spring teaching, Year 3
This module covers the topics of general equilibrium and welfare economics, including the important issue of market failure. General equilibrium is illustrated using Sen's entitlement approach to famines and also international trade. Welfare economics covers concepts of efficiency and their relationship to the market mechanism. Market failure includes issues such as adverse selection and moral hazard, and applications are drawn from health insurance, environmental economics and the second-hand car market.
Harmonic Analysis and Wavelets
15 credits
Autumn teaching, Year 4
You will be introduced to the concepts of harmonic analysis and the basics of wavelet theory: you will discuss the concepts of normed linear spaces and Hilbert spaces, with a focus on sequence spaces and spaces of functions, most notably the space of square-integrable functions on an interval or on the real line. You will be introduced to the ideas of best approximation, orthogonal projection, orthogonal sums, orthonormal bases and Fourier series in a separable Hilbert space.
You will then apply these concepts to the concrete case of classical trigonometric Fourier series, and both Fejer's theorem and the Weierstrass approximation theorem will be proved.
Finally, you will apply the introduced concepts for Hilbert to discuss wavelet analysis for the example of the Haar wavelet and the Haar scaling function. You will be introduced to the concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function for the case of the Haar wavelet), but will also be defined in general. The concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function) will initially be introduced for the case of the Haar wavelet, but will also be defined in general.
Introduction to Mathematical Biology
15 credits
Autumn teaching, Year 4
The module will introduce you to the concepts of mathematical modelling with applications to biological, ecological and medical phenomena. The main topics will include:
Perturbation theory and calculus of variations
15 credits
Spring teaching, Year 4
The aim of this module is to introduce you to a variety of techniques primarily involving ordinary differential equations, that have applications in various branches of applied mathematics. No particular application is emphasisedRing Theory
15 credits
Autumn teaching, Year 4
In this module we will explore how to construct fields such as the complex numbers and investigate other properties and applications of rings.
Special topics: Quaternions, valuations, Hurwitz ring, the four squares theorem.
Topology and Advanced Analysis
15 credits
Spring teaching, Year 4
This module will introduce you to some of the basic concepts and properties of topological spaces. The subject of topology has a central role in all of Mathematics and having a proper understanding of its concepts and main theorem is essential as part of an undergraduate mathematics curriculum.
Topics that will be covered in this module include:
Topological spaces
Base and sub-base
Separation axioms
Continuity
Metrisability
Completeness
Compactness and Coverings
Total Boundedness
Lebesgue numbers and Epsilon-nets
Sequential Compactness
Arzela-Ascoli Theorem
Montel's theorem
Infinite Products
Box and Product Topologies
Tychonov Theorem.
MMath Project
30 credits
Autumn & spring teaching, Year 4
The work for the project and the writing of the project report will have a major role in bringing together material that you have mastered up to Year 3 and is mastering in Year 4. It will consist of a sustained investigation of a mathematical topic at Masters' level. The project report will be typeset using TeX/LaTeX (mathematical document preparation system). The use of mathematical typesetting, (mathematics-specific) information technology and databases and general research skills such as presentation of mathematical material to an audience, gathering information, usage of (electronic) scientific libraries will be taught and acquired during the project.
E-Business and E-Commerce Systems
15 credits
Autumn teaching, Year 4
This module will give you a theoretical and technical understanding of the major issues for all large-scale e-business and e-commerce systems. The theoretical component includes: alternative e-business strategies; marketing; branding; customer relationship issues; and commercial website management. The technical component covers the standard methods for large-scale data storage, data movement, transformation, and application integration, together with the fundamentals of application architecture. Examples focus on the most recent developments in e-business and e-commerce distributed systems.
Financial Portfolio Analysis
15 credits
Spring teaching, Year 4
You will study valuation, options, asset pricing models, the Black-Scholes model, Hedging and related MatLab programming. These topics form the most essential knowledge for you if you intend to start working in the financial fields. They are complex application problems. Your understanding of mathematics should be good enough to understand the modelling and reasoning skills required. The programming element of this module makes complicated computations manageable and presentable.
Harmonic Analysis and Wavelets
15 credits
Autumn teaching, Year 4
This module introduces you to the concepts of harmonic analysis and the basics of wavelet theory. We will discuss the concepts of normed linear spaces and Hilbert spaces, with a focus on sequence spaces and spaces of functions, most notably the space of square-integrable functions on an interval or on the real line. You will be intoroduces to the ideas of best approximation, orthogonal projection, orthogonal sums, orthonormal bases and Fourier series in a separable Hilbert space, and apply these to the concrete case of classical trigonometric Fourier series. You will also use these strategies to prove both Fejer's theorem and the Weierstrass approximation theorem. Finally you will apply the concepts for Hilbert spaces to discuss wavelet analysis using the example of the Haar wavelet and the Haar scaling function. The concepts of an orthogonal wavelet and a multiresolution analysis (with a scaling function) will initially be introduced for the case of the Haar wavelet, but will also be defined in general.
Introduction to Cosmology
15 credits
Autumn teaching, Year 4
This module covers:
observational overview: In visible light and other wavebands; the cosmological principle; the expansion of the universe; particles in the universe.
cosmological models: solving equations for matter and radiation dominated expansions and for mixtures (assuming flat geometry and zero cosmological constant); variation of particle number density with scale factor; variation of scale factor with time and geometry.
inflation: definition; three problems (what they are and how they can be solved); estimation of expansion during inflation; contrasting early time and current inflationary epochs; introduction to cosmological constant problem and quintessence.
initial singularity: definition and implications.
connection to general relativity: brief introduction to Einstein equations and their relation to Friedmann equation.
Mathematical Models in Finance and Industry
15 credits
Spring teaching, Year 4
Topics include: partial differential equations (and methods for their solution) and how they arise in real-world problems in industry and finance. For example: advection/diffusion of pollutants, pricing of financial options.
Object Oriented Programming
You will be introduced to object-oriented programming, and in particular to understanding, writing, modifying, debugging and assessing the design quality of simple Java applications.
You do not need any previous programming experience to take this module, as it is suitable for absolute beginnersTechnology-Enhanced Learning Environments
15 credits
Spring teaching, Year 4
This module emphasises learner-centred approaches to the design of educational and training systems. The module content will reflect current developments in learning theory, skill development, information representation and how individuals differ in terms of learning style. The module has a practical component, which will relate theories of learning and knowledge representation to design and evaluation. You will explore the history of educational systems, as well as issues relating to: intelligent tutoring systems; computer-based training; simulation and modelling environments; programming languages for learners; virtual reality in education and training; training agents; and computer-supported collaborative learning
Specific entry requirements: A levels must include both Mathematics and Further Mathematics, grade A.
International Baccalaureate
Typical offer: 35 points overall
Specific entry requirements: Higher Levels must include Mathematics, with a grade of 6.
Advanced Diploma
Typical offer: Pass with grade A in the Diploma and A in the Additional and Specialist Learning.
Specific entry requirements: The Additional and Specialist Learning must be an A level in Mathematics (grade A). Successful applicants will also need to take A level Further Mathematics as an extra A level software development, actuarial work, financial consultancy, accountancy, business research and development, teaching, academia and the civil service. All of our courses give you a high-level qualification for further training in mathematics.
Recent graduates have taken up a wide range of posts with employers including:
actuary at MetLife
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associate tutor at the University of Sussex
health economics consultant at the University of York
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accountant at KPMG Mathematical and Physical Sciences
The School of Mathematical and Physical Sciences brings together two outstanding and progressive departments - Mathematics, and Physics and Astronomy. It capitalises on the synergy between these subjects to deliver new and challenging opportunities for its students and faculty advice |
Problem Solving Approach to Mathematics for Elementary School Teachers
9780321331793
ISBN:
0321331796
Edition: 9 Pub Date: 2006 Publisher: Addison-Wesley
Summary: Setting the Standard for Tomorrow's Teachers:This best-selling text continues as a comprehensive, skills-based resource for future teachers. In this edition, readers will benefit from additional emphasis on active and collaborative learning. Revised and updated content will better prepare readers for the day when they will be teachers with students of their own. An Introduction to Problem Solving. Sets, Whole Numbers..., and Functions. Numeration Systems and Whole-Number Computation. Integers and Number Theory. Rational Numbers as Fractions. Decimals, Percents, and Real Numbers. Probability. Data Analysis/ Statistics: An Introduction. Introductory Geometry. Constructions, Congruence, and Similarity. Concepts of Measurement. Motion Geometry and Tessellations. For all readers interested in mathematics for elementary school teachers [more99 Purchased as new and in great condition. We cannot guarantee the availability of CD/DVD or other resource materials such as access code etc if the book is so described by the [more]
ALTERNATE EDITION: Annotated Instructor. Same as the student edition. Cannot guarantee the availability of CD/DVD/Access codes. Ships now if ordered before 2pm CST[less] |
Marblehead ACT Math Science is the systematic study of the feasibility, structure, expression, and mechanization of the methodical
processes (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and
access to information, whether such information is encoded |
Introduction
What is Maple?
Maple is a computer program for people doing mathematics. Using Maple to do your calculations should make the work more interesting, allow you to focus more on the concepts, and help you to avoid mistakes in calculation.
How to use this tutorial
This document is intended to get you started, and show you how to learn more. It is intended to be used while sitting at a terminal running Maple in a windowed environment, by entering the commands and thinking about the output.
To use any software effectively, some knowledge of the computer's operating system is required. This document will assume that you are already familiar with the rudiments of windows -- things like point, click and drag, how to use menus, and the standard way to open and close files. Maple is essentially the same on Microsoft Windows, Macintosh, and the X windows system, but there are minor differences in their interface.
This tutorial assumes that you are running Maple in one of the previously listed environments. If you are using a character-based terminal, for example in a telnet session, the Maple commands will be the same although the interface is different (no mouse, no menus, and typewriter graphics).
In order to be more broadly understood, we don't include some things which require a lot of mathematical knowledge, for example linear algebra. Subject oriented guides are also available -see our By Subject page.
We'll be using some standard conventions throughout this document.
Example
Explanation
File -> Open
Choose the file menu, and select Open.
a := 5;
Input to be typed at the Maple prompt.
a := 5
Output from Maple.
An important tip.
Where to find Maple
Maple is available for many different kinds of computers at Indiana University Bloomington |
Archive for the 'Problem Solving Techniques' Category
This post is the first of a series of hints and techniques for students of math, all based on my experience as a math tutor and teacher…
Much of what a student must learn in a math course amounts to mastering the steps in a well defined procedure. For example, multiplying two binomials (e.g. (x-3)(y2+z) ) |
calculus based physics Vs. algebra based physics
calculus based physics Vs. algebra based physics
Quote by DefennnderSome high schools don't require physics [unfortunately]... and, if it is offered, it won't be calculus-based since calculus would be taught in the senior year, if at all. (If the high-school follows a "physics-first" curriculum, it certainly won't be calculus-based.)
Now for college...
I agree calculus is essential for science and engineering... but, as you've observed, not for a major in the arts and literature.... although it does help round out a student in a liberal arts institution. In addition, I would guess that there are more non-science majors than science-majors in college. So, there is a need for an algebra-based class.... although in an ideal scientifically-minded world there would only be a calculus-based one.
I was at one school that had three levels of introductory calculus-based physics... for bio and premed majors, for chem majors, and for physics and math majors. I guess that school saw the need to give the appropriate attention depending on the needs of the student, as well as the resources to devote to it. In a similar way, some schools will have algebra-based and calculus-based intended for less- and more-scientific majors.
This discussion highlights one of the main difficulties in professional training and education. Because science is constantly advancing, it takes longer and longer to gain mastery of the relevant material. Also, it leads to increasingly narrow specialization by practicioners. Most of what I have to say is for the US educational system- the European system is different, and AFAIK, students are tracked into professional/vocational programs at a very early age.
So, why not teach calculus in high school? Two main reasons- first, the teachers are not sufficiently trained in the material. Second, why teach it? Given that a tiny fraction of K-12 students go into fields requiring proficiency in calculus/physics, especially as compared to say, having proficiency in the english language (or a foreign language!).
What's the difference between calculus based Physics I and non-calculus based Physics I? Primarily conceptual. For both classes, students are expected to memorize certain formulas and are expected to plug-and-chug to solve problems. Using calculus allows for a simpler way of introducing time-dependent things (and later, spatially dependent things), at the cost of having to learn a whole new block of irrelevant math: I can't speak for anyone else, but I stopped doing "delta-epsilon" proofs and all that nonsense freshman year.
Personally, I think science curricula in K-12 needs an overhaul, and undergraduate Physics programs are also in need of an overhaul. Both are outdated products of the 60s and 70s.My high school didn't require us to take calculus (I did anyway, apparently I was a year ahead of everybody or something). The "regular" track ended with trig.
Anyway, the physics was basic algebra-based physics.
F = ma, my mass is 5kg and my acceleration is 4 meters per second per second. What force is being applied?
Why do educators still teach algebra-based physics when they could simply teach the calculus mathematics first, then afterwards go straight to calculus-based physics? It saves the trouble of having to memorise equations when doing algebra-based physics.
I don't think there's any more equations to remember. The constant acceleration equations are used so often in introductory physics, calculus or not, that it's useful to remember it anyway. I don't think there's much more to remember.
To echo what others have said, there hardly is a difference. It makes some things easier to do, but all in all, it reduces to algebra. You might get problems with varying work, and have to integrate, or look at a graph and find the area under the line (usually the lines make triangles, so don't really need calculus) or do some derivatives to find maximum values, so not much a difference. It manly gives you different ways to do problems.
To really udnerstand physics, i think you have to understand calculus, but calculs largley came from physics so they are intertwined. Just about all physics equations are dervied with some help from calculus. It allows for more realistic problems to be solved, but as far as high school physics, you dont really need it.
I just dusted off my very old Halliday and Resnick, copyright 1966, and they certainly went well beyond algebra-based physics. Here are a few topics in which calculus played an integral role: Work as a line integral; the rocket equation; coupled, damped, and forced harmonic oscillators; simple fluid dynamics and thermodynamics. Moreover, many topics which are presented as givens in pre-calculus physics are derived in that ancient version of Halliday and Resnick; e.g., Kepler's laws of motion. Has the Halliday, Resnick, and Walker text dumbed things down since I went to school back in the stone age?
Sorry, I know this is off topic- but this sounds like a really nice book (Halliday et al.), do you have any idea where I could get the book? And, for that matter, would you recommend it?
as someone stupid enough to sign up for courses without checking to see if they'll actually go towards my degree (i know, i'm a ****ing idiot) and thus ending up taking both algebra and calculus based physics, i can tell you that there's not a hell of a lot of difference. you learn all the same concepts and equations: in my experience there was absolutely nothing new that i picked up in calc based physics. the classes only varied in that the prof spent more time going over the whys and hows of the equations and how they worked (a lot of which derived from calculus, like s=a/2(t^2)+vi(t)+si ). that's the way it is at my college at least, there could be huge differences at other schools but in my experience there was virtually no difference. IMO, you could take a class in algebra based physics, take a calculus course afterwards, and be just as well off as someone who took both calc-based physics and calculus itself at the same time (hell, you could be better off: calculus makes a hell of a lot more sense when you're learning it if you already know a thing or two about velocity and acceleration)
Basically with calculus we are able to expand upon the ideas presented with an algebraic approach to physics. Not only can the algebraic equations be derived using calculus but there are some cases where it is much more practical (and easier) to use calculus.
For instance say we wanted to find a velocity of a function at a certain time, with only knowing it's position at any given time. Without calculus the best we can do is approximate this. But since a velocity is just a change in position, if we find the change in position over an infinitely small time interval we can find the actual velocity of an object. This would be an example of differentiation.
An example of integral calculus would be something like this. Say you have a rigid rod and you wanted to calculate the force of gravity the rod exerts on another object at sometime. Well to do this we need to chop the rod up into finitely small parts and find the force for all of these parts, then sum them together to get the total force. Without calculus goodluck summing up the force of an infinite number of pieces of a rod.
Also you can have differential equations (Just shows how a particular function is changing) and you might want to calculate a value of the function at a particular point. A good example of this would be a spring that is dampened. |
The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Intermediate Algebra, 3e is part of the latest offerings in the successful Dugopolski series in mathematics. In his books, students and faculty will find short, precise explanations of terms and concepts written in clear, understandable language that is mathematically accurate. Dugopolski also includes a double cross-referencing system between the examples and exercise sets, so no matter where the students start, they will see the connection between the two. Finally, the author finds it important to not only provide quality but also a wide variety and quantity of exercises and applications |
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Introductory Algebra (9th Edition)
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Prealgebra Review; The Real Number System; Equations, Inequalities, and Applications; Graphs of Linear Equations and Inequalities in Two Variables; Systems of Equations and Inequalities; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Applications; Roots and Radicals; Quadratic Equations
The Student Support Edition of Introductory Algebra: An Applied Approach, 7/e, brings comprehensive study skills support to students and the latest technology tools to instructors. In addition, the ... |
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In discrete mathematics and combinatorics courses, students learn to master the use and combinations of integers, graphs, sets, and logic statements. These are the best graduate schools for discrete mathematics and combinatorics. |
Category:Multilinear algebra
multilinear algebra extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concept of a tensor and develops the theory of 'tensor spaces'. In applications, numerous types of tensors arise. The theory tries to be comprehensive, with a corresponding range of spaces and an account of their |
Overview - HANDS-ON ALGEBRA
A vast assortment of ready-to-use games and activities make Hands-On Algebra! an invaluable resource for teachers of Grades 7-12 looking to make algebra more meaningful and fun. The 159 reproducible games and lessons teach all of the major concepts covered in first-year algebra recommended by the NCTM. Business and industry are requiring more employees to have a better understanding of mathematics than ever before, in particular a greater knowledge of algebra. Teaching techniques once used only for college-bound students must now be adjusted to better serve students of all ability levels.
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The book is divided into the following five sections: -Real Numbers, Their Operations, and Their Properties (11 objectives) -Linear Forms (8 objectives) -Linear Applications and Graphing (12 objectives) -Quadratic Concepts (12 objectives) -Special Applications (9 objectives)
Special Features The Appendix contains an assortment of four tile patterns that can be easily photocopied for student use in completing the games and activities located throughout the book.
About the Author Frances McBroom Thompson has taught mathematics at the junior and senior high school levels, and has served as a K-12 mathematics specialist. She holds a B.S. in mathematics education from Abilene Christian University in Texas, a master's degree in mathematics from the University of Texas at Austin, and a doctoral degree in mathematics education from the University of Georgia in Athens. |
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Practice makes perfect. Our algebra worksheets are great resource for finding extra problems to complete while studying for an exam or for further understanding of a homework assignment. Many of our worksheets contain answer keys so you can check your work immediately.
Parents
Want to make sure your kid is doing their homework? Print out a few of our worksheets and work though some problems together or use a worksheet as a study guide on the night of a big test. Our free algebra worksheets with answer keys are also a great resource for homeschool parents.
Below you can find our collection of algebra worksheets and education resources. Regardless of the grade or topic you are working on, you are sure to find an appropriate worksheet for the lesson. |
A rigorous, concise development of the concepts of modern matrix structural analysis, with particular emphasis on the techniques and methods that form the basis of the finite element method. All relevant concepts are presented in the context of two-dimensional (planar) structures composed of bar (truss) and beam (frame) elements, together with simple discrete axial, shear and moment resisting spring elements. The book requires only some basic knowledge of matrix algebra and fundamentals of strength of materials. |
Equation Editor in Google Docsmeans that anyone with a computer that can go online is able to do his or her math work in a word processor. The built in equation editor is easy to use, and offers a convenient way of inserting mathematical notation and maths symbols into a document. Perhaps the only thing that would make this equation editor more useful would be keyboard shortcuts for each of the symbols.
1. Don't start with the Math. The teachers have discussed how many students shut down if you start with the math. Rather than introducing formulas, vocabulary terms, and numbers, start with problems, puzzles, and situations. Rather than using the problem to practice math – introduce a problem that requires math to solve it.
2. Try to avoid text-only problems. Some students struggle to start a math problem because of difficulties with langauge. Where possible, start with images, videos, manipulates or hands-on introductions to the math. Chunking out the sub-questions or giving them one at a time isn't really a solution – find ways to get rid of the written language completely. Dan Meyer's name has come up many times as the master of this.
We hear a lot of design manifestos around here. But Bret Victor's stuck out: He wants to kill math. He's no Luddite, though — he thinks mathematics is one of the most powerful, transcendent ways humans have for understanding and changing the world. What he wants to kill is math's interface: opaque, abstract, unfamiliar, hard. "The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols," he writes. Now he's created a prototype iPad interface that turns differential equations into something that doesn't feel math-ey at all: visual, intuitive, and touchableEnter Desmos, a startup out of Connecticut, that has built a graphing calculator alternative that may shake up the industry on two key fronts: it's Web-based, and it's free.
Do we need students to spend $100 on a graphic calculator?
So much potential—if only it worked in HTML5 instead of Flash. Then it'd be available on the over 200 million iOS devices out there. There's always this app for less than $2. Still much cheaper than my old TI-83 Plus.
A geometric construction of the parabola. The blue point is called the focus, and the horizontal line is the directrix. The blue lines show all the points which are at an equal distance from the red point and the blue focus point. The point of the blue line directly above the red dot contributes to the parabolic curve, because the parabola is defined as the set of all points equidistant to the focus and the directrix. [more] [code] |
Linear Algebra : A Modern Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlyi... MOREng geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra. |
Saxon Teacher provides comprehensive lesson instructions that feature complete solutions to every practice problem, problem set, and test problem, with step-by-step explanations and helpful hints. These Algebra 1 Algebra 1 3rd Edition. Five Lesson CDs and 1 Test Solutions CD included.
Too much time and frustration
Date:June 29, 2012
Karen
Location:North Carolina
Age:45-54
Gender:female
My son has used Saxon very successfully since 1st grade until he got halfway through Algebra 1. The concepts are not presented in a rational progression; today's topic may be totally unrelated to yesterday's and tomorrow's topics. Also, there are never enough new concept problems to work through in order to thoroughly cement each day's lesson in the student's understanding. My son needed many more new concept problems and less review problems on each lesson and better continuity. He was constantly having to review previous lessons. We are using a different curriculum now which great success and enjoyment.
Love the CDs
Date:February 10, 2011
WI Mom
Age:35-44
Gender:female
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
I just received this kit today, and I am loving the teacher lesson & test cds. The simulated whiteboard is amazing! My daughter goes to public school, and has always had trouble understanding math. We use the Saxon curriculum as a way to help her at home. We do lessons in the summer months to keep her in a math state of mind. Worth every penny.
I homeschool my two 9th grade granddaughters. We are using Saxon Math with Saxon teacher and we love it. The teacher's demonstrations and explanations of each problem is so clear that the girls are actually enjoying math this year. Thank you for this new help. |
MATHEMATICS
Pre-requisite(s):
SCE H or GCE A level in Mathematics. This course may not be included in a minimum curriculum with EG 1503.
Note(s):
The course starts from the beginning of the subject, but it is advantageous to be familiar with the material on Calculus contained in the Scottish Highers syllabus.
Calculus allows for changing situations and complicated averaging processes to be described in precise ways. It was one of the great intellectual achievements of the late 17-th and early 18-th Century. Early applications were made to modeling planetary motion and to calculating tax payable on land. Now the ideas are used in broad areas of mathematics and science and parts of the commercial world. The course begins with an introduction to fundamental mathematical concepts and then develops the basic ideas of the differential calculus of a single variable and explains some of the ways they are applied.
3 one-hour lectures and 1 one-hour tutorial per week; support 1006
ALGEBRA
CREDIT POINTS 15
Course Co-ordinator: Dr A Gonzales
Pre-requisite(s):
SCE H or GCE A level in Mathematics.
The basic course includes a discussion of the following topics: complex numbers and the theory of polynomial equations, vector algebra in two and three dimensions, systems of linear equations and their solution, matrices and determinants.
3 one-hour lectures and 1 one-hour tutorial per week. Support tutorials to be arranged by the Course Coordinator, as need arises.
Formative Assessment and Feedback Information
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.
In-course assessment will be marked and feedback provided to the students.
Support tutorials to be arranged by the Course Coordinator, as need arises.
MA 1007
INTRODUCTORY MATHEMATICS 1
CREDIT POINTS 15
Course Co-ordinator: Dr M Boyle
Pre-requisite(s):
S or GCSE or equivalent in Mathematics. This course is not open to students with the equivalent of a Higher in Mathematics at grade B or above.
This is a basic course aimed primarily at helping students achieve greater accuracy, speed and confidence in mathematics. It is suitable both for those who may need mathematics in future study and for students who want to improve their abilities without any intention of studying the subject beyond first year. The course is taught using the interactive computer software CALMAT, enabling students to work in their own way and time but with immediate feedback. Support from staff is available on a daily basis. There is a requirement to attend a single weekly test for continuous assessment. The topics covered include basic arithmetic and algebraic operations, linear and quadratic equations, logarithms and the interpretation of graphs, and an introduction to the calculus7
INTRODUCTORY MATHEMATICS 2
CREDIT POINTS 15
Course Co-ordinator: Dr M Boyle
Pre-requisite(s):MA 1007 or equivalent. This course is not open to students with the equivalent of a Higher in Mathematics at Grade B or above.
The course emphasizes accuracy in performing calculations involving trigonometry, exponentials, techniques and application of differentiation and integration, vectors, complex numbers and matrices. The course is taught and examined using the CALMAT computer software8
CALCULUS II
CREDIT POINTS 15
Course Co-ordinator: Prof V Gorbunov
Pre-requisite(s):
SCE H or GCE A level in Mathematics; MA 1005 (recommended). This course may not be included in a minimum curriculum with EG 1503.
The course is a continuation of Calculus I from the 1st session. It develops the basic ideas concerning the integration of a function of one variable. It introduces Taylor series and determines these series for the most common functions. It also provides a first introduction to differential equations which are fundamental in applications of Mathematics to other sciences.
3 one-hour lectures and 1 one-hour tutorial per week. Support 2005
INTRODUCTION TO ANALYSIS
CREDIT POINTS 15
Course Co-ordinator: Dr C Lopez
Pre-requisite(s):MA 1005 or, with the permission of the Head of Mathematical Sciences, both MA 1007 and MA 1507.
Resit: 1 two-hour written examination paper. The CAS mark awarded will be the maximum of 100% resit and 80% resit with 20% in-course assessmentFields.
Solving a linear system over a field; Definition and examples of fields (Q, R, C, Fp ); Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system over a field.
Linear maps
Definition of a linear map between two K-vector spaces; Kernel, image, injective, surjective linear maps;
Matrix of a linear map; Rank of a matrix; Invertible matrices; Determinants; Change of basis and the matrix of a linear map Information |
Math 7 - 8: A two-year pre-algebra class with an inquiry-based hands-on approach to learning using MathScape, Course 2 and 3 published by Glencoe/McGraw Hill (2005)
Students will practice and improve their number sense, measure sense and estimation skills, review and extend their arithmetic, calculator, and thinking skills by working with fractions, decimals, percents, large and small numbers and negative numbers. Students will study variables, expressions, equations, multiple representations of data, and other algebra topics. Students will extend their understanding of geometry, including transformations and 2 and 3 dimensional figures, and their knowledge of probability and statistics. They will investigate the uses of mathematics outside the classroom.
Successful completion of Math 7
and Math 8 will prepare a student to take Algebra in high school.
Pre-Algebra is designed to prepare seventh grade students for success in Algebra I. The emphasis will be on continued development of pattern recognition, computational skills, elementary algebra topics, geometric relationships, problem solving and the use of technology. Students will extend their knowledge of probability and statistics and analyze data to make decisions and defend conclusions.
Algebra I: A one-year high school level algebra class using Algebra 1, An Integrated Approach published by McDougal Littell (1991, 1994)
Students will review and extend their knowledge of problem solving, data analysis, and the use of technology (i.e., scientific calculator, graphing calculator, computer). They will extend their knowledge of the theory, use and understanding of the fundamental operations to real numbers. Students will learn to express quantitative statements in the language of algebra, solve equations and inequalities, use rational expressions in equations, graph using the coordinate plane, perform operations with polynomials and irrational numbers, and solve quadratic equations. They will use their mathematical knowledge to solve problems.
Prerequisites: A or B in Pre-Algebra in Grade 7
Geometry: A one-year high school level geometry class using Geometry for Enjoyment and Challenge published by McDougal Littell (1993)
This course covers the study of plane and three dimensional geometry. There is an emphasis on clarity and precision of language and the logical development of geometric principles in deductive reasoning and proof. This will include work with points, lines, planes, angles, congruent triangles, circles, polygons and transformations.
Prerequisites: A or B in Algebra I in Grade 7
Math Support provides assistance to students who want to strengthen their foundation in 7th grade math. |
Program from Raffles Institution for Math Enrichment
Prerequisites:
Basic arithmetic
Duration:
15 hours | Self-paced
learning more
Students will learn:
• To identify prime
and composite numbers
and list them
• The difference
between a divisor and
a factor
• To find the Highest
Common Factor and Least
Common Multiple
• Divisibility rules
to determine divisibility
by a number
• That geometrical
and numerical patterns
can be represented
symbolically
• About Triangular
numbers, Fibonacci sequence,
Pascal's Triangle
etc...
US$ 34.99
Prerequisites:
Basic arithmetic
Duration:
10 hours | Self-paced
learning more
Topics covered:
Angle Properties, including
angles at a point, on
a straight line, vertically
opposite angles, angles
formed by parallel lines,
angles formed by triangles.
Polygons, sum of interior
and exterior angles formed
by convex polygons.
Students will learn:
• That angle is
a measure of rotation
• That angles can
be classified according
to their unique properties
• That interior
and exterior angles of
polygon are dependent
on its number
of sides.
• To use appropriate
angle properties to calculate
unknown angles
of regular and irregular
polygons.
US$ 34.99
Prerequisites:
Basic geometry, Arithmetic
Skills
Duration:
15 hours | Self-paced
learning more
Topics covered:
Area and perimeter of
triangles, parallelograms,
trapeziums and rectangles,
Circumference and Area
of circles.
Students will learn:
• To classify triangles
and quadrilaterals
• To calculate the
perimeter and area of
various quadrilaterals
• To calculate the
circumference and area
of circle
• To use the above
facts to calculate the
perimeter and area
of
compound figures
US$ 34.99
Everyday Arithmetic
The course explains the concepts of equivalent fractions, simplifying fractions, mixed numbers and improper fractions. Then it explores decimals and percentages and how they relate to fractions. Once you've mastered the basics of fractions, decimals and percentages, you'll be able to apply them to different problems in everyday situations.
Prerequisites:
Arithmetic skills, Basic algebra
Duration:
20 hours | Self-paced
learning moreEveryday Arithmetic
The course explains the
concepts of equivalent
fractions, simplifying
fractions, mixed numbers
and improper fractions.
Then it explores decimals
and percentages and how
they relate to fractions.
Once you've mastered the
basics of fractions, decimals
and percentages, you'll
be able to apply them
to different problems
in everyday situations.
Topics covered:
Fractions, Decimals, Percentages,
Conversion from one form
to the other, Word problems
Students will learn:
• What are fractions
- proper, improper and
mixed numbers?
• About equivalent
fractions with visual
demonstrations.
• To represent fractions
and mixed numbers on a
number
line.
• What are decimals
and how it relates to
fractions?
• To order fractions
and decimals
• The four operations
on fractions and decimals
• What are percentages
and how it relates to
fractions and
decimals?
• To compare fractions,
decimals and percentages
and to
convert one
form to the another.
• How it helps to
solve problems in everyday
situations.
Prerequisites:
Basic knowledge of whole
numbers, Fractions &
Decimals, Integers
Duration:
15 hours | Self-paced
learning more
Students will learn:
• That the real
numbers form an extension
of the rational numbers
• That real numbers
are manifested in real-life
situations
• How to compare
and contrast whole numbers,
integers, rational,
and irrational numbers
• How to use a calculator
to calculate complicated
sums with real
numbers
• That estimation
can be used to judge the
reasonableness of results
• How to round off
numbers in different ways,
to different degrees
of accuracy and for different
purposes in real life
• How to convert
numbers to scientific
notation or standard form
and vice versa
• How to solve problems
of standard form which
require the use
of calculator and without
a calculator
US$ 34.99
Prerequisites:
Knowledge of whole numbers
and real numbers (fractions,
decimals, factors, multiples,
HCF, LCM)
Duration:
20 hours | Self-paced
learning more
Students will learn:
• How mathematical
and real-life situations
can be represented
and analysed using algebraic
symbols and rules
• How to manipulate
and simplify algebraic
expressions
• That algebra is
a tool used to solve problems
in real life
• How to solve linear
equations by obtaining
equilibrium on both
sides
• That real-life
situations can be modeled
using equations
US$ 44.99
Prerequisites:
Basic knowledge of real
numbers (fractions, decimals)
Basic algebra (algebraic
terms and expressions)
Duration:
10 hours | Self-paced
learning more
Students will learn:
• That mathematical
problems can be expressed
via
symbolic representation.
• How to solve problems
involving the use of units
of mass, length,
time and money.
• How to solve problems
involving ratio and proportion.
• How to recognise
and use common measures
and rate.
US$ 34.99
Prerequisites:
Basic knowledge of real
numbers, ratio, rate and
proportion.
Basic algebra (algebraic
terms and expressions)
Duration:
10 hours | Self-paced
learning more
Students will learn:
• That there are
a variety of strategies
which can be applied to
solve mathematical
and real-life problems.
• How to solve consumer
problems using arithmetic
operations.
US$ 34.99
Prerequisites:
Mensuration I
Duration:
15 hours | Self-paced
learning more
Students will learn:
• To compare and
classify geometric figures.
• To calculate arc
length and area of a sector.
• To calculate and
solve problems involving
surface area and volume.
• To solve mathematical
and real life problems.
US$ 34.99
Intermediate Algebra
In this course you will learn to expand algebraic expressions using identities and also to factorise algebraic expressions. You will note that expansion and factorisation are reverse processes of each other. You will also learn to manipulate and simplify algebraic fractions.
Prerequisites:
Basic Arithmetic
Duration:
20 hours | Self-paced
learning moreIntermediate Algebra
In this course you will
learn to expand algebraic
expressions using identities
and also to factorise
algebraic expressions.
You will note that expansion
and factorisation are
reverse processes of each
other. You will also learn
to manipulate and simplify
algebraic fractions.
Students will learn:
• Expansion and
factorisation of algebraic
expressions can
be represented
geometrically.
• Expansion and
factorisation are reverse
processes of each
other.
• The use of algebraic
identities helps to expedite
the solving
of numerical
problems.
• Manipulate and
simplify algebraic fractions.
• Manipulate to
change the subject of
a formula such that
equivalence
is maintained.
Prerequisites:
Fractions, ratio and proportion
Simple Algebra (algebraic
expressions, solving linear
equations and powers)
Duration:
10 hours | Self-paced
learning more
Students will learn:
• How Pythagoras'
Theorem can be used to
solve a variety of mathematical
and real-life problems.
• What trigonometric
ratios are.
• How they can be
applied to measure distances
and angles in
real-life situations.
• How to find the
trigonometrical values
of sine, cosine and tangent
of an angle with the help
of a calculator.
• How to solve problems
involving trigonometrical
ratios in right-angled
triangles.
• How to solve problems
involving angle of elevation
and angle
of depression.
US$ 34.99
Prerequisites:
Simple Algebra (algebraic
expressions, solving linear
equations and powers)
Duration:
8 hours | Self-paced
learning more
Students will learn:
• About how statistics
is useful in real-life
situations and how people
use statistical data to
suit their purposes
• That data can
be represented in different
forms, each with
its own
advantages and disadvantages.
• How to represent
data appropriately e.g.
pie chart, bar graphs,
pictograms, dot diagrams,
stem and leaf diagrams,
line graphs
and histograms with equal
intervals.
• How to interpret
graphs or charts of given
situations.
• How to evaluate
the mean, median and mode
for
ungrouped data.
• How to select
and justify the use of
appropriate central tendencies.
US$ 34.99
Prerequisites:
Algebra I (algebraic formulae,
expressions, algebraic
fractions, solving linear
equations)
Duration:
16 hours | Self-paced
learning more
Students will learn:
• About how to plot
and sketch quadratic graphs
• How the shape
of a quadratic graph depends
on the coefficients
• That there are
different ways that we
can solve quadratic equations
• The procedure
for factorising a quadratic
equation - what factorising
means and how to do it
quickly
• The derivation
of the quadratic formula
(for solving any quadratic
equation) and how to use
it
• That real-life
problems can give rise
to quadratic equations
and that we
can solve the equations
using the methods learnt
US$ 34.99
Congruence
andPrerequisites:
Fractions, ratio and proportion,
Basic geometry
Duration:
8 hours | Self-paced
learning moreCongruence and
Prerequisites:
Fractions, ratio and proportion,
Basic geometry
Duration:
8 hours | Self-paced
learning less
Topics covered:
Congruence and Similarity,
Proof of congruent and
similar triangles, Area
and volume of similar
figures and solids.
Students will learn:
• The meaning of
the terms 'similar' and
'congruent'
• That a proportional
change in the lengths
of a shape will result
in a similar shape.
• How to derive
and apply the relationships
between similar objects.
US$ 34.99
Prerequisites:
Real number system, Basic
algebra
Duration:
15 hours | Self-paced
learning more
Students will learn:
• To identify the
base and the exponent
in an index notation
• The meaning of
negative, fractional and
zero indices.
• To use the laws
of indices for all rational
exponents.
• To solve exponential
equations of the form
a = bx
where a =
bn.
• The applications
of indices and indicial
equations in real life
situations.
US$ 34.99
Prerequisites:
Number system, Basic Inequality,
Simple geometrical figures
Duration:
15 hours | Self-paced
learning more
Students will learn:
• That mathematical
information can be represented
by set notations
• How Venn diagram
helps in organising, recording
and communicating
mathematical ideas
• That set notations
can be used to solve mathematical
and real-life
problems
• To organise data
using set notation and
Venn diagram
• To formulate and
solve problems using set
theory
Prerequisites:
Algebra I and II (Solving
linear equations, Solving
simultaneous linear equations,
Solving quadratic equations,
Simultaneous non linear
equations in 2 unknowns.)
Duration:
20 hours | Self-paced
learning more
Students will learn:
• About how graphs
can help us in analysing
trends,
patterns
and relationships
• How the Cartesian
coordinates system is
used to represent
algebraic relationships
• To use graphs
as a pictorial representation
of algebraic equations
and to model real-life
situations
• To use graphs
to analyse numerical data
for trends,
patterns and
relationships
• To draw graphs
of linear functions
• To solve simultaneous
linear equations using
a graphical method
• To interpret and
use graphs in practical
situations
US$ 44.99
Prerequisites:
Algebra II (Expansion and
factorisation, identities,
algebraic fractions, solving
quadratic equations),
Graphs of Quadratic Functions
and their properties.
Duration:
20 hours | Self-paced
learning more
Students will learn:
• How to find the
maximum or minimum value
of quadratic
function by completing
the square
• How to sketch
quadratic functions by
observing the value of
'a' and expressing
the function in the form
y = a(x-h)2+k
• To determine the
equation of quadratic
function from the graph
• To choose and
apply different methods
to solve quadratic equations
efficiently and elegantly
• To investigate
how the nature of roots
is related to the 'discriminant'
and use the results to
solve for unknown constants
in an equation
• To extend the
knowledge on the nature
of roots and discriminant
to points of intersection
of line and a curve
• To establish the
relationship between roots
and coefficients of a
quadratic equation to
solve questions
US$ 44.99
Prerequisites:
Positive, negative, zero
and fractional indices,
Laws of indices and indicial
equations.
Duration:
25 hours | Self-paced
learning more
Topics covered:
Operations on Surds, Rationalisation
of denominator, Laws of
Logarithms including
change in base, Solving
exponential and logarithmic
equations, Graphs of exponential
and logarithmic functions.
Students will learn:
• What are Surds
and their rules
• Simplify numbers/expressions
in surds
• To convert exponential
form to logarithmic form
• To simplify logarithmic
expressions using the
laws of logarithms
• To solve exponential
and logarithmic equations
• To illustrate
exponential and logarithmic
functions graphically
and the relationship between
the two functions.
• To apply the exponential
and logarithmic functions
to solve problems
in real-life
US$ 44.99
Prerequisites:
Algebra (Expansion and
factorisation, Algebraic
Fractions, Solving quadratic
equations by factorisation
and by formula)
Duration:
20 hours | Self-paced
learning more
Topics covered:
Operations of polynomials,
The remainder and factor
theorems, Factorising
and solving cubic equations,
Expressing algebraic fractions
as partial fractions,
Use the Binomial Theorem
for the expansion of (x
+ y)n.
Students will learn:
• That the real
numbers form an extension
of the rational numbers.
• That we can divide
polynomials in a similar
way to
numbers, getting
a quotient and remainder.
• Understand, state
and use the Remainder
and Factor Theorems
to factorise/solve polynomial
expressions or equations.
• How to find the
remainder when a polynomial
is divided by a linear
factor.
• How to find factors
of polynomials.
• How to factorize
cubic expressions or polynomials
of higher degree
using the Factor Theorem
• Translate problems
involving remainder and
factor
theorems
into mathematical equations
and solve them.
• That rational
functions can be written
as partial fractions.
US$ 44.99
Prerequisites:
Basic Algebra, Fractions,
Decimals and Percentages
Duration:
15 hours | Self-paced
learning more
Students will learn:
• That probability
is the mathematical formulation
of
likelihood to
quantify risks and chance.
• To calculate the
theoretical probability
and make inferences from
data to estimate the probability
of an event
• To predict possible
outcomes of real life
situations.
• To list all the
possible outcomes for
more complex experiments
systematically, using
possibility diagram and
tree diagrams
• To calculate the
probability of combined
events using Addition
and Multiplication Rules
US$ 34.99
Prerequisites:
Fractions, Decimals and
Percentages, Statistics I, Basic probability
Duration:
15 hours | Self-paced
learning more
Students will learn:
• That data can
be represented effectively
by pictorial means
• To construct a
grouped frequency table
• To represent grouped
data using histogram with
equal and unequal
intervals
• To find the central
tendencies for grouped
data
• To draw cumulative
curves using a cumulative
frequency table
• To find quartiles
and percentiles from the
cumulative frequency
curves
• To use box plots
to compare data sets
US$ 34.99
Prerequisites:
Cartesian coordinates,
Plotting straight lines
on a graph
Duration:
15 hours | Self-paced
learning more
Topics covered:
Coordinate plane, Length
and midpoint of line segments,
Equations of straight
lines, Area of polygons
in coordinate plane.
Students will learn:
• To derive and
apply the formulae for
midpoint, distance and
gradient of
line joining two points
• To find the equation
of straight lines and
area of plane figures.
• To identify and
investigate the relationship
between parallel and
perpendicular lines.
• To apply these
properties and formulae
to solve problems
in Cartesian
plane.
US$ 34.99
Prerequisites:
Basic geometry, Properties
of triangles and polygons,
Congruency
Duration:
20 hours | Self-paced
learning more
Students will learn:
• The symmetrical
and the geometrical properties
of circles.
• The angle properties
of cyclic quadrilaterals.
• To calculate unknown
angles and solve problems
using the circle
properties.
US$ 44.99
Matrices
This course introduces the concept of Matrices. Here you will learn to represent real life data in the form of a matrix; add, subtract, multiply two matrices and to find the inverse of a matrix. Explore the use of matrices as a tool to solve mathematical and real-life problems.
Prerequisites:
Real numbers, Arithmetic, Algebra
Duration:
12 hours | Self-paced
learning moreMatrices
This course introduces
the concept of Matrices.
Here you will learn to
represent real life data
in the form of a matrix;
add, subtract, multiply
two matrices and to find
the inverse of a matrix.
Explore the use of matrices
as a tool to solve mathematical
and real-life problems.
Prerequisites:
Pythagoras' theorem and
Trigonometry (The sine,
cosine and tangent ratios
for acute angles in a
right-angled triangle.)
Duration:
18 hours | Self-paced
learning more
Prerequisites:
Pythagoras' theorem and
Trigonometry (The sine,
cosine and tangent ratios
for acute angles in a
right-angled triangle.)
Students will learn:
• How to find the
trigonometrical ratios
of any angle
• What is a basic
angle? How to find the
basic angle, given any
angle?
• To solve simple
trigonometric equations
of the form
sin x = k,
cos x = k
and tan x = k where k
is a constant
• To apply the sine
rule, the cosine rule
to find unknown angles
or sides in a triangle
• How to find the
area of a triangle given
two sides and an angle
between them
• To solve real
life problems involving
bearings using the above
rules
• What is a radian?
A radian is a unit of
measure for angles and
has a simple relationship
with the degree measure
• That circular
(radian) measure can be
used to solve mathematical
and real-life problems
US$ 44.99
Prerequisites:
Algebra, Trigonometry,
solving trigonometric
equations, Laws of Logarithms,
solving exponential and
logarithmic equations.
Duration:
25 hours | Self-paced
learning more
Topics covered:
The idea of Limits, Differentiation
of polynomial functions,
Functions of the form
xn, Trigonometric,
Exponential and Logarithmic
functions, The Chain rule,
The Product rule and The
Quotient rule.
Students will learn:
• About the concept
of limits
• How limits are
essential to the invention
of differentiation
• That gradients
can be formulated using
limits
• To use differentiation
from First Principles
to find derivatives and
gradients
• To use techniques
of differentiation to
differentiate many
functions
• To extend their
knowledge of differentiation
to trig functions, and
other functions
US$ 44.99
Prerequisites:
Calculus I (Differentiation
of polynomial functions,
functions of the form
xn, Trigonometric,
Exponential and Logarithmic
functions)
Duration:
16 hours | Self-paced
learning more
Prerequisites:
Calculus I (Differentiation
of polynomial functions,
functions of the form
xn, Trigonometric,
Exponential and Logarithmic
functions)
Students will learn:
• The concept of
Tangent and Normal
• To describe the
graph of non-linear functions
and discuss
its
appearance in terms of
the basic concepts of
maxima
and
minima, rate of change
• To infer, from
concepts of approximation
and rate
of change, how
one change results in
other changes and summarize
as accurately
as possible, the amount
of change
resulted and
how fast the change is
changing.
US$ 34.99
Prerequisites:
Algebra, Trigonometry,
Calculus I
Duration:
10 hours | Self-paced
learning more
Students will learn:
• The relationship
between derivatives and
integrals;
• To derive the
formulae for integrating
various simple functions:
polynomials, trigonometric,
exponential
• To find the equation
of a curve whose gradient
function and a
particular point on the
curve are given.
• The difference
between definite and indefinite
integrals and to
evaluate them
US$ 34.99
Prerequisites:
Calculus III, Distance,
Time & Speed
Duration:
14 hours | Self-paced
learning more
Topics covered:
Area under a curve, Area
between two curves, Calculus
and Kinematics, Displacement-time,
velocity-time and acceleration-time
graphs, Problem solving
using kinematics.
Students will learn:
• That finding "area
under the curve"
is one of the ways to
solve a variety
of problems.
• To apply the techniques
of integration to evaluate
the area of plane
figures bounded by one
or more curves
• To use definite
integrals to find the
changes in
displacement
and velocity
of motions.
• To solve problems
relating to graphs of
displacement, velocity
and acceleration as functions
of time.
US$ 34.99
Prerequisites:
Algebraic skills, Sketch
linear and quadratic graphs
Duration:
12 hours | Self-paced
learning more
Students will learn:
• That functions
are relations governed
by fixed rules and domains.
• To formulate composite
and inverse functions
completely and
accurately.
• To generate modulus
functions.
US$ 34.99
Vectors
Vectors are mathematical objects characterized by both magnitude and direction. Vectors have various physical and geometrical applications. In this course you will learn to add and subtract vectors; column vectors and unit vectors. You will explore the possibility of vectors in solving many real life problems.
Prerequisites:
Real numbers, Basic Arithmetic, Coordinate geometry
Duration:
10 hours | Self-paced
learning moreVectors
Vectors are mathematical
objects characterized
by both magnitude and
direction. Vectors have
various physical and geometrical
applications. In this
course you will learn
to add and subtract vectors;
column vectors and unit
vectors. You will explore
the possibility of vectors
in solving many real life
problems.
Students will learn:
• That vectors are
mathematical objects that
are
characterized
by magnitude and direction.
• To model and solve
problems involving polygons
and
vectors, with
the help of vector diagrams.
• To solve coordinate
geometry problems using
column
vectors.
• To solve problems
involving bearings and
proportions
using operations
of vectors.
• That vectors can
be used to represent physical
concepts
and to solve
mathematical and real
life problems.
US$ 34.99
Trigonometry III
In this course, we will see other trigonometric
ratios, cosecant, secant and cotangent; the
relation between degrees and radians; trigonometric
identities and to graph these functions. Here
you will see the similarities and differences
between the amplitudes, periods and symmetries
of trigonometric graphs. You will also learn
how to use the identities as well as the graphs
to solve the trigonometric equations.
Prerequisites:
Trigonometric ratios of acute angle, Circular measure (angles in radians)
Duration:
20 hours | Self-paced
learning moreTrigonometry III
In this course, we will
see other trigonometric
ratios, cosecant, secant
and cotangent; the relation
between degrees and radians;
trigonometric identities
and to graph these functions.
Here you will see the
similarities and differences
between the amplitudes,
periods and symmetries
of trigonometric graphs.
You will also learn how
to use the identities
as well as the graphs
to solve the trigonometric
equations.
Students will learn:
• How to find the
trigonometrical ratios
of any angle
• What are positive
angles and negative angles?
How to find
the basic
angle, when any angle
is given?
• What is CAST ?
• Trigonometric
identities and their applications
• How to solve trigonometric
equations using basic
angles
• Graphs of trigonometric
functions and their properties.
• How we could solve
the trigonometric equations
using
graphs
US$ 44.99
Prerequisites:
Trigonometry III
Duration: 15 hours | Self-paced
learning more |
In applied mathematics, write your solutions in
a way which makes it clear what you are showing,
but avoid excessive concern for rigour.
2.
Write your answers grammatically and
concisely.
3.
Check the accuracy of your calculations by
verifying that the answer is sensible.
4.
Use diagrams freely for experimentation and
illustration, but not for deduction.
Writing
mathematics discusses in general terms the task of
writing out the solution accurately and completely.
When you read Part
2: Proof, you will find some examples taken mainly
from pure mathematics, where the task is to write out a
proof at the appropriate level of `rigour'. In applied
mathematics, very little (but still some) of your work
will involve writing out formal proofs of precisely
formulated general propositions. You will spend much
more time developing techniques to solve particular
problems, without trying to push up against the limits
of their applicability.
Aiming for rigour in your applied work can lead you
into inappropriate and distracting arguments.
In your analysis courses you may well work through
proofs of very simple and familiar propositions, such
as that the derivative of the function x® x2 is the function
x® 2x. It takes a while
to see why it is important to do this: it is that you
need to put the foundations of calculus on a sound
basis in order to build on them later. If you rely on
intuitive and vague definitions of concepts like limit
and derivative, you will eventually come up against the
same barriers that stalled the development of
mathematics in the eighteenth century. In pure
mathematics, the danger is that, in exploring the
foundations, you accidently allow in intuitive
arguments based on your informal understanding of the
concepts you are playing with. Hence the emphasis on
the discipline of rigour, of taking great care to check
that your argument follows logically, step-by-step from
the definitions. There is a corresponding danger in
your applied work that you will be so unnerved by
concern for rigour that you will be unable to write
down ``if f(x) = x2, then f¢(x) = 2x'' without proving it.
Taken to its extreme, this attitude would imply that
you could not use integrals at all in your first two
terms because you do not begin the rigorous theory of
integration until your third term. This would be to
misunderstand the purpose of rigour, which is precisely
to allow you to use the familiar rules of calculus (and
the less familiar ones that you will meet in the coming
year) with confidence. The purpose is to reinforce that
confidence, not to undermine it.
It is very easy to misinterpret these remarks as
saying that ``rigour has no place in applied
mathematics; any argument, however sloppy, will do''.
That is wrong. All that is being said is that to sum up
the instructions for writing good applied
mathematics under the heading of `rigour' would be
misleading. The important point is that your written
work should be clear, accurate, and
concise (I shall expand on this below). Rigour is,
in any case, a relative term. One of the disconcerting
lessons of twentieth century mathematics is that, if
you insist on proving everything by strict rules of
inference from a finite set of axioms, then your
mathematical horizons will be very limited. A
celebrated theorem of Gödel's implies that you
will not even be able to prove rigorously all the
propositions in arithmetic that you know to be true by
informal argument. In almost all your work, pure and
applied, you will construct arguments by building on
other results that you take for granted. Read what is
said about this in
Part 2: What can you assume? and look carefully at
some of the examples in Part 2: Proof when you work through
them. In your applied work, you will build on the
results you prove in your pure work.
Clear writing
A solution to a mathematical problem takes the form
of an argument. It should be written in good
grammatical English with correct punctuation. It should
make sense when you read it out loud. This applies to
the mathematical expressions as well as to the
explanatory parts of the solution. A solution should
never take the form of a disconnected sequence of
equations. When you are writing up a calculation, you
must make clear the logical connection between
successive lines (does the first equation imply the
second, or the other way around?), and you must make
the equations fit in a coherent way into your sentences
and paragraphs (see the remarks in Part 2: Making the proof
precise). One minor point: many mathematicians are
poor spellers. If you are not confident about your
spelling, keep a dictionary on your desk, and use it. A
good way to improve your style is to browse
occasionally in Fowler's Modern English
usage.
You will never write a clear argument unless you are
clear in your own mind what it is it that the argument
is proving, and you make this clear to your reader.
Sometimes it is simplest to do this by using the
`proposition-proof' style of pure mathematics, but more
often this is inappropriate in applied mathematics (it
looks very artificial to formulate as a `proposition' a
result that is special to a particular problem). It is
very helpful, both for yourself and for your reader, to
say what you are going to do before you do it, for
example, by writing something like ``We shall now show
that every function given by an expression of the form
... satisfies the differential equation''. It is also
helpful to break up a long argument into short steps by
using sub-headings. For example, if you are asked to
show that ``X is true if and only if Y is true'', then
you might head the first part the argument with ``Proof
that X implies Y'' and the second with ``Proof that Y
implies X'' (see
Part 2: Implications).
Of course it is in the nature of much of applied
mathematics that you have to do quite a lot of thinking
to extract from the original formulation of the problem
the precise statements that you have to establish. Even
something as apparently simple as
Solve the equation y¢¢ = y
contains potential pitfalls. The correct answer is: y =
Aex+Be-x, where A and B are
arbitrary constants. Your argument in this case will
establish two things: first, that every function of the
form y = Aex+Be-x satisfies the
equation, and, second, that every function that
satisfies the equation is of the form y =
Aex+Be-x. In a simple example
like this, you can establish both statements by the
same short calculation, and it would be rather fussy to
break the argument up into two parts. But you do not
have to go much further to find an example in which you
can go badly wrong if you simply manipulate without
thinking. Consider the following problem.
Solve the simultaneous differential equations
y¢ = z, z¢ = y.
If you ignore what has been said above, you might be
tempted to write the following.
However, if you take particular values for the
`arbitrary constants' A, B, C, D, say, A = 1, B = 0, C
= 0, D = 0, then you rapidly find that your `answer'
does not work. The problem is that it is not clear what
the `argument' in the solution is establishing. If you
look carefully, you will see that the first line
implies the second line, that the first two lines
together imply the third, and that the third implies
the fourth. However, when you try to go backwards, you
cannot get from the second line to the first. To solve
this problem without confusing yourself and your
reader, you should break it up into two parts, along
the following lines.
Solution. Suppose that y and z are functions
such that y¢ = z
and z¢ = y. Then
y¢¢ = z¢ = y,
z¢¢ = y¢ = z.
But the general solution to the differential
equation y¢¢ = y is y =
Aex+Be-x, where A and B are
constant. Therefore y and z must be of the form
y =
Aex+Be-x,
z =
Cex+De-x,
for some constants A, B, C and D. [This does
not say that all y and z of this form are
solutions.]
Conversely, suppose that y and z are of this
form. Then
y¢ =
Aex-Be-x,
z¢ =
Cex-De-x.
Therefore y¢ = z
and z¢ = y if A = C
and B = -D.
We conclude that the general solution is y =
Aex+Be -x, z =
Aex-Be -x, where A and B are
arbitrary constants.
Even in such a very simple problem, you must think
carefully about the logical structure of your argument
if you are going to avoid mistakes. Two final remarks:
(1) you should have spotted in the initial stage of
thinking about this problem that the solution would
contain two arbitrary constants, and not four; (2) if
you think about rigour, then there are a lot of other
questions that come up here, such as ``What are the
domains of the functions? Are they twice
differentiable?'', and so on. A skill that you must
learn by practice is that of finding the appropriate
level of rigour. There are no absolute rules. What is
appropriate depends on the context. Too little rigour,
and you will end up saying things that are untrue; too
much will be distracting.
Accurate manipulation
For the most part, this is a matter of taking
trouble, and giving yourself time to check your work
carefully. However, the following tips may help.
(i)
If you have sketched out a solution in rough, do
not just make a fair copy of your notes. Having seen
how to solve the problem in rough, put you notes
aside, and write out the argument from scratch,
checking each step carefully as you go. It is very
hard to see mistakes when you are simply copying,
rather than reworking.
(ii)
If you are prone to making careless slips, treat
your work with suspicion, and look for ways of seeing
that bits of it must be wrong. In mechanics problems,
you can often pick up sign errors by thinking about
whether your answer makes good physical sense. If
your trajectory for a projectile implies that it
falls upwards rather than downwards, then you have
made a mistake. If you have found a formula involving
parameters for the probability of some event, check
that it always gives an answer between 0 and 1. If a
particular choice of parameter values gives a
negative probability, then you have made a mistake.
Test your conclusions against common sense. If you
calculation gives 2.31 as the expected number of
tosses of a coin needed to get three heads in a row,
then you have made a mistake.
(iii)
Wherever possible, check your answer. For
example, always substitute your solution back into a
differential equation (this will also pick up the
sort of problem we met in the example above). If this
is too messy, try doing it with special values of the
constants. It may be too much of a labour to check
that
y =
cos-1
æ
è
Ö
klog(sec2x +
xx)+x2
ö
ø
satisfies some complicated differential equation, but
it may be much easier when the constant k vanishes.
(iv)
Never bring a rough and sloppy piece of work to a
tutorial in the hope that your tutor will not spot
the mistakes. The chances are that your tutor will
not spot the mistakes, in which case nobody learns
anything; if your tutor does spot them, then your
tutor learns something about you, but you learn
little about mathematics. If you are uncertain about
something you have written, even after spending a lot
of time on it, draw it to your tutor's attention, and
ask to go through it carefully together.
Concise writing
Pascal wrote in a letter to a friend ``I have made
this letter longer than usual, only because I have not
had time to make it shorter''. Long-winded arguments in
mathematics are hard to follow. It is well worth
spending time and effort to extract the essential steps
from your original rough notes and to present your
argument in as concise as form as is consistent with
clarity. But do not be surprised if you find it hard
work, sometimes much harder than spotting the solution
in the first place.
There are two points to keep in mind here: first,
tutors very rarely criticise undergraduate work for
being over-concise. Second, a good test to apply is the
`text-book test': ``if my solution were printed as a
worked example in a text-book, would I find it helpful
and easy to follow''
Diagrams
One other topic needs special mention: the use of
diagrams. It is a classic howler, and one that is
almost too easy for a tutor to spot, to argue ``from
the diagram it is obvious that ... ''. If you try it,
you will be left in no doubt that such arguments cannot
be rigorous (incidentally, you should in any case avoid
phrases like ``it is obvious that'': either it is
obvious, in which case you do not have to say that it
is obvious, or it is not, in which case you should be
more honest). Undergraduates who have been chastened by
the scornful reaction to a `diagramatic' proof
sometimes draw the false conclusion that diagrams have
no place in mathematics. This is quite wrong. First,
you should use diagrams freely in the experimentation
stage. Second, it is quite legitimate to use diagrams
to help your reader to follow an argument, even in the
most abstract parts of pure mathematics. The mistake is
to make deductions from a diagram. It is similar to the
mistake of arguing a general proposition from a single
example. In fact, it is bad practice to suppress
diagrams which have played an important part in the
construction of your solution, particularly if you give
away the fact that you have a diagram in mind by using
phrases like ``above the x-axis'' or ``in the upper
half-plane''. Finally, it is quite legitimate to use a
diagram to set up notation. For example, there is
nothing wrong with using a diagram in a geometric proof
to specify the labelling of points (``where A, B, C are
as shown ... ''); or in analytical proof to give the
definition of a function that takes different constant
values in different ranges (a picture here may be much
easier to take in at a glance than a long sequence of
expressions with inequalities defining the various
parts of the domain). The only test you must satisfy
is: is the use of the diagram clear and
unambiguous? |
Mathematical
Supports the most common and useful functions The mathematical console SigmaConsole supports the most common and useful functions. ItOCOs easy to use: to evaluate an expression, simply write it, using operators (+ - * / ^), parenthesis and mathematical functions and press ENTER. You can also...
A handy, fast, reliable, precise tool if you need to perform mathematical calculations. A handy, fast, reliable, precise tool if you need to perform mathematical calculations. The Calculator was designed with purpose to fit Netbooks and Notebooks with small display. Of course, the calculator can be used on laptop and desktop...SciCa is a scientific calculator, which is able to evaluate complex mathematical expressions. SciCa is a scientific calculator, which is able to evaluate complex mathematical expressions. In addition, this program enables you to visualize two-dimensional functions (y=y(x)-functions) graphically.The sole intention of this program is to...
Expression Solver is a mathematical software for you to use. Expression Solver is a mathematical software for you to use. It computes the value of a mathematical equation / expression. It is able to work with simply operators, numbers, variables, and functions and both variables and functions can be user...
With this AutoCAD add-on you can create mathematical curves. With this AutoCAD add-on you can create mathematical curves.Curves can be defined as explicit, parametric or polar functions.Function's formula can also be changed dynamically by changingparameter 'p' value(parametric modeling).Use standard...
LeoCalculator is an application for performing calculation of mathematical expressions these could include not only basic operations but also functions and brackets. LeoCalculator also permits to use of predefined variables. LeoCalculator is an application for performing calculation of mathematical expressions that could include not only basic operations but also functions and brackets.
Edit box "Expression" has to contain a string of mathematical expression that is...
A program VSCalculator is a visual textual calculator. The all expressions for the calculation are presented as the text. The representation of expressions as text is very comfortable at the big and difficult calculations. The rules of a writing of the mathematical text are simple and intuitively clear. At construction of expressions it is possible to use the standard functions, constants, variables, commands.
Math Suga is a complete utility to calculate mathematical equations, lets you to calculate mathematical equations with various features. Math Suga is a complete utility to calculate mathematical equations, lets you to calculate mathematical equations with various features. A techincal documentation program with the following features
1. Writing Equations
2. Graphing Equations
3....
TFunctionParser and TComplexParser are invisible DELPHI component for evaluating mathematical functions. TFunctionParser and TComplexParser are invisible DELPHI component for evaluating mathematical functions. The function term is a user given string like sin(x)*x. The function term can be changed during runtime. These are the features of the latest...
TFunctionParser is an Automation/COM server that parses mathematical functions and evaluates them at runtime. TFunctionParser is an Automation/COM server that parses mathematical functions and evaluates them at runtime. About 100 functions and operations are predefined. The user can define variables, constants and functions.
TFunctionParser Features:
1....
InftyEditor is a mathematical app. InftyEditor is a mathematical app. It allows you to to input all sorts of mathematical expressions.
Here are some key features of "InftyEditor":
? You can input any math expressions keeping your hand on the HOME Position of your keyboard.
? The |
Evanston, IL Cal main difference (besides focusing on algebra and geometry instead of precalc) included myself in attendance during the main lecture to aid students during in-class exercises and quizzes. These classes were a bit fast-paced in comparison to those during the main school year. In one summer we would hold classes for two entirely different groups of algebra pupilsThis course serves as a refresher in many of the topics of Algebra II and Trigonometry, as well as an introduction to the concept of Limits, which play a significant role in calculus. The basic mathematical methods and techniques required for success in calculus are reviewed and expanded upon. This topic is typical taught as a component of Algebra II and/or Precalculus. |
Inteval notation worksPractice worksheet covering interval notation. Students are asked to change inequalites and graphs to interval notation as well as translate interval notation to inequalities and draw the appropriate number line.
Word Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
9925 years experience teaching secondary mathematics in Texas.
Currently, serve as the math departmental chairman at a 5-A high school. Pioneered interactive whiteboard use with integrated powerpoint lessons in my district. |
sábado, 28 de julho de 2012
The Mathematical Collage has been written to meet an Associate Degree general education requirement of a mathematics course with a Beginning Algebra prerequisite. The text shows that mathematics is alive in today's world and helps students see the beauty and power of mathematics. Its contents consists of chapters on the lore of numbers, finance matters, measurement geometry and trigonometry, probability and statistics, and math in sports, It also includes Mathematical Excursions, short trips into various areas where mathematics is used, such as math and the tourist, math and the internet, math and voting, math and nursing, math and the automobile, math and cooking, math and the angler, math and the World Series of Poker.
quinta-feira, 26 de julho de 2012
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.
This volume is concerned with the alignment between the way the mathematical performance of students is assessed and the reform agenda in school mathematics. The chapters in this book have been prepared to raise a set of issues that scholars are addressing during this period of transition from traditional schooling practices toward the reform vision of school mathematics. Chapters are: (1) "Issues Related to the Development of an Authentic Assessment System for School Mathematics" (T. A. Romberg and L. D. Wilson), (2) "A Framework for Authentic Assessment in Mathematics" (S. P. Lajoie), (3) "Sources of Assessment Information for Instructional Guidance in Mathematics" (E. A. Silver and P. A. Kenney), (4) "Assessment: No Change without Problems" (J. De Lange), (5) "The Invalidity of Standardized Testing for Measuring Mathematics Achievement" (R. E. Stake), (6) "Assessment Nets: An Alternative Approach to Assessment in Mathematics Achievement" (M. Wilson), and (7) "Connecting Visions of Authentic Assessment to the Realities of Educational Practice
Contents
Preface vii
1 Issues Related to the Development of an Authentic Assessment System for School Mathematics
THOMAS A. ROMBERG AND LINDA D. WILSON
This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch or sketches, a description of the curve, a discussion of pertinent facts, and a bibliography. Depending upon the curve, the discussion may cover defining equations, relationships with other curves (identities, derivatives, integrals), series representations, metrical properties, properties of tangents and normals, applications of the curve in physical or statistical sciences, and other relevant information. The curves described range from the familiar conic sections and trigonometric functions through the less well known Deltoid, Kieroid and Witch of Agnesi. Curve related systems described include envelopes, evolutes and pedal curves. A section on curve sketching in the coordinate plane is included.
domingo, 1 de julho de 2012
A survey of math for liberal arts majors. This book is a survey of contemporary mathematical topics: voting theory, weighted voting, fair division, graph theory, scheduling, growth models, finance math, statistics, and historical counting systems. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.
The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics.
quinta-feira, 28 de junho de 2012
The idea of this book was suggested to me by Kindergarten Gift No. VIII. - Paper-folding. The gift consists of two hundred variously colored squares of paper, a folder, and diagrams and instructions for folding. The paper is colored and glazed on one side. The paper may, however, be of self-color, alike on both sides. In fact, any paper of moderate thickness will answer the purpose, but colored paper shows the creases better, and is more attractive. The kindergarten gift is sold by any dealers in school supplies ; but colored paper of both sorts can be had from stationery dealers. Any sheet of paper can be cut into a square as explained in the opening articles of this book, but it is neat and convenient to have the squares ready cut. |
This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy.
Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading.
Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates
Warwick Tucker is professor of mathematics and principal investigator for the Computer-Aided Proofs in Analysis (CAPA) Group at Uppsala University in Sweden. He has been honored with several awards, including the European Mathematical Society´s Prize for Distinguished Contributions in Mathematics, the R. E. Moore Prize for Applications of Interval Analysis, and the Swedish Mathematical Society´s Wallenberg Prize.
Endorsements:
´Validated Numerics contains introductory material on interval arithmetic and rigorous computations that is easily accessible to students with little background in mathematics and computer programming. I am not aware of any other book like it. The exercises and computer labs make it ideal for the classroom, and the references offer a good starting point for readers trying to gain deeper knowledge in this area.´--Zbigniew Galias, AGH University of Science and Technology, Kraków
´A significant contribution, particularly since there are not many texts in this area. Validated Numerics will be read by those interested in interval arithmetic, numerical analysis, and ways to make computer simulations more robust and less susceptible to errors. It is well written and well organized.´--A. J. Meir, Auburn University |
Huntington Beach SAT the basic function library. Knowing the basic properties of common will save you a lot of time in your calculus studies. Basic functions include trigonometry functions, exponential function, polynomials, and many more |
Algebra 2 covers Systems and Matrices, Analytic Geometry, Arithmetic and Geometric Sequences, the Binomial Theorem, Permutations, and Combinations and the Basics of Probability. I break down the concepts of algebra 2 into manageable pieces that you can understand. By doing this, algebra becomes less intimidating and easier to learn. |
College Mathematics I –
mth208ca
(3 credits)
This course begins a demonstration and examination of various concepts of algebra. It assists in building skills for performing specific mathematical operations and problem solving. These concepts and skills serve as a foundation for subsequent quantitative business coursework. Applications to real-world problems are emphasized throughout the course. This course is the first half of the college mathematics sequence, which is completed in MTH 209: College Mathematics II.
Linear Functions
Identify the domain and range of a function, as expressed per set theory.
Linear Equations & Inequalities
Use linear equations and inequalities in real-world applications.
Solve linear inequalities.
Use equations to solve word problems and formulas.
Solve linear equations.
Evaluate forms of linear equations.
Fundamentals of Expressions
Create expressions using real-world applications.
Apply mathematical laws and order of operations principles to solve math problems.
Evaluate expressions.
Solve problems containing fractions.
Classify real numbers.
Identify real and variable elements |
Here is a copy
of the Department of Mathematics syllabus
that applies to all MAT and STA classes.
Monday, August
20
For Wednesday, August 22:Solve
the cryptogram that you received and create two cryptograms (around 120
characters).One cryptogram should show
word length and punctuation; the other should not – it should be blocked
in 5-letter blocks.
Wednesday,
August 22
For Friday, August 24:Solve the
cryptogram that you received that included word length and punctuation.Be prepared to discuss your solution and how
you constructed the key for the ciphertext that you created.
Next week we will discuss how you
did with the ciphertext that did not have word length and punctuation.
Friday, August
24
Create a Caesar cipher to exchange on
Monday.Do not give word length or punctuation;
block in five-letter blocks. |
Heya guys! Is someone here know about prentice hall chapter 4 project worksheet 1? I have this set of problems about it that I just can't understand. Our class was asked to answer it and understand how we came up with the solution. Our Math professor will select random students to solve the problem as well as explain it to class so I require thorough explanation about prentice hall chapter 4 project worksheet 1. I tried answering some of the questions but I think I got it completely wrong. Please assist me because it's urgent and the due date is quite close already and I haven't yet figured out how to answer this.
I know how annoying it can be if you are not getting anywhere with prentice hall chapter 4 project worksheet 1. It's a bit hard to give you advice without a better idea of your problems. But if you can't afford a tutor, then why not just use some piece of software and see if it helps. There are an endless number of programs out there, but one you should consider would be Algebrator. It is pretty easy to use plus it is quite affordable.
I fully agree with that. It truly is a great software. Algebrator helped me and my classmates again and again till you actually understand it, unlike in a classroom where the teacher has to move on due to time constraints. Go ahead and try it.
A great piece of math software is Algebrator. Even I faced similar difficulties while solving graphing, radicals and perfect square trinomial. Just by typing in the problem workbookand clicking on Solve – and step by step solution to my algebra homework would be ready. I have used it through several algebra classes - Remedial Algebra, College Algebra and Remedial Algebra. I highly recommend the program.
For more information you can try this link: There is one thing that I would like to highlight about this deal; they actually offer an unrestricted money back assurance as well! Although don't worry you'll never need to ask for your money back. It's an investment you won't regret. |
All the key areas of the SAT of Mathematics are covered in this iTooch SAT Math app including Numbers and Operations, Algebra, Geometry and Statistics. Short and helpful chapter summaries review key facts and over 1,400 example problems give students plenty of practice so that the methodology of working through problems is clear. Thanks to this app, future exposure to complex SAT math structures should seem less daunting.
This app allows you to cover a spectrum of problems; you can make sure you've got the basics covered and stretch yourself with some of the more difficult questions. Real-world problems are used in many cases, so that the importance of learning these skills is clear. It can be used to help students prepare for the SAT and/or review high-school level math concepts in general in a fun and interactive way.
Apps automatically sync in the background in order to load new activities whenever an Internet connection is available.
Meet the SAT Math Team:
Hannah Kirk
SAT Math author, Hannah Kirk, is a British mathematics graduate with a professional background in research. She holds a BSc Economics and Mathematics from the University of the West of England and an MSc Econometrics from the University of Manchester. Her research interests revolve around international development issues. Hannah has experience as a private tutor of mathematics for pupils undertaking the equivalent high school graduation exam in England.
Eileen Heyes
SAT Math editor, Eileen Heyes has a BA in journalism from California State University, Long Beach. She wrote and edited at newspapers for 30 years while trying to decide what she wanted to be when she grew up. She is the author of three nonfiction books for teens and two mysteries for children. In learning the storytelling craft, she has studied screenwriting and improv, earned a certificate in Documentary Arts, and volunteered in the street cast of a Renaissance Faire. She takes it all back into the classroom as a writer-in-residence with the United Arts Council of Wake County, North Carolina. Originally from Los Angeles, she now lives in Raleigh with her brilliant husband and one of her two interesting, articulate sons. |
Outcome
Type
Tuition Fees
Sponsors
College: College of Physical and Engineering Science
Department: Department of Mathematics and Statistics
Instructors
Prof. Joe Cunsolo
Description
Getting Ready for Calculus is a non-credit course designed as a preparation for university-level mathematics.
This course is for you if you lack a solid mathematics background and/or skills and find that you need to take more mathematics to reach your educational and/or career goals. In designing this course, the Department of Mathematics recognizes the diverse mathematical backgrounds and concerns of students. The material in this course spans Grade 9 through to and including part of the OAC Calculus course. The course starts with a basic review of algebra from Grades 9 and 10, and then it focuses on the mathematical material from Grades 10, 11 and 12 that allows the introduction of material from the OAC Calculus course. This design allows you to develop a more solid grounding in the mathematics that is needed for university-level mathematics courses.
Call us (519-767-5010) if you have any questions regarding this unique preparatory course.
Note: This is a non-credit course |
I believe having a good foundation in pure math is very, very helpful for approaching applied math (in my experience, and as my teachers have also taught me). I believe the more math you know, the better off you will be.
To address your question on how much pure math to learn, I suggest at the very minimum the following: Real Analysis , Basic Functional Analysis, Graduate Real Analysis (Lebesgue Integration, Measure Theory, Lp Spaces), some familiarity with point set topology, and some familiarity with basic algebra.
To reiterate, learn your real analysis first. If you have absolutely zero background in proving things, start with a nice introductory book such as Elementary Analysis by Ross, which is an excellent introduction to analysis. Then, work your way up to a typical undergraduate course in real analysis (especially focus on the concepts of pointwise and uniform convergence of functions), which I personally strongly recommend N. L. Carothers extremely affordable and phenomenal textbook titled Real Analysis. Others will recommend Walter Rudin's Principles of Mathematical Analysis, and it is also quite good, but I prefer Carothers. These subjects will show you how calculus really works, and how the concept of convergence of functions works, which is very important for approximation theory, PDEs, etc. The reason these concepts are important is because in applied math (at least for me), we typically want to guess a function by using functions from some finite dimensional subspace (as in finite elements or other forms of approximation theory), so we want to have a solid, rigorous and meaningful way of saying "This approximate guess we constructed from our numerical algorithm will be very close to the true function we want to approximate".
Once you know these subjects, try out Kreyszig's Functional Analysis book, so you learn about the appropriate spaces to do analysis. All three fields you highlighted (Inverse problems, PDEs, Approximation Theory) rely on real and functional analysis, so learn it! If you're feeling up to it, approach graduate real analysis to learn measure theory and the Lebesgue integral (which will give you a solid footing in the concept of Lp spaces, which are spaces of functions often used in PDEs and numerical analysis). I recommend Folland's analysis book.
I personally really enjoy topology, so I'd say give Munkres Topology book a whirl and see if you enjoy it. I recommend this because its a wonderful subject and because it is important if you want to pursue any differential geometry (which has many, many applications! Physics uses this constantly).
You should be at least familiar with some basic algebra (groups, rings, fields), but I personally don't use too much algebra (at least, not explicitly). However, I would never say "don't learn it", because you'd be shocked at where these things pop up. Also, if you happen to take an interest in cryptography or computational algebraic geometry, this will be fundamental. I'll let someone else recommend a good introductory algebra textbook.
Elsewhere in this post, myFriendsCallmeRaz recommended going to the library and checking out Keener's book Principles of Applied Mathematics. I used this book for two semesters, and personally detest the writing, and yet I still completely agree with his suggestion. I don't like how its written, but it contains an incredible amount of information. It will teach you basic functional analysis and operator theory, calculus of variations, and more importantly, why we care about these fields. These are all pure topics, but you can use them to understand how to solve PDEs, how to construct a numerical algorithm to solve PDEs( the Galerkin method follows from results in functional analysis), learn how to mathematically derive the way a wire sags between two poles (calculus of variations, catenary), and other things.
Once you feel comfortable with all of this (this will take a long time!), you will have your basics down, and you will understand the fundamental language used in subjects like approximation theory and PDEs. I'm not saying you'll be able to pick up a paper in approximation theory and say "Ah, how clear", but you will have the basic tools down. Knowing your basics is crucial!
In that, do you not think that going into Applied Math to begin with is good enough?
I'm not exactly sure how to interpret this. I enrolled in a Ph.D. program and my program is just "Mathematics".I know some schools have separate "applied math" programs, and I honestly can't comment on them because I'm not familiar with them. When considering applying for a Ph.D. program, you should be very careful and study the school and how their program works. I can't comment on them, because there are so many and I really only know how my school works. At my school, however, I took the same breadth courses as any typical pure math student and was in no way separated as an "applied" student until I chose an adviser in an applied field (approximation theory, which the more I learn about, feels more and more pure to me). In my experience, my pure math classes have been helpful to me, not a hindrance. The only downside to the way I approached things is that I did not take many computational sort of classes which emphasize programming and scientific computation, so I have had to pick that up on my own. Hopefully other students in an Applied Math Ph.D. program can discuss how their programs work.
Feel free to ask any more questions (especially if you want some clarification on analysis, approx theory, etc.). Good luck! |
Analytic Trigonometry Lesson 1: Fundamental Identities begin the journey into Analytic Trigonometry through exploring basic identities. This lesson contains an eight-page "bound book" style Foldable (C) with an accompanied SmartBoard lesson. There is also a *.pdf file of the completed Foldable and Smart Notes. This teaching method minimizes wasted class time since the "skeleton" of the lesson is pre-printed. Students stay engage and focused.
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2156.5 |
Be aware of the need for mathematical theory to support numerical problem solving techniques.
Understand the relationship between the theoretical solution of a problem and a computational solution.
Extend his/her mathematical abilities in linear algebra and analysis.
Construct programs and use current mathematical programming tools such as LINPACK and the International Mathematical and Statistical Library (IMSL) to solve problems involving systems of equations, interpolation and least squares approximation of functions.
COURSE OUTLINE:
Floating Point Arithmetic and Rounding Errors
Taylor's Theorem
Non-linear Equations
Solution of Systems of Linear Equations Using Direct and Iterative Methods, Error Analysis and Norms |
Mathematical Application In Agriculture - 04 edition
Summary: This book teaches the many mathematical applications used in crop production, livestock production and financial management in the agriculture business, skills which are essential for success as an agriculture professional. By giving readers a solid foundation in arithmetic, applied geometry and algebra as they relate to agriculture, the material presented will help develop their ability to think through the many mathematical challenges they will face. Case studies, ...show moresample problems, charts, and graphs fully illustrate the important concepts presented.
Product Benefits:
Sample problems contain multiple operations so that students must put information together to get the desired final answer
All are real problems in agriculture, leading students to learn agricultural facts
The flexible presentation of the material lends itself to being taught in any order31.28 +$3.99 s/h
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feedback. Prerequisites: High school calculus |
Im probebly one of the dumest people in the world! I need help with the math probebly one of the dumest people in the world! I need help with the math!
Hello,
What books would you recommend reading for the math required to do 3D? Wait Wait now I need something written in ENGLISH not "Author is a pain and uses difficult words to make reader unhappy language" and "Author uses stupid examples that dont blend in with the text language" . Well thanks in advance! |
What is Pre Algebra?
Answer
Pre algebra is the most basic math course in the field of algebra. Pre algebra is comprised of a review of natural and whole numbers in the number system, it is an introduction to new types of numbers such as imaginary and complex numbers, it is comprised of the factoring of numbers, prime number introduction, and finally, pre algebra is also comprised of simple roots and powers. |
Mathematics
Creativity is the essence of Science at Western. Engage your intellectual curiosity to recognize the deeper patterns formed from observations, experimentation, facts and probabilities.
Discover and explore fundamental concepts that lead to the mathematical formulas used in every branch of science, engineering, statistics, computer science, and economics. Go on to learn about the new ideas in mathematics that will drive those disciplines in the future. Today's students benefit from millennia of mathematical thought; learning exciting and powerful new ways to look at the world |
Algebra 1
Algebra 1 is part of algebraic mathematics which can be define as branch of mathematics in which we represent the components of a specified Set or the numbers by use of symbols, alphabetical letters to express general relationship between the components of set. Algebra 1 is a broad topic which covers several topics like from addition and subtraction Positive and Negative Numbers to Solving Rational Equations.
2: Solution of Linear Equations: In this topic of algebra 1 we learn about writing equation one to multi step to solving them by using property of addition(2x+3x=5x),subtraction(5x-2x=3x),multiplication(7x $\times$ 8x = 56 $\times$ 2)and division($\frac{12x}{4x}$ = 3) with variable on each side. Also the properties of ratio(a:b) and proportion(a:b::c:d),percentage(%) are come under this branch.
3: Factoring: This topic of algebra 1 contain greatest common factor, factorizing of trinomials (ax2 + bx + c) by splitting middle term or by method of perfect Square.
4: Statistics: It is another branch of algebra 1 under it introductory matrices, measure of variation, making of Histograms, sampling and bias are come.
5: Probability: This branch of algebra 1 contains possibility of occurring of an event from a group of events under (distributional, conditional, binomial etc.). It also contains Permutation (npr) and Combination (ncr).
6: Solving system of linear equation and inequalities: linear equation of one and two variables, and method of solving them by substitution, elimination, completing square method, solving by graphical method are come under this branch of algebra 1. |
Aims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.
At the completion of this subject, students should be able to: 1. Draw the surface for a given equation and find the gradient and second derivative at any point on the surface. (K2, S1) 2. Calculate small changes in a function of several variables. (K2, S1) 3. Estimate errors of measurement for a function of several variables. (K2, S1) 4. Find derivatives of a function of several variables using relevant chain rules. (K2, S1) 5. Find the directional derivatives at a point on a surface. (K2) 6. Find stationary points on a surface. (K2, S1) 7. Solve first order separable differential equations. (K2, S1) 8. Solve first order linear differential equations using an integrating factor. (K2, S1) 9. Find the orthogonal family to a given family of curves. (K2, S1) 10. Solve second order homogeneous linear differential equations with constant coefficients. (K2, S1) 11. Solve second order nonhomogeneous linear differential equations with constant coefficients. (K2, S1) 12. Do calculations involving binary, octal and hexadecimal numbers. (K2, S1) 13. Design simple switching and logic circuits using Boolean algebra and Karnaugh maps. (K2, S1) 14. Perform simple operations involving matrices and determinants by hand. (K2, S1) 15. Solve simultaneous equations using Cramer's rule, inverse matrices and Gaussian elimination. (K2, S1) 16. Calculate the paths of projectiles in 2D. (K2, S1) 17. Find the curvature and radius of curvature of a given curve. (K2, S1) 18. Do calculations involving complex numbers. (K2, S1)
Swinburne Engineering Competencies for this Unit of Study This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies: K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer and information science concepts as tools. S1 Engineering Methods: Applies engineering methods in practical applications.
Differential equations: First order separable differential equations, first order linear differential equations, orthogonal trajectories, second order linear differential equations with constant coefficients and simple right hand sides. |
Algebra 2/Trigonometry Course Description (from NY State Education Department)
The three high school mathematics courses (Integrated Algebra,
Geometry, Algebra & Trigonometry) are built around five process
strands: Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation as well as five content strands:
Number Sense and Operations, Algebra, Geometry, Measurement, and
Statistics and Probability. Within these courses, students
will be expected to make connections between the verbal, numerical,
algebraic, and geometric representations of problem situations.
These courses will require students to apply and adapt a selection
of strategies and algorithms to solve a variety of problems.
It is expected that these strategies and algorithms will be
implemented using both traditional and technological tools.
Algebra 2 and Trigonometry
is the capstone course of the three units of credit required for a
Regents diploma. This course is a continuation and extension
of the two courses that preceded it. While developing the
algebraic techniques that will be required of those students that
continue their study of mathematics, this course is also intended to
continue developing alternative solution strategies and algorithms.
For example, technology can provide to many students the means to
address a problem situation to which they might not otherwise have
access.
Within this course, the number
system will be extended to include imaginary and complex numbers.
The families of functions to be studied will include polynomials,
absolute value, radical, trigonometric, exponential, and logarithmic
functions. Problem situation involving direct and indirect
variation will be solved. Problems resulting in systems of
equations will be solved graphically and algebraically.
Algebraic techniques will be developed to facilitate rewriting
mathematical expressions into multiple equivalent forms. Data
analysis will be extended to include measures of dispersion and the
analysis of regression that model functions studied throughout this
course. Associated correlation coefficients will be
determined, using technology tools and interpreted as a measure of
strength of the relationship. Arithmetic and geometric
sequences will be expressed in multiple forms, and arithmetic and
geometric series will be evaluated. Binomial experiments will
provide a basis for the study of probability theory and the normal
probability distribution will be analyzed and used a a n
approximation for these binomial experiments. Right triangle
trigonometry will be expanded to include the investigation of
circular functions. Problem situations requiring the use of
trigonometric equations and identities will also be investigated.
Students will sit for a NYS Regents Examination at
the end of this course. |
Specification
Aims
Brief Description of the unit
A graph consists of a set of vertices with a set of edges connecting
some pairs vertices. Depending on the context, the edges may represent
a mathematical relation, two people knowing each other or roads
connecting towns, etc. The graph theory part of the course deals with
networks, structure of graphs, and extremal problems involving graphs.
The combinatorial half of this course is concerned with
enumeration, that is, given a family of problems P(n), n a natural number, find a(n), the number of
solutions of P(n) for each such n. The basic device is the generating function, a
function F(t) that can be found directly from a description of the problem and for which
there exists an expansion in the form F(t) = sum {a(n)gn(t); n a
natural number}. Generating
functions are also used to prove a family of counting formulae to prove combinatorial
identities and obtain asymptotic formulae for a(n).
Learning Outcomes
On successful completion of the course students will be:
able to formulate problems in terms of graphs, solve graph
theoretic problems and apply algorithms taught in the course;
able to use generating functions to solve a variety of combinatorial problems.
Future topics requiring this course unit
None.
Syllabus
Graph Theory
Introduction. [1 lecture]
Electrical networks. [2]
Flows in graphs, Max-flow min-cut theorem. [3]
Matching problems. [3]
Extremal problems. [3]
Combinatorics
Examples using
ordinary power series and exponential generating functions, general properties of such
functions. [3]
Dirichlet Series as generating functions. [1]
A general family of problems described in terms of
"cards, decks and hands" with solution methods using generating functions. [3]
Generating function proofs of the sieve formula and of
various combinatorial identities. Certifying combinatorial identities. [2] |
Lecture 9: WildLinAlg9: Three dimensional affine geometry
Embed
Lecture Details :
Three dimensional affine geometry is a big step from two dimensional planar geometry. Here we introduce the subject via a 3d coordinate system, showing some ZOME models, explaining how to draw such a coordinate system in the plane, and seeing how points in space are naturally associated to triples of [x,y,z] of numbers. We discuss points, lines and planes in 3D, and point out the important distinction between affine space and a vector space.
NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry---see his WildTrig YouTube series under user `njwildberger'. There you can also find his series on Algebraic Topology, History of Mathematics and Universal Hyperbolic Geometry.
Course Description :
This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry. |
You were born to greatness. Having a life mission implies that that world has need of you. In fact, the world has been preparing you to fill this need with one incredible life experience after another. Finding and fulfilling your potential will lead you to your highest experience in this life. Believe it, you have a mission. It is the gateway to your personal greatness. Greg Anderson
WELCOME!
This year, I am teaching Math 9, Math 10, Math 11, Math 12, and Integrated Math 1. I will incorporate lectures, hand-on demonstrations and student-creations in order for students to discover their highest learning potential. For more information about each class and competencies, please click onto the specific tab.
This course continues with the concepts of rational numbers, positive and negative exponents, problem solving, writing and evaluating written expressions, and working with equations. Students continue to build on earlier skills,working with single–two step word problems andgradually progress to solvingmulti-step algebraicproblems, utilizing various strategies. Students are also introduced to solving and graphing linear equations, defining slope and y intercept, and mixed uniform rate work problems. Basic geometry, Pythagorean Theorem, defining angles, perimeter, and areas of various geometric shapes will be continued graph ordered pairs via mapping and table, solve an equation of a straight line, given the domain and range, and solve for slope, two coordinate points and an equation of a straight line.
5) Student will solve and graph inequalities, compound inequalities, and system of equations using various methods.
6) Student will find unknown measures of the sides of two similar triangles and solve problems using the Pythagorean Theorem.
7) Student will solve for perimeter and areas of various polygons.
8) Student will calculate Probability and Odds. Students will interpret graphical representations for a set of data and the use of mean, median, mode, etc.
Textbook:Algebra 1 (Glencoe) Textbook will be used in class and for homework. Points Earned
Grade = Total:
100-93=Aunch
F
Math 10
125
G
Math 9
123
H
Prep
I am looking forward for a great year!!
Math 11
Mrs. Mak
2012-2013
bwong-mak@ londonderrry.org 432-6941, x 2914
Students continue to build further knowledge from Math 10, and new algebraic concepts, such as polynomials, inequalities, geometry, and trigonometry are introduced. Hands on applications, utilizing compasses, transits, protractors are emphasized, while solving geometric concepts. Several realistic projects are introduced, allowing students to demonstrate their problem solving and mathematical skills solve and graph the following: simple/compound inequalities, singular and systems of linear equations.
5) Student will solve system of equations by elimination and substitution.
6) Student will solve for perimeter / area of polygons, determine unknown measures of the sides of two similar triangles and solve problems using the Pythagorean Theorem.
8) Student will calculate Probability and Odds. Students will interpret graphical representations for a set of data and the use of mean, median, mode, etc.
Textbook:
Algebra 1 (McDougal Littel) Textbook will be used in class and for homework
Supplies:
1) 3 Ring Binder
2) 5 Subject
3) Assignment Notebook
4) Pencils, Highlighters
5) CalculatorStudents are provided with the skills to solve a variety of problems that demonstrate how mathematics is used in everyday life an in the business world. Topics include mathematics used in: budgeting, purchasing/renting homes /apartments, automobiles, insurance, establishing a bank loan, cooking, salary, taxes, and investments. These applications reinforce and extend the student's mastery of mathematical concepts. Several projects throughout the semester will be performed to allow students to demonstrate their understanding and application of math skills.
Competencies:
1) Student will be able to understand the importance of budgeting, evaluate methods of income and expenses and graphically display budget information on EXCEL.
2) Student will be able to understand and record deposits and withdrawals to checking accounts. Additionally, students will learn to reconcile between two accounts: (personal & bank).
3) Student will be able to determine best buys, unit price, and discounts on various products.
4) Student will be able to research and determine various housing options: renting vs. purchasing apartments & homes based upon income and need. Establishing good credit necessary to obtain loans with low interest will be introduced.
5) Student will be able to develop food recipes, including a variety of whole number and fraction conversions.
6) Student will be able to research a variety of autos and determine the pros and cons for new, used, and leased cars. Additionally, students will research the best insurance policies necessary for vehicle selected.
7) Student will be able to know salary calculation, its related taxes, and their specific purposes, such as payroll, FICA, Federal, etc.
8) Student will be able to learn and create investment portfolio options, including stocks, mutual funds, bonds, etc.
Textbook: Financial Peace University (Dave Ramsey) DVD & Workbooks
Practical Mathematics for Consumer (Staudacher & Turner)
Consumer Mathematics (AGS)
Magazines, Newspaper Articles teacher's DISCRETION & APPROVAL for all LATE assignments submitted for a passing grade.
Semester Grades: Courses at the high school are performed on a SEMESTER basis and grades are determined as follows:
This course focuses on a review and re-teaching of the four basic operations: addition, subtraction, multiplication, and division of positive and negative integers including whole numbers, fractions, and decimals. Students will learn to read, interpret, write, and solve world problems while incorporating the use of calculators to check their work. The course also offers an introduction to understanding concepts in algebra, including order of operations, factoring, and solving single-two step problems. Probability, proportions, percents, ratios, data analysis & application, and basic geometry is also introduced in solving algebraic equations. Real world life experiences are used to reinforce all algebraic concepts.
Competencies:
1) Student will simplify and evaluate numerical and algebraic expression utilizing order of operations, distributive property, rules of exponents and absolute value.
2) Student will be able to add, subtract, multiply, divide, and factor monomials and polynomials.
3) Student will convert and solve verbal statements to algebraic expressions and equations.
4) Student will be able to convert and solve problems with proportional reasoning.
5) Student will solve and graph simple inequalities and find the perimeter and area of simple polygons.
6) Student will graph ordered pairs via mapping and table, solve an equation of a straight line, given the domain and range, and solve for slope, two coordinate points and an equation of a straight line.
7) Student will create and interpret graphical representations for a set of data, using mean, median mode, and range.
Textbook:
Algebra Readiness (McGraw Hill) & Pre-Algebra (Glencoe). These books will be used in class for classwork and homework.
Supplies:
1) 3 Ring Binder
2) 5 Subject Dividers
3) Assignment Notebook
4) Pencils, Highlighters
5) Calculator
Expectations:
1) Be on time
2) Be prepared
3) Do your homework / Make up missing work
4) Be respectful of other classmates
DO YOUR BEST!!!
Grading:
A TOTAL point system will be used for each quarter.
Quarter Grade = Points Earned
Total Possible Points.
A student earns points for everything they do:
Classwork= 5 pts. Quizzes= 50 pts.
Homework= 3-5 pts. Tests= 100 approval and discretion of the teacher for all make-ups submitted after two (2) weeks to receive a "passing grade".
Semester Grades:
Courses
100-93= AUNCH
F
Math 10
125
G
Math 9
123
H
Prep
Looking forward for a great year!
Integrated Math 1
Co- Taught By:Mr. Tallo & Mrs. Mak
This course is the first of four in the Integrated Algebra/Geometry curriculum sequence. Integrated Math I will focus on developingthe student's basic understanding of algebraic and geometric principles. Real life problem solving skills are stressed through "hands- on" manipulatives and various projects. The course includes the following topics: basic math skills/ operations, single-two step equations, linear functions, geometric planes, its perimeter, area/surface area, proportions, statistics, and probability.
3) Student will solve one & two step equations. Student will simplify ratios and proportions.
4) Student will demonstrate and apply conceptual understanding of points, lines, planes, angles, and the relationships between them.
5) Student will write, solve, and graph linear functions.
6) Student will determine probability and odds. Student will also create/ interpret graphical representations and use appropriate statistics to communicate information about data.
7) Student will find the surface area and volumes of various three dimensional geometrical solids.
Textbook:Algebra 1 (Glencoe) will be used in class and for homework.
Supplies:
3 Ring BinderDO YOUR BEST!!!
Grading:
A TOTAL point system will be used for each quarter.
A student earns points for everything they do:
Classwork= 5 pts. Quizzes= 10-25 pts.
Homework=3-5 pts. Tests= 50pts.
Quarter Grade = Points Earned
Total Possible Points.
Absent Days & Makeup:
When absent, notes and homework are available in the Study Lab, in their individual folders. Missed homework (due to an Excused absence) can be made up for FULL credit. Late homework can be made up for PARTIAL credit. Prior approval and teacher discretion will be necessary when accepting LATE WORK past 2 weeks.
Semester Grades:
Courses at the high school are performed on a SEMESTER basis and grades are determined as follows: |
Southeastern PrecalculusKnowing what a derivative means and how an integral is used are just two of the basic elements. Understanding Calculus lead Newton into greater understanding of Physics and which has lead us to many other places as well. Chemistry is all about the Periodic Table. |
Series overview MathsWorks for Teachers has been developed to provide a coherent and contemporary framework for conceptualising and implementing aspects of middle and senior mathematics curricula. more...
Boost Your grades with this illustrated quick-study guide. You will use it from college all the way to graduate school and beyond. FREE chapters on Linear equations, Determinant, and more in the trial version. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Table of Contents. I.... more...
Drawn from the literature on the asymptotic behavior of random permanents and random matchings, this book presents a connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the U-statisticsMatrices are effective tools for modelling and analysing dynamical systems. This book presents the basics of the Cayley-Hamilton theorem and elementary operations of polynomial and rational matrices. It covers topics such as: normal matrices; rational and algebraic polynomial matrix equations; and more. more... |
Pompano Beach MathI
...Advanced functions such as Ln and Exponential functions are also explained in the subject. The focus on differences become crucial when dealing with advanced mathematics. Calculus branches into two sections, differential and integral calculus. |
Linear Algebra
Math 265 is a first course in Linear Algebra (Math 365 is
a second course). Over
75% of all mathematical problems encountered in scientific or industrial
applications
involve solving asystem of linear equations. Linear systems arise in
applications
to areas such as business, demo graphy , ecology, electronics, economics,
engineering,
genetics, mathematics, physics, and sociology. Linear algebra involves much more
than solving systems of linear equations, it also involves abstract and
geometric
thinking. You will have to use analogies, and learn to think geometrically in
more than
3 dimensions. Linear algebra is commonly the first course that a student
encounters
that requires abstract thought. For this reason, students all over the world
struggle
when they first meet linear algebra. If you can not devote at least 8 productive
hours
of work per week to this course, then I recommend you take this course later
when
you can devote the necessary time and effort.
Calculators and computers can be very useful as an aid to computation, for
checking
hand computations, and as a laboratory for quickly exploring new ideas. I
encourage
the intelligent use of calculators and computers. My discussions about
calculator
usage will be confined to the TI83 Plus. You will likely need to improve the
accuracy
and speed of your arithmetic : calculators are not allowed on tests and the final
exam.
In particular, there exist links for practising arithmetic
and testing algebraic skills.
We shall cover chapters 1, 2, 3 (chapters 5, 6, 7 are covered in Math 365). I
should
stress though that the lecture notes, not the textbook, form the body of
examinable
material. I strongly encourage you to read the relevant parts of the textbook
before
attending lectures, review your lecture notes after each lecture, and do all the
assigned
problems! The way to become a good violin player is to practice. To become good
at
this course (and hence pass) you must practice. You will learn much more doing
the
exercises yourself than watching an expert solve them for you!
If you are unable to attend a lecture, you should get a copy of the notes from a
classmate who takes good notes. Consider forming your own study groups : you can
learn a lot by explaining solutions to a friend , and by hearing solutions.
After each test I will post adjacent to my office a list of scores and
approximate
grades, so you can determine your relative position in the class. You should
double-
check the time of the final exam by using Safari. The exam will be in our
assigned
classroom.
Students requiring special accommodation, because of a physical or mental
disabil-
ity, should see me in the first week of the course. Also, if you are quite sick
or suffer
a notable hardship, then please let me know promptly. Claims of lengthy hardship
that are disclosed the day before the final exam receive less sympathy. Although
the
Registrar will notify you of your final grades, you can find out your
(unofficial) grades
earlier by using Safari.
I plan to make each Tuesday a problem-solving class. Please bring your
textbook
on these days. A brief description of the course content, and the approximate
number
of lectures spent on each topic is: solving systems of linear equations (4),
matrix
algebra and elementary matrices (4), determinants with applications to
areas/volumes
and computing inverses (5), vector spaces, subspaces, and dimension (7), the
matrix
of a linear transformation and change of basis (3). The course outcomes are: (i)
that
students learn to think abstractly, laterally, logically and critically, and
(ii) that
(passing) students have a reasonable mastery of the concepts underlying the
above
topics.
Math 265 Homework Problems
Below is a list of homework problems from the textbook, S. J. Leon, Linear
algebra
with applications, 7th ed., 2006. You should solve all homework problems before
Tuesday, and importantly you should write out your solutions neatly using
correct
notation, correct spelling, and grammatically correct English sentences. I shall
deduct
points on exams for poor setting out, especially for omitting brackets andequal
signs .
On problem-solving days you should bring your textbook, your worked solutions,
and
your questions. The chapter tests, abbreviated CT below, are helpful to test
your
knowledge before an exam |
With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras. less |
Peer Review
Ratings
Overall Rating:
This site contains a large collection of tutorial resources. The math topics covered include Pre-calculus, Calculus, Geometry, Trigonometry, Elementary Statistics, Probability, and applications of mathematics in physics and engineering. Many of the tutorials include interactive Java-based applets that help with deeper understanding of mathematical concepts.
Learning Goals:
To provide tutorials in various areas of mathematics, including precalculus, calculus, geometry, and statistics.
Target Student Population:
Undergraduate students taking courses in any of the areas covered.
Prerequisite Knowledge or Skills:
Basic algebra.
Type of Material:
This material is designed as tutorials, but many of the applets could also be used in classroom demonstrations.
Recommended Uses:
In-class demonstration or as a part of a guided or self-guided study.
Technical Requirements:
A Java-enabled Web browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
: This site contains a wealth of tutorial resources, both interactive and non-interactive, in algebra, calculus, geometry, probability and statistics. The non-interactive resources include solved problems and practice quizzes (some inside applets). The interactive resources mostly involve guided assignments using graph-based applets. While some of these assignments are straightforward, such as finding the number of x-intercepts on a graph, many others explore deeper concepts such as the relationship between the difference quotient of a function and the slope of a tangent line. These deeper explorations are generally experiment-based in that the student is instructed to change various parameters and observe the results. All of the graphs expand to full screen which should make them useful also for classroom demonstrations.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
With clear and ample instructions and detailed examples, students seeking help in undergraduate mathematics should be well-rewarded by visiting this site. However, the more sophisticated interactive tutorials may require the aid of an instructor. This is not the fault of the site; it is simply a recognition that learning through experimentation requires skills and motivation that many students lack. And while the site says nothing about its value for classroom demonstrations, there is obviously a great potential here.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Most of the Java applets are intuitive and easy to use. There is quite adequate instruction provided for the technical aspects throughout the site, and the problems and solutions are well-explained. Even in the non-interactive parts, one finds a great number of illustrative graphs.
Concerns:
Initially, some of the applets would not work in Firefox. After upgrading Java and then re-installing the upgrade, these difficulties seem to be resolved. Internet Explorer played all the applets without a hitch.
While most applets are easy to use, there are exceptions. For example, the "Explore Graphs of Functions" applet requires the use an "edit box" in the pull-down menu. Finding this and using it to change parameter values and function definitions is awkward.
While navigation is straightforward for the most part, for a site as complex as this one with many interconnecting hyperlinked topics, a subject index would be highly desirable. So, for example, if one were studying the derivative and could look that up in the subject index, all examples, quizzes, and applets pertaining to the "derivative" could be easily explored. As it is, one must click on all calculus topics both in the table of contents and in the left-hand margin of the front page and then search the linking pages for references to the derivative. It is a bit slow and cumbersome. |
Short description Key Stage 4 (KS4) maths eBooks comprise three principle sections. These are, notably: (Read more) maths eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Statistics Data) there are individual modules produced within each principle section which are published as eBooks.
Rounding Numbers, Accuracy and Bounds, Estimation and Checking is a module within the Number and Algebra principle section our Key Stage 4(KS4) publications. (Less) |
... concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus. Microsoft Mathematics includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help ...
... to developing embedded image recognition algorithms or teaching calculus. Mathematica is renowned as the world's ultimate application for computations. But it's much more—it's the only development platform fully integrating most problems in arithmetic, algebra, trigonometry and introductory/intermediate calculus for middle- to high-school students and first year university students. All solutions are accompanied by step by step verbal and written ...
... number, and polynomial arithmetic, etc. It does some calculus and is very easy to compile, learn, and ... simplify, combine, and compare algebraic equations · Perform calculus transformations · Help with series analysis · Perform ...
... and complex algebraic expressions. UltimaCalc lets you do calculus: differentiate an expression, or find its integral and ask how this was found. You can factorise polynomials, multiply and divide one ...
... the application of the construction concept in Algebra, Calculus, etc. Use its full potential to create interactive and dynamic math calculations and visualizations and you will discover new ways to ... |
The mission of the Mathematics discipline is to
advance knowledge of mathematics: by teaching
mathematics and its processes, by research in
mathematics and mathematical pedagogy, and by
dissemination of this knowledge to students and
the community we serve.
Historically, the study of mathematics has been
central to a liberal arts education. The
mathematics curriculum serves as an integral part
of students' active pursuit of a liberal arts
education.
The mathematics program serves
students who major or minor in mathematics,
seek secondary mathematics teaching licensure,
major or minor in programs that require a
mathematical background, or wish to fulfill
components of a general education.
The mathematics curriculum is designed to help
students develop competence in mathematical
techniques and methods; to sharpen the
students' mathematical intuition and abstract
reasoning as well as their reasoning from
numerical data; to encourage and stimulate
the type of independent thinking required for
research beyond the confines of the textbook; and
to provide students
with the basic knowledge and skills to make
mathematical contributions to modern society.
The program seeks to enable students to see and
communicate how the development of
mathematics has been part of the development of
several civilizations and is intimately interwoven
with the cultural and scientific development of
these societies. The curriculum prepares students
to enter graduate school, pursue careers in applied
mathematics, or teach mathematics.
The Mathematics Discipline has seven full-time
tenured or tenure-track faculty with a wide range
of background and expertise. All mathematics faculty have years
of teaching experience and at UMM, they teach
all Math courses from the freshmen level to the senior level.
In particular, faculty members with expertise in pure mathematics
are able to offer advanced courses in
Abstract Algebra ,
Combinatorics,
Differential Geometry,
Number Theory,
Real & Complex Analysis, and
Topology; while
faculty members with expertise in applied mathematics
are able to offer advanced courses in
Partial Differential Equations,
Mathematical Modeling,
Optimization and Operations Research,
Applications of Graph Theory, and
Applied Numerical Analysis.
In addition to being able to offer a plethora of advanced mathematics
courses, with their diverse expertise, UMM's mathematics faculty
are able to successfully involve their students
in undergraduate research projects specifically in
almost all of the aforementioned areas in mathematics.
Here are a few typical questions asked about UMM's Mathematics
Program: |
Textbook: Concepts of Mathematical Modeling by Walter J. Meyer (Dover Edition, ISBN
0486435156) Search multiple booksellers here
Amazon offers to students a free one-year subscription to "Amazon Prime", which allows you to receive books sold directly from Amazon within two business days for free! Sign up here. Make sure your order says "Eligible for Amazon Prime / Free Super Saver Shipping". Our book is here Software: Mathematica (learn about Mathematica access on MyQC)
This class covers: Various sections of the book, along with Mathematica tutorials.
Homework:
Homework is due weekly and is the key component to your learning of
the material, so DO IT!!! Each homework will be posted on the course web page the previous week.
Written Homeworks:
The written homeworks contribute towards your homework grade.
They will consist (normally) of five questions. I expect all answers to be fully justified, unless otherwise
noted. Each of the problems will be graded on a scale from 0-4, as follows:
4
**Perfect**
3
A well-written solution with slight errors.
2
A good partial solution.
1
A very partial solution or a good start.
0
No work, a weak start, or an unsupported answer.
I require you to follow some relatively strict guidelines.
It is especially important that your homework be legible and clearly presented, or I may not grade it.
It is important to learn how to express yourself in the
language of mathematics. In the homework, you should show your work and explain how
you did the problem. This is the difference between an Answer
and a Solution. It should be obvious to the person reading the homework how you
went about doing the problem. This will often involve writing out explanations for your
work in words. Imagine that you need an example to help refresh your memory for another
class in six months!
Late Written Homework:
I understand that outside factors may affect your ability to turn in
your homework on time. During the semester you will be allowed five total grace days. If a homework is due on
Wednesday and you turn it in on Friday, this counts as two of your five grace days. Once you have zero grace
days, I will not accept late homework. If you are not planning to be in class, let me know and get it to
me beforehand. This is your responsibility. I can accept clearly scanned homework by email.
Final Project:
In addition to the homeworks, you will be working in a group of around three students, where you will use the
techniques from class to model a real-life situation of your choosing. Click here for more information.
Study Groups:
It is useful to form study groups to work on homework.
Be sure to include an acknowledgment to your groupmates on your homework.
At the beginning the problems will seem easy enough to plug and chug on your own,
but as the quarter progresses the questions become quite complex indeed.
Study groups good. Copying solutions bad. When a group works on a problem, everyone can participate.
But when you write up the answers to the problems, write it up in your own way.
I will take off points from all parties if multiple solutions are the same.
Study groups have several advantages:
You can practice and learn how to solve more problems in less time (doing as many problems as possible is the key to success),
The best way to really learn something is to explain it to someone else (misunderstandings that you never knew you had will appear under someone else's questioning),
No two people solve the same problem the same way; in a group, you may discover new and more efficient ways to solve the same problem,
seeing that others also struggle with this material helps to put your own level of understanding in a better perspective and will hopefully reduce some of your
anxiety,
in making the homework assignments, I assume that you will be working in groups.
Exams:
There will be two exams during the semester.
They will be a class period in length and no calculators or study aides are allowed (or are necessary).
There will be no make-up exam except in the case of a documented emergency.
In the event of an unavoidable conflict with the midterm (an athletic meet, wedding, funeral, etc...),
you must notify me at least one week before the date of the exam so that we can arrange for you
to take the exam BEFORE the actual exam date.
I am happy to help you with your homework and other class-related questions during my office hours. I have official
office hours as posted on my schedule. In addition, you are welcome to make an
appointment or stop by my office in Kiely 409 at any time.
Cheating/Plagiarism: DON'T DO IT! It makes me very mad and very frustrated when students cheat. Cheating is the quickest way to lose the respect that I have for each student at the beginning of the semester. Both receiving and supplying the answers on an exam is
cheating. Copying homework solutions is considered cheating. Copying text from sources for your project is cheating. I take cheating very seriously. If you cheat, you will
receive a zero for the homework/exam and I will report you to the academic integrity committee in the Office of Student
Affairs. If you cheat twice, you will receive a zero for the class.
**Please do realize that working together on
homework as described above is not cheating.** |
Stoneham, MA Math these and other topics:
- math for finance including interest and annuities
- systems of linear equations and matrices
- linear programming
- Markov chains
- difference equations
- logic and sets
- probability and elementary statistics
Matrix methods and Linear Progra |
David Rubenstein
TAKS Study Guides
This link provides free study guides for all 4 TAKS subjects. Click the interactive button under the correct subject and you will be provided with a list of objectives to choose from. Each objective will bring you to an interactive page where you will be given an overview of the objective, notes and information on the topics and practice questions.
Virtual TI-83 Calculator
This link provides you with a free graphing calculator. This is a computer based version of the TI-83. Follow the link and click to download. This will download a .zip file. You will have to double click to extract the files. Tell it where to save the extracted files. In the new folder, there is a file (at the bottom) which is a .exe or application file. This will open the calculator.
TI-84 Video Tutorials
This website provides free videos that can help you to better use your graphing calculator in class and on tests. All of the videos are for the TI-84 but most of the topics and information covered also apply to the TI-83 which you can download a version of from the previous link. |
By the end of the course students should be able to:
- apply numerical methods to solve a variety of mathematical problems with relevance to engineering;
- demonstrate an understanding of the limitations and applicability of the methods
- demonstrate skills in solving similar problems using MATLAB programs
L4 and L5 Numerical solution of ODE&ęs
Introduction to solution of Ordinary Differential Equations, derivation and application of the Euler Method. Application of Euler, Euler-Cauchy and Runge-Kutta Methods. [Associated MATLAB exercises run in labs during same period]
L8 and L9 Numerical differentiation
Nature of the problem: situations in which it arises in civil engineering problems. Finite difference formulae. The concept of finite differences, two, three and higher point formulae. Errors. Central, backward and forward differences. Method order. Application of difference formulae to estimate derivatives. Examples. Polynomial fitting by least squares. Algebraic differentiation. Problems likely to be encountered.
L10 Revision
Applications and worked examples, to further demonstrate use of methods for solving Civil Engineering problems with guidance on checking correct implementation and common errors to avoid.
Tutorials: Titles & Contents
Some exercises in this module are undertaken in the Computer Laboratory using MATLAB. The aim is to build on the course Computer Tools for Civil Engineers 2 (CTC2) to give further experience and confidence in the use of numerical analysis packages on computers. Other examples are worked into revision exercises.
Computer Exercise 1: Non-linear Equations
This computer lab exercise is undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of non-linear equations using Fixed Point, Newton-Raphson, Bisection and False Position methods. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, with investigation of issues such as convergence and tolerances. The lab exercises are designed to teach the student that problems which look difficult from an algebraic viewpoint can be simple numerically, and vice versa.
Computer Exercise 2: ODE&ęs
This computer lab exercise is also undertaken over two weeks. Students are asked to develop MATLAB scripts for the solution of ODE&ęs. The methods used are Euler, Euler-Cauchy and Runge Kutta. Example scripts are provided for some of these, others must be developed from scratch. These are then applied to the solution of various mathematical problems, some set in the context of Civil Engineering problem, with investigation of issues such as numerical errors and convergence and tolerances.
Assessment of the coursework is undertaken in the fifth week of labs, with a set of short questions testing ability to apply the above methods to some similar problems. It is conducted using MATLAB, with submission via the course intranet pages on WebCT.
There are also revision exercises for completion by hand run in weekly tutorial sessions. These will cover the same material as that of the teaching course, but provide the hands-on experience that students require to gain confidence in application of the methods, learning to resolve difficulties, correct misunderstandings, etc. The examples provided are typical of the questions asked during the examinations. |
2009 was the first year students could enrol in one or both of the new Mathematics Courses. The Courses consist of units of study which are intended to be studied in pairs over the whole school year. The Courses are Mathematics General (MAT) and Mathematics Specialist (MAS).
The first WACE (West Australian Certificate of Education) exam for the new Mathematics courses was conducted in 2010.
Students may choose from one to four courses over Years 11 and 12.
Subjects should be chosen with a view to satisfy pre-requisites for later studies with TAFE or the universities.
For potential students who are unsure whether they have the necessary pre-requisites to study with SIDE, student services personnel are available to provide advice. We recommend completion of the Enrolment Unit for the chosen unit.
The Mathematics General course has been designed to cater for the full range of student abilities and their mathematics achievement at the beginning of their senior years of schooling. The units are written as a sequential development of mathematical concepts, understandings and skills.
They are grouped in four stages. Preliminary units provide opportunities for practical and well supported learning to help students develop skills. Stage One units emphasise practical uses of mathematics for daily life and the workplace. Stage Two and Stage Three units extend the mathematical development in all areas, providing preparation for daily life, the workplace and further studies.
All units in the Mathematics Specialist Course are at Stage 3 and provide opportunities to extend knowledge and understandings in challenging academic learning contexts.
SIDE is Western Australia's leading K-12 distance education provider. Thousands of students across Western Australia and the wider world undertake their education with specialist teachers based in Leederville, an inner suburb of Perth. Founded in 1918, the school has become a cutting-edge "eschool".
By any measure, Wan-Yi Sweeting is an extraordinary young woman. She came to Australia aged 11, to board at a large Perth girls' school. At 13, she was selected for the WA Tennis Academy, which meant a hectic international touring schedule, and she chose to continue her schooling with SIDE.
Read more... |
MAA Review
[Reviewed by Fernando Q. Gouvêa , on 02/11/2001]
The Old Testament book of Ecclesiastes reminds us that "of the making of many books there is no end" and "there is nothing new under the sun." And when it comes to mathematics textbooks this often seems to be the case. Here, on the other hand, is something truly different.
Introductory books on number theory seem, these days, to always begin at the same place and cover similar territory. Whatever differences one finds between books have to do with details of approach and style or with what is done in the more advanced chapters, after the obligatory chapters dealing with divisibility, congruences, linear diophantine equations, primitive roots, and quadratic reciprocity.
Now, of course there's nothing wrong with that sequence; in fact, one can certainly argue that it represents some of the most important foundational ideas in the subject. On the other hand, number theory is such a large subject, and so much of it is initially accessible without too many pre-requisites, that one would expect to see a different take on the subject every once in a while. And that, happily, is what we have here, both in content and in style of presentation.
Burger's book proposes to introduce students to a range of number-theoretical ideas, theorems, and problems by having the students themselves discover the results and prove the theorems. Thus, the book presents the material largely through a sequence of problems surrounded by some expository text which usually focuses on the significance of the theorems rather than on their proofs. The chapters, actually called "modules," typically end with "Big Picture Questions" which invite the student to attempt to consider what has been done so far, where it might be going, and why it is interesting.
The main thread through the book is diophantine approximation. For the first ten modules, the focus is on approximating irrational numbers by rationals while controlling the size of the denominator of the approximants. This is a rich area of number theory, connected to continued fractions, Farey sequences, and transcendence theory. It is also an area that is accessible to undergraduates, so it is a particularly good choice for this kind of book. The modules build towards some significant results: a description of the Markoff spectrum, solving the Pell equation, and the work of Liouville and Roth on transcendental numbers.
The next two chapters are basically a detour through arithmetical algebraic geometry. They look at Pythagorean triples from a geometric point of view and quickly visit the theory of elliptic curves. Then come chapters on Minkowski's "geometry of numbers" and applications to simultaneous diophantine approximation and the four squares theorem. After a module on "distribution modulo 1," the final modules deal briefly with p-adic numbers, ending with a discussion of Hensel's Lemma and the local-global principle.
As that summary suggests, the first half of the book feels tightly integrated around a basic theme, building towards some significant theorems. The second half is more like a quick tour, with stops at several interesting locations but no extensive development and no culminating theorems. This may make sense in a course setting, where one would be virtually certain of finishing the first ten modules but might want to pick and choose among the last ten.
Overall, this is a very nice guide through this material. The first ten modules are the best and most interesting part of the book, well worth working through. The section on "arithmetical algebraic geometry" is probably the weakest, but the book picks up steam again when it goes into the "geometry of numbers" section. The module on "distribution modulo 1" has an interesting theorem at its center, though perhaps the proof given here is not the most illuminating one. (On the other hand, the proof I really find more illuminating has far more pre-requisites.) The section on the p-adics should be lots of fun for the students, and goes just deep enough to suggest that there is some substance to the subject.
Since the book is designed to be given to students in a seminar-style course, it does not contain solutions of any of the problems. For some problems, hints are provided; these vary from very meager to quite detailed. There are discussions, at the back of the book, of some, but not all, of the "Big Picture Questions." All this is just right for a course where students are expected to work through the material and develop their own proofs and examples, but it lays a heavy burden on the instructor. No "teacher's solution manual" is provided. If you propose to lead your students into this jungle, you had better have a pretty good idea of the lay of the land before you start, or you'll all end up lost together. This is particularly true when it comes to the "big picture."
For professors with the requisite background, this may be just the right book to use in an upper-level undergraduate seminar. Students working through this book will learn some nice material, and will probably also emerge from the course with a much greater confidence in their ability to do mathematics.
Fernando Q. Gouvêa is Associate Professor of Mathematics at Colby College in Waterville, ME. He works in number theory (focusing especially on modular forms and Galois representations) and also has a strong interest in the history of mathematics.
BLL* — The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. |
purpose of this book is to present material on elementary statistical methods in a succinct manner, to extend the introductory ideas into analysis of variance and experimental design, and to explain without formal mathematical proof the assumptions on data necessary for the v ...
We use math every day, sometimes without even realizing it! Kid-friendly, real-life situations show readers how they can put math to work in their day-to-day activities. A variety of problem-solving activities and graphic organizers make these books ideal for young learners. . |
textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems. |
Age-Specific Population Models
Allen E. Martin
Abstract
An age-specific population model is built, based on Fibonacci's rabbit problem. The model is examined using spreadsheets, matrices, iteration and exponential regression. The investigations are based on the assumption that students will have a graphing calculator and/or spreadsheet available to them. The suggested investigations encourage students to use a variety of representations and seek links between them. This module might be used as a lead-in to a discussion of Leslie models for population growth, or as an enrichment project after a discussion of exponential regression.
In Liber Abaci, Leonardo of Pisa (Fibonacci, ca. 1202) proposed one of the earliest mathematical models for population growth. The problem situation stated below is a reworking of Fibonacci's original problem which generates an introductory age-specific population model.
Imagine that we start with one pair of rabbits (one female and one male). After N days, this pair matures to reproductive age and immediately produces a new pair. After N more days, the first pair again produce offspring. Thus, each pair of rabbits will reproduce two times during their lifetime (exactly one pair immediately at the start of each new stage, where "pair" always means one female and one male), at intervals separated by N days, and each new pair of rabbits will go on in a similar fashion.
The problem statement suggests that the rabbit population can be broken down into three groups: "newly born", "young adults" and "mature adults". Each pair of newly born rabbits survives to become young adults and to produce one new pair of offspring at this stage. Each pair of young adults survives to become mature adults and to produce another pair of offspring. Finally, each pair of mature adults moves on to "rabbit heaven"; no survival is allowed after stage 3.
This process of moving through the age-structure and the patterns that emerge can be represented several ways:
with diagrams, to break down and understand the dynamics of the problem
with spreadsheets, to capture patterns and create graphs
with matrices, to emphasize the age-structure and make it more explicit
with recursive formulas (iteration), to capture the dynamics algebraically for further analysis
Analysis by Diagram
The first step in understanding the model is to find a way to "make sense" of the problem situation. A chart or diagram like the one shown below is helpful. The columns display the age structure for each of the first 6 time steps. The rows show the first 6 generations.
Diagram Breakdown of the Rabbit Population
Generation
1
NB
YA
MA
2
NB
YA
MA
NB
YA
MA
3
NB
YA
MA
NB
YA
MA
NB
YA
MA
4
NB
YA
MA
NB
YA
NB
YA
NB
YA
NB
YA
5
NB
YA
NB
NB
NB
NB
NB
NB
NB
6
NB
Time Step
1
2
3
4
5
6
Newly Born
1
1
2
3
5
8
Young Adult
0
1
1
2
3
5
Mature Adult
0
0
1
1
2
3
Total
1
2
4
6
10
16
This diagram captures many of the key aspects of the growth process of this rabbit population. Viewing the chart by columns, we can see the age-specific breakdown for each time-step. For example, in the 4th column we see that there are 3 newly born, 2 young adults and 1 mature adult. Viewing the chart by rows, we see the progression of the pairs born in a given generation as they move through the age-specific categories for the rabbit population. For example, the two pairs born in the 3rd generation become young adults in the next column, contributing 2 pairs of newly born to the 4th generation below them; they then survive to produce one last time, contributing to the 5th generation.
Analysis by Spreadsheet
The information contained in the diagram can then be summarized in a spreadsheet like the one shown below.
Time
Newly
Young
Mature
Total of
Step
Born
Adults
Adults
Rabbits
1
1
0
0
1
2
1
1
0
2
3
2
1
1
4
4
3
2
1
6
5
5
3
2
10
6
8
5
3
16
7
13
8
5
26
8
21
13
8
42
9
34
21
13
68
10
55
34
21
110
Once the spreadsheet has been created, we can view large amounts of data conveniently, include the data in reports, and easily create graphs. Also, we can vary the assumptions of the model and explore variations of the problem situation quickly.
Investigation #1
Starting with 1 pair of "newly born" rabbits, suppose that each pair of rabbits survives through 4 time steps, instead of three.
(a) Create a "diagram analysis" to break this problem situation down
(b) Create a spreadsheet that shows the data for each of the 4 age categories
(c) Create a graph showing Newly Born vs. Time Step
Investigation #2
Suppose that each pair of rabbits survives through 3 time steps (as in the original setup), but that each pair of young adults has 2 pairs of newborns. Also suppose that mature adults have only 1 pair each.
(a) Create a table showing each age category and the total number of rabbits for time steps = 1, 2, 3, ... , 10
(b) Create a graph showing Newly Born vs. Time Step
Analysis with Matrices
Let's return to the original problem situation. For any given time step, the population can be conveniently broken down into its age-specific groups with matrix notation.
So the information in the diagram and spreadsheet can be expressed as follows:
Step123456 n
Structure
Now, as the population moves from one time step to the next, we see that
Bold ---> Ynew , Yold ---> Mnew, and then Ynew + Mnew ---> Bnew
This transformation can be accomplished by matrix multiplication!
This can be expressed in a more compact form:
where T is the transition matrix
and Pold & Pnew are the population matrices.
This multiplication can be accomplished on a calculator with "Answer-Key" iteration. First enter the transition matrix into matrix [A], then the initial population matrix into matrix [B]. Next call matrix [B] and press <enter>. Then call matrix [A] and multiply by ANS. Finally, press <enter>, <enter>, <enter>, ... to get the 2nd, 3rd, 4th, ... generations.
Analysis by Iteration
As can be seen in both the diagram and the spreadsheet, the values of each age group can be determined from previous values. These patterns can be expressed iteratively.
Let = # of newly born in the nth time step
= # of young adults in the nth time step
= # of mature adults in the nth time step
then, moving from one time-step to the next, we can see that
,
and then
Note: It follows that
Since all three age groups have the characteristic Fibonacci-like pattern
(b) Extend this table further out to the right (by letting n = 10, 20, 30, ...); then describe what happens to the values of .
(c) Sketch a graph of vs. n.
In the third investigation, we find that grows exponentially:
for n = 1, 2, 3, ..., 10
and, for n = 1, 2, 3, ..., 20
.
The fourth investigation reinforces this, since the ratio gets very close to 1.618 as n gets large; hence .
In fact, if we assume that and apply this to the iteration , we get
The roots of this equation are
Key Observation:Notice the striking similarity between the base of the exponential, the limiting value of the ratio and one of the roots of this "characteristic polynomial". What is going on here? The next two investigations will explore this similarity further.
Investigation #5 --
In investigation #1, we found that the "newly born" followed the pattern shown above. Using this ...
(a) Determine the characteristic polynomial for this iteration, then graph this polynomial on your calculator. How many real roots does it have? Approximate any real roots you find. |
It may be a good idea to get a Rubik's cube, as many examples we will see may be easier to understand with a cube in front of you. There are several online cube solvers (I particularly like this one), and they may be used as well, but I still recommend you get a physical copy.
The book presents many examples using the mathematics software SAGE. SAGE, developed by William Stein, is open source and may be freely downloaded. Consider installing it in your own computers so you can practice on your own. SAGE is very powerful and you will probably find it useful not just for this course.
(It was recently proved that Rubik's cube can be solved in 20 moves or less, and 19 moves do not suffice in general.)
Contents: The usual syllabus for this course lists
Introduction to abstract algebraic systems – their motivation, definitions, and basic properties. Primary emphasis is on group theory (permutation and cyclic groups, subgroups, homomorphism, quotient groups), followed by a brief survey of rings, integral domains, and fields.
Joyner's textbook emphasizes group theory through permutation representations. The theory is illustrated by several permutation games. Other natural examples of groups come from geometric considerations. We will see many additional examples.
(An interesting example of groups arising from geometric considerations are the plane symmetry groups, which one can see nicely illustrated in La Alhambra. I visited Granada in 2005 and have uploaded to Google+ some pictures from the trip, where you can see further examples.)
Prerequisites: 187 (Discrete and foundational mathematics). Knowledge of 301 (Linear algebra) will be useful, though I will review the matrix theory we will need.
Grading: There will not be exams. Instead, the grade will be determined based on homework.
I will frequently assign problems (many will come directly from the book) and provide deadlines. Some of these problems are routine, others are more challenging, a few may give you extra credit points due to their difficulty. Although collaboration is allowed, each student should write their own solutions. If a group of students collaborate in a problem, they should indicate so at the beginning of their solutions. Also, if additional references are consulted, they should be listed as well. It may happen that while reading a different book you see a solution for a homework problem. This is fine, as long as it is not done intentionally, and I trust your honesty in this regard. For some problems, I may specify that no collaboration is allowed.
No problems will be accepted past their deadline, and deadlines are non-negotiable.
I will pay particular attention not only to the correctness of the arguments, but also to how the arguments are presented. Your final grade will be determined based on the total score you accumulate through the term.
It may be that you do not see how to completely solve a problem, but you see how to solve it, if you could prove an intermediate result. If so, indicate this clearly, as it may result in partial credit. On the other hand, the fact that you write something does not mean you will get partial credit.
In addition, you will be assigned a project (to work in groups of two or at most three), to be turned in at the latest by the scheduled time of the final exam. This will constitute 20% or your total grade.
Attendance to lecture is not required but highly recommended.
As the term progresses, I will be getting pickier on how you write your solutions. Introduce and describe all your notation. Use words as necessary; strings of equations and implications do not suffice. You may lose points even if you have found the correct answer to a problem but it is not written appropriately. Do not turn in your scratch work, I expect to see the final product. I am not requiring that you typeset (or LaTeX) your solutions, but I expect to be able to read them without any difficulty. Additional remarks are encouraged; for example, if a problem asks you to prove a result and you find a proof of a stronger statement, this may result in additional extra credit points.Your final project must be typeset; I encourage you to consult with me through the semester in terms of how it looks and its contents.
Once your total score is determined, II will use this website to post any additional information, and encourage you to use the comments feature. If you leave a comment, please use your full name, which will simplify my life filtering spam out.
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3 Responses to 305 – Abstract Algebra I
[...] Although I have several ideas in mind, feel free to suggest your own topic. As mentioned on the syllabus, I expect groups of two or three per project. The deadline for submission is the scheduled time of [...]
[...] we now have computers and projection equipment on each classroom. I am using this quite a bit in my abstract algebra class. Except that, during the first few weeks, it was more often than not that the keyboard would [...] order type $\beta$, or the col […] |
This web site contains a collection of educational math programs.
It has a chemistry calculator that can balance virtually any equation and follow up
with dozens of stoichiometry and equilibrium problems using a spreadsheet.
There is a sophisticated loan calculator, Conway's life game simulator,
a Tesselation demonstrator, and
for the future, lots of java and TI83 programs that promote educational math
concepts. |
Trigonometry, CourseSmart eTextbook, 3rd Edition
Description
Dugopolski's Trigonometry gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find enough carefully placed learning aids and review tools to help them do the math without getting distracted from their objectives. Regardless of their goals beyond the course, all students will benefit from Dugopolski's emphasis on problem solving and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this edition.
Instructors will also find this book a pleasure to use, with the support of an Annotated Instructor's Edition which maps each group of exercises back to each example within the section; pop quizzes for every section; and answers on the page for most exercises plus a complete answer section at the back of the text. An Insider's Guide provides further strategies for successful teaching with Dugopolski. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
P. Algebraic Prerequisites
P.1 The Cartesian Coordinate System
P.2 Functions
P.3 Families of Functions, Transformations, and Symmetry
P.4 Compositions and Inverses
Chapter P Highlights
Chapter P Review Exercises
Chapter P Test
1. Angles and the Trigonometric Functions
1.1 Angles and Degree Measure
1.2 Radian Measure, Arc Length, and Area
1.3 Angular and Linear Velocity
1.4 The Trigonometric Functions
1.5 Right Triangle Trigonometry
1.6 The Fundamental Identity and Reference Angles
Chapter 1 Highlights
Chapter 1 Review Exercises
Chapter 1 Test
2. Graphs of the Trigonometric Functions
2.1 The Unit Circle and Graphing
2.2 The General Sine Wave
2.3 Graphs of the Secant and Cosecant Functions
2.4 Graphs of the Tangent and Cotangent Functions
2.5 Combining Functions
Chapter 2 Highlights
Chapter 2 Review Exercises
Chapter 2 Test
Tying it all Together
3. Trigonometric Identities
3.1 Basic Identities
3.2 Verifying Identities
3.3 Sum and Difference Identities for Cosine
3.4 Sum and Difference Identities for Sine and Tangent
3.5 Double-Angle and Half-Angle Identities
3.6 Product and Sum Identities
Chapter 3 Highlights
Chapter 3 Review Exercises
Chapter 3 Test
Tying it all Together
4. Solving Conditional Trigonometric Equations
4.1 The Inverse Trigonometric Functions
4.2 Basic Sine, Cosine, and Tangent Equations
4.3 Multiple-Angle Equations
4.4 Trigonometric Equations of Quadratic Type
Chapter 4 Highlights
Chapter 4 Review Exercises
Chapter 4 Test
Tying it all Together
5. Applications of Trigonometry
5.1 The Law of Sines
5.2 The Law of Cosines
5.3 Area of a Triangle
5.4 Vectors
5.5 Applications of Vectors
Chapter 5 Highlights
Chapter 5 Review Exercises
Chapter 5 Test
Tying it all Together
6. Complex Numbers, Polar Coordinates, and Parametric Equations
6.1 Complex Numbers
6.2 Trigonometric Form of Complex Numbers
6.3 Powers and Roots of Complex Numbers
6.4 Polar Equations
6.5 Parametric Equations
Chapter 6 Highlights
Chapter 6 Review Exercises
Chapter 6 Test
Tying it all Together
Appendix A: Solutions to Try This Exercise
Appendix B: More Thinking Outside the Box
Answers to All |
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