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Math Program
The purpose of this math program explanation is to clarify math placement in the Middle School. It includes course descriptions, information on how placement decisions are made, and indicates how the progression of math classes functions (table above).
We believe building a strong foundation in algebra is essential for success in subsequent mathematics courses. Algebra is the turning point from using arithmetic skills to solve basic math problems with specific numeric values, to creating generalized formulas for equations that use variables that represent more than one value. The abstract reasoning and analytical thinking skills required for an in-depth understanding of algebra is both difficult and developmental. Students entering the Upper School as freshmen who do not demonstrate this foundation of knowledge and do not take or review Algebra I in 9th grade will find themselves struggling when they take later courses, such as Pre-Calculus. Therefore, all Middle School math courses focus on skill-building, problem-solving, and algebraic thinking. We know these are the critical elements of a strong mathematics foundation.
What is Math 6?
Math 6 is a course designed to solidify, strengthen, and deepen foundational math skills. In addition, the course emphasizes creative problem-solving strategies and generalizing patterns to push the growth of each student's abstract thinking and logical reasoning ability. The beginning of algebraic thinking is woven throughout the curriculum. The students are also introduced to computer programming during our gender-based grouping.
What is Math 7/Pre-Algebra?
Math 7/Pre-Algebra is a course designed as a continuation of the topics in Math 6 with the goal of extending student understanding of basic math facts and skills. Application of this knowledge to problem-solving situations is expanded, logical reasoning skills are strengthened, and foundational concepts are explored. Emphasis is placed not only on math proficiency, but also on building the habits of learning that are critical to understanding in a math environment. Pre-Algebra topics are incorporated into the course.
What is Pre-Algebra?
Pre-Algebra is a very broad term used to describe courses that prepare students for the study of algebra. This course includes topics that involve arithmetic review and the introduction of skills and concepts for algebra, geometry, and statistics. Our program emphasizes mastery of the facts and skills of mathematics and the development of abstract concepts, logical reasoning, and application of skills through problem-solving challenges.
What is Algebra?
Algebra courses vary greatly from one school to another in terms of their depth and rigor. At Catlin Gabel, our vigorous program emphasizes abstract thinking and logical reasoning. Topics covered in algebra include evaluation and simplification of algebraic expressions, solving and graphing linear equations, linear systems, operations with polynomials, radical and rational expressions, and factoring. Four dimensions of understanding are emphasized to maximize performance: skill in carrying out various algorithms; developing and using mathematics properties and relationships; applying mathematics in realistic situations; and representing or picturing mathematical concepts.
What is Algebra 1A?
This course allows students to complete the study of Algebra over two years to ensure a thorough understanding of the topics and to build a strong foundation for higher-level mathematics.
What is Accelerated Pre-Algebra and Algebra?
The accelerated version of these classes move at a quicker pace, which allows time for additional extensions and greater emphasis on conceptual understanding and abstract reasoning.
How are math placements decided?
We strive to place students in a class that will meet their individual needs as learners. To ensure a fair process, objective measures are relied upon heavily and subjective opinions are introduced only for unusual circumstances. Although there are courses and typical math paths, we recognize that students change, mature, develop more abstract reasoning and improve their critical thinking abilities, hence a student may be moved up or down over the course of the year to best serve their learning needs.
In 6th grade, the first weeks of school are used to assess each student's basic math skills, abstract thinking, problem-solving ability, and spatial reasoning. Several placement assessments are used during this time, including 5th grade teacher input, standardized tests, pre-algebra readiness assessments, and baseline exams. In 6th grade, the great majority of the students are placed in Math 6, a vigorous math curriculum reviewing and solidifying elementary math skills, deepening the conceptual understanding of these topics, extending these skills to more complex number sets, and exploring new topics. In addition, abstract thinking and problem-solving strategies are stretched and expanded. Students who place in the 99th percentile on standardized tests with Independent School norms will be placed in an advanced math class. This is a small group of students who have demonstrated mastery over the 6th grade math curriculum and whose intuitive learning style cannot be accommodated in a heterogeneous group.
Between 6th and 7th grades, students are further grouped by math proficiency and learning pace. For our current students, placement into 7th grade math classes happens at the end of 6Between 7th and 8th grades, the groups continue along the same lines as 7What is the difference between the terms accelerated and advanced, because I see the Middle School uses both?
Accelerated means the pace of the class is faster. The students in those courses understand new concepts quickly and are facile with abstract ideas. The teacher is able to move quickly, minimize direct instruction, present broader concepts, and deepen abstract thinking.
Advanced means the content of the class is at a different level of mathematics. Our advanced math classes are essentially one year ahead of the scope and sequence of our grade-level offerings. These courses are not designed simply for strong math students, but for those who are clearly outliers and already have mastered the content of that year's math class. In addition, the content and instruction are adapted for the intuitive learning style of these outliers.
Is there movement of students during the course of the year?
Yes. If a teacher assesses a student is not able to meet the expectations of a course or is far exceeding the expectations of a course, the student will be moved to a more appropriate placement.
What if I have questions about my child's math placement?
Parents are always welcome to contact their child's math teacher, or Barbara directly, to discuss placement decisions and their child's math progress. |
Welcome to the Mathematics Department
Monday, 28 March 2011 11:02
Department Philosophy:
To understand mathematics is to have at one's disposal a source of intellectual delight as well as a tool of great practical usefulness. Mathematical power is achieved through exploration, reasoning, problem solving, communication, and connections. Students in our mathematics classes work toward achieving the Medfield High School learner outcomes as they connect ideas within mathematics and between mathematics and other intellectual activity. MHS mathematics courses challenge students of all ability levels and encourage them to excel academically.
Department Objectives:
The student will:
Explore mathematical ideas in ways that maintain enjoyment of and curiosity about mathematics
Explain and justify solutions to problems
Recognize the relationships among different topics in mathematics and apply mathematical thinking to solve problems in other disciplines.
Recognize and apply deductive and inductive reasoning.
Use multiple approaches to investigate and understand mathematical content |
The Department
Algebra and Geometry Section
The Algebra and Geometry Section includes the following fields of Mathematics: Abstract Algebra, Differential Geometry, Number Theory, Mathematical Logic, Differential and Algebraic Topology, Algebraic Geometry, etc.
Algebra developed mainly in the 19th and 20th centuries and its aim was the solution of specific problems in Geometry, Number Theory and the Theory of Algebraic Equations. It also contributed to a better understanding of the existing solutions to such
problems. Today, Algebra's contribution to other sciences, such as that of Computer Science, is invaluable.
Differential Geometry constitutes one of the main branches of mathematics and deals with the study of metric concepts on
manifolds, such as metrics and curvature. The classic period of Differential Geometry was the 19th century, during which the local
theory of curves and surfaces - now known as elementary Differential Geometry - developed as an application of Infinitesimal Calculus. In the 20th century the field developed rapidly, based on the recent achievements of the theory of Partial Differential Equations, Algebraic Topology and Algebraic Geometry. The dynamics and fruitfulness of Differential Geometry is also a result of its interaction with other sciences, such as Physics (Theory of Relativity), etc. |
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Mathematics, BS
What Is the Study of Mathematics?
Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
As.
-From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences
Why Should I Consider this Major?
The special role of Mathematics in education is a consequence of its universal applicability. The results of Mathematics-theorems and theories-are both significant and useful; the best results are also elegant and deep. Through its theorems, Mathematics offers science both a foundation of truth and a standard of certainty.
In addition to theorems and theories, Mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power-a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the information-laden world in which we live.
-From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences
Empowered with the critical thinking skills that Mathematics develops, recent Mathematics graduates from Western have obtained positions in a variety of fields including actuarial science, cancer research, computer software development, business management and the movie industry, among many others. The skills acquired in our program have prepared graduates for further academic studies in Mathematics, Computer Science, Physics, Biology, Chemistry, Oceanography and Education.Coursework
Requirements
MATH 204 Elementary Linear Algebra
MATH 224 Multivariable Calculus and Geometry I
MATH 225 Multivariable Calculus and Geometry II
MATH 226 Limits and Infinite Series
MATH 304 Linear Algebra
MATH 312 Proofs in Elementary Analysis
Note: The pair MATH 203 and 303 may be substituted for MATH 204 and 331.
Choose either:
MATH 124 Calculus and Analytic Geometry I
MATH 125 Calculus and Analytic Geometry II
or
MATH 134 Calculus I Honors
MATH 135 Calculus II Honors
or
MATH 138 Accelerated Calculus
One course from:
MATH 302 Introduction to Proofs Via Number Theory
MATH 309 Introduction to Proofs in Discrete Mathematics
No fewer than 31 approved credits in mathematics or math-computer science, including at least two of the following pairs:
One course from:
MATH 303 - Linear Algebra and Differential Equations II
MATH 331 - Ordinary Differential Equations
Together with one of:
MATH 415 - Mathematical Biology
MATH 430 - Fourier Series and Applications to Partial
Differential Equations
MATH 431 - Analysis of Partial Differential Equations
MATH 432 - Systems of Differential Equations
Only one of the pairs from the above group can be used
The following pair:
MATH 341 - Probability and Statistical Inference
MATH 342 - Statistical Methods
The following pair:
MATH 401 - Introduction to Abstract Algebra
MATH 402 - Introduction to Abstract Algebra
The following pair:
MATH 421 - Methods of Mathematical Analysis I
MATH 422 - Methods of Mathematical Analysis II
The following pair:
MATH 441 - Probability
MATH 442 - Mathematical Statistics
The following pair:
M/CS 335 - Linear Optimization
M/CS 435 - Nonlinear Optimization
The following pair:
M/CS 375 - Numerical Computation
M/CS 475 - Numerical Analysis
Supporting Courses
At least 19 credits from 400-level courses in mathematics or math-computer science except MATH 483, and including at most one of MATH 419 or MATH 420.
One of:
CSCI 139 Programming Fundamentals in Python
CSCI 140 Programming Fundamentals in C++
CSCI 141 Computer Programming I
MATH 207 Mathematical Computing
Note: If the supporting sequence from CSCI below is chosen, this requirement is fulfilled.
One of the following sequences:
PHYS 161 - Physics with Calculus I
PHYS 162 - Physics with Calculus II
PHYS 163 - Physics with Calculus III
OROR
CSCI 141 - Computer Programming I
CSCI 145 - Computer Programming & Linear Data Structures
CSCI 241 - Data Structures
CSCI 301 - Formal Languages and Functional Programming
And one of:
CSCI 305 - Analysis of Algorithms and Data Structures I
CSCI 330 - Database Systems
CSCI 345 - Object Oriented Design
CSCI 401 - Automata and Formal Language Theory
OR
ECON 206 - Introduction to Microeconomics
ECON 207 - Introduction to Macroeconomics
ECON 306 - Intermediate Microeconomics
And one of
ECON 375 - Introduction to Econometrics
ECON 470 - Economic Fluctuations and Forecasting
ECON 475 - Econometrics
Language competency in French, German or Russian is strongly recommended for those students who may go to graduate school.
Students who are interested in the actuarial sciences should complete: MATH 441 and 442, M/CS 335 and 435, M/CS 375 and 475 as part of their major programs.
GURs:
The courses below satisfy GUR requirements and may also be used to fulfill major requirements.
QSR: CSCI 139, 140, 141, 145; MATH 124, 125, 134, 135, 138
SSC: ECON 206, 207
LSCI: CHEM 121, 122, 123, 125, 126, 225; PHYS 161, 162, 163
"The Department of Mathematics has very highly qualified faculty who excel as both teachers and scholars. We have expertise in both pure and applied mathematics as well as statistics and math education. Our instructional focus is to establish a sound understanding of the fundamental concepts as well as mastery of the related analytical and computational skills. We have small classes and strive for active involvement of students in their learning. Our graduates are extremely well prepared for the workplace and for more advanced studies in math and related fields."
- Tjalling Ypma, Faculty
"The focus of the math department is to give students a strong background in problem solving and applying those skills. There is a wide range of mathematicians at Western, making it easy to find professors who share your interests and help you maximize your potential. They take teaching and advising very seriously; my advisor was always available for help with my resume' and planning my courses and my future. I am confident that Western has prepared me for success in graduate school and beyond. Whether your goals are professional or academic, being a Math major at Western will help you to succeed."
- Malcolm Rupert, Student
Notable Alumni
Jeanie Light
Software engineer, Google
Software engineer, Google
Charles Clark
Co-Director, Joint Quantum Institute, National Institute of Standards and Technology |
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This course is an extension of Algebra, Geometry and Trigonometry with the inclusion of a unique set of definitions. This course deals with domain, range, inverse functions, sequence, Binomial expansion, Matrices, Vectors in 2 and 3 dimensions, Integration and Application of integration, probability and statistics, basic coverage of differential calculus, and more.
Class time will be used to review homework questions, introduce "new" concepts, discuss the significance of the concepts, and apply the concepts to solve problems. In addition to learning concepts and solving problems, the students will learn to become comfortable with presenting their problems solving in a methodical manner.
COURSE REQUIREMENTS & REQUIRED MATERIALS
1. TEXT: HAESE & HARRIS, Third edition, ( Mathematics SL)
2. A scientific calculator (graphics if possible)
3. A full-size binder for the purpose of organizing ALL class notes, class handouts, homework assignments, quizzes, and tests.
*** These materials need to be in class with you everyday!
GOALS & OBJECTIVES
1. To be introduced to new mathematical tools and maintain an open mind while learning
3. To demonstrate responsibility, organization, and good study habits.
4. To prepare for advanced courses in both math and science.
5. To sharpen problem -solving skills
6. To begin to develop the ability to think through a solution and present it in an organized, thoughtful, and well-spoken way.
Participation: All students are required to participate in class discussions, offer solutions to problems, and demonstrate their knowledge of the subject at the board.
Homework: Homework is assigned on a daily basis and will be collected every class.
Exams: A test will be given on a weekly basis; tests follow the completion of each chapter.
GENERAL: To be a successful IB candidate you must apply yourself fully and to the best of your abilities at all times and on all assignments. Effort and the application of good work habits also contribute to a good grade. |
Calculus Functions Study Guide
Introduction
Calculus is the study of change. It is often important to know when something is increasing, when it is decreasing, and when it hits a high or low point. Much of the business of finance depends on predicting the high and low points for prices. In science and engineering, it is often essential to know precisely how fast quantities such as temperature, size, and speed are changing. Calculus is the primary tool for calculating such changes.
Numbers, which are the focus of arithmetic, are no longer the objects of our study. This is because they do not change. The number 5 will always be 5. It never goes up or down. Thus, we need to introduce a new sort of mathematical object, something that can change. These objects, the centerpiece of calculus, are functions.
Functions
A function is a way of matching up one set of numbers with another. The first set of numbers is called the domain. For each of these numbers in a set, the function assigns exactly one number from the other set, the range.
For example, the domain of the function could be the numbers 1, 4, 9, 25, and 100; and the range could be 1,2,3,5, and 10. Suppose the function takes 1 to 1,4 to 2, 9 to 3, 25 to 5, and 100 to 10. This could be illustrated by the following:
1 → 1
4 → 2
9 → 3
25 → 5
100 → 10
Because we sometimes use several functions at the same time, we give them names. Let us call the function we just mentioned by the name Eugene. Thus, we can ask, "Hey, what does Eugene do with the number 4?" The answer is "Eugene takes 4 to the number 2."
Mathematicians are notoriously lazy, so we try to do as little writing as possible. Thus, instead of writing "Eugene takes 4 to the number 2," we often write "Eugene(4) = 2" to mean the same thing. Similarly, we like to use names that are as short as possible, such as f (for function), g (for function when f is already being used), h, and so on. The trigonometric functions in Lesson 4 all have three-letter names like sin and cos, but even these are abbreviations. So let us save space and use f instead of Eugene.
Because the domain is small, it is easy to write out everything:
f(1) = 1
f(4) = 2
f(9) = 3
f(25) = 5
f(100) = 10
However, if the domain were large, this would get very tedious. It is much easier to find a pattern and use that pattern to describe the function. Our function f just happens to take each number of its domain to the square root of that number. Therefore, we can describe f by saying:
f(a number) = the square root of that number
Of course, anyone with experience in algebra knows that writing "a number" over and over is a waste of time. Why not just pick a variable to represent the number? Just as f is our favorite name for functions, little x is the most beloved of all variable names. Here is the way to represent our function f with the absolute least amount of writing necessary:
f(x) = √x
This tells us that putting a number into the function f is the same as putting it into √. Thus,
f(25) = √25 = 5 and f(4) = √4 = 2.
Parentheses Hint
It is true that in algebra, everyone is taught "parentheses mean multiplication." This means that 5(2 + 7) = 5(9) = 45. If x is a variable, then x(2 + 7) = x(9) = 9x. However, if f is the name of a function, then f(2 + 7) = f(9) = the number to which f takes 9. The expression f(x) is pronounced "f of x" and not "f times x." This can be confusing, so an apology is necessary. Mathematicians use parentheses to mean several different things and expect everyone to know the difference. Sorry!
Example 1
Find the value of g(3) if g(x) = x2 + 2.
Solution 1
Replace each occurrence of x with 3.
g(3) = 32 + 2
Simplify.
g(3)=9 + 2 = 11
Example 2
Find the value of h(–2) if h(t) = t3 –2t2 + 5.
Solution 2
Replace each occurrence of t with –2.
h(–2) = (–2)3– 2(–2)2 + 5
Simplify.
h(–2) = – 8 – 2(4) + 5 = – 8 – 8 + 5 = –11
Plugging Variables into Functions
Variables can be plugged into functions just as easily as numbers can. Often, though, they can't be simplified as much.
Example 1
Simplify f(w) if f(x) = √x + 2 x2 + 2.
Solution 1
Replace each occurrence of x with w.
f(w) = √w + 2w2 +2
That is all we can say without knowing more about w.
Example 2
Simplify g(a + 5) if g(t) = t2 – 3t +1.
Solution 2
Replace each occurrence of t with (a + 5).
g(a + 5) = (a + 5)2 – 3(a + 5) + 1
Multiply out (a + 5)2 and –3(a + 5).
g(a + 5) = a2 + 10a + 25 – 3a – 15 + 1
Simplify.
g(a + 5) = a2 + 7a + 11
Example 3
Simplify .
Solution 3
Start with what needs to be simplified.
.
Use f(x) = x2 to evaluate f(x + a) and f(x).
Multiply out (x + a)2.
.
Cancel out the x2 and the –x2.
.
Factor out an a.
.
Cancel an a from the top and bottom.
2x + a
Composition
Now that we can plug anything into functions, we can plug one function into another. This is called composition. The composition of function f with function g is written fg. This means to plug g into f like this: fg(x) = f(g(x))
It may seem that f comes first in fg(x), reading from left to right, but actually, the g is closer to the x. This means that the function g acts on the x first.
Example 1
If f(x) = √x + 2x and g(x) = 4x = 7, then what is the composition fg(x)?
Solution 1
Start with the definition of composition.
fg(x) = f(g(x))
Use g(x) = 4x + 7.
fg(x) = f(4x + 7)
Replace each occurrence of x in f with 4x + 7 .
fg(x) = √4x+ 7 + 2(4x+ 7)
Simplify.
fg(x) = √4x+ 7 + 8x + 14
Conversely, to evaluate gf(x) , we compute:
gf(x) = g (f (x))
Use f(x) = √x + 2x.
gf (x) = g(√x + 2 x)
Replace each occurrence of x in g with √x + 2x.
gf (x) = 4(√x + 2x) + 7
Simplify.
gf (x) = 4√x + 8x + 7
Notice that fg(x) and gf (x) are different. This is usually the case.
Example 2
If f(x) = x2 + 2x + 1 and g(x) = 5x + 1, then what is fg(x)?
Solution 2
Start with the definition of composition.
fg(x) = f(g(x))
Use g(x) = 5x + 1.
fg(x) = f(5x + 1)
Replace each occurrence of x in f with 5x + 1 .
fg(x) = (5x + 1)2 + 2(5x + 1) + 1
Simplify.
fg(x) = 25x2 + 20x + 4
Domains
In the beginning of the lesson, we defined the function Eugene as:
f(x) = √x
However, we left out a crucial piece of information: the domain. The domain of this function consisted of only the numbers 1,4,9,25, and 100. Thus, we should have written
f(x) = √x if x = 1,4,9,25, or 100
Usually, the domain of a function is not given explicitly like this. In such situations, it is assumed that the domain is as large as it possibly can be. The domain consists of all numbers that don't violate one of the following two fundamental prohibitions:
Never divide by zero.
Never take an even root of a negative number.
If you divide by zero, the entire numerical universe will collapse down to a single point. If dividing by zero were allowed, then all numbers would be equal. Four would equal five. Negative and positive would be equivalent. "It's all the same to me" would be the correct answer to every math question. While this might be appealing to some people, it would make calculus, the study of change, impossible. If only one number existed, there could be no change. Thus, we automatically rule out any situation where division by zero might occur.
Example 1
What is the domain of
Solution 1
We must never let the denominator x – 2 be zero, so x cannot be 2. Therefore, the domain of this function consists of all real numbers except 2.
The prohibition against even roots (like square roots) of negative numbers is less severe. An even root of a negative number is an imaginary number. Useful mathematics can be done with imaginary numbers. However, for the sake of simplicity, we will avoid them.
Example 2
What is the domain of g(x) = √3x + 2?
Solution 2
The numbers in the square root must not be negative, so 3x + 2 ≥ 0, thus . of all numbers greater than or equal to .
Do note that it is perfectly okay to take the square root of zero, since √0 = 0. It is only when numbers are less than zero that even roots become imaginary. |
Algebra Tutor
AlgebraTutor is a set of books and videos designed to help you get through Algebra class. Covering most of the topics found in college and high school algebra, its like having a "dummies" book with video help but without the fluff. Includes a book with 200 pages of material and hundreds of solved examples plus 6 video tutorials - all showing solved examples. The emphasis is on showing you how to solve algebra problems in a step-by-step fashion. Plus - each chapter includes an end of chapter quiz complete with answers so you can test your learning progress.
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Algebra tutor makes algebra easy for anyone to learn. Using a teach by example approach you get these tutorial books: |
The Oxford Users' Guide to Mathematics is one of the leading handbooks on mathematics available. It presents a comprehensive modern picture of mathematics and emphasises the relations between the different branches of mathematics, and the applications of mathematics in engineering and the natural sciences. The Oxford User's Guide covers a broad spectrum of mathematics starting with the basic material and progressing on to more advanced topics that have come to the fore in the last few decades. The book is organised into mathematical sub-disciplines including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimisation, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. The book is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics. It also includes a comprehensive bibliography of key contemporary literature as well as an extensive glossary and index. The wealth of material, reaching across all levels and numerous sub-disciplines, makes The Oxford User's Guide to Mathematics an invaluable reference source for students of engineering, mathematics, computer science, and the natural sciences, as well as teachers, practitioners, and researchers in industry and academia.
Reviews
"With so much mathematics in compact form, this book will be useful as a quick reference for those working in such fields as physics, engineering, and economics, as well as for mathematicians."--CHOICE
You can earn a 5% commission by selling Oxford User's Guide to Mathematics |
Assessment Rules
CMod description
This module introduces the concepts of complex numbers.
These include the graphical representation of complex numbers, complex
arithmetic and Demoivres theorem, real and imaginary parts, complex mapping,
representations of harmonic waves and AC circuits, application to solution of
differential equations in quantum mechanics. |
These exemplorary presentations are ideal tools for those teaching GCSE Mathematics.
They cover all the theory for Shape, Space, Measures and Data
Handling and,
in addition, provide worked examples, summaries and introductory exercises
to test studentsí understanding - with solutions. Whilst aimed principally
at whole class teaching, they can be used by individual students or small groups
to help them when they have missed work or when they are revising.
Each page is revealed in stages so that students have plenty of time to ask
and answer questions. In many cases real life situations and data has been
used, including that related to weather, health, money, land use and a variety
of other applications.
Text, diagrams and examples are animated to explain and enliven the work and
teachers can control the speed at which the presentations run and pause whenever
they wish.
Materials cover the tiers, Foundation and Higher (for teaching
from September 2007)
Extensive use is made of graphs and illustrations to
explain and enliven theory
Summaries are given suitable for note-taking and
for photocopying
Written by an experienced GCSE teacher and examiner
Good mathematical practice
is followed throughout
Mathematical terminology is gradually introduced and
correct notation is used
All you need is a Data Projector or Interactive Whiteboard and a computer
running Microsoft Powerpoint (Office 2002 or later). |
Algebra II picks up, of course, where Algebra I leaves off. And now we have the benefit of a years worth of geometry to provide further insight into some algebraic topics.
A quick and speedy review of some previously learned algebra leads to intensive work with polynomial functions and their distant cousins, the rational functions. The transcendental functions of exponentiation and the logarithm are covered in detail as well.
Expect some things that look familiar, but questions and applications that do not. Expect to be pushed to really THINK about what these functions do, how they do it, and how they behave. Expect to leave this course with a better understanding of why some functions make better real life models for a particular situation than others.
Looking forward to meeting each of you and successfully working our way through the course!
Visit our Class Edmodo site for announcements, handouts, and other useful information related to Algebra 2: |
This is an
honors-level course for students who have been highly successful in middle
school mathematics. This course will be a more extensive study of the
algebraic concepts traditionally covered in Algebra 1. It is an
intense program that includes all topics taught in Algebra 1 as well
as additional enrichment topics. Students in this course must take a
state-mandated end-of-course test. |
Description
Calculus Know-It-All: Beginner to Advanced, and Everything in Between By Stan Gibilisco
Publisher: McGraw-Hill/TAB Electronics 2008 | 806 Pages | ISBN: 0071549315 | PDF
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* Andquot;Extra CreditAndquot; and Andquot;ChallengeAndquot; problems to stretch your mind
StanAnd#39;s expert guidance gives you the know-how to:
* Understand mappings, relations, and functions
* Calculate limits and determine continuity
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* Analyze graphs using first and second derivatives
* Define and evaluate inverse functions
* Use specialized integration techniques
* Determine arc lengths, surface areas, and solid volumes
* Work with multivariable functions
* Take college entrance examinations with confidence
* And much more! |
78915052
ISBN-13:
9780878915057
Publisher:
Research & Education Association
Release Date:
January, 1998
Length:
1104 Pages
Weight:
Unavailable
Dimensions:
10.1 X 6.8 X 2.1 inches
Language:
English
Calculus Problem Solver (REA) (Problem Solvers Solution Guides) tex... Read moreDETAILS- The PROBLEM SOLVERS are unique - the ultimate in study guides.- They are ideal for helping students cope with the toughest subjects.- They greatly simplify study and learning tasks.- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.- They cover material ranging from the elementary to the advanced in each subject.- They work exceptionally well with any text in its field.- PROBLEM SOLVERS are available in popular subjects.- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.- Most are over 1000 pages.- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.
Customer Reviews
Excellent
Posted by Robert T Carroll on 09/16/2003
I was recently offered a high school teaching job, so I needed to brush up on my calc, and this book did the trick. Unlike other books, this one "teaches by example". I always found that too many college professors & textbooks spend too much time trying to "explain" the concept. My experience has been to skip the lecture part, do the problems, and in doing so, the concept will come to you. The fact that the problems are all solved in detail is also a plus. A lot of texts simply list the answer to the problem, so you're often left wondering how they got it. This won't be an issue with this text.
Great for University Students!
06/16/2000
The Calculus Problem Solver is an excellent book for University students or even high school students taking Calculus. This book is clearly organized with a table of contents and an index. It provides an explanation on each topic, followed by tons of practice problems with full solutions. It beats regular textbooks because the solutions are fully explained using words and calculations so the reader understands exactly how to solve each problem. It is also low on wear and tear, I bought my book used and have trucked it to school and back and it has remained in tact. I would recommend this book to every Calculus student and or Physics student as this book also provides topics ranging from first year Physics to Advanced.
Calculus: Oh how i love it
Posted by Calc Lover on 04/18/2000
This book is a great solution guide to ANY Calculus I,II,III textbook. Basically contains all problems which are solved out in a sytematic approach. Lets you follow the solution from beginning to end with comlpete understanding. I recommend this book for people who need help with Calculus and for people who just cant get enough problems, ITS GREAT.
Step by Step
01/09/2004
I have been out of college for 7 years. I began Grad school last quarter. This book gave me the basic steps to relearn and remember Calculus. It takes you through each kind of problem without skipping steps or assuming you already know what you are doing. A big crutch for understanding single and multivariable calculus. -I passed the placement exam and then used the book to assist in other engineering classes.
This is exactly what the title says
Posted by ophelia99 on 01/03/2005
Even if you understand the principles, the handful of problems in the average textbook are too few to really drill you on the procedures. It's a little like the difference between understanding some music theory and being able to play an instrument. Practice, for those of us who are not math prodigies, is essential. If you are willing to put in the hours and hours, this hugh collection of solved problems is well worth the price. |
Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the "Bulletin of the American Mathematical Society" as " [more]
Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the "Bulletin of the American Mathematical Society" as "a very welcome addition to the mathematical literature." 1963 edition.[less] |
In
this unit students are expanding their understanding of algebraic
relations to include models in which more than two variables are
involved. By the end of this unit students should have a good understanding
of a variety of means for exploring different multiple variable
situations through the use of tables, graphs, and symbolic representation. Lesson 1: In this lesson
students will explore how the changes in one variable affects the
values of other variables. Lesson 2: Students will
work with multiple variable situations that involve algebra, geometry,
and trigonometry. In the second lesson students solve problems involving
the law of Sines and the law of Cosines. Lesson 3: The investigations
involve two or more output variables related to the same input variable.
The students explore such systems of equations and determine algebraic
models, tables, and graphs for them. Student will also explore inequalities
related to these systems. Lesson 4: Linear programming
is used to motivate interest in and to show one reason for graphing
linear inequalities. Students will be discovering the feasible region
for linear programming problems, what the boundaries are of the
region, and finally the best solution is always a vertex of the
region.
Objectives:
To develop an understanding of and the ability
to solve problems involving multiple variable relations where
one equation relates more than two variables.
To develop the ability to solve mulitiple variable
equations for one variable in terms of the other variables.
To
model situations
with systems
of equations
and inequalities
where two
or more
output variables
are related
to the
same input
variables,
and to apply
those systems
to solve
problems. |
Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications. The companion website on contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers.
Please note the previous printing included a disk attached to the back of the book.
Please note the previous printing included a disk attached to the back of the book.
The material is now only available on the companion website -
Customer Reviews:
Instructors, please don't use this as a course book
By Jordan Bell - March 8, 2011
I am currently the marker for a first course on linear programming which uses this book. I find that the definitions of key terms are buried in the text, like the definition of a basic solution on p. 95. The description of the simplex algorithm in section 2.1 is mixed together with a particular linear programming problem. I would prefer to have a general description and then many detailed examples, rather than a mix of both and then only two examples. I have a similar complaint with section 2.3 on the two phase method.
This book is expensive. There are books published by Dover that cover the simplex algorithm, duality, and integer programming that cost a tenth as much as this book, and an instructor should look at those before assigning a book that costs this much. Also, it is ludicrous now to have newly purchased books come with floppy disks.
A good book
By Bryan Urizar - December 19, 2010
This is a good book. Everything is well explained and each section has many examples. The only thing I would complain about is that the examples should probably have been placed before the theorem statement/proof as it would help the reader understand the proof. The material is all very straightforward and shouldn't cause any headaches. Overall an excellent book which I'd recommend to anyone who would like to learn linear programming.
For anyone trying to learn linear programming out a class room setting it is also good as the back has answers to odd numbered questions. |
Summary:
Clear explanations, an uncluttered and appealing layout, and examples
and exercises featuring a variety of real-life applications have made
this text popular among students year after year. This latest edition
of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC
GEOMETRY retains these features. The problems have been consistently
praised for being at just the right level for precalculus students
like you. The book also provides calculator examples, including
specific keystrokes that show you how to use various graphing
calculators to solve problems more quickly. Perhaps most
important-this book effectively prepares you for further courses in
mathematics.
Classification:
Book Details:
Physical Description: 902 pages
Edition Info: Hardcover; 2007-02 |
Summary
In this Spreadsheets Across the Curriculum activity, students are guided step-by-step to build a spreadsheet that estimates the real cost of driving out of the way for less-expensive gasoline. To better illustrate the modeling process, the module begins with the simplest case of factoring in only the extra gas consumed and is then expanded to consider not only the additional wear-and-tear expense, but also the non-monetary cost of travel time. This module should demonstrate both the power of basic mathematics to analyze authentic relevant scenarios as well as the ease at which this can be accomplished using spreadsheets.
Gain experience with using numbers and mathematical calculations to examine their opinions.
Context for Use
I wrote the module out of dismay with how the media hypes their "cheap gas price" reports and yet continually fails to provide any context as to when and how this information will actually serve its intended purpose, namely to save the consumer money. However, without an audience of own, my thoughts would all be for naught. Luckily, a module exploring the trade-offs involved in driving some distance to get cheaper gas is perfect for Davenport University's College Mathematics course (MATH120). A major focus of this class is to develop the students' ability to apply the concepts learned in basic algebra to both the content of their major as well as their daily life. .
The module is meant to be the first step into real modeling (i.e., thinking beyond the basic textbook story problem). The module is given around the fifth week of classes after the students have completed sessions on applying linear, quadratic, logarithmic and exponential functions as well as systems of linear equations. The reason for the later placement is so students will have time to complete a series of short Excel skill-building assignments. This way, students can start on the module with full confidence in their spreadsheeting abilities. Alternatively, the module could be given to correspond with coverage of linear functions, but then additional time would need to be dedicated to the Excel portions of the module.
I prefer to have a discussion about gas prices and the cheap-gas reports prior to showing the students the module. I open the discussion by showing the students a cheap-gas website or a cheap-gas report from a recent copy of the local newspaper, and then I ask them if they've seen these reports and if anyone actually follows up on them (and how). Typically the conversation stalls with students either believing there is value in making a trip for cheaper gas or that the trip isn't worthwhile; significantly, students in the latter group are unable to provide evidence as to why it isn't worthwhile except for "I don't want to take the time." At this point, I give them the overview of modeling that appears on Slide 2 of the module and immediately follow that up by asking the students to identify everything they think may be relevant to making this decision (Students who already have a strong opinion regarding what they would do in this situation can be coaxed back to "neutral" by asking them to put this in business context where their boss would like actual data before making a choice).
After that introduction, I start to walk the students through the actual module. (They seem to like the fact that they have already brought up most if not all or more of the variables mentioned in the module). As we sort through the variables, the most natural question that arises is what information is actually available to us, which then leads us right into what assumptions are we going to make. For example, the fuel cost to make the trip is the first variable most people consider. Finding this cost depends on the distance we need to travel, the price we pay for the gas, and the fuel efficiency of the vehicle we're driving; hence, we need to establish values for each of these. I chose the numbers I used because (a) they are believable and (b) they work out nicely - which we then proceed to do. The great thing about this is that if students don't like my numbers, they can run their own numbers later.
As is often done in real-world problem solving, we have started our considerations with a simple case. So next we increase the complexity by incorporating the other variables. We discover that gathering the relevant information can become difficult (and possibly impractical) to find, thus requiring additional assumptions if we wish continue. We also find that the scale of the problem may render some variables irrelevant. Lastly, and building on the idea that this may not be worth our time, we take a look at the non-monetary costs (for many scenarios this road can easily lead to a discussion of ethics).
Although we only change gas prices in this module, I have set up the spreadsheet in a manner that allows one to alter distance traveled and wear-and-tear costs.
Description and Teaching Materials
The module is a PowerPoint presentation with embedded spreadsheets. IfThe module is constructed to be a stand-alone resource. It can be used as a homework assignment or lab activity. It can also be used as the basis of an interactive classroom activity.
Assessment
The last slide of the module is a set of questions that can be used for assessment.
The instructor version includes a slide of questions that can be used as a pretest. |
Mathematics Assistance
The Math Assistance Area (MAA) is a resource center for students enrolled in any COD
math course through Math 2232, including classroom, flexible learning, and online
classes. The MAA provides support through its faculty staff and its print and technology
resources.
The MAA is staffed by full- and part-time COD mathematics faculty, providing one-on-one
help to students with homework problems or by clarifying concepts from their math
coursework. Sessions are kept to 15 minutes when other students are waiting, but students
may have unlimited turns.
The MAA also has the current textbooks used in all COD math courses as well as solution
manuals, computers, videos, and calculators. All materials must be used in the MAA
with the exception of calculators which may be checked out for short periods of time.
The Math Assistance Area is primarily a drop-in center, but 15-minute appointments
can be made for students with time constraints.
Resources:
LearningExpress Library is a comprehensive, interactive online learning platform of
practice tests and tutorial course series designed to help patrons—students and adult
learners—succeed on the academic or licensing tests they must pass |
4. Factorization Formulae: Introduction, Formulae for conversion of sum or difference into
products, formulae for conversion of product into sum or difference, trigonometric functions of
angles of a triangle.
5. Locus : Introduction, Definition and equation of locus, points of locus, shift of the origin.
6. Straight Line : Revision. Inclination of a line, slope of a line, equation of lines, parallel to coordinate axes, intercepts of a line, revision of different forms of equations of a line, slope point
form, slope intercept form, two point form, double intercept form other forms of equations of a
line, parametric form, normal form, general form, Theorem : A general linear equation Ax + By+
C =0, provided A and B are not both zero, simultaneously, always represents,straight line.
Theorem 2 : Every straight line has an equation of the form Ax +By + C = 0, where A, B and C
are constants (without proof), Reduction of general equation of a line into normal form,
intersection of two lines, parallel lines, perpendicular lines, identical lines, condition for
concurrency of three lines, angle between lines, distance of a point from a line, distance between
two parallel lines, equations of bisectors of angle between two lines, family of lines, equation of
a straight line parallel to a given line, equation of a straight line perpendicular to a given line,
equation of family of lines through the intersection of two lines.
8. Vectors : Definition, magnitude of a vector, free and localized vectors, types of vectors, zero
vector, unit vector, equal vector, negative of a vector, collinear vectors, coplanar vectors,
coinitial vector, like and unlike vector, scalar multiple of a vector, triangle law, parallelogram
law, polygon law, properties of addition of vectors, three dimensional co-ordinate geometry, coordinate axes & coordinate planes in space, co-ordinates of a point in space, distance between
two points in a space, unit vectors along axes, position vector of a point in space, product of
vectors, scalar product, definition, properties, vector product, definition, properties, simple
application, workdone by force, resolved part of a force, moment of a force.
9. Linear Inequations : Linear in equations in one variable – solution of linear inequation in one
variable & graphical solution, solutions of system of linear in equations in one variable, Linear in
equations in two variable – solution of linear inequation in one variable & graphical solution,
solution of linear in equations in two variable & graphical solution, solutions of system of linear
inequations in two variables, Replacement of a set or domain of a set, Transposition.
10. Determinants : Revision, determinant of order three–definition, expansion, properties of
determinants, minors & co-factors, applications of determinants condition of consistency, area of a
triangle, Cramer"s rule for system of equations in three variables.
Maharashtra Board Best Sellers
In order to keep pace with technological advancement and to cope up with Maharashtra Board examinations, Pearson group has launched Edurite to help students by offering Books and CDs of different courses online. |
Mathematics - AS/A2 Levels
Entry Requirements
Five GCSEs at Grades A* - C including English Language and Mathematics at Grade B Higher Tier.
Further Mathematics is available through attendance at one twilight session per week at The University of Northampton and revision classes at the University of Warwick.
Course Content
A Level Mathematics is one of the most useful subjects you can study, as the successful mathematician possesses a problem-solving ability that is valuable in many occupations. This course builds on the algebra, trigonometry and geometry you learned at GCSE Level and develops the topics of calculus into Pure Mathematics. Modules also include Statistics (the identification of patterns in data) and Mechanics (developing mathematical models of physical forces). You should enjoy problem-solving, have a tenacious, disciplined approach and be prepared to practise between lessons the skills you have acquired |
Dickinson College is a four-year, residential, liberal
arts institution serving approximately 1,800 students. During
the past decade, the introductory science and
mathematics courses at the college have been redesigned to
emphasize questioning and exploration rather than passive learning
and memorization. The Workshop Calculus
project1, now in its sixth year of development, is part of this college-wide effort.
Workshop Calculus is a two-semester sequence
that integrates a review of pre-calculus concepts with the
study of fundamental ideas encountered in Calculus I:
functions, limits, derivatives, integrals and an introduction to
integration techniques. The course provides students who have had
three to four years of high school mathematics, but who are
not prepared to enter Calculus I, with an alternate entry
point into the study of higher-level mathematics. It seeks to
help these students, who might otherwise fall through the
cracks, develop the confidence, understanding and skills
necessary to use calculus in the natural and social sciences and
to continue their study of mathematics. After completing
both semesters of Workshop Calculus, workshop students
join their peers who have completed a one-semester Calculus
I course, in Calculus II.
All entering Dickinson students who plan to take
calculus are required to take the MAA Calculus Readiness
Exam. Students who score below 50% on this exam are placed
in Workshop Calculus, while the others enter Calculus I.
The two strands serve the same clientele: students who plan
to major in mathematics, physics, economics or other
calculus-based disciplines. While both courses meet 5 hours a
week, Calculus I has 3 hours of lecture and 2 hours of
laboratory sessions, while there is no distinction between
classroom and laboratory activities in Workshop Calculus, which
is primarily hands-on.
A forerunner to Workshop Calculus consisting of a
review of pre-calculus followed by a slower-paced version
of calculus was developed in response to the fact that
30-40% percent of the students enrolled in Calculus I were
having difficulty with the material, even though they appeared
to have had adequate high school preparation.
Students' reactions to the course, which was lecture-based with
an emphasis on problem solving, were not positive. They
did not enjoy the course, their pre-calculus skills did not
improve and only a few ventured on to Calculus II. In
addition, colleagues in client departments, especially economics
and physics, continued to grumble about the difficulty
students had using calculus in their courses. Workshop Calculus
was
the department's response.
With the Workshop approach, students learn by
doing and by reflecting on what they have done. Lectures
are replaced by interactive teaching, where instructors try
not to discuss an idea until after students have had an
opportunity to think about it. In a typical Workshop class, the
instructor introduces students to new ideas in a brief, intuitive
way, without giving any formal definitions or specific
examples. Students then work collaboratively on tasks in
their Workshop Calculus Student Activity Guide [1]. The
tasks in this manual are learner-centered, including computer
tasks, written exercises and classroom activities designed to
help students think like mathematicians — to make
observations and connections, ask questions, explore, guess, learn
from their errors, share ideas, and read, write and talk
mathematics. As they work on assigned tasks, the instructor mingles
with them, guiding their discussions, posing additional
questions, and responding to their queries. If a student is
having difficulty, the instructor asks the student to explain what
he or she is trying to do and then responds using the
student's approach, trying not to fall into
let-me-show-you-how-to-do-this mode. The instructor lets — even encourages
— students to struggle, giving only enough guidance to
help them overcome their immediate difficulty. After
completing the assigned activities, students participate in
class discussions, where they reflect on their own experiences.
At this point, the instructor can summarize what has
been happening, present other theoretical material or give a
mini-lecture.
Method
Assessment activities are a fundamental part of the
Workshop Calculus project. With the help of external
collaborators2, we have analyzed student attitudes and learning
gains, observed gender differences, collected retention data
and examined performance in subsequent classes.
This information was used to help make clearer the tasks
expected of students laid out in our Study Guide. More
significantly, it has provided the program with documented
credibility, which has helped the Workshop program gain the
support of colleagues, administrators, outside funding agencies,
and even the students themselves. The following describes
some of the tools we have used. For a more in-depth
description of these assessment tools and a summary of some of
the results, see [2].
a. Collecting Baseline Data. During the year prior
to introducing Workshop Calculus, baseline information
was
collected concerning students' understanding of
basic calculus concepts. Workshop Calculus students were
asked similar questions after the new course was implemented.
For example, students in the course prior to the Workshop
version were asked:
What is a derivative?
If the derivative of a function is positive in a given
interval, then the function is increasing. Explain why this is true.
In response to the first question, 25% of the
students stated that the derivative represented the slope of the
tangent line, and half of these students used this fact to give
a reasonable explanation to the second question.
The remaining students answered the first question by giving
an example and either left the second question blank or wrote
a statement that had little relationship to the question;
they could manipulate symbols, but they didn't understand
the concepts.
This data showed the need to emphasize
conceptual understanding of fundamental concepts and to have
the students write about these ideas. Consequently,
Workshop students learn what an idea is — for example, what
a derivative is and when it is useful — before they learn
how to do it — in this case, the rules of differentiation —
and they routinely write about their observations.
b. Administering Pre- and Post-tests. Workshop
Calculus students answer questions prior to undertaking
particular activities and then are re-asked the questions later.
For example, on the first day of class, students are asked to
write a short paragraph describing what a function is,
without giving an example. Although they all claim to have
studied functions in high school, many write gibberish, some
leave the question blank, and only a few of students each
year describe a function as a process. After completing
the activities in the first unit of their activity guide (where
they do tasks designed to help them understand what a
functions is, without being given a formal definition of
"function"), nearly 80% give correct, insightful descriptions of
the concept of function.
c. Analyzing Journal Entries. At the end of each of the
ten units in the Workshop Calculus activity guide, students
are asked to write a journal entry, addressing the
following questions:
Reflect on what you have learned in this unit. Describe
in your own words the concepts that you studied and
what you learned about them. How do they fit together?
What concepts were easy? Hard? What were the
main, important ideas? Give some examples of these ideas.
Reflect on the learning environment for the course.
Describe the aspects of this unit and the learning environment
that helped you understand the concepts you studied.
If you were to revise this unit, describe the changes
you would make. What activities did you like? Dislike?
The students' responses provide the instructor with
valuable insight into their level of understanding; their candid
replies also provide important feedback about what works and
doesn't work and about changes that might need to
be made.
d. Asking Comparative Test Questions. Student
performance in Workshop Calculus has been compared to students at
other institutions. For instance, on the final exam for
Workshop Calculus, in the spring of 1994, students were asked
four questions from an examination developed by Howard
Penn at the US Naval Academy to assess the effectiveness of
using the Harvard materials at the USNA versus using a
traditional lecture-based approach [3]. (See the Appendix for
these questions.) We are pleased to report that the
Workshop Calculus students did about as well as the USNA
students who were using the Harvard materials, even though
the Academy is certainly more selective than Dickinson College.
e. Conducting Critical Interviews. A representative
group of Workshop students have been interviewed in
structured ways, to help determine what they are thinking as they
work on a given problem and to determine their level of
understanding of a particular concept. For this, a questionnaire
is administered to students, and we categorize responses
and approaches used, even taping one-on-one "critical
interviews" with a representative group of students,
transcribing the interview sessions, and analyzing the results. After
using the first version of the Workshop Calculus materials
in the spring of 1992, this approach was used, for instance,
to analyze students' understanding of "definite integral."
After analyzing students' responses on the questionnaire and
during the interview sessions, we realized that some students
could only think about a definite integral in terms of finding the
area under a curve and had difficulty
generalizing.3 Based on this observation, the tasks pertaining to the development of
definite integral in the Student Activity Guide were revised.
f. Scrutinizing the End-of-Semester Attitudinal
Questionnaire. At the end of each semester, students are asked to rate
the effectiveness of various activities, such as completing
tasks in their activity guide, participating in discussions with
peers, using a computer algebra system. They are also asked
to rate their gains in understanding of fundamental ideas
— such as their understanding of a function, or the
relationship between derivatives and antiderivatives — to compare
how they felt about mathematics before the course with how
they
feel after completing the course, and to describe the
most and least useful activities in helping them learn mathematics.
Student responses are analyzed for gender
differences. For instance, both male and female students who
took Workshop Calculus in 1993-1994, claimed, on the
average, that they felt better about using computers after
completing the course than before. Men showed a greater increase
in confidence, however, and even after the course, women
were not as comfortable using computers as the men were initially.
g. Gathering Follow-up Data. Information about
student attitudes is also collected from students who took either
the Workshop Calculus sequence or the regular Calculus
I course, one or two years after they complete the
course (irrespective of whether they have gone ahead
with mathematics or not).4 Their responses are used to
determine the impact of the course on their attitudes
towards mathematics and their feelings about the usefulness
and applicability of calculus in any follow-up courses.
For instance, students are asked whether they strongly
agree, somewhat agree, somewhat disagree, or strongly
disagree to 46 statements, including:
I am more confident with mathematics now, than I
was before my calculus course.
I feel that I can apply what I learned in calculus to
real world problems.
On the whole, I'd say that my calculus class was
pretty interesting.
In addition, we gather data about Workshop
Calculus students who continue their study of mathematics and/or
take a course outside the Mathematics Department that
has calculus as a pre-requisite, asking questions such as:
How many Workshop students continued their study
of mathematics by enrolling in Calculus II?
How do the Workshop students perform in Calculus II
in comparison with those who entered via the
regular Calculus I route?
How many Workshop students became
mathematics majors?
How do Workshop students do in courses outside
the Department that have calculus as a pre-requisite?
Findings and Use of Findings
With the exception of the critical interviews, the
assessment tools used for Workshop Calculus are easy to
administer and the data can be easily analyzed. Moreover, these
tools can be used in a variety of courses at a variety of
institutions. In general, our assessment process requires developing
a
clear statement of intended outcomes, designing and
utilizing supportive assessment tools, and analyzing the data
and summarizing the results in ways that can be easily and
readily understood (for instance, bar charts or graphs are helpful).
Success Factors
Something should be said here for the advantages of using
a variety of assessment measures. We feel that our
program benefits from the breadth of our methods for
collecting information about performance, teaching, learning, and
the learning environment. In particular our focus is
on understanding how students are thinking, learning,
and processing the courses. Often assessment measures
raise more questions than they answer, and when students
are asked questions, they may be reading and responding
on different wavelengths from those we are broadcasting
on. We have found that an advantage to using a
"prismatic" assessment lens is that we obtain a variety of ways
of exploring issues with students, and therefore we
become closer to understanding students and more inspired to
make the changes that will be beneficial to all of us.
Good assessment offers students feedback on what they
themselves report. We feel that our methods are appreciated by
students, and that the department is perceived as caring as
reforms are instituted. Good assessment also promotes
ongoing discussion. And our measures have certainly helped
to stimulate ongoing faculty dialogue, while unifying
the department on the need for further assessment. It has
been six years since the Workshop Calculus project began
and we are still learning!
[3] Penn, H., "Comparisons of Test Scores in Calculus I
at the Naval Academy," in Focus on
Calculus, A Newsletter for the Calculus Consortium Based
at Harvard University, 6, Spring 1994, John Wiley &
Sons, Inc., p. 6.
Appendix
Q1 showed five graphs and asked which graph had
f´(x) < 0 and
f´´(x) < 0.
Q2 showed the graph of a function h and asked at which
of five labeled points on the graph of h is
h´(x) the greatest.
Q3 showed the graph of a function which was
essentially comprised of two line segments—from
P(-1,0) to Q(0,-1) and from
Q(0,-1) to R(3,2)—and asked to approximate the integral of the function from -1 to 3.
Q4 showed the graph of the derivative of a function,
where f´ was strictly positive, and asked at which of five
labeled points on the graph of f´ is
f(x) the greatest.
——————
1 The Workshop Calculus project has received support from the Knight Foundation, the US Department of Education Fund
for Improvement of Postsecondary Education (FIPSE) and the National Science Foundation (NSF).
2 Ed Dubinsky, from Georgia State University, and Jack Bookman, from Duke University, helped assess student learning gains
and attitudes in Workshop Calculus. They were funded by FIPSE. |
Complex Variables: Second Edition (Dover Books on Mathematics)
Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. 1990 edition. Appendices.
Customer Reviews:
mediocre
By A Customer - May 27, 2004
This book contains a wealth of information, and at this price, one really shouldn't complain, but if you're looking to really understand complex analysis as a mathematical subject, keep looking. My main problem with the book is that while it states plenty of facts on the subject, the explanations for them (i.e. proofs, examples, counterexamples) are unclear, incomplete, or absent. There's enough "theorem"... "proof" talk to scare off those unaccustomed to it, but the information contained therein is often of little use to those who ARE. In trying to cover both bases, I think the author ends up failing both. If you're looking to learn complex variables for applications, find a book that covers just that. If you're looking for analysis, do likewise. I was impressed by Stein and Shakarchi's "Complex Analysis", which gives an introductory, but thorough and sufficiently rigorous, treatment of the subject.
Great text
By A Customer - August 15, 2000
It is wonderful to see this great book on undergraduate complex analysis back in print at even a more affordable price. I've used it in in one of my junior level courses and been totally satisfied with it. I will use a part of it again in a continuation course.What is nice about this book is that it is a textbook, and not a cookbook nor a book that tries to include everything and fails at all of them. This book never lists too many results; instead it aims at the understanding of the subject matter. Its treatment of Cauchy's theorem clearly exposes the fact that different points of view (derivatives, series, integrals) in the complex plane lead to the same object, analytic functions. The sections on geometric and applied topics, such as linear fractional transformations and fluid mechanics, are a delight to read.The book assumes nothing other than calculus (Green's theorem) as background. Topological concepts are kept at a reasonable level and some are... read more
Excellent excercises, poor explainations
By A Customer - January 18, 2003
I used this book for a complex variable course as part of my engineering study. I found this book very insufficient to explain things well as a beginner in the subject. There were often problems I could not understand because the book only offered a couple line explaination and no example. In fact almost all the class thought the book was terrible and didn't even read it. Now my school Rochester Institute of Technology has returned to its previous book. If you are well versed in math and want to explore another realm, go ahead with this book, but if you are no mathematician try something else.
Focusing on applications rather than theory, this book examines the theory of Fourier transforms and related topics. Suitable for students and researchers interested in the boundary value problems of ...
Written by a pioneer in the development of reliability methods, this text applies statistical mathematics to the analysis of electrical, mechanical, and other systems employed in airborne, missile, ... |
The purpose of the mathematics standards is to equip all of Elite's students the mathematical skills, understanding, and attitude that they will need to be successful in their careers and daily lives.
For Elite Prep the mathematics standards adopts "The Common Core State Standards" which provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them.
The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future,
our communities will be best positioned to compete successfully in the global economy.
This course is designed as the first course in a traditional program for all students who are required to take three or more years of college preparatory mathematics. Initially, concepts mastered in the previous math course are expanded. In addition, this course covers solving and graphing equations and inequalities, solving word problems, graphing on a coordinate plane, solving simultaneous equations, properties of exponents, operations with polynomial expressions, working with quadratic functions, and data analysis.
This course is for mathematically oriented students who desire an extensive and comprehensive treatment of the topics of geometry. This course, along with Honors Algebra 2, is designed for students who plan to take the maximum units of mathematics in high school. Because this is an honors course, the grades are weighted for class rank purposes. Students selecting Honors Geometry must check the district web site in June to obtain a summer preview project, which is due on the first day of school in September.
Prerequisite: Strong performance in Algebra 1 in the eighth grade and teacher recommendation Geometry, along with Algebra 1 and Algebra 2, serves as the starting point for further work in mathematics.
The course is divided into two main parts. The first part covers basic figures of geometry, writing deductive proofs, congruent triangles, corresponding parts of congruent triangles, parallel lines and planes. The second part includes concepts of similarity, a study of quadrilaterals and circles, work with area and volume, constructions, and the Pythagorean Theorem with applications to plane and solid figures. Geometry 9 is intended specifically for those ninth graders who successfully completed Algebra 1 in Grade 8. It is not weighted as an honors course. In addition to the proficiencies listed for the regular Geometry course, the Geometry 9 curriculum includes an extensive review of Algebra 1 topics. Students selecting Geometry 9 must check the district web site in June to obtain a summer preview project, which is due on the first day of school in September.
This course is for mathematically oriented students who desire an extensive and comprehensive treatment of the topics of Algebra 2. This course, along with Honors Geometry, is designed for students who plan to take the maximum units of mathematics in high school. Students who plan to take this course should have had an average of ―A or B in Algebra 1. Because this is an honors course, the grades are weighted for class rank purposes.
This course completes a traditional three-year college preparatory sequence. It begins with a brief review of concepts learned in Algebra 1 and includes more advanced topics such as quadratic equations and functions, polynomial equations and functions, properties of exponents, logarithms, verbal problems, and arithmetic and geometric sequences and series. The course is for potential college candidates who wish to benefit from the study of a rigorous secondary mathematics course. Seniors who previously had difficulty in mathematics should consider Essentials of Algebra 2.
This course is a must for the serious math student and prerequisite for the study of calculus. Topics covered include trigonometric functions, conic sections, analytic proofs, polar coordinates, graphs of higher degree equations, and rotation of axes. This course provides a more detailed and rigorous treatment of the subject than Trigonometry and Precalculus. This course is a prerequisite for students who plan to take either Advanced Placement Calculus course. Because this is an honors course, the grades are weighted for class rank purposes.
Prerequisite: Trigonometry and Analytic Geometry (Honors) or Trigonometry and Precalculus.
This course is the last portion of an accelerated mathematics program for students who do not take an Advanced Placement Calculus course. It continues the work begun in previous honors courses, with primary emphasis on differential and integral calculus. This course is designed to be an introduction to calculus material for students who will be taking a calculus course in college, and it is not as intensive as either Advanced Placement Calculus course. Hence, while students who enroll in this course may elect to take an Advanced Placement exam, not all the required material will be covered by the time of the exam. A TI-83 graphing calculator is used throughout the course.
Because this is an honors course, the grades are weighted for class rank purposes.
Prerequisites: Trigonometry and Analytic Geometry (Honors) or Trigonometry and Precalculus.
This course consists of a full high school academic year of work and is comparable to one semester AB must check with the math department in June to obtain a preview packet which is due in September. Because this is an advanced placement course, the grades are weighted for class rank purposes.
This course consists of a full high school academic year of work and is comparable to two semesters BC must check with the math department in June to obtain a preview packet which is due in September. Because this is an advanced placement course, the grades are weighted for class rank purposes.
This class is recommended for college-bound juniors and seniors planning to take the SAT and/or ACT. Almost all undergraduate colleges and universities require that prospective students take either the ACT or the SAT; most students take both. Taking this course will prepare students for all of the question types found on the SAT and ACT. We will analyze each of the test question areas and give special consideration to math and verbal refreshers and techniques aimed at relieving test-taking anxiety. Topics include sentence completions and reading comprehension for the reading section, grammar and essay writing for the writing section, scientific concepts for the science section, and basic and advanced math concepts (including fractions, decimals, percentages, ratios, proportions) and algebraic and geometric concepts for the math sections. |
Class News
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Course Information
Instructor: Herman Gluck
Lecture:
T, Th 3:00 - 4:30 p.m DRL 4C4
Recitation Sections:
M, W 6:30-8:30 p.m. in DRL 4C6.
During our recitation sessions you will presenting solutions to homework problems (those that you have already worked on the previous week and handed in) in front of the class at the blackboard. The goal is to practice laying out a mathematical argument, communicate it effectively, and be able to spot gaps in proofs.
Homework problems are handed in at lecture and returned to you at recitation after it has been graded. Selected problems from each assignment will be graded in detail while the rest may be graded less in depth.
Presenting Solutions:
The goal in written mathematics is to communicate a formal proof clearly enough that a reader can understand the proof without special ingenuity on their part. One must therefore have an idea of who the hypothetical reader is. For us, the hypothetical reader is someone who hasn't thought about the problem and therefore doesn't know what details will come up in the proof or how they will be addressed. We assume though that the reader knows what we know outside of the particular problem at hand and, likewise, is as competent with the current material as we are. This means they know the definitions and they are comfortable taking facts for granted that have been proven earlier in the course.
It is necessary, then, that when we present the solutions to the class that we engage in a little bit of acting - none of us fits the description of the hypothetical reader! The audience should also act the part, asking questions where the solution is ambiguous or unclear. Of course, if you legitimately don't see a step then definitely ask a question too. Likewise for the speaker, feel free to break character and ask a question. (When standing at the blackboard, it is normal to get confused about what you knew when sitting down - don't be ashamed!).
When you present the problem at the blackboard you should be both speaking and writing your solution. Normally it is a good idea to verbally give an overview or an intuitive idea before you do each step. When you write, you should speak aloud what you are writing, either literally or paraphrasing. To reiterate: you should almost always be speaking, either facing the class (while not writing) or while writing (and speaking what you write). As for what you write, it should be complete sentences and self contained, meaning there should not be an essential step which you spoke but did not write. Make sure to use the whole blackboard instead of erasing a single panel over and over. |
Note: This course has a lab requirement. The labs will be assigned by your instructor and will be a significant portion of your course grade. The labs will be delivered online and will require computer and internet access, but may be completed in any location with such access, on or off campus.
Students will learn pre algebra, review arithmetic, and learn how to use them in their daily lives. Topics include the arithmetic operations, long multiplication and division, decimals, fractions, percents, signed numbers, natural number exponents, order of operations, introduction to the concept of variables, combining like terms, solving linear equations, application problems and the use of geometric formulas. |
OOC: Can't help there I'm afraid - I dropped maths first chance I got XD you could try Student room? There's normally a lot of people there who can help if you're stuck with something :)
ooc: A lot of people do XD I barely chose it myself. Student room?
It's a forum thing where people can go and get help with work stuff and discuss things - a lot of people in my year used it and they said it was helpful so… :P It should turn up on google if you look for it there.
I shall definitely give it a look, it sounds like it may help a lot :D Thank you! |
Middle School Mathematics
About Middle School Mathematics
The FCPS Mathematics Program of Studies (POS) define the instructional programs that must be implemented in mathematics in the middle school. Each POS describes the curriculum content and identifies the essential knowledge and skills taught in the instructional program.
Mathematics Course Sequence
Mathematics courses, from Grade 6 through Grade 12, should be completed in sequence since each course provides the prerequisite knowledge and skills for the follow-on course. |
Designed for the undergraduate course in multivariable and vector calculus. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples.
This book is aimed primarily at undergraduates in mathematics and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. It also provides numerous computer algebra illustrations and tutorials using MATLAB or MAPLE.
DAVID A. SANTOS (late) held positions at Community College of Philadelphia, the University of North Texas, the University of Puerto Rico, and the University of Pennsylvania. He held an AB in Mathematics from the University of Chicago and a Ph.D. from the University of Michigan. |
Find a Marcus Hook can guide, but students must do the work.Introduction to the basics of symbolic representation and manipulation of variables. Liberal use of concrete examples. May require review of arithmetic concepts, including fractions and decimals. |
D Martin, Glasgow University, UK
This blend of local coordinate methods and intrinsic differential geometry enables workers to read and do calculations in relativity and high energy particle research. It provides foundations for study in gauge theory, differential geometry and differential topology. Mathematical Reviews
Dr Martin's very readable differential geometry text for graduate students in physics could also be used for
independent study. American Mathematical Monthly
- provides a comprehensive account of basic manifold theory for post-graduate students - introduces the basic theory of differential geometry to students in theoretical physics and mathematics - contains more than 130 exercises, with helpful hints and solutions
This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject. |
Customer Reviews for New Leaf Publishing Group Exploring The World Of Mathematics
Show your students that numbers don't have to be difficult---in fact, they can be enjoyable! More than just another textbook, this supplement to your curriculum traces the history of mathematics principles and theory; features simple algebra, geometry, and scientific computations; and offers practical tips for everyday math use. Includes biblical examples, fun activities, chapter tests, and lots of illustrations and diagrams. 160 pages, softcover from New Leaf The World Of Mathematics
Review 1 for Exploring The World Of Mathematics
Overall Rating:
5out of5
Engaging
This book gives a history of the development of mathematics with some instruction on how to do the various types of math worked in. The text was engaging and easy to understand. Much of the book was suitable for middle schoolers, though some chapters were more high school level. There were useful black and white charts and illustrations. At the end of each chapter, there were 10 questions--most tested if you learned the important points in the chapter, but some were math problems based on what was learned. The answers were in the back.
The book occasionally referred to things in the Bible, like explaining the cubit as an ancient measurement of length. The author had math start with the ancient Egyptians (since, according to him, it wasn't needed before then because people were roaming herders).
Chapter 1 talked about ancient calendars and how the modern calendar was developed. Chapter 2 talked about marking the passage of time. Chapter 3 talked about the development of weights and measures from ancient ones to modern non-metric systems. Chapter 4 talked about the development of the metric system.
Chapter 10 talked about algebra and analytical geometry. Chapter 11 talked about network design, combinations & permutations, factorials, Pascal's triangle, and probability. Chapter 12 talked about the development of counting machines, from early mechanical calculators to modern digital calculators. Chapter 13 talked about the development of modern computers. Chapter 14 gave some math tricks and puzzles.
Share this review:
+1point
1of1voted this as helpful.
Review 2 for Exploring The World Of Mathematics
Overall Rating:
5out of5
Date:November 11, 2007
Cindy Downes
Because I was taking College Algebra last semester, I picked up the book, Exploring the World of Mathematics, to read in order to supplement my understanding of math. Great choice! Not only did I learn more about mathematic principles but I learned more about the history of math, how math applies to everyday life, and even how math is used in scriptures!I suggest that sometime during your child's 5th-8th grade years, you go through each chapter with him - maybe as a summer course or one day a week on Friday. Most kids will like the book, too, as it teaches them how to solve logic problems that can fool their friends! Like this one: Have your friend secretly choose a number from one to ten. Tell him to add six to the number, double the results, and divide his answer by four. Next subtract half of the original number. When he is done, you can tell him what his number is 100% of the time. You'll have to read the book to find out how! |
Math Class Formats
TMCC offers math classes in a variety of formats to accommodate varying student needs and preferences. Students should check with the mathematics department when in doubt as to the format of a particular class.
Lecture format. Class meets twice a week for one hour and fifteen minutes on one of the TMCC sites. Traditional and/or non-traditional learning/instruction methods may be used (lecture, group work, discovery modules, in-class exercises, question-and-answer sessions, etc.). A lecture math class may include an online component (for example, homework and quizzes).
Computer-based format (Math 95 and 96). These classes meet in a classroom equipped with computers. Students work with interactive software, completing homework and assessments on the computer. Faculty instruct on an individual and/or small group basis. Access to a computer outside of class time is required in order to complete coursework. Computer-based math classes are described in the TMCC class schedule as: "COMPUTER-BASED CLASS: ASSIGNMENTS WILL BE COMPLETED ON A COMPUTER. STUDENTS NEED COMPUTER ACCESS OUTSIDE CLASS TIME."
Online format. Syllabus, class notes, videos, homework, quizzes, practice tests, etc. are delivered online. Students interact with the instructor and with their classmates online. Students must come to the college to take their midterm and final exams (unless proctoring arrangements have been made with the instructor).
Hybrid format. Online class but meets on campus one day per week for discussion.
Self-paced lab format. Class meets twice a week for one hour and fifteen minutes in a math lab. Students work individually and at their own pace. Homework isn't collected. Students take exams after studying the appropriate sections of the textbook. The instructor helps students on an individual and/or small group basis. |
Functions Modeling Change: A Preparation for Calculus is more than just an ordinary textbook for MacArthur High School students. It is a book that one of their teachers, Ann Davidian, helped to author and three MacArthur students contributed to.
Seana Grey and Victoria Yen, both of whom graduated from MacArthur last year and Eric Motylinski, a senior at MacArthur this year, all worked on the book to keep it current and up to date. Motylinski actually even contributed a problem to the book, which is used in classrooms across the country. All three students are recognized in the acknowledgments section of the book and Davidian is listed with the nine college professors and one other high school teacher who authored the textbook.
According to Davidian, there were eight high schools, approximately five years ago who were chosen to pilot pre-calculus materials that were written by the Harvard Consortium, part of a project by the National Science Foundation to increase the standard of what students are learning. Davidian noted that MacArthur was one of the original eight schools chosen and the school has been working on this project ever since.
The preliminary edition of the textbook came out in 1997, at which point the then-authors decided to come out with a first edition of the textbook. It was at that point that Davidian was asked to join the process as an author.
The main authors of the book, Deborah Hughes-Hallett and Eric Connally asked each of the other authors to look at various problems, to rewrite problems and to write new problems. Hughes-Hallett asked Davidian if she had any students who would be interested in updating some of the information for the first edition. Many of the problems were word-based problems with information that was several years old and no longer correct. When Davidian asked the students whom she felt were up to the task if any of them were interested, Grey, Yen, and Motylinski responded.
One example of the work that the MacArthur students did on the textbook was a section of the book on the AIDS epidemic, which Yen and Grey updated with the current data. Motylinski, other than updating many problems for the book, came up with his own idea for a problem while on a skiing vacation. Davidian e-mailed the problem to the authors and according to the proud teacher, "They loved it." Among other things Motylinski updated problems which he felt needed to be changed because they used deutschmarks in the problem and the Euro is the form of currency now being used. It was issues like these that the students felt were important in keeping the book updated.
When asked what this experience meant to the students, Davidian responded, "They're thrilled. To be published at the age of 18!" Davidian went on to note that it is exciting for her students this year to see that past students contributed to their textbook.
"The exciting part about working with this whole project was we were in it from the ground floor. When we first started using the materials they were page proofs on a looseleaf and it was the first draft and then we went through and every year had different materials," said Davidian. The teacher noted that it was not only an exciting experience for the students but for herself as well.
Dr. Herman Sirois, superintendent of the Levittown School District, said that he is very proud that Davidian and her students have been published and noted that the Harvard Consortium program has been so successful that it is now being used at Division Avenue High School as well. "The level of instruction and quality of instruction to produce these three children, the next layer of quality must be up there as well," said Sirois. "I think it's a reflection of what we're coming to expect from our district...I think it's nice for the kids and it's nice for the district too." |
IGCSE Mathematics for Edexcel Practice Book 2nd Edition
Trevor Johnson,Tony Clough
IGCSE Mathematics Practice for Edexcel, 2nd edition has been updated to ensure that this second edition fully supports Edexcel's International GCSE Specification A and the Edexcel Certificate in Mathematics. Containing a wealth of exam-style questions and written by experienced examiners, teachers and authors, this is the perfect resource for Higher Tier students both during their course and when they are revising for their exams.
IGCSE Mathematics Practice for Edexcel, 2nd edition can be used in conjunction with IGCSE Mathematics for Edexcel, 2nd edition and IGCSE Mathematics Teacher's Resource for Edexcel, or as a standalone resource.
This second edition has been revised to ensure it fully supports the requirements of Edexcel's International GCSE Specification A and the Edexcel Certificate in Mathematics.
Contains a wealth of exam style-questions covering every aspect of the specification to provide Higher Tier students with the support they need during the course and as they revise for their exams.
Can be used as a stand-alone resource or alongside IGCSE Mathematics for Edexcel, 2nd edition and IGCSE Mathematics Teacher's Resource for Edexcel, guaranteeing complete flexibility.
About the Author(s):
Trevor Johnson is currently a chief examiner for a leading awarding body. He is an experienced author and was formerly Head of Maths in a Staffordshire comprehensive school.
Tony Clough is currently a senior examiner for a leading awarding body. He was Head of Maths for 22 years and has written extensively for Key Stage 3, GCSE and A Level. |
Mathematics
To achieve the goal, the department develops and improves its curriculum integrating strengths of American, Japanese and other countries' curricula. In particular, American textbooks contain various types of basic practice problems, which help students build a solid foundation of each mathematical concept, while Japanese textbooks and problem solving books contain many problems requiring multiple steps for their solution, which help students develop ability to apply their knowledge to solve complex problems. Both American and Japanese textbooks are used. Indian textbooks are also used to take advantage of their clear and easy-to-understand presentation of proofs of theorems and formulas.
The curriculum is constructed taking the cognitive development of each student into account. In general, more abstract concepts are introduced at higher grade levels. At each grade level, students are placed in one of two to three levels that best fits their cognitive and mathematical development. The goal for each level is set so that students will feel that they can reach the goal if, but only if, they put effort into studying mathematics. Each grade level has the following goal:
9th Grade
In the 9th grade, all students are required to take the course "Algebra and Geometry." The goal of this course is to develop student competence to deal with mathematical expressions, the basic language of mathematics. In particular, the course is designed to develop students' fluency in algebraic manipulations with polynomials and irrational numbers and to develop the ability to construct geometric proofs. Students are placed in either an intermediate or an honors level class, based on the results of a placement test. The course includes the following topics: Equations, Inequalities, Exponents and Polynomials, Polynomials and Factoring, Systems of Equations, Radical Expressions and Equations, Relations and Functions, Quadratic Equations, Introduction to Probability and Statistics; Congruent Triangle, Applying Congruent Triangles, Quadrilaterals, Similarity, Circles, Polygons and Areas, Surface Area and Volume.
10th Grade
In the 10th grade, all students are required to take the course "Algebra and Trigonometry." The goal of this course is to continue developing student competence to deal with mathematical expressions. The course develops fluency in algebraic manipulations, especially with rational and radical expressions, and in solving quadratic equations. Students are placed in either an elementary, intermediate or honors level class based on the results of a placement test. The course includes the following topics: Equations and Inequalities, Systems of Equations and Problem Solving, Polynomials and Polynomial Equations, Equations of Second Degree, Rational Expressions and Equations, Polynomial Functions, Powers, Roots, and Complex Numbers, Quadratic Equations, Relations, Functions and Graphs, Quadratic Functions and Transformations, Exponential and Logarithmic Functions, Trigonometric Functions, Trigonometric Identities and Equations, Counting and Probability.
11th Grade
In the 11th grade, all students are required to take the course "Pre-calculus." The goal of this course is to develop student competence in logical and abstract thinking. Building on the competence developed in previous courses, 11th grade students fully utilize their ability to understand mathematically-expressed abstract concepts and to express their own ideas mathematically. This training logical and abstract thinking will be extremely valuable throughout their lives. Students are placed either in an elementary, intermediate, or honors level class, based on their Algebra and Trigonometry course grades. The course includes the following topics: Trigonometric Functions, Introduction to Three dimensional Geometry, Vector Algebra, Permutations and Combinations, Binomial Theorem, Probability, Straight Lines, Conic Sections, Matrices, Determinants, Sequence and Series, Mathematical Induction, Three Dimensional Geometry.
The mathematics core curriculum is structured on mathematical content areas. To develop students' problem solving ability of utilizing knowledge of various mathematical content areas, 11th graders can elect "Advanced Problem Solving" course. Although the course mainly focuses on mathematical problems, it may include real world social, economical, and environmental problems as well. For students to qualify for the course, they must (1) be in an honor level Algebra and Trigonometry class at the end of the 10th grade and (2) participate in the American Mathematics Competition (AMC-10) during the 10th grade. The course includes the topics as follows: Combinatorics, Complex Numbers, Inversion in Plane, Mathematical Induction, Proofs by Contradiction, Sequence/Series, Basic Probability, Law of Sine/Cosine, Basic Mod Computation, Basic Functions and Graphs, Basic Geometry, Checking the Validity of the Answer, Working Backward, Work with Algebra and Geometry on a Same Problem, Analogy (Find Similar Problem), and Use of Symmetry.
12th Grade
In the 12th grade, all students are required to study calculus, and students who wish to major in science, mathematics, medicine, pharmacy, or engineering at college are required to study linear algebra as well. Students who wish to major in economics and commerce in college are strongly encouraged to take linear algebra. Other students may take linear algebra as an elective course. The goal of these courses is to introduce 12th graders directly to their study of mathematics at Keio University and other colleges in Japan and the United States.
"Calculus for Non-Science Majors" course includes the following topics and students will be placed either in an elementary or intermediate level class by grades of Pre-Calculus: Limits of Functions, Derivatives (The Chain Rule, Implicit Differentiation, Parametric Representation, Differentiation of Exponential and Logarithmic Functions, Higher Derivatives), Applications of Differentiation (Maxima and Minima, Inflexion Points, Graph Sketching), Indefinite Integrals (Method of Substitution, Integration by Parts, Partial Fractions), Definite Integrals and Applications (Areas and Volumes).
"Advanced Calculus & Linear Algebra for Science Majors" course is a requirement for students applying to faculty of science and technology, faculty of medicine and faculty of Pharmacy. The calculus part in this course deals with single variable calculus and includes the following topics: Limit of Functions, Continuity, Differentiation, Sketching a Graph, Integration including Integration by Parts and Integration by Substitution, Surface area, Volume, Polar Coordinates, Differential Equations and Infinite Sequences and Series. Linear algebra part in this course includes the following topics: Basic Notions of Vector Spaces, Systems of Linear Equations, Determinants, Eigenvalues and Eigenvectors, Inner Product Spaces up to Orthogonal Projection and Gram-Schmidt Orthogonalization. The calculus part will be taught in the first three quarters of the school year and the linear algebra part will be taught in the forth quarter. This is a very demanding fast paced course and all the students enrolled in the course are expected to devote a lot of time and effort to study outside of class by reading textbooks and solving problems in the textbooks |
Math
The College Prep math curriculum focuses on building a strong conceptual base that helps students to become flexible thinkers, able to apply the mathematics they have learned to a rapidly changing world.
Math teachers have designed materials for incremental learning and to address a variety of learning styles, including visual, auditory, and kinesthetic. Students learn concepts and skills by solving carefully sequenced problems; in class, students often work in cooperative groups. Teachers coordinate courses and review frequently so students retain important ideas from year to year. Instead of separate courses in algebra, geometry, and trigonometry, all three areas are addressed in each course of an integrated curriculum. Course materials introduce applications to science and other related fields and provide historical context.
Calculators and computers are important tools of modern mathematics. Teachers instruct students in their appropriate use, but also require a firm grasp of basic skills. Students are required to solve many problems without using calculators. The Math Department uses placement examinations, recommendations, and interviews to ensure that each student enrolls in the most suitable course sequence. Almost all students take four years of mathematics, even though only three are required. Math Club meets regularly to share ideas and investigate problems beyond the scope of the normal curriculum. All interested students are welcome to participate. The club also provides opportunities for students to take part in local and national mathematics competitions.
Math I
Concepts and applications of algebra, problem solving, and geometry are the main topics in this course, designed to prepare students with diverse mathematical backgrounds for Math II. Students learn how to use the scientific calculator to solve problems and use manipulatives extensively to develop spatial visualization skills. They often work together in small groups in the classroom, developing their collaborative skills and their ability to explain mathematics clearly. Students review and practice algebra skills in a wide variety of situations. Topics include proportional reasoning, geometric similarity and transformations, area and perimeter, linear and quadratic equations, and introductory statistics and probability. This course is coordinated with Integrated Laboratory Science.
Math II
This course covers topics from geometry and algebra. The curriculum encourages connections among topics by continually interweaving them. Emphasis is placed on the development of geometric intuition, deductive logic, proof, and a strong foundation in algebra. Group work is encouraged; activities are done in groups, sometimes with physical models and or computers. Class discussions and group activities enrich the learning experience by developing problem-solving and communication skills.
Math III/IIIA
The concept of function serves as a framework for this course. Mathematical modeling (deriving a mathematical expression from real-world data) is introduced, and students do experiments and use graphing calculators to gather information. Students purchase a course-specific graphing calculator and are instructed in its use. Algebraic skills are practiced within the context of solving problems, and geometric interpretations and graphing are emphasized. Students continue the study of linear and quadratic equations begun in Math I and Math II, adding new functions to their repertoire: polynomials, trigonometric functions, exponentials, and logarithms. This course is offered at two levels: Math IlIA and Math III. Both are college preparatory and cover functions and applications. Math IIIA is accelerated, covering topics usually included in algebra honors, trigonometry and precalculus. It prepares students for Level IIC of the College Board SAT Subject Test in Mathematics. Math III covers topics normally taught in advanced algebra and trigonometry.
Math Analysis & Intro Calculus
This course begins with material from pre-calculus, including a study of functions (polynomial, exponential, logarithmic and trigonometric) and their graphs. It continues with topics in analytic geometry, linear algebra, vectors and discrete mathematics. The course introduces topics from calculus, such as limits, continuity and derivatives and their applications. Students learn the material through lecture, group work, and homework.
Applied Math
This
course explores topics across a broad spectrum, including pre-calculus,
calculus, economics, finance, and statistics. The emphasis will be on
applications of mathematics to a variety of fields. In the first semester, we
will introduce some of the ideas of set theory, statistics (linear regression
models), economics (supply, demand) and finance (including simple and compound
interest). Second semester, we will continue with more finance (annuities and
loan amortization), probability, single variable statistics (normal curve
distributions) and calculus (limits, rates of change, derivatives, and
integrals). The goal is to expose students to a variety of techniques and
applications that will be useful in diverse academic pursuits as well as life
in general.
Math V: AP Calculus
This two-semester course covers differential and integral calculus at the college level. There are two versions. Math VAB is the basic course, covering techniques and applications of derivatives and integrals. It prepares students for the "AB" Advanced Placement Examination. Designed for the strongest math students, Math VBC covers the same material, as well as topics like infinite series and multivariable calculus and prepares students for the "BC" Advanced Placement Examination. The department advises students on which course to take based on their previous math work at College Prep. VBC is not recommended for students receiving lower than an A- in Math Analysis and Introduction to Calculus.
AP Statistics
How accurate are opinion polls? Where is the economy really heading? Can you believe the latest "study" about health and diet? The media appear to give definitive answers to questions like these, without examining how strong or weak the evidence really is. In Statistics, we look at how data are gathered and presented, and how certain the conclusions drawn from them are likely to be. This means using standard formulas, but we will also look at the math behind the formulas, including probability and its applications. There are lab exercises (sometimes with edible "equipment") and mini-projects in which students design and carry out original investigations. There are also informal discussions of items in the news. This two-semester course is equivalent to a semester of statistics in college and prepares students for the AP exam. It may be taken after or at the same time as Applied Math, or Math Analysis and Introductory Calculus.
The Art of Problem Solving
High
school math includes many beautiful topics, but there is so much more math that
is accessible to bright and curious high school students like you that we don't
include in our curriculum. There just isn't time to do it all. For those of you
hungry for more math, The Art of Problem Solving is for you. It is a
one-semester math elective which will cover topics in arithmetic, number
theory, and counting and probability, as well as some algebra and geometry that
isn't already covered in Math I, II, or III/IIIA. Students must have completed
Math III/IIIA or equivalent to enroll. You don't have to like math contests to
take this course, but if you do like them, this course might help you improve
your scores. However, the best reason to take this course is that you will
learn new math, and equally importantly, it will be interesting and fun.
Course Spotlight
AP Statistics
How accurate are opinion polls?
Where is the economy really heading?
Can you believe the latest "study" about health and diet?
The media appear to give definitive answers to questions like these, without examining how strong or weak the evidence really is. In Statistics, we look at how data are gathered and presented, and how
certain the conclusions drawn from them are likely to be. This means
using standard formulas, but we also look at the math behind the
formulas, including probability and its applications. |
An Introduction to Optimization, 2nd Edition
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business |
Author: Delbert L. Hall Email: [email protected] Publisher: Spring Knoll Press Trim Size: 8.5" x 11" Pages: 146 ISBN: 0615747795 ISBN-13: 978-0615747798 Price: $19.95 Tentative Date of Release: March 1, 2013 Description: The job of
an entertainment rigger is to safely suspend objects (scenery, lights,
sound equipment, platforms, and even performers) at very specific
locations above the ground. The type, size and location of the
structural members from which these objects must be suspended vary
greatly from venue to venue. Additionally, the size, weight, and
location of each object varies from object to object. To ensure that
each object is safely suspended at the proper location, math is
essential. If you want to be a top-notch rigger, you have to know
math. Math does not have to be hard. It is a lot like baking - you
need a good recipe, and then you just have to follow it - EXACTLY. The
purpose of this book is to provide you with the recipe for solving
rigging problems. Once you learn the recipes, you will be able figure
out many rigging problems. This book is more than a list of formulas -
it will also help users grasp some of the principles behind the physics
of rigging. By understanding these principles and the math behind
them, entertainment riggers should be able to look at many rigging
situations and determine if it is "obviously safe," or "obviously
unsafe," without actually doing any math. However, there are many
cases where the load is just uncertain, or the answer is not obvious, and
the math needs to be done. This book may be of particular interest to
individuals who wish to become a certified rigger. Many of the
mathematical problems and other information presented in this book are
intended to prepare individual for the types of questions they might
encounter on a certification exam – in both theatre and arena rigging.
Table of Contents Part I. Conversions Lesson 1: Converting between Imperial and Metric
Part IV. Truss Lesson 10: Center of Gravity for Two Loads on a Beam Lesson 11: Uniformly Distributed Loads on a Beam Lesson 12: Dead-hang Tension on One End of a Truss Lesson 13: Simple Load on a Beam Lesson 14: Distributed Load on a Beam Lesson 15: Cantilevered Load on a Beam Lesson 16: Chain Hoists, and Truss, and Lights, Oh My! |
This new edition of a classic American Tech textbook presents
basic mathematic concepts typically applied in the industrial,
business, construction and craft trades. By combining
comprehensive text with
illustrated examples of mathematics problems, this book
offers easy-to-understand instructions for solving math-based
problems encountered on the job. Many different trade areas are
represented throughout the book.
Each of the twelve chapters contains an Introduction providing an
overview of the chapter content. Examples of specific mathematic
problems are displayed in illustrated, step-by-step formats.
Following visual as well as written processes provides the reader
with a sequenced opportunity to learn each concept. Learned
knowledge is then applied in Practice Problems, which immediately
follow Examples in the book. Students are encouraged to use the
space provided in the margins to answer these questions.
Tips located throughout the text assist in the development of
mathematics skills.
Calculator tips are also provided in each chapter to offer an
alternative method of solving problems and equations. Points
to Know are included to enhance the learner's understanding of how
mathematics principles are applied to the trade professions.
Additionally, photographs provide visual examples of how these
principles relate to on-the-job skills.
Practical Math is designed to be a basis for a mathematics course
or as a supplement to many other American Tech books and training
products. |
The Mathematics Survival Kit
The Mathematics Survival Kit
Professor Jack Weiner taught at the University of Guelph from 1974 to 1976. He spent the next five years at Parkside High School in Dundas, Ontario. In 1982, he was re-recruited by Guelph and has been happily teaching and writing there ever since. He has won both the University of Guelph Professorial Teaching Award and the prestigious Ontario Conderation of University Faculty Associations Teaching Award. He has been listed as ...
How to get an 'A' in Math!
1) After class, DON'T do your homework! Instead, read over your class notes. When you come to an example done in class...
2) DON'T read the example. Copy out the question, set your notes aside, and do the question yourself. Maybe you will get stuck. Even if you thought you understood the example completely when the teacher went over it in class, you may get stuck.
And this is GOOD NEWS! Now, you know what you don't know. So, consult your notes, look in the text, see your teacher/professor. Do whatever is necessary to figure out the steps in the example that troubled you.
From the Best of Our Knowledge
ALBANY, NY (2007-11-12) THE MATHEMATICS SURVIVAL KIT ,
Pt. 1 of 2 -
If you listen to public radio on the weekends, you have likely heard a university math professor who is also the Math Guy. But if your tastes run more to television, you may have also seen the Friday night CBS show, Numbers, in which a curious young math wiz named Charlie, solves crimes using mathematics. Regardless of your viewing or listening habits, it's apparent more emphasis is being placed on math.
Now, comes The Mathematics Survival Kit. It's written by Professor Jack Weiner from the University of Guelph in Ontario, Canada. Weiner has partnered with education software provider, Maple, to produce an interactive e-book version of his math survival book. The University of Guelph has taken the lead introducing e-books , intelligent assessment systems, and podcasts nto its math curriculum. This next generation of educational technology provides teachers with ore time to motivate students and improve their comprehensive retention. |
Apologia Science
The quality of mathematics is extremely important to me, as math and science go hand-in-hand. There are many students who cannot handle my chemistry course, for example, because they have not had a good algebra course. That is why I strongly encourage you to look at Videotext Interactive's algebra course. It is, truly, the best that I have seen.
The course teaches real mathematics. It does not use tricks or shortcuts. Instead, it teaches the student to think mathematically. That's what is missing from many algebra courses! The use of animation and graphics is excellent. They do not detract from the learning, as is the case with some video courses I have seen. Instead, they enhance the student's ability to understand what is happening in each and every step along the way.
If you want your student to really learn algebra, then you should use this course. In short, this course is a scientist's dream come true! Every science-oriented student should use it |
This updated manual opens with an overview of the SAT Math Level 1 test, followed by a section covering the most important tactics for succeeding on the test. Separate chapters review basic arithmetic, fractions and decimals, ratios and proportions, basic algebra, plane geometry, solid and coordinate geometry trigonometry, functions, statistics, and miscellaneous math topics. Three full-length model tests are presented with complete solutions for every problem. |
Mathematics education; history of mathematics; pure mathematics (general, year 12 mathematics students performance, interface between school and university, history of mathematics, finite group theory |
Math 9 is the first step in preparing students for the study of calculus by providing important skills in algebraic manipulation and interpretation at the college level. Topics will include a review of basic algebraic concepts; lines; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions, identities, inverse functions and equations; applications of trigonometry; systems of equations and matrices; conic sections; sequences, series and combinatorics. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous.
Math 10 prepares students for the study of calculus by providing important critical thinking and problem solving skills. The central theme of the course is the analysis of mathematical functions as models of change. Families of functions - linear, exponential, logarithmic, power, periodic, polynomial, rational - will be introduced, compared and contrasted. Course content will include an introduction to functions and functional notation; transformation of functions; composite, inverse and combinations of functions; vectors and polar coordinates; series; parametric equations; complex numbers. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous.
Prerequisite:
Mathematics 9 and proficiency with the TI-83 graphing calculator as gained from, for instance, Math 2098154
LEC
SS110
DACHKOVA E
13.50
3.0
DAILY
0900A-1145A
GIL
06/17/02 - 07/12/02
MATH 12
Mathematics for Elementary Teachers
This course is intended for students preparing for a career in elementary school teaching. Emphasis will be on the structure of the real number system, numeration systems, elementary number theory, and problem solving techniques. Technology will be integrated throughout the course.
Prerequisite:
Mathematics 208, or successful completion of a high school geometry course and Mathematics 233.
Operations with signed numbers, evaluation of expression containing numbers and letters, simplifying algebraic expressions, equations, word problems, exponents, polynomials, factoring and special products, fractions, graphing, systems of equations, radicals, and quadratic equations. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205B or 206 with a grade of "C" or better. This course may be taken for Mathematics 205B credit (2.5 units) by those students who have successfully completed Mathematics 205A with a grade of "C" or better.
Advisory:
Mathematics 402 or assessment test recommendation.
Transferable:
No
Sect#
Type
Room
Instructor
Hours
Units
Days
Time Start-End
Footnotes
Campus
Date Start-End
8103
LEC
CH109
KING K
15.00
5.0
DAILY
1030A-0120P
GIL
Full term
9027
LEC
SS206
STAFF
15.00
5.0
MTuWTh
0600P-0920P
GIL
Full term
MATH 208
Survey of Practical Geometry
A survey of practical geometry with an emphasis on applications to other disciplines and everyday life. Parallel lines, triangles, circles, polygons, three dimensional figures, vectors, and right triangle trigonometry will be covered. There will be a weekly lab. |
Past Course Descriptions
Course Listings - Spring 2008
This is an introduction to mathematics at the beginning college level. MATH 112 will explore topics in contemporary mathematics with a problem-solving approach.
The class meetings will include lectures, problem-solving sessions, and group work. The final grade will be based on quizzes, exams, a project, and/or a comprehensive final. This course is not intended to prepare students for further courses in mathematics. Mathematical-reasoning intensive.
Study of number systems, number theory, patterns, functions, measurement, algebra, logic, probability, and statistics with a special emphasis on the processes of mathematics: problem solving, reasoning, communicating mathematically, and making connections within mathematics and between mathematics and other areas. Open only to students intending to major in education. Every year. Mathematical-reasoning intensive.
Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry. Includes computer programming experiences using Geometer=s Sketchpad. Every year. Mathematical-reasoning intensive.
This is a standard pre calculus
(4 credits)
Andrews, Douglas
Prerequisites: Math Placement Level 23 or higher
A study of statistics as the science of using data to glean insight into real-world problems. Includes graphical and numerical
1 201 Calculus I
(4 credits)
Parker, Adam and Alan Stickney
Prerequisite: MATH 120 or Math Placement Level 25
or minoring in mathematics, computer science, physics, or chemistry. MATH 201 and MATH 202 can also count as Asupporting science@ AEssentials of Calculus@. Talk with your advisor or with any math professor for advice on which calculus course is most appropriate for youDepending on the instructor, the
(4 credits)
Higgins, William and Parker, Adam
Prerequisite: MATH 201
This is the second course in Wittenberg=s three semester calculus sequence. MATH 202 is primarily concerned with integration and power series representations of functions. Topics covered include indefinite and definite integrals, the Fundamental Theorem of Calculus, integration techniques, elementary differential equations, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor=s Series
The final grade in the course will be based on homework, quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.
MATH 210 Fundamentals of Analysis
(4 credits)
Higgins, William
Prerequisite: MATH 202
Functions, set theory, sequences, the topology of the real line, and methods of mathematical proof. Particular emphasis is given to careful, accurate definition and proof of mathematical concepts. Grades may be based on several tests, quizzes, homework assignments, and a final examination. WRITING INTENSIVE. Mathematical-reasoning intensive.
MATH 212 Multivariable Calculus
(4 credits)
Stickney, Alan
Prerequisite: MATH 202
This course completes the basic calculus sequence. It covers the calculus of functions of several variables and associated analytic geometry. Students are required to have a TI-83, TI-84, or TI-86 graphing calculator for use in class, for homework assignments, and for tests. The final grade in the course is based on quizzes, tests, and a comprehensive final exam. Mathematical-reasoning intensive.
Computational science is the field of study that integrates science, computer science, and applied mathematics. This course is an introduction to the principles and approaches of computational science. This includes the understanding, development, and use of mathematical models as well as their effective computer implementation using computer languages such as Mathematica®. This course is specifically designed to be accessible to a wide range of students, especially those with an interest in applications of biology, chemistry, geology, physics, or economics.
A spectrum of problems taken from these areas will be addressed. Topics include: Using Mathematica®, The Scientific Process, The Experimental Method, Types of Science Models (for Evaluation, Simulation, and Optimization), Sources of Errors, Dimensional Analysis, Model Sensitivity, Solving Equations, Computer Arithmetic vs. Exact Arithmetic, Limits of Computation, Data Fitting, Visualization Methods, and Ethical Issues. Applications of computational science in our everyday lives will be investigated. A weekly two hour and ten minute computer laboratory is required. The student will be expected to be familiar with the use of a scientific graphing calculator. This course is cross-listed as MATH 260. Students may enroll in either COMP 260 or MATH 260, but not both. Mathematical-reasoning intensive.
the course will cover relations and functions, counting arguments, discrete probability, number theory and graph theory. The course is required for the major and minor in computer science and can be used as an elective for the mathematics major. The course grade will be determined by quizzes, graded homework assignments, in-class tests and a comprehensive final.
MATH 337 Statistical Design
(4 credits)
Andrews, Douglas
Prerequisite: MATH 227
Whereas the introductory statistics sequence focuses primarily on exploratory and formal analysis of data that have already been observed, this course focuses primarily on how to design the comparative observational and experimental studies in which data is collected for formal analysis. Students will learn: 1) to choose sound and suitable design structures, 2) to recognize the structure of any balanced design built from crossing and nesting, 3) to assess how well standard analysis assumptions fit the given data and to choose a suitable remedy or alternative when appropriate, 4) to decompose any balanced dataset into components corresponding to the factors of a design, 5) to construct appropriate interval estimates and significance tests from such data, and 6) to interpret patterns and formal inferences in relation to the relevant applied context. Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing. Students who have taken a different introductory statistics course may be admitted with permission of instructor. Mathematical-reasoning intensive.
MATH 365 Abstract Algebra
(4 credits)
Stickney, Alan
Prerequisite: MATH 205 and MATH 210
This course will focus on abstract algebraic structures such as groups, rings, and fields with particular attention to groups. There will be an emphasis on presenting arguments with a full explanation of the reasoning. Grades will be based on written homework, work done in class, and exams. WRITING INTENSIVE. Mathematical-reasoning intensive.
MATH 380 Computational Algebraic Geometry
(4 credits)
Parker, Adam
Prerequisite: MATH 205
Algebraic geometry is the study of systems of polynomial equations in one or more variables. The solution to such a system is a geometric object called a variety and much of algebraic geometry is concerned with how algebraic properties of the system are related to geometric properties of the variety. Results in this field tend to be quite abstract and complexity increases rapidly, making examples hard to compute.
This changed in the mid 1960's with the discovery of a generalized division algorithm called Buchberger's algorithm. With this new computational tool, it became possible to manipulate systems of polynomials efficiently. As a result, algebraic geometry has become accessible to a wider audience of both students and researchers.
This course will concentrate on the algorithmic and computational aspects of algebraic geometry. Topics covered will include, but not be limited to Hilbert Basis Theorem, the Nullstellensatz, resultants, and Buchberger's algorithm. The final course grade will be based on homework, tests, class participation, and a computer project. Mathematical-reasoning intensive. |
Seek to increase basic knowledge without necessarily considering its practical use
Many pure/theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research.
Applied
Use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences.
Start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables.
Use computers to analyze relationships among the variables and solve complex problems by developing models with alternative solutions. |
This module introduces you to the wide range of mathematical skills that are necessary for studying engineering at degree level. You learn the fundamentals of algebra, trigonometry, and basic statistics, and you are provided with an introduction to vectors, matrices, complex numbers, and differential and integral calculus. |
Code: EISMTI9
Introduction of Entrancei Foundation
"Remember that effective time management makes you more rather than less flexible. It allows you to do the things that you really want to do rather than the things you really have to do" entrancei foundation is the ideal program for students who wish to start early in their quest for a seat at the IITs. This program helps the student not only to excel in IIT-JEE but also in Olympiads & KVPY by building a strong foundation, enhance their IQ & analytical ability and develop parallel thinking processes from a very early stage in their academic career. Entrancei foundation study material will have more time to clear their fundamentals and practice extensively for IIT-JEE, their ultimate goal!
Serious students aspiring for success with a good rank in the IITs understand the importance of starting early in their preparation for IIT-JEE. As the JEE becomes more competitive now, it is necessary to build a strong fundamentals base, as early as possible.
Entire course will be cover two subject mathematics and science. In science the study material covers all three subjects' physics, chemistry and biology.
Single comprehensive study material. Additional problems will be supplemented wherever necessary students should not require any additional books etc.
Work Books for Home Assignment.
Chapter Practice Problems On each chapter students will be given practice problems which they have to done by the student before the beginning of the next chapter. Thus helping every student to have a very strong command over fundamental concept knowledge very crucial for getting Top ranks.
This study material will lay strong foundation for NTSE, IITJEE,AIEEE and school syllabus.
Single comprehensive study material. Additional problems will be supplemented wherever necessary students should not require any additional books etc.
Gives you more time to adapt to the quantum jump in level of difficulty with better ease as there is more time for understanding and consolidation over a longer spread academic plan.
Optimum utilization of time available.
Early starters will always have more time before the actual Board & Engineering Entrance / Other Competitive Exams as their course curriculum will finish much before the batches starting later.
More time to consolidate on one's performance and for self revision, polishing of examination temperament & removal of last moment doubts. This is very vital to help a student achieve a quantum jump in the His / Her Rank.
Subject Details in Entrancei Foundation Study Material
Name of the chapters covers in Entrancei Foundation in Mathematics:
Limit
Logarithm
Real number
Surds
Analytical geometry
Three dimensional geometry
Polynomial
Quadric equation
Sets
Permutation
Function
Matrices
Trigonometry
Numbers
Name of the Chapters covers in Entrancei Foundation in Physics :
Physic basics
Measurement ,unit and dimension
Mathematics for physics
Vector
Kinematics
Newton law of motion
Friction
Circular motion
Work, power and energy
Centre of mass
Conversion of linear motion
Impulse
Collinions
Name of the Chapters covers in Entrancei Foundation in Chemistry :
Chemistry Basics
Atomic Structure
Gaseous State
Stochiometry
Rate Of Chemical Reaction
Chemical Reaction
Chemical Equilibrium
Acid And Base
Solution
Periodic Classification
Compound Of Nitrogen
Compound Of Phosphorus
Language Of Chemistry
Behavior Of Gases
Atom And Molecule
Name of the Chapters covers in Entrancei Foundation in Biology :
Living Organisms Show Organisation
Cell - The Structural And Functional Unit
Non Renewable And Alternate Resources
Organisms, Habitat And Ecological Balance
Biosphere
Pollution
How to buy this Study Material :
Entrancei Junior for Class 9: Consists of 8 workbooks of mathematics and science
Price: 2399 /-Offer Price: 1690/
(Additional 150 Rs will be charged for courier)
For biology additional 360 Rs will be charge so the fee for all subjects will be 1690+360=2050 biology study material is not compulsory.
Price: 2799 /-Offer Price: 2050/
To purchase Entrancei Study Material fill this form and instructions will send on your mail id. |
MATH 71 - Intermediate Algebra
(5 units)
This course reviews and extends concepts from elementary algebra, and introduces new
content to prepare students for a variety of subsequent mathematics courses. Polynomial,
rational, radical, exponential and logarithmic expressions are simplified, equations solved
and functions graphed and studied; linear and nonlinear systems of equations and
inequalities; conic sections; sequence, series and the binomial theorem. Application
problems appear throughout the course.
Course Measurable Objectives:
Solve linear equations and inequalities in one variable, including applications. Solve absolute value equations and inequalities. Find and interpret the slope of a line. Find the equation of a line given information about the line. Solve systems of linear equations in two and three variables. Analyze and solve applications.
Solve quadratics by the square root principle, completing the square, and the quadratic formula; apply these techniques to other types of equations and to applications.
Define a function and find the domain and range; find the inverse of a function. Perform operations with linear, quadratic, logarithmic and exponential functions; graph and solve applications of these functions. Identify and graph the conic sections. Solve nonlinear systems of equations. |
Billerica Precalculus numerous tools and facts that you need to understand and then you build on them throughout the year. At the end of this course, a student should be able to make and critique logical arguments and calculate missing parts of a geometric diagram. Pre-calculus is the study of function families and their behavior |
Activities Manual for Beginning and Intermediate Algebra, 2nd Edition
ISBN10: 0-534-99873-9
ISBN13: 978-0-534-99873-8
AUTHORS: Garrison/Jones/Rhodes
Don't go to class without it! ACTIVITIES MANUAL FOR BEGINNING AND INTERMEDIATE ALGEBRA provides you with activities and exercises that will help you succeed in math. Activities clarify algebra concepts, help you draw the correct conclusions, and include real world data to help you see the relevance of what you are learning to your own life |
Mathematics for Plumbers and Pipe Fitters
Mathematics for Plumbers and Pipe Fitters
Mathematics for Plumbers and Pipefitters
Mathematics for Plumbers and Pipefitters
Summary
Fully updated for optimal learning, Mathematics for Plumbers and Pipefitters, 7E remains a trusted resource for essential math concepts in the plumbing and pipefitting trades. With an emphasis on real-world examples that will prepare readers to successfully transfer their knowledge to on-the-job situations, this book utilizes the most currently used fitting materials to demonstrate key concepts. Simplified, clear explanations and a straightforward approach, combined with new units on changes of state, pressure and heat, and mechanical advantage, make this an ideal tool for anyone entering the field. |
Applied mathematics (minor subject)
An applied mathematician works with solving problems which lie beyond the realm of regular mathematics, and therefore Applied mathematics is the programme for you if you want to work with mathematics and still keep in mind how mathematics can be of use in your future career.
Applied mathematics is not a particular branch of mathematics, but rather a way of working with mathematics. In the Applied mathematics programme, you will learn to create models of and solve problems from the practical world by utilising advanced mathematical tools.
The Applied mathematics programme gives you the opportunity to solve complex problems and to create new insight and recognition. Applied mathematics is for you if you want to learn to utilise advanced mathematical tools and computers to model, analyse and solve complex problems in the business sector or in research. An applied mathematician masters and is able to further develop the mathematical tools which have contributed to the development of the modern society of information. |
**Tests will be given at the end of each chapter. Quizzes will be given as needed.
**Homework will be assigned every day. Students are expected to complete all homework in the assigned time frame.
Major Topics To Be Covered
Linear Equations/Inequalities
Functions
Systems of Equations
Exponents
Operations on Polynomials (including factoring)
Quadratic Equations
Classroom Expectations
Respect yourself and others – this includes the classroom environment
Always try hard and do your best
Be in your seat and ready to learn when the bell rings.
Follow all school rules
NO CELL PHONES!!!
Discipline
Most discipline issues will be handled in class according to following list, but occasionally student behavior will warrant removal from class. Parents may be contacted anywhere along the process.
In-class correction
Time in hallway to complete behavior contract
Out of class detention
Office referral
Homework
Most homework is worth 5 points and can be obtained by doing the following:
1. Heading: Put your name, period and date.
2. Copy problems when possible.
3. Show your work/explanation.
4. Done in PENCIL.
5. Complete and on time.
5/5 points = 100 % = A 4/5 points = 80% = B-
3/5 points = 60% = D- 2/5 points = 40% = F
1/5 points = 20 % = F
There will be assignments graded by performance - the number of problems you have missed. These assignments can be redone for a better grade.
Late Work: Late work with nice effort is worth 70%. Late work must be turned in within 1 week after chapter test, otherwise assignment will remain a zero.
Help!!! You can come in before or after school or during lunch. I am usually here at 7 a.m. and stay after until 4 – 4:30 p.m. It really doesn't hurt!!
My Responsibility As Your Teacher Is To
Treat you with respect and care as an individual.
Provide you an orderly classroom environment.
Provide the necessary discipline.
Provide you the appropriate motivation.
Teach you the required content.
BINDER TABS: The student should have a math section in their big binder for Miller. The following tabs are required in their math section:
(Tab A) Notes/Vocabulary
(Tab B) Homework
(Tab C) Assessments (Tests and Quizzes)
Weekly e-mails/Carle's webpage
Shortly after the school year starts, I like to send weekly e-mails out to parents and students. This e-mail gives classroom information about the week and sometimes for the school, and I attach the homework schedule for the week. If you would like to be on this list, please include your e-mail below. You can also find the week's schedule, last week's schedule, grades, weekly e-mail message and more at my webpage on the Aberdeen's Website at HYPERLINK " You must go to Miller Jr. High School, staff, and then Laura Carle.
Please sign and return the form at the bottom with your child. This is their first assignment, so please sign and return ASAP for points. (This paper will be handed back.) If you have any questions or concerns send a note, call at 538-2100, or visit me at the school from 7:00-7:50 a.m. or 2:40-4:00 p.m. |
This talk will describe developments in Mathletics, a freely-available computer-aided assessment (CAA) system that exploits the open code facilities of Question Mark Perception by using random parameters with all question components, including equations written in MathML and diagrams written in SVG. Thus each of the existing 1700 question styles realises to thousands or even millions of questions for the students, each with rather full feedback that seeks to alert the student to where they have gone wrong by recognising common mistakes or mal-rules.
Pedagogic issues such as choice of question type and "reverse engineering" to keep control of arithmetic/algebraic difficulty will be discussed. The technology, and much of the pedagogy, is exportable to other disciplines where quantitative methods are taught. |
chapter we looked at first order
differential equations. In this chapter
we will move on to second order differential equations. Just as we did in the last chapter we will
look at some special cases of second order differential equations that we can
solve. Unlike the previous chapter
however, we are going to have to be even more restrictive as to the kinds of
differential equations that we'll look at.
This will be required in order for us to actually be able to solve them.
Here is a list of topics that will be covered in this
chapter.
Basic Concepts Some of the basic concepts and ideas that are
involved in solving second order differential equations.
Mechanical Vibrations An application of second order differential
equations. This section focuses on
mechanical vibrations, yet a simple change of notation can move this into
almost any other engineering field. |
introduces the concept of algebraic thinking, offering a framework for the use of classroom questions to foster the development of algebraic thinking in students from grades six through ten; presents accounts, from teacher's and learner's perspectives, of why the issue is important; and includes a set of related mathematics activities. |
Introduction to junior/senior-level courses in Advanced Calculus, Analysis I, Real Analysis taken by math majors. The first semester is usually a general requirement; the second semester is often an option for the more motivated students. Designed to challenge advanced students while bringing weaker students up to speed, this text is an advantageous alternative to most other analysis texts which either tend to be too easy (designed for an Intermediate Analysis course) or too difficult (designed for students headed for a Ph.D. in Pure Math... MOREematics)both of which usually tend to slight multidimensional material. Hailed for its readability, practicality, and flexibility, this text presents the Fundamental Theorems from a very practical point of view. Introduction to Analysis starts slowly and carefully, with a focused presentation of the material; saves extreme abstraction for the second semester; provides optional enrichment sections; includes many routine exercises and examples; and liberally supports (with examples and hints) what little theory is developed in the exercises. Offering readability, practicality and flexibility, Wade presents Fundamental Theorems from a practical viewpoint. Introduces central ideas of analysis in a one-dimensional setting, then covers multidimensional theory. Offers separate coverage of topology and analysis. Numbers theorems, definitions and remarks consecutively. Uniform writing style and notation. Practical focus on analysis. For those interested in learning more about analysis. |
%amstex
\documentstyle{amsppt}
\magnification=\magstephalf
\TagsOnRight
\NoRunningHeads
\document
\hfuzz=20pt
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\parskip.25truein
\topmatter
\title {COMPUTER TECHNOLOGY AND PROBLEM SOLVING}
\endtitle
\author {Ken S. Li, Steve Ligh and Randall G. Willis}\endauthor
\affil Southeastern Louisiana University\\
Department of Mathematics\\
Hammond, LA 70402 \endaffil
\endtopmatter
\document
\subhead{1.\quad Introduction}\endsubhead
The advancement of technology during the past $10$ years has greatly affected
how we teach, what we teach and how our students learn in our undergraduate
courses. Computer technology is greatly influencing the way we do mathematics
and the problems which are accessable to our students. Before the introduction
of Mathematica, Maple and other computer algebra systems, algebraic manipulation
discouraged many students from studying mathematics and it is this reason that
makes students think that mathematics is the most difficult subject. This
dillusion keeps students from appreciating mathematics as a subject full of
power and ideas and that it requires a lot of critical and logical thinking.
By using computer algebra systems like Mathematica, Maple and Derive we can
spend less time on doing algebraic manipulation, routine problem solving
and sketching useless graphs, and spend more time on understanding concepts,
and applying them to solve more realistic and challenging problems. The
numerical and graphical capabilities of these software make students see what
they could never before even imagine. These powerful capabilities can also
help students make discoveries with our careful guidance. Many things which
could not be done before now can be done easily with the help of computers.
Many numerical methods which were very difficult to implement on a computer
can now be done in meaningful and simple way with the help of computer
algebra systems. With training in the use of computer technology in their
mathematics classes, students are more capable of applying mathematics in
their major fields and in the business world. Certainly the classroom
experience will be more relevant to the "real world". In this paper we will
use two types of problems that we can give to our calculus students to
illustrate the computer can be used to aid in the solution of mathematics
problems, how they will enhance students' understanding of calculus and
improve their problem solving skills, why computer technology alone can not
solve the problems and why mathematics reasoning is still of vital importance.
\subhead{2.\quad Tangent line problem}\endsubhead
A typical problem given to students in the first semester of calculus is
"Find an equation of the line tangent to the graph of $f(x)=x^2$ at the point
$(2,f(2))$". With the advent pf computer algebra systems and their excellent
graphics capabilities, a new type of tangent line problem is accessable to
students taking calculus. We will begin by stating the problem in general, and
then work out a specific example. The problem can be stated as follows: "Let
$f(x)$ be a differentiable function. Under what conditions does there exist a
differentiable function $g(x)$ such that the lines tangent to the
graph of $y=g(x)$ are of the form $y=ax+f(a)$ for all $a$ in the domain of
$f$? If $g(x)$ exists, then find an expression for it in terms of $f(x)$". A
complete discussion of this problem can be found in [1] and [2].
\noindent \bf{Example:} \rm Let $f(x)=x^2$. Is there a differentiable function $g(x)$ whose
tangent lines are of the form $y=ax+a^2$ for all $a\in R$? If so, what is
$g(x)$?
\noindent \bf{Solution:} \rm We begin by using a computer algebra system to sketch lines
of the form $y=ax+a^2$. The graphs of these lines can be generated by the
programs listed below.
\medskip
\noindent \bf{Maple program} \rm
\newline $>f:=x->x^2;$
\newline $>f1:=a->a*x+f(a);$
\newline $>line:=proc(low,high,step)$
\newline $>c1:=\{\ \};$
\newline $>for\ i\ from\ low\ by\ step\ to\ high\ do$
\newline $>c1:='union' (c1,{f1(i)});$
\newline $>od;$
\newline $>end;$
\newline $>line(-10,10,1/10):$
\newline $>plot(c1,x=-10..10, y=-10..10, scaling=CONSTRAINED);$
\bigskip
\noindent \bf{Derive commands} \rm
\newline $vector(ax+a^2,a,-10,10,1/10)$
\newline $Simplify$
\newline $Plot$
\newline $Plot$
\bigskip
\noindent \bf{Mathematica program} \rm
\newline $Clear[t]$
\newline $t=Table[a*x+a^2,{a,-10,10,0.1}];$
\newline $Plot[Evaluate[t],\{x,-10,10\},PlotRange->\{-10,10\}, AspectRatio->1]$
\bigskip
The picture shown on the computer suggests that the function $g(x)$ exists and
$g(x)$ is a quadratic function of the form $g(x)=-\alpha x^2$, where
$\alpha >0$. The equation of the line tangent to the graph of $y=g(x)$ at
the point $(\beta,g(\beta))$ is given by $y=-2\alpha\beta x+\alpha\beta^2$.
This tangent line is of the form $y=ax+a^2$ if only if $a=-2\alpha\beta$
and $a^2=\alpha\beta^2$. Since $\alpha>0$ we see that these equations are
satisfied when $\alpha=\frac{1}{4}$. Hence the function $g(x)=-\frac{1}{4}
x^2$ has tangent lines of the form $y=ax+a^2$. We would like to point out
that without the ability to visualize the set of lines of the form
$y=ax+a^2$, this problem would be extremely difficult for students to solve.
Hence the computer aids in the solution of this problem by allowing us to
visualize the problem and then make a conjecture about the existence and form
of the function $g(x)$ that we are trying to find.
\vfill \eject
\subhead{3.\quad Area Problem}\endsubhead
In our calculus course we have adopted the reform oriented Harvard Calculus book.
Our intention is to teach the students not just the rules and procedures of
differentiation and integration, but more about the concepts, geometric and
numerical aspects, and real world applications of calculus. With the development
of advanced computer algebra systems like Mathematica, students are able to
reinforce their understanding of calculus concepts and ideas by solving more
challenging, realistic and meaningful problems. We want to train our students
to be problem solvers. One type of problem every student who takes calculus
should be able to solve is finding area of a region in a plane bounded by
curves. In Mathematica finding the area of the region bounded by the curve
with the equation $x^4+y^4=a^4$ is not much more difficul than finding the
area of the region bounded by the circle with the equation $x^2+y^2=a^2$.
Both can be done by evaluating a definite integral. What about finding the
area of the region bounded by the curve whose equation is $x^{100}+y^{100}=
a^{100}$? Is it a difficult task? This depends on if you use computer
technology. Without using a computer algebra system or computer programming
or a graphing calculator this would be an insurmountable task. With
Mathematica students can find the area easily by numerically evaluating
the integral $\int_{-a}^{a}(a^{100}-x^{100})^{\frac{1}{100}}\,dx$ for a specific
value of $a$ and doubling it. With proper training it is now possible for
our students to make discoveries. From the graph drawn by Mathematica they
observe that the graph of $x^{100}+y^{100}=a^{100}$ is almost a square. Hence
the area inside the curve $x^{100}+y^{100}=a^{100}$ is almost $4a^2$.
Now let us show our students that Mathematica can be used to solve more
complicated and difficult area problems. One of these problems is to find
the area of the region that consists of the points whose total distance from
the vertices of a unit square is less than or equal to $2+\sqrt{2}$. It is
our belief that this problem cannot be done by pencil and paper method.
It is not easy even with assistance of Mathematica.
The reason is that the $y$-coordinate cannot be explicitly in terms of the
$x$-coordinate. For this problem just
understanding the concept of integral and the connection between area and
integral is not near enough, critical thinking and problem solving skills
are necessary. How can we solve the problem? The first step is to get the
picture of the region. Let us place the square in the rectangular coordinate
plane so that the vertices of the square are the points $(0,0),\ (0,1),\
(1,0),\ $ and $(1,1)$. Then one can see, using distance formula,
that the region is bounded by the
curve whose equation is
$$\sqrt{x^2+y^2}+\sqrt{x^2+(y-1)^2}+\sqrt{(x-1)^2+y^2}+\sqrt{(x-1)^2+
(y-1)^2}=2+\sqrt{2}.$$
One may use CountourPlot to sketch the curve. In order to find the area, one
proceeds to find values of $y$ for some values of $x$ and use a Riemann sum or
the trapezoidal rule to get an approximate value of the area. A different approach
may be used to sketch the curve and find the area. In this approach we introduce
parameter and derive parametric equations that correspond to the rectangular
equation. Both $x$-coordinate and $y$-coordinate are functions of a parameter.
Hence one can express the area of the region as an explicit definite integral can
be computed by built-in numerical method. The program written in Mathematica
used to sketch the curve and compute the area is given below:
\newline $Clear[x,y,s,t,a,b,c,e,f,g,g1,g2,g3,g4,g5,g6,g7,g8,area]$
\newline $s=2+Sqrt[2]-t;$
\newline $a=4*(t^2-s^2);$
\newline $b=-8*s^2*(t^2-1);$
\newline $c=4*s^2*(t^2-1)+(t^2-1)(s^2-1)(t^2-s^2);$
\newline $x[t\_]:=Evaluate[N[(-b-Sqrt[b^2-4*a*c])/(2*a)]];$
\newline $e=4(t^2-1);$
\newline $f=-4(t^2-1);$
\newline $g=4*t^2*(x[t])^2-(t^2-1)^2;$
\newline $y[t\_]:=Evaluate[N[(-f+Sqrt[f^2-4*e*g])/(2*e)]];$
\newline $g1=ParametricPlot[\{x[t],y[t]\},\{t,1.00001,$
\newline $(2+Sqrt[2])/2-0.00001\},AspectRatio->1];$
\newline $g2=ParametricPlot[\{x[t]+0.5,3=ParametricPlot[\{4=ParametricPlot[\{g5=ParametricPlot[\{x[t],1-y[t]\},$
\newline $\{t,1.00001,(2+Sqrt[2])/2-0.00001\}];$
\newline $g6=ParametricPlot[\{x[t]+0.5,1-7=ParametricPlot[\{1-8=ParametricPlot[\{1-Show[g1,g2,g3,g4,g5,g6,g7,g8]$
\newline $area=8*NIntegrate[(y[t]-1)*x'[t],\{t,1,(2+Sqrt[2])/2\}]+1$
\medskip
\Refs
\ref\no 1 \by S. Ligh and R. Wills \pages 32--52
\paper On Linear Functions II \yr1995 \vol 29, No. 1
\jour Mathematics and Computer Education \endref
\ref\no 2 \by S. Ligh and R. Wills \pages 9--18
\paper On Linear Functions III \yr1996 \vol 30, No. 1
\jour Mathematics and Computer Education \endref
\enddocument
\bye |
Algebra II
Algebra II picks up where Algebra I leaves off. Quadratic relations are expanded to include Conic sections in Algebra II while expontenial and logarithmic functions are introduced and explored. Linear equations are reviewed then expanded to three variable graphs. Quadratic graphs will now deal with the complex numbers and completing the square is taught as a thrid method of determining the parabola's zeros. Algebra I uses primarily the quadratic formula and factoring. Matrices and determinants are explored in depth. Matrix operations of addition, subtraction and mulitplication are practiced while using Cramer's rule for determinants. Sequences and series are introduced as arithmetic or geometric. Recursive rules for sequences and infinite geometric series begin the student's journey into abstract mathematics. Trigonometric graphs, identies and equations are added to basic trig ratios begun during geometry. |
Algebra
The Student Study Guide contains additional step-by-step worked out examples, exercises, practice tests, and practice finals. Solutions to all ...Show synopsisThe Student Study Guide contains additional step-by-step worked out examples, exercises, practice tests, and practice finals. Solutions to all exercises, tests, and final examinations are found in the Student Study Guide. It also contains Study Skills and note-taking suggestions |
Summary
A combination of a basic mathematics or prealgebra text and an introductory algebra text, Integrated Arithmetic and Basic Algebra, Third Edition, provides a uniquely integrated presentation of the material for these courses in a way that is extremely beneficial to students. As opposed to traditional texts that present arithmetic at the beginning and algebra at the end, this text integrates the two whenever possible, so that students see how concepts are interrelated rather than learning them in isolation and missing the "big picture." The ideas and algorithms shared by arithmetic and algebra are introduced in an arithmetic context and then developed through the corresponding algebraic concept. For example, operations with rational numbers and rational expressions are discussed together, whereas most texts discuss operations with rational numbers early on and operations with rational expressions much later. The Jordan/Palow text helps students recognize algebra as a natural extension of arithmetic using variables. This approach aligns directly with NCTM and AMATYC standards, which suggest playing upon students' previous knowledge to teach new concepts.
Table of Contents
Basic Ideas
Reading and Writing Numerals
Addition and Subtraction of Whole Numbers
Multiplication of Whole Numbers
Division of Whole Numbers
A Brief Introduction to Fractions
Addition and Subtraction of Decimal Numerals
Multiplication and Division of Decimal Numerals
Addition and Subtraction of Integers and Polynomials
Variables, Exponents and Order of Operations
Unit Conversions and Perimeters of Geometric Figures
Areas of Geometric Figures
Volumes and Surface Area of Geometric Figures
Introduction to Integers
Addition of Integers
Subtraction of Integers and Combining Like Terms
Polynomial Definitions and Combining Polynomials
Laws of Exponents, Products and Quotients of Polynomials
Multiplication of Integers
Multiplication Laws of Exponents
Products of Polynomials
Special Products
Division of and Order of Operations with Integers
Quotient Rule and Integer Exponents
Power Rule for Quotients and Using Combined Laws of Exponents
Division of Polynomials by Monomials
An Application of Exponents: Scientific Notation
Linear Equations and Inequalities
Addition Property of Equality
Multiplication Property of Equality
Combining Properties in Solving Linear Equations
Using and Solving Formulas
Solving Linear Inequalities
Traditional Applications Problems
More Traditional Applications Problems
Geometric Applications Problems
Using and Solving Formulas
Graphing Linear Equations and Inequalities
Ordered Pairs and Solutions of Linear Equations with Two Variables
Graphing Linear Equations with Two Variables
Graphing Linear Equations using Intercepts
Slope - Intercept Form of a Line
Point - Slope Form of a Line
Graphing Linear Inequalities with Two Variables
Relations and Functions
Systems of Linear Equations
Defining Linear Systems and Solving by Graphing
Solving Linear Systems of Equations Using Elimination by Addition
Solving Systems of Linear Equations Using Substitution
Applications Using Systems of Linear Equations
Systems of Linear Inequalities
Factors, Divisors, and Factoring
Introduction
Prime Factorization and Greatest Common Factor
Factoring Polynomials with Common Factors and by Grouping
Factoring General Trinomials with Leading Coefficient of One
Factoring General Trinomials with First Coefficient Other Than One
Factoring Binomials
Factoring Perfect Square Trinomials
Mixed Factoring
Solving Quadratic Equations by Factoring
Multiplication and Division of Rational Numbers and Expressions
Fractions and Rational Numbers
Reducing Rational Numbers and Rational Expressions
Further Reduction of Rational Expressions
Multiplication of Rational Numbers and Expressions
Further Multiplication of Rational Expressions
Division of Rational Numbers and Expressions
Division of Polynomials (Long Division)
Addition and Subtraction of Rational Numbers and Expressions
Addition and Subtraction of Rational Numbers and Expressions with Like Denominators
Least Common Multiple and Equivalent Rational Expressions
The Least Common Denominator of Fractions and Rational Expressions
Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators |
This 14-lesson series introduces each concept in an easy-to-understand way and by using example problems that are worked out step-by-step and line-by-line to completion. Includes Permutations (79 minutes); Combinations #11;(4..
Having trouble engaging your algebra students? This set of PowerPoint® slides highlights student-centered situations to teach algebra. The problems are rigorous enough to require true problem-solving and accessible enough to allow all stude..
Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understanding of key concepts. 13..
GRADES 9-12. Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understandi..
Everything you need for a class of up to 30 students. Kit contains: 30 Algebra Tile™ Student Sets (each set includes a 35-piece, two-color set of Algebra Tiles™), a 70-piece overhead set of Algebra Tiles™, an instructional ..
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. |
Daily Warm-Ups Algebra for Common Core State Standards
Each title in our new set of Daily Warm-Ups contains more than 100 focused activities to challenge your studentsí thinking. These three books support implementation of the Common Core State Math Standards, including the Common Core Mathematical Practices, with a firm foundation of important concepts and problem-solving skills.
Daily Warm-Ups: Algebra for Common Core State Standards features problems addressing the following topics: Number and Quantity; Algebra; Functions; and Statistics and Probability.
Materials include:
Reproducible teacher book
More than 100 varied problems directly addressing CCSS
Includes CD-ROM with detailed correlations, student problems ideal for projecting within the classroom, and an answer key |
Exploring, Investigating and Discovering in Mathematics
May 23, 2011 - 22:52 — Anonymous
Author(s):
V. Berinde
Publisher:
Birkhäuser
Year:
2003
ISBN:
3-7643-7019-X
Price (tentative):
€34
MSC main category:
00 General
Review:
The book is a collection of problems from elementary mathematics. It can be of substantial help in work with gifted secondary school students. On the other hand, it also contains problems on determinants, special sequences, functional equations, primitive functions, difference and differential equations, so that it will be useful for work with students of basic courses on analysis and algebra. The collection is divided into 24 groups. Over 100 problems are presented with solutions, and another 150 are accompanied by hints and clear ideas how to proceed on the way to a solution. Using included material, the author leads readers from active problem solving to exploration of methods to obtain new problems and to an active use of the gained inventive skills. The book is based on the author's personal long lasting cooperation with the Romanian journal Gazeta Matematica. |
Introduction to Real Analysis
Author: , Date: 28 Feb 2012, Views: ,
ISBN: 0471433314 | 2011 | PDF | 402 pages | 9.17 MB
This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible |
Nine PlanetsA Multimedia Tour of the Solar System: one star, eight planets, and more
Search for Bowie, MD Calculus Tutors
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...Matlab can handle vast amounts of input data and manipulate the data in accordance with the instructions that the user provides. It has amazing plotting capabilities with both 2-D and 3-D plots. It also provides a vast array of statistical functions including means, variances, medians, and modes of data sets.
...I beg
DexterReviewing basic algebraic concepts (e.g. variables, order of operation... |
All of the following courses satisfy the Mathematics
K Exploration course requirement in our core curriculum, Becoming Responsibly Engaged in the World. This guide is meant to
help students choose the mathematics course that is best for the student and
the student's ability level. We recommend that a majority of Concordia's
students choose a course from Section A below to fulfill their core Math K
requirement. If you have any questions or comments, please contact us in the
mathematics department, 4151 or [email protected].
A.General
Level Mathematics Courses: Math 105, 203, 205, CSC 125
MATH
105 — Exploring Mathematics, 4 credits. E. This course uses
real-world problems and situations to improve students' problem-solving skills,
to improve their ability to apply mathematics, and to enhance their
appreciation of the importance of mathematics in our modern world. Topics will
be chosen from taxicab geometry, voting theory, fair division, apportionment,
scheduling, networking, probability, statistics, consumer mathematics, logic,
game theory, and symmetry. Prerequisite:
high school algebra.
MATH
203 — Finite Mathematics, 4 credits. E. This course
examines combinatorics, probability, matrices, systems of linear equations, linear
inequalities and mathematics of finance. Examples and applications are drawn
from various behavioral sciences and social sciences. Prerequisite: high school
higher algebra. Recommended for business, social science and other majors, and
those preparing for a statistics course in their major, due to an emphasis in
this course on the foundations of probability.
MATH
205 — Introduction to Statistics, 4 credits. E. This is
an introductory course in statistical methods. The object of this course is to
provide students with a conceptual introduction to the field of statistics,
including the determination of the appropriate procedures for data analysis and
the proper interpretation of results. The theory will be illustrated by
examples from biology, engineering, industry and medicine. In addition, a
statistical software program will be used to facilitate the understanding of
statistical concepts and analysis of data sets. Prerequisite: high school
higher algebra. Recommended for science and other majors looking for a full
introductory treatment of statistics.
MATH
102 — Fundamental Concepts of Modern Mathematics,
4 credits. E. Numeration, number systems, geometry and other topics addressed
in the elementary school curriculum. Required for students majoring in
elementary education; enrollment restricted to elementary education majors.
MATH
110 — Precalculus, 4 credits. E. A study of the function
concept and properties of the polynomial, exponential, logarithmic and
trigonometric functions. Prerequisites: high school geometry and higher algebra.
Recommended for those preparing for Calculus I, or those who really enjoy
higher high school algebra, the study of functions, and trigonometry.
MATH 121 — Calculus I, 4 credits. E.
An introduction to the concepts of limit and continuity, the derivative and its
applications, and an introduction to the definite integral. Some review of trigonometry
and analytic geometry is included. Prerequisite: MATH 110 — Precalculus or
equivalent. Recommended for those with a strong pre-calculus background, or
those who want a full review of introductory calculus. |
Solving single variable equations in the algebra classroom
This report recognizes the common mistakes students make solving single variable equations and attempts to connect these errors to varying levels of developmental readiness. Striving to meet the needs of all students, this report offers an alternative to lecture based mathematics lessons by exploring the benefits of a unit based curriculum. The unit poses an overarching problem for the students to investigate and answer, while the students still receive the instruction on solving algebraic equations. The goal is to move beyond traditional procedures when solving equations to help students become more familiar with symbol manipulation involved in solving real world story problems. |
Linear algebra is perhaps the most important field of mathematics for
computations and applications. Linear problems turn up at every step of
every computation and there are well established, powerful methods to
solve them. Linear methods are at the heart of computer graphics, every
form of data analysis, and is the first approximation to every problem
in every field of science. In this course, we will learn the
computational methods, the images and the concepts of linear
algebra.
Grading: Your final grade will be made out of 25% Midterm 1, 25% Midterm 2, 40% Final Exam and 10% Homework.
Reading: I will assign reading in the textbook. You are
responsible for doing this reading in advance of class. This will allow
me to use class time more efficiently to clear up points of confusion
and present alternate perspectives.
Vermeer demonstrates an excellent understanding of
perspective. Did he know that it could be described using matrices?
Homework Policy: You may collaberate on homework, but you must
write up and turn in your own problem set, and you must disclose any
people with whom you worked. Homework is due Wednesdays in
class. If you cannot turn in your homework at that time, you must
contact me in advance to arrange another time.
You are free to seek help from me, from each other (disclosed as
above), and from the tutors at the Mathlab. You
absolutely MAY NOT post homework problems to internet
discussion boards.
If you get help from someone outside this group, it should be limited
in nature, and must be disclosed.
Exams: The first midterm will take place in class on Monday,
October 1. The second midterm will be in class Friday, November 16 9. The
final exam will be Thursday, December 20, 1:30-3:30. If you have a
medical condition requiring special accomodation during exams, please
inform me and provide medical documentation before hand.
Will
Hunting realizes that he can count paths through a
network using matrices. If you want to learn more about this, take
Math 465 or 565.
Syllabus: Readings and problems sets are to be completed before or on the corresponding class date. More details will appear on this calendar as the term progresses. |
Formats
Book Description
Publication Date: Oct 1 2006Product Description
Review
"Have you ever looked at your child's homework and been stumped by mathematical terms you haven't seen in years? This book will help alleviate hours of frustration for students. Math Dictionary includes a large variety of mathematical terms that often come up in student. Students will easily be able to locate the term and identify its meaning through definitions, examples, diagrams, and some photos. This book clearly explains how to find greatest common factor, differences in bar graphs, how to write in expanded form, and other often-confusing terms." --Library Media Connection
About the Author
Eula Ewing Monroe is a former classroom teacher. She lives in Provo, Utah, where she teaches mathematics education at Brigham Young5.0 out of 5 starsEnthusiastically recommended for junior high and high school libraries.Nov 4 2006
By Midwest Book Review - Published on Amazon.com
Format:Paperback
Math Dictionary: The Easy, Simple, Fun Guide To Help Math Phobics Become Math Lovers by Eula Ewing Monroe (teaches mathematics education at Brigham Young University) is a straightforward reference to basic mathematical terms for readers of all ages and backgrounds, from junior high and high school students to adults in need of a quick refresher. From "average" (including mean, median and mode) to "partial products algorithm" to "zero-dimensional" and much more, the terms cover general arithmetic, geometry, algebra, graphing, probability, statistics, and much more. Advanced mathematical terms such as those used in calculus are not covered. Each definition is spelled out in plain terms, often with simple diagrams to illustrate, eliminating any confusion. Amusing "Did You Know?" quips spice up Math Dictionary with amusing anecdotes such as how the number "googol" (ten to the hundredth power) got its name. Enthusiastically recommended for junior high and high school libraries.
12 of 13 people found the following review helpful
5.0 out of 5 starsCourtesy of Teens Read TooNov 8 2006
By TeensReadToo - Published on Amazon.com
Format:PaperbackReviewed by: Jennifer Wardrip, aka "The Genius"
1 of 1 people found the following review helpful
5.0 out of 5 starsWonderful ToolSep 26 2009
By L. Rentz - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
This math dictionary is an excellent resource for my development as an Elementary Teacher. This tool is user and kid friendly. My household use this referecnce source faithfully. My daughter is a Business Management Major and my son is in Middle School. We love the clear definitions and examples showing what the operation(s)look like. |
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Product Description:
160 math teasers and 40 alphametics will provide hours of mind-stretching entertainment. Accessible to high school students. Solutions. Four Appendices |
97801389412 Mathematics: A Source Book for AIDS, Activities, & Strategies
The art of teaching math lies in the ability of the instructor to motivate and inspire individuals to look beyond the numbers and understand the concepts. This book is designed to revive this art, focusing more on the aspects of learning the ideas behind the math rather than the sheer mechanics of mathematical operation. This text addresses the art of teaching mathematics while also providing specific aids and activities in arithmetic, geometry, algebra and probability and statistics for use in the classroom. The authors pay close attention to the role, importance, methods and techniques of motivation. They present ideas that will generate attention, interest, and surprise among students, and will thus foster creative thinking. The material in the text is based on talks given by the authors at professional meetings, as well as the actual application of their ideas in undergraduate and graduate classes they taught. Additionally, many laboratory and discovery activities have been used by authors in teaching junior and senior high school math classes. Instructors of mathematics, school administrators, math specialists, and parents |
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Description students with the skills and confidence they need in mathematics to succeed in their university courses.
Table of contents
Why this book was written How to use this book Part A - Basic Skills 1. Numbers 2. Algebra 3. Functions and Graphs 4. Differentiation 5. Integration Part B - Additional Topics 6. Optimisation 7. Finance 8. Regression 9. Index Numbers Appendix: Suggestions for Further Study Appendix: Using Computer Programs Solutions to Exercises
Features & benefits
It is designed as a handy reference purchase for interested students and also for lecturers to recommend to students identified as having problems in mathematics.
The book can also be used as a text in mathematics orientation courses for university economics, commerce and business administration students.
It assumes no prior high-level mathematical knowledge on behalf of the student. Only a familiarity with numbers and basic arithmetic is assumed.
Mathematics is becoming increasingly important in economics and business degrees which often excludes those without mathematical skills particularly minority groups. This book hopes to help reverse this trend by showing students that everyone can be successful at maths.
The author is an experienced lecturer familiar with the problems many students face with mathematics. He has written a book that will help retain otherwise good students who may leave economics and business because of a fear of mathematics.
The book includes exercises with solutions.
Author biography
Dr Paul Oslington is a Professor of Economics at Australian Catholic University in Sydney. |
College Algebra With Modeling And Visualization - Text Only - 3rd edition
Summary: Gary Rockswold focuses on teaching algebra in context, answering the question, ''Why am I learning this?''
Applications: The author believes that students become more effective problem-solvers by being exposed to applications throughout the course. Therefore, a wide variety of unique, data-based, contemporary applications are included in nearly every section.
Making Connections: This feature points out how concepts presented throughout the course are interrelated. It also provides students with a perspective on how previously learned material applies to the new material they have learned.
Checking Basic Concepts: This feature consists of a small set of exercises provided after every two sections. These exercises can be used by students for review purposes, or by the instructor as group activities. They require 10-15 minutes to complete and could be used during class if time is available.
End of Chapter Material: Each chapter ends with a summary of key concepts, review exercises, and extended and discovery exercises.
Chapter R Reference: Basic Concepts from Algebra and Geometry: This contains much of the material from intermediate algebra and basic geometry in a separate appendix at the back of the text. This material is referenced by Algebra and Geometry Review Notes in the margins of the text.
Graphing Calculator Appendix: This allows students to work more easily on their own with the calculator and frees up class time for the instructor. This material is referenced by Graphing Calculator Help Notes in the margins of the text book bentSnag A Deal Cypress, TX
0321279085 Book contains writing and or highlighting, shows some wear to cover and or DJ cover |
Mathematica Classroom Gets Students Interested in Math
High school math will never be the same at Torrey Pines High
School in San Diego, California. Abby Brown and her students are pushing the
limits of traditional learning with Mathematica.
When
Brown first began teaching, she used a single Mathematica license
to quickly and accurately graph functions and typeset traditional math symbols
for tests, quizzes, and handouts. A few years later, her school in conjunction
with San Diego State University began a special program that gives advanced
math students a chance to earn college credit in Calculus II, Multivariable
Calculus, and Linear Algebra. To supplement these new courses, Brown used
Mathematica to create visual aids such as graphs of tangential planes
and matrix operation demos. She displayed the graphics during lectures with a
projector attached to her computer. "Visualization is so valuable, and
Mathematica is a tremendous tool for this," Brown explains.
Brown found even more ways to incorporate Mathematica into her
lessons when her school purchased enough licenses to allow students to use it
in math and science classes as well as in the central computer lab. "My
philosophy focuses heavily on teaching using multiple methods of
representation," says Brown. "My students' projects center on this, and
Mathematica works well for combining graphical, symbolic, numerical,
and verbal techniques."
Although Brown notes that she finds Mathematica most useful for
teaching advanced courses, even her Algebra I students are captivated by the
graphics and show improvement when she incorporates them into the course. One
year, several Algebra I students didn't believe that the curve 1/x would never
cross the x-axis. Using Mathematica, the students were able to
investigate their theory by zooming in on the plot repeatedly, searching for an
intersection. When they were satisfied that their teacher was correct, the
students presented their final graphs to the class.
Using Mathematica is sometimes a challenge for Brown's students, but
they are good at learning from their classmates' mistakes and helping each
other with nuances of the code. The most common problems involve forgotten
commas and capital letters. Brown has found that "with more practice, they
learn to spot these errors and make fewer of them." Giving students early
exposure to Mathematica will help them succeed in future math and
science courses and can help increase their interest in technology-related
fields.
Recently, Brown led several workshops to teach her colleagues how to take
advantage of Mathematica as a teaching tool. She also wrote a tutorial
titled "Exponentials vs. Factorials" to demonstrate how
Mathematica can aid teaching in ways that aren't possible with a textbook or
a graphing calculator.
Brown has also created a website that is a great resource for students and
teachers. There is an activity section with puzzles, problems, and codes for
students to solve. Ideas on how Mathematica can add a new dimension to
math courses are available, and sample teaching modules in Mathematica
notebook form can be downloaded. Brown has also included information on her
teaching philosophy, sample student presentations, and links to other
math-oriented web resources. View the site
for more details. |
Schaum's Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.A monograph is concerned with exchange rings in various conditions related to stable range. It discusses diagonal reduction of regular matrices and cleanness of square matrices. It includes topics such...Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book provides a comprehensive exploration of Mumford-Tate...
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book provides a comprehensive exploration of Mumford-Tate... |
Synopses & Reviews
Publisher Comments* Assumes virtually no prior knowledge
* Numerous worked examples, exercises and challenge questions
Modular Mathematics is a new series of introductory texts for undergraduates. Builiding on both the skills and knowledge acquired at A level, each book provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
Synopsis:
provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
Synopsis"Synopsis"
by Elsevier,
provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
"Synopsis"
by Elsevier, |
have
A non-measurable set in (0, 1] 6.975, Fall 2004Let + stand for addition modulo 1 in (0, 1]. For example, 0.5 + 0.7 = 0.2, instead of 1.2. If A (0, 1], and x is a number, then A + x stands for the set of all numbers of the form y + x where y A. You may wa
Homework No. 3 - SolutionO restart; with(student);1. For the two soils whose characteristics are given below, and for the variable diffusivity case:a) Compute the infiltration as a function of time for constant q1 = n at the surface. b) Assuming a rain
Getting Started in Mathematical BiologyFrank Hoppensteadtathematicians are sometimes known in high school biology classes for their tendency to faint during dissections and their ability to cook experiments to fit straight lines. In spite of these impre
MATHEMATICS IN BIOLOGYSPECIAL SECTIONtions provide models of the same general form. Although the different systems have important special features (e.g., the conservation laws), surely we would like to communicate the more general idea that dynamics are
Why Is Mathematical Biology So Hard?Michael C. ReedAlthough there is a long history of the applications of mathematics to biology, only recently has mathematical biology become an accepted branch of applied mathematics. Undergraduates are doing research |
Mathematical Biology Pages - Brandeis University
In contemporary biology there are many areas which depend heavily on rather advanced mathematics. This site demonstrates a few of these through Shockwave, Java, and JavaScript explorations. Dixon's Population Pages (exponential growth, nonlinear terms
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Mathematical Interactivities - David Hellam
Interactive mathematical challenges, mostly written in Flash, covering number, algebra, data, shape, and space for K-12 students. Site also includes a forum for teachers to discuss this sort of resource, its development, and its use in the classroom.
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Mathematica: Tour of Features - Wolfram Research, Inc.
Pages that guide you through an interactive demonstration of some of Mathematica's capabilities. New features; using the program as a calculator; power computing; accessing algorithms; building up computations; handling data; visualization; Mathematica
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Mathematics Applications - Arlen Strader
Areas of mathematics for which Strader has developed Java applets: Algebra, Probability, Statistics, Set Theory, and Geometry. Statistics, developed for an undergraduate behavioral statistics class, is the most developed; algebra and geometry are aimed
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mathematics.com - ENGINEERING.com
Interactive material to download or work with online; articles on current technology topics; resources and links of interest to mathematicians; technology products offered for sale. Online calculators and applets for geometry, trigonometry, calculus,
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Mathepower - Markus Hendler
Online calculators for most calculations covered in the first ten years of school, from basic operations through the first stages of algebra. Available in English, German, and French.
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Math Forest - Tobias Grönberg
Five games for students to practice arithmetic online. Math Forest provides teachers a tool to manage and analyze student results. Preview the games and teacher tool, or sign up for a free trial.
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MATHGYM Mathematics Training Programme - Paul Dooley
A tutorial from Australia designed to help 10-16-year-olds develop mathematical problem-solving ability, with five SETs of 20 problems typical to many math competitions. Students are given a Training Problem to solve, with necessary background theory,
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Mathkinz
Free printable math worksheets for home and school use, early grades through middle school, with links to math games and online quizzes.
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mathlab.com - Mehrdad Simkani
A Java applet of unmarked straightedge and collapsible compass tools to virtually draw the lines and circles fundamental to Euclidean geometry. The help page explains how to use the Euclid applet, and contains descriptions for constructing found in propositions
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Math Learning Site
This site offers a library of over 2000 lessons in video format, as well as pretests, exams, and a performance report accessible by parents and/or teachers. Lessons are accessible by subscription, with a money-back guarantee and an online demo.
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Specification
Aims
This course unit aims to introduce the basic ideas and techniques of linear algebra for use in many other lecture courses. The course will also introduce some basic ideas of abstract algebra and techniques of proof which will be useful for future courses in pure mathematics.
Brief Description of the unit
This core course aims at introducing students to the fundamental concepts of linear algebra culminating in abstract vector spaces and linear transformations. The first part covers systems of linear equations, matrices, and some basic concepts of the theory of vector spaces in the concrete setting of real linear n-space, Rn. The second part briefly explores orthogonality, and then goes on to introduce abstract vector spaces over arbitrary fields and linear transformations. The subject material is of vital importance in all fields of mathematics and in science in general.
Learning Outcomes
On successful completion of this course unit students will be able to
be able to solve systems of linear equations by using Gaussian elimination to reduce the augmented matrix to row echelon form or to reduced row echelon form;
understand the basic ideas of vector algebra: linear dependence and independence and spanning;
be able to apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination;
know how to find the row space, column space and null space of a matrix, to find bases for these subspaces and be familiar with the concepts of dimension of a subspace and the rank and nullity of a matrix, and to understand the relationship of these concepts to associated systems of linear equations;
be able to find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial and will know how to diagonalize a matrix when this is possible;
be able to find the orthogonal complement of a subspace;
be able to recognize and invert orthogonal matrices;
be able to orthogonally diagonalize symmetric matrices;
be familiar with the general notions of a vector space over a field and of a subspace, linear independence, dependence, spanning sets, basis and dimension of a general subspace;
be able to find the change-of-basis matrix with respect to two bases of a vector space;
be familiar with the notion of a linear transformation, its matrix with respect to bases of the domain and the codomain, its range and kernel, and its rank and nullity and the relationship between them;
be familiar with the notion of a linear operator and be able to find the eigenvalues and eigenvectors of an operator.
Future topics requiring this course unit
Almost all Mathematics course units, particularly those in pure mathematics. |
Overview
Main description
Considered to be the hardest mathematical problems to solve, word problems continue to terrify students across all math disciplines. This new title in the World Problems series demystifies these difficult problems once and for all by showing even the most math-phobic readers simple, step-by-step tips and techniques. How to Solve World Problems in Calculus reviews important concepts in calculus and provides solved problems and step-by-step solutions. Once students have mastered the basic approaches to solving calculus word problems, they will confidently apply these new mathematical principles to even the most challenging advanced problems.
Each chapter features an introduction to a problem type, definitions, related theorems, and formulas.
Topics range from vital pre-calculus review to traditional calculus first-course content.
Sample problems with solutions and a 50-problem chapter are ideal for self-testing.
Fully explained examples with step-by-step solutions.
Author comments
Eugene Don (Coram, NY) is Professor of Mathematics at Queens College of the City University of New York. He is also the author of Schaum's Outline of Mathematica.
Back cover copy
WORD PROBLEMS??
NO PROBLEM!!
Be prepared when you get to the word-problem section of your test! With this easy-to-use pocket guide, solving word problems in calculus becomes almost fun.
This anxiety-quelling guide helps you get ready for those daunting word problems, one step at a time. With fully explained examples, it shows you how easy it can be to translate word problems into solvable calculus problemsand get the answers right!
You get complete directions for solving problems commonly found in high-school and college text books. There's no word problem too tough for How To Solve Word Problems in Calculus!
Sanity-saving features include:
Step-by-step approach to word problems
Complete explanations of every step
Fully explained answers
Dozens of sample problems
Problems of every type
Skill-checking practice drill
If you don't have a lot of time but want to excel in class, this book helps you: |
Mathematics classes that will help with physics (list included)
Mathematics classes that will help with physics (list included)
I was wondering if anybody could give me some suggestions on which mathematics courses will be of the most use for theoretical physics. I am a sophomore at Wayne State university and am taking intro to quantum mechanics and a first course in optics this semester.
And I was just wondering if somebody could help me with finding out which classes would be most helpful to pursue studies in theoretical physics. I am dual majoring in mathematics, but I am mainly concerned not with getting a degree, as with getting knowledge
So I have to confine myself to an area and theorize there? The undergrad stuff at my school is this.. I have left (in semester order)
Thermodynamics/stat mechanics, mechanics 1
quantum physics 1, mechanics 2
Quantum physics 2, electromagnetism 1
Electromagnetism 2, modern physics lab
4 semesters. But over the summers they do not offer these classes, so I want to take a lot of math classes over the summers to be the best I can be, I really like quantum mechanics a lot, I want to take a lot of quantum mechanics classes as a grad student, if that helps isolate classes.
I was told elementary analysis (which is the class required to get into all those upper level classes on that list) is good, as well as partial differential equations and complex analysis, but then I heard algebra was good, probability theory, basically every teacher I ask tells me something different so I don't know what to do.
It is quite hard to say since little of math (at least at the level you are considering taking) is useless for physics... following your own interests towards math can help too!
But anyway definitely take an analysis class, and definitely an abstract algebra class (for QM). Taking classes like complex analysis, probability theory, more abstract algebra, more analysis etc can all definitely be useful, but understand that whenever math is necessary in a physics class, you usually learns that math within the physics class, just much more quick and dirty and bare-boned than in a full math class, but it's not like you'll ever get stuck if you don't take them. That being said two very important mathematics topics that usually get taught quite shabbily within a physics context (although it is definitely very useful to know them properly) are: representation theory (very important for QM) and differential geometry (very important for GR). (The problem is that they might be grad courses in your math department.)
If you are really planning on going to the mathematical physics sides of things, i.e. you know you will be studying a lot of math in the future, then take as much analysis, algebra and topology classes to ensure a firm foundation for self-study down the road! is a class called elementary analysis which is the prereq for all the higher math courses. I'm not great at math, I mean, I get A's, but I don't really feel like I understand it, so I want to focus on the things that I can apply towards physics. Unfortunately the elementary analysis is not offered this summer so I will have to take it next year so next summer I can take some algebra and perhaps something else. They do offer a lot of topology and things like that. I should just become a monk and go to school for the rest of my lifeNot at the undergrad level I think. I think for someone who sees himself as a future theorist, it makes sense to study (at least) linear algebra, real analysis, differential geometry, and maybe differential equations, representation theory, complex analysis, linear/harmonic analysis (i.e. Fourier series and stuff), and abstract algebra. Representation theory is super important, but some of it is taught in QM courses. So I can't say that it's essential to take a course on it, but I would definitely recommend it. A similar comment can be made about several of the other topics, in particular differential equations and stuff about Fourier series and integrals. You need some abstract algebra, but I'm not sure you need to take a course. It may be enough to read the early chapters in some book.
If you want to go into mathematical physics, you also need topology, measure and integration theory, and functional analysis.
Quote by Levi Tate was a course like that at my university. I thought it was pretty useless to be honest. In my humble opinion, it's better to take "real" math courses.
Quote by Levi Tate
There is a class called elementary analysis which is the prereq for all the higher math courses.
You will probably need this just to be able to read books on more advanced topics.
Thanks a lot. I suppose I will just reference this thread and reopen the conversation as I get a bit closer. There is so much, it is a bit boggling. I suppose for right now I will content myself to focusing on understanding my classes now.
And thank you everybody else as well. This gave me a lot to think about and I plan to revisit this question as I, and you, progressAs for linear algebra: I assumed one class treated both of those aspects, but if not yes I agree.
As for abstract algebra: actually I agree that the material itself in an abstract algebra is not that important for QM (as in, all the theorems) but what seems immensely valuable to me from such a class is the reasoning skills you obtain when thinking about algebra (and it is a kind of mathematical maturity that is the distinct from the maturity you get from an analysis class, at least in my own experience). My opinion is that once you get the basics down ice-cold, it is much more possible to add to that the specific relevant physics-related pieces that you can self-study (e.g. representation theory), whereas to get the basics down can easily take the length of a proper math course on analysis and abstract algebra respectively.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereq.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereqHis course doesn't cover modules. And you really don't need group theory to be able to understand quotient spaces and the isomorphism theorems. In fact, I might even say that it's better to first see quotient spaces in the setting of linear algebra than in group theory. |
matrices
Course: CS 2130, Fall 2009 School: East Los Angeles College Rating:
Word Count: 2410
Document Preview capital letters to denote complete matrices1. For example: 11 4 A = 7 2 10 4 7 5 -6
The individual entries in a matrix are called the elements of the matrix. We denote the element in row i, column j of the matrix A by aij, that is we use the corresponding lower case letter with two subscripts denoting the row (i) and column (j) numbers. Thus a11 = 11, a21 = 7, a12 = 4, a23 = 5. If A is an n n matrix, we say that A is a square matrix of order n. A 1 n matrix is called a row vector of order n. An m 1 matrix is called a column vector of order m. When referring to the elements of a row vector the row number is (of course) always 1 and so is often omitted. Thus the element in column j of a row vector V is often denote as vj rather than v1j. Similarly the element in row i of a column vector U is usually denoted by ui rather than ui1 as the column number is always 1. and U = [1 2 3 4] 3 V = 4 5 is a row vector of order 4 and u1 = 1, u2 = 2, u3 = 3, u4 = 4.
is a column vector of order 3 and v1 = 3, v2 = 4, v3 = 5.
If the elements of a matrix are all integers we speak of a matrix over Z (the integers). If the elements of a matrix are all real numbers we speak of a matrix over R (the Reals). If the elements of a matrix all belong to the integers modulo n we speak of a matrix over Zn. Two matrices A and B are equal if and only if they are the same size that is each has the same number of rows and columns that is both are m n for some integers m and n and corresponding elements are equal that is aij = bij for 1 i m and 1 j n Matrix Addition and Subtraction We can add or subtract matrices A and B only if they are the same size. The element in row i column j of the sum of two matrices is the sum of the corresponding elements of the two matrices. Thus A and B are m n matrices, their sum C = A + B is also m n and cij = aij + bij
1
for 1 i m and 1 j n.
In hand-written text matrices are usually denoted by underlining the capital letter with a curly line.
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Similarly if A and B are m n matrices, their difference D = A B is also m n and dij = aij bij For example 11 4 A = 7 2 10 4 and 7 5 -6 for 1 i m and 1 j n. 3 7 B= 2 4 1 2 2 8 -8 5 3 then 2 8 11 12 C= A+B= 9 2 2 11 2 -4
and
14 3 D = A - B = 5 6 9 6
Scalar Multiplication Multiplication of a matrix A by a scalar a (a single number) produces a matrix of the same size as the original whose elements are the corresponding elements of A each multiplied by a. Thus if A is an m n matrix then B = aA is also m n and bij = aaij Example 3 1 2 If A = 6 5 4 3 6 then 3A = 18 15 9 12 for 1 i m and 1 j n. .
Matrix Multiplication Suppose A and B are m p and q n matrices respectively. Then we can form the matrix product AB if and only if p=q, that is if the number of columns of A is equal to the number of rows of B. We say A and B are conformant for the product AB. In this case C = AB is an m n matrix and the element in row i, column j of the product matrix C = AB is given by
p
cij = aik bkj = ai1b1 j + bi 2 b2 j + ai 3b3j ... + aipb pj
k =1
Note that to obtain the element in row i column j of AB we multiply corresponding elements in the ith row of A and the jth column of B and then add up these p multiples. The number of rows in the product matrix AB is the number of rows in A and the number of columns is the number of columns in B. Thus, for example, given that 3 7 5 4 2 3 4 6 7 A= and B = 2 4 3 then C = AB = 1 2 5 4 9 9 1 2 2 Note that since A is 2 3 and B is 3 3, AB is 2 3 and, for example, the element in row 1 column 2 is formed from row 1 of A and column 2 of B: 2 (7) + 3 4 + 4 2 = 6 Similarly the element in row 2 column 3 is formed from row 2 of A and column 3 of B: (1) (5) + (2) 3 + 5 2 = 9.
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Note that in the above example BA does not exist, since B is 3 3 and A is 2 3. We say A and B are not conformant for the product BA. Note also that square matrices are conformant for multiplication if and only if they have the same size. Even if A and B are square matrices of the same size it is NOT usually the case that AB = BA. For example, if 1 2 5 6 A= and B = 7 8 3 4 19 22 then C = AB = 43 50 23 34 and D = BA = 31 46
We say that in general matrix multiplication is not commutative. In a few special cases we can find square matrices A and B such that AB = BA, in this case we say A and B commute. The Zero Matrices The zero matrix Om n is the m n matrix with all its elements equal to zero Thus the 2 2 and 3 2 zero matrices are 0 0 0 0 O2 2 = O32 = 0 0 0 0 0 0 If the size of the matrix is clear from the context the subscripts are omitted and the zero matrix is represented simply by O. Let A be any m n matrix, then the following properties of the zero matrix are fairly obvious: A + O m n = Om n + A = A AOnp = Om p OqmA = Oqn
The Identity Matrices The identity matrix In is a square matrix of order n with ones on the main diagonal and zeros elsewhere. Thus the 2 2 and 3 3 identity matrices are 1 0 I2 = 0 1 1 0 0 I 3 = 0 1 0 0 0 1
If the size of the matrix is clear from the context the subscript is omitted and the identity matrix is represented simply by I. If A is any 2 3 matrix then AI3 = I 2 A = A. Thus multiplying a matrix the by identity matrix of the appropriate size leaves the matrix unchanged. For example 3 2 1 2 1 0 0 4 2 0 1 0 = 5 1 0 0 1 3 2 4 5 4 2 3 1 0 2 3 and = 0 1 1 2 5 1 2 4 5
More generally we find that if A is m n then AIn = Im A = A. In particular if A is square of order n we have AIn = I n A = A. Thus any square matrix commutes with the identity matrix of the same size.
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Powers of a Square Matrix Let A be a square matrix of order n. Then we can form the matrix product AA which is also n n; this product is denoted by A2. Similarly we can form the products: A3 = A2A, A4 = A3A, ......., Am = Am1 A for any integer m1
where we define A1 = A and A0 = In. We saw above matrix multiplication is not normally commutative and however it can be shown that any two powers of a square matrix A always commute, thus: A3 = A2A = AA2 and more generally Am = Am1 A = AAm1 37 54 and also C = A2 A = 81 118 for any integer m1. Thus any two powers of a matrix commute. For example, if 1 2 7 10 2 A= then A = 15 22 3 4 37 54 thus B = AA2 = 81 118
The Transpose of a Matrix The transpose of an m n matrix A is the n m matrix formed from A by interchanging the rows and columns of A. The transpose of A is denoted by AT (or sometimes by A'). Thus, for example, if
Suppose that A is m p and that B is p n, then A and B are conformant for the product AB which is m n . Note that BT is n p and that AT is p m and therefore BT and AT are conformant for the product BTAT which is n m. In fact the following result holds: (AB)T = For example, if 1 2 A= and 3 4 3 5 1 B= 1 8 0 1 then A = 2
T
BTAT 3 4 3 1 and B = 5 8 1 0
T T
1 2 3 5 1 5 21 1 thus AB = = 3 4 1 8 0 13 47 3 3 1 1 B A = 5 8 1 0 2
T T
5 13 and (AB) = 21 47 1 3
whereas
5 13 3 T = 21 47 = (AB) 4 1 3
Laws of Matrix Algebra In the laws that follow, a and b are scalars (single numbers) and A, B and C are matrices of an appropriate size such that the matrix sums and products indicated exist. Commutative Law for Addition A+B= B+A 4
A Barnes 2000
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NO commutative Law for Multiplication Associative Law for Addition Associative Laws for Scalar Multiplication Associative Law for Matrix Multiplication Distributive Laws (Matrix) (Scalar) Properties of Zero Matrix Properties of the Identity Matrix Scalar Multiplication Properties
AB BA (A + B) + C = A + (B + C) a(AB) = (aA)B = A(aB) (ab)A = a(bA) (AB)C = A(BC) (A + B)C = A(B + C) = a(A + B) = (a + b)C = AC + BC AB + AC aA + aB aC + bC
O + A= A+ O = A OA = O AO = O IA = A 1A = A AI = A 0A = O
Symmetric and Anti-Symmetric Matrices If A is a square matrix with A = AT, we say that the matrix A is symmetric. If A is a square matrix with A = AT, we say that the matrix A is anti-symmetric (or skewsymmetric). The symmetric part of a square matrix A is the matrix (A + AT). The anti- (or skew-) symmetric part of a square matrix A is the matrix (A AT). Not surprisingly the symmetric part of a square matrix is symmetric! This follows since (A + A T)T = (AT + (A T)T) = (AT + A) = (A + A T)
Similarly the anti-symmetric part of a square matrix is anti-symmetric! The proof is left as an exercise. For example, if 1 2 A= 3 4 then 1 1 2.5 (A + AT ) = 2 2.5 4 and 1 0 -0.5 (A A T ) = 0 2 0.5
Matrices in Ada There is no direct support for matrix algebra in Ada. However it is relatively easySRT210Week ThreeWeek OverviewChange Management Revision Control Time ManagementChange management is an organized effort to implement changes to a systemChange ManagementTypically, change management involves the following elements: Th
CS2130 Programming Language ConceptsUnit 11 More on Function and Procedure Abstractions Defining New Operators Some languages, for example Ada and C+, allow new overloadings of existing operator symbols to be defined. For example in Ada:TYPE Vector
CS2130 Programming Language ConceptsUnit 2 Concurrent Programming So far in this degree programme you have mainly considered sequential programs in which statements are obeyed in a single thread of control, that is where only one instruction sequenc
CS2130 Programming Language ConceptsUnit 16 Encapsulation and Abstraction Client/Server Model Most modern programming languages provide a means of grouping related services together in some program entity. This entity is variously called a package,
CS2130 Programming Language ConceptsUnit 10 Function and Procedure AbstractionsExpressions & Commands Revisited Recall that an expression is anything that can be evaluated to produce a value whereas a command modifies program state (the internal s a" > double we would define#include <math.h> Concurrent |
ADVANCED ALGEBRA LESSONS
Whether needing help with advanced algebra homework or reviewing for tests, Mr. X can help math students better understand Advanced Algebra. Our lessons are designed to reinforce the instructor's message. We also have a library of sample algebra problems with examples of solved problems for each advanced algebra lesson. Check out our free samples below, as well as the advanced algebra curriculum. Advanced algebra lessons and problems are included with a subscription to Mr. X. |
EDUC6103
Mathematics Curriculum Studies 2
10 Units 6000 Level Course
Available in 2013
Fairfield High School
Semester 2
WebLearn GradSchool
Semester 1
Previously offered in 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2004
This course introduces students to the key concepts underlying a deep understanding of number, arrangements, number distribution and combinatorics. This course will consider the historical development of number and will examine current related pedagogical models within the field of secondary mathematics including assessment policy and structure.
Objectives
On satisfactory completion of this course students should be able to: - understand the key concepts related to number theory, combinatorics, binomial theory and difference equations - appreciate the mathematical knowledge and beliefs that learners bring to a learning task - apply a range of strategies for teaching secondary mathematics - recognise the common misconceptions that students may have in regard to the mathematical content covered. - apply a range of strategies for assessing students learning
Content
- basic number theory including modular arithmetic - Permutations and Combinations theory (cominatorics) and applications to probability and games of chance - Binomial distribution and its relationship to algebraic expansion and probability - Difference equations and applications to fibonnaci numbers and linear algebra - teaching strategies related to mathematical content - common misconceptions related to the mathematical content - Assessment requirements of the Board of Studies NSW |
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics or thermodynamics can be described, in general, by formulating partial differential equations (PDEs). Though complicated boundary - value problems still remain a mystery, at least to the extent of seeking their analytical solutions, there exists a variety of problems with relatively simplistic posture that may yield solution without computing. In the present course, effort is being made to present the fundamental material on the subject in an easy manner, but without sacrificing much of the mathematical rigour.
GOALS:
To familiarize with some easy cases of modeling of PDEs.
To comprehend and apply the method of separation of variables as one of the tools to solve BVPs.
To understand Fourier expansion of functions and to apply it in the solution of PDEs.
To gain knowledge in some special functions derived from infinite series, like Bessel functions and Legendre Polynomials and to study their properties.
To have an exposure to problems dealing with rectangular, circular and spherical membrane. |
Math Composer is a powerful yet easy to use tool for creating all your math documents. It is a simple way for math teachers and instructors to create math worksheets, tests, quizzes, and exams. This... |
Mathematics at Huntington
The Mathematics Department believes that there is a level of mathematics study available to every student. The mathematics program emphasizes computational skills, problem-solving techniques, and mathematical structure. Students learn skills and concepts, and practice analytical and critical thinking. They study the uses of the computers, statistics and measurement.
Algebraic and geometric structure, logic, and analysis provide a sequential program for the college-bound. The decisions made about the courses taken in high school affect each student for the rest of their lives. The teaching faculty, the school counselor, the school administrators, and parents can all advise in the course selection process, but the student should be fully involved in the final decision and be ready to bear the responsibility for that decision. For this reason it is imperative to read course descriptions with considerable thought and care.
In selecting your courses for next year, several factors should be considered. These factors include graduation requirements and your job or school plans for the future. All students are required to complete successfully three credits of mathematics and demonstrate a minimum level of proficiency on a New York State exam. |
Experience mathematics--and develop problem-solving skills that will benefit you throughout your life--with THE NATURE OF MATHEMATICS. Karl Smith introduces you to proven problem-solving techniques and shows you how to use these techniques to solve unfamiliar problems that you encounter in your day-to-day world. You'll find coverage of interesting historical topics, and practical applications to real-world settings and situations, such as finance (amortization, installment buying, annuities) and voting. With Smith's guidance, you'll both understand mathematical concepts and master the techniques.
Additional versions of this text's ISBN numbers
Purchase Options
List$260 |
My NMSI Story
Watch clips of U.S. students and teachers speaking about their participation in the National Math and Science Initiative's Advanced Placement Training and Incentive Program (APTIP). Upload your own video narrative about APTIP, which has expanded American
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National Math & Science Initiative
This non-profit organization "facilitates the national scale-up of programs that have a demonstrated impact on math and science education in the United States." Programs include the Training and Incentive Programs, which encourage excellence among teachers
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New Mathwright Library - James White; Bluejay Lispware
An Internet-based library of interactive workbooks on topics commonly encountered in undergraduate mathematics, from college algebra and precalculus through multivariable calculus, differential equations, and mathematical modelling. Workbooks, together
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Newton Papers - University of Cambridge
View and download Isaac Netwon's handwritten papers: his own annotated copy of Principia Mathematica; the so-called "Waste Book," a large notebook that he inherited from his stepfather, and which Newton filled with notes and calculations when forced toOscience.info - Subash Chandra
Introductions to limits and continuity, derivatives and antiderivatives, functions and graphs, matrices and determinants, properties of triangles, set theory, basic trigonometric formulae, and trigonometric functions and identities. See also Oscience'sPersonal Tutor - Memory Banks Pty. Ltd., Australia
Maths and science software designed to complement the secondary school math syllabus. A comprehensive learning system usually used by students and schools as a supplement and aid to coursework, but thorough enough that it can be used by individuals withoutPhysics and Math Help Online - Bryan Gmyrek
Tutoring available through e-mail. Previously answered questions are archived on the site, and a tutorial on The Plank Radiation Law - Blackbody Spectrum is available. The author also provides a physics help newsletter and a list of sites for further
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Plot multiple two- or three-dimensional graphs, including of parameterized functions and derivatives, in one and the same graph. Key in equations with the WYSIWYG formula editorThe PostCALC Project - Duke University
The PostCALC Project is a branch of the Connected Curriculum Library that presents interactive, mathematically-based modules designed for high school students who have finished a year-long course in calculus. These modules, each appropriate for several
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igonometry
Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling ...Show synopsisGain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling TRIGONOMETRY 6e, International Edition. This book's proven approach presents contemporary concepts in brief, manageable sections using current, detailed examples and high-interest applications. Captivating illustrations drawn from Lance Armstrong's cycling success, the Ferris wheel, and even the human cannonball show trigonometry in action. Unique Historical Vignettes offer a fascinating glimpse at how many of the central ideas in trigonometry began. TRIGONOMETRY 6e, International Edition, uses a standard right-angle approach with an emphasis on the study skills most important for success both now and in advanced courses, such as calculus. The book's proven blend of exercises, fresh applications, and projects is combined with a simplified approach to graphing and the convenience of new Enhanced WebAssign--a leading, time-saving online homework tool--and the innovative CengageNOW teaching system. With TRIGONOMETRY 6e, International Edition, you'll find everything you need for a thorough understand of trigonometry concepts now and the solid foundation you need for future coursework and career success |
Customer Reviews for Mcgraw-hill Education Key To Algebra, Books 1-10
Key To Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language and examples are easy to follow. Word problems relate algebra to familiar situations, helping students understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system. This kit contains only Books 1-10. Answers Notes for Books 1-4Books 5-7 and Books 8-10 are available separately, as well as the Key to Algebra Reproducible Tests Key To Algebra, Books 1-10
Review 1 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
easy to use!
I purchased this for my oldest son, who is now about to graduate. He did very well with it although book 4 was a little challenging. It is well written and easy to understand. I will be using it next year with my other son. I believe he will do very well with it. The only problem I have is that some times in the teachers guide, the answer is provided with no explaination as to how the answer is achieved. Since there were only a few like that we just skipped them. Other than that, it is great! I have recommended it to several of my homeschooling friends, and will continue to do so for years to come.
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+1point
1of1voted this as helpful.
Review 2 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
Date:October 12, 2005
Nancy Evans
I never had Algebra in school and never thought I could teach it! I was given your curriculum from an old homeschooler. The first day I looked at it I reviewed 1 and 1/2 books just to see if I could understand it, and I did! It gave me a new confidence teaching a subject I knew little about. Wow! Thank you key curriculum Press.
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Review 3 for Key To Algebra, Books 1-10
Overall Rating:
5out of5
Date:September 10, 2005
Donna
Now using it on student number 5. Easy to teach from and learn from and well retained information. |
Mathematics for Economists
Learning goals
In order to understand and apply modern economic theories and concepts as well as to meet the requirements for course study it is necessary for students to be able to use learn basic mathematical theories. This Course has the goal to provide students with these mathematical resources. |
Numbers in parentheses
indicate session (1-8) at which topic was covered.
Grade 8By the end
of grade eight,
students will understand various numerical representations, including
square roots, exponents and scientific notation; use and apply
geometric properties of plane figures, including congruence and the
Pythagorean theorem; use symbolic algebra to represent situations and
solve problems, especially those that involve linear relationships;
solve linear equations, systems of linear equations and inequalities;
use equations, tables and graphs to
analyze and interpret linear
functions; use and understand set theory and simple counting
techniques; determine the theoretical probability of simple events; and
make inferences from statistical data, particularly data that can be
modeled by linear functions. Instruction and
assessment should include the appropriate use of manipulatives
and technology use linear algebra to
represent, analyze and solve problems. They will use equations, tables,
and graphs to investigate linear relations and functions, paying
particular attention to slope as a rate of change.
M8A3. Students
will understand relations and linear functions. (1)
a. Recognize a relation as a correspondence between varying quantities.
(1) b. Recognize a function as a correspondence between
inputs and outputs where the output for each input must be unique.
(1) c. Distinguish between relations that are functions
and those that are not functions.
(1) d. Recognize functions in a variety of
representations and a variety of contexts.
(1) e. Use tables to describe sequences recursively and
with a formula in closed form.
(2) f. Understand and recognize arithmetic sequences as
linear functions with whole number input values.
(2) g. Interpret the constant difference in an
arithmetic sequence as the slope of the associated linear function.
(2) h. Identify relations and functions as linear or
nonlinear.
(1-2) i. Translate among
verbal, tabular, graphic, and algebraic representations
DATA ANALYSIS AND
PROBABILITY Students will use and understand set theory and simple
counting techniques; determine the theoretical probability of simple
events; and make inferences from data, particularly data that can be
modeled by linear functions.
M8D4. Students
will organize, interpret, and make inferences from statistical data
a. Gather data that can be modeled with a linear function.
b. Estimate and determine a line of best fit from a
scatter plot.
MATH
I
ALGEBRA
Students will explore functions and
solve simple equations. Students will simplify and operate with
radical, polynomial, and rational expressions.
(5) c.
Graph transformations of basic functions including vertical shifts,
stretches, and shrinks, as well as reflections across the
x- and y-axes.
(4) d. Investigate and explain the characteristics of a
function: domain, range, zeros, intercepts, intervals of increase and
decrease, maximum and minimum
values, and end behavior.
(4) e. Relate to a given context the characteristics of
a function, and use graphs and tables to investigate its behavior.
(4) f. Recognize sequences as functions with domains
that are whole numbers.
(4) g. Explore rates of change, comparing constant rates
of change (i.e., slope) versus variable rates of change. Compare rates
of change of linear, quadratic,
square root, and other function families.
(4) h. Determine graphically and algebraically whether a
function has symmetry and whether it is even, odd, or neither.
(2) i. Understand that any
equation in x can be interpreted as the equation f(x)
= g(x), and interpret the solutions of the
equation as the x-value(s)
of the intersection point(s) of the graphs of y = f(x)
and y = g(x).
Mathematics
2This is the second course in a
sequence of courses designed to provide students with arigorous program of study in mathematics. It
includes complex numbers; quadratic, piecewise, and exponential
functions; right triangles, and right triangular trigonometry;
properties of circles; and statistical inference. (Prerequisite: Successful
completion of Math 1). Instruction and assessment should include
the appropriate use of manipulatives and
technology investigate piecewise,
exponential, and quadratic functions, using numerical, analytical, and
graphical approaches, focusing on the use of these functions in
problem-solving situations. Students will solve equations and
inequalities and explore inverses of functions.
MM2A1. Students
will investigate step and piecewise functions, including greatest
integer and absolute value functions. (3)
a. Write absolute value functions as piecewise functions.
(3) b. Investigate and explain characteristics of a
variety of piecewise functions including domain, range, vertex, axis of
symmetry, zeros, intercepts, extrema, points of
discontinuity, intervals over which the function is constant, intervals
of increase and decrease, and rates of change.
(3) c. Solve absolute value equations and inequalities
analytically, graphically, and by using appropriate technology.
MM2A2. Students
will explore exponential functions. (6)
a. Extend properties of exponents to include all integer exponents.
(7) b. Investigate and explain characteristics of
exponential functions, including domain and range, asymptotes, zeros,
intercepts,
intervals of increase and decrease, rates of change, and end behavior.
(7) c. Graph functions as transformations of f(x)
= ax.
(8) d. Solve simple exponential equations and
inequalities analytically, graphically, and by using appropriate
technology.
(7) e. Understand and use basic exponential functions as
models of real phenomena.
(7)
f. Understand and recognize geometric sequences as exponential
functions with domains that are whole numbers.
(7) g.
Interpret the constant ratio in a geometric sequence as the base of the
associated exponential function.
MM2A4. Students
will solve quadratic equations and inequalities in one variable. (5)
a. Solve equations graphically using appropriate technology.
(5) b. Find real and complex solutions of equations by
factoring, taking square roots, and applying the quadratic formula.
(5) c. Analyze the nature of roots using technology and
using the discriminant.
d. Solve quadratic inequalities both
graphically and
algebraically, and describe the solutions using linear inequalities.
MM2A5. Students
will explore inverses of functions.
(8) a. Discuss the
characteristics of functions and their inverses, including
one-to-oneness, domain, and range.
(8) b. Determine inverses of linear, quadratic, and
power functions and functions of the form f(x) = a/x,
including the use of restricted
domains.
(8) c. Explore the graphs of functions and their
inverses.
(8) d. Use composition to verify that functions are
inverses of each other.
MM2D2. Students
will determine an algebraic model to quantify the association between
two quantitative variables. a. Gather and plot data that
can be modeled with linear and quadratic functions.
b. Examine the issues of curve fitting by finding
good linear fits to data using simple methods such as the median-median
line and "eyeballing".
c. Understand and apply the processes of linear and
quadratic regression for curve fitting using appropriate technology.
d. Investigate issues that arise when using data to
explore the relationship between two variables, including confusion
between correlation and causation.
MM3A1. Students
will analyze graphs of polynomial functions of higher degree.
a. Graph simple polynomial functions as translations of the function f(x)
= axn.
b. Understand the effects of the following on the
graph of a polynomial function: degree, lead coefficient, and
multiplicity of real zeros.
c. Determine whether a polynomial function has
symmetry and whether it is even, odd, or neither.
d. Investigate and explain characteristics of
polynomial functions, including domain and range, intercepts, zeros,
relative and absolute extrema, intervals
of increase and decrease, and end behavior. |
Compressed Math 7 The math curriculum used in the Tumwater School District is aligned to the newest Washington state math standards. This course is a compressed version of seventh and eighth grade state standards and will prepare students to transition to eight grade algebra. We will be using materials from Connected Mathematics Project (CMP2), along with supplemental resources and materials. |
Emaths.Info - Vinod Sebastian
Math tools, formulas, tutorials, videos, tables, and "curios," such as the unusual properties of 153, 1729, and 2519. See in particular Emaths' interactive games, which include the N queens problem, Towers of Hanoi, and partition magic, which finds a
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The Geometer's Sketchpad - Key Curriculum Press
Geometry software for Euclidean, coordinate, transformational, analytic, and fractal geometry, recommended for students from grade 5 through college. Developed for geometry, students now also use Sketchpad's flexibility and reach to explore algebra, trigonometry, |
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