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Essentials of Trigonometry - With CD - 4th edition
Summary: Intended for the freshman market, this book is known for its student-friendly approach. It starts with the right angle definition, and applications involving the solution of right triangles, to help students investigate and understand the trigonometric functions, their graphs, their relationships to one another, and ways in which they can be used in a variety of real-world applications. The book is not dependent upon a graphing calculator2.79 9780534494230
$4.50 +$3.99 s/h
Good
Nettextstore Lincoln, NE
200563 +$3.99 s/h
Good
Campus_Bookstore Fayetteville, AR
Used - Good Hardcover. texbook only 4th Edition May contain highlighting/underlining/notes/etc. May have used stickers on cover. Ships same or next day. Expedited shipping takes 2-3 business days; sta...show morendard shipping takes 4-14 business days. ...show less
2006 Hardcover Good NO CD. Includes iLrn Tutorial and Studen Solutions Manual.
$30.00 +$3.99 s/h
Good
Textbook Barn Woodland Hills, CA
Hardcover Good 0534494234
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The History of Mathematics History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social con... MOREtext behind mathematics' greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library.
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0486204308
9780486204307
History of Mathematics:Volume II of an unusually clear and readable two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Evolution of arithmetic, geometry, trigonometry, calculating devices, algebra, calculus, more. Includes problems, recreations, and applications.
Back to top
Rent History of Mathematics 1st edition today, or search our site for David E. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Dover Publications, Incorporated.
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Mathematics program intended for Middle School pupils (age 11-14). This Title comprises 19 chapters of complete courses completed with exercises covering every subject undertaken. The exercises are corrected step by step using the Evalutel Teaching Method which reconciles the struggle against failure in school and the valorisation of the most talented .... Free download of GEOMETRY 1 : Symmetries, Thales, Pythagoras, Figures, constructions … 1.01.002 5.0 Beta Portable 4.9.233.0 Test for Mac 4.2.58
... In numerology numbers 1 to 9 have certain geometry. Numbers relate to a pattern of energies and vibrations. The bad, good and the information about previous birth and the effects of previous in present birth and every trait of a human being can be highlighted. Numbers express more than we .... Free download of MB Runes Numerology 1.15 Windows 2.1.05 Mac OS X 2.1.05
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Summary
Strong algebra skills are crucial to success in applied calculus. This text is designed to bolster these skills while students study applied calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra topics and points out potential problem spots. the table of contents is organized so that the algebra topics are arranged in the order in which they are needed for applied calculus.
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Click below to play a sample Core Video from our CSET Mathematics Subtest 1 Online Prep program. This particular video focuses on proof by mathematical induction, a topic that commonly appears on written response questions.
When you purchase any of our CSET Mathematics Subtest 1 Online Prep programs, you'll get Core Videos like this one covering every key number theory and algebra concept you need to pass. You'll learn the same key subject matter you would in our live classes, as well as strategies for success on the various multiple choice and constructed response question types you can expect on the exam. Then, once you are confident with the underlying subject matter, you can watch our Smart-STEM Virtual Tutoring videos, in which a tutor will show you how to apply your knowledge to the specific question types you are most likely to encounter on the actual test.
Both our Core Videos and Smart-STEM Virtual Tutoring videos are included in all our Online Prep programs!
These Core Videos Are Included in All Our CSET Mathematics Subtest 1 Online Prep Programs...
Below is a complete list of the Core Videos that are included in all our CSET Mathematics Subtest 1 Online Prep programs. These videos have been created by our industry-leading team of Teachers and Subject Matter Experts based on the official Content Specifications published for the CSET, along with research and feedback from students and test takers, so you get an engaging, easy-to-use, and highly-focused program that makes the absolute most of your study time and teaches you the exact content knowledge and strategy you need to pass the exam.
Number Sense: Properties of Real and Complex Numbers
Fields and Rings
Complex Number Operations
Ordering of Rational and Real Numbers
Linear Programming
Rational Root Theorem and Factor Theorem
Zeros of Functions
Quadratic Formula
Polynomial Equations and Inequalities
Binomial Theorem
Fundamental Theorem of Algebra
Properties of Functions
Solutions to Functions
Specific Functions
Graphing Functions
Increasing/Decreasing Functions
Linear Algebra
Cross Products
Dot Products
Unit Vectors
Matrices - Determinants
Matrices
Matrix Multiplication
Systems of Equations
Properties of Natural Numbers
Mathematical Induction(You are currently viewing this free sample video.)
Greatest Common Divisor
Euclidean Algorithm
Fundamental Theorem of Arithmetic Factors
Least Common Multiple and Square Roots
Enroll in CSET Mathematics Online Prep, and you can begin watching all these Core Videos right now! You'll also get instant access to a host of other great features, including Smart-STEM Virtual Tutoring Videos in which an expert tutor will discuss each question on your full-length, CSET Mathematics Subtest 1 (Version 1) Practice Test, teaching you proven strategies for applying the subject matter knowledge you've gained from our Core Videos to the specific types of questions you are most likely to encounter on the real exam.
Connect with us for discounts, sample prep videos, test tips for credential candidates, in-class ideas for working teachers, grants, job opportunities in education and more.
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Intermediate Algebra With Early Functions and Graphing/Hornsby developmental mathematics paperback series has helped thousands of students succeed in math. In keeping with its proven track record, this revision includes a sharp new design, many new exercises and applications, and several new features to enhance student learning. Among the features added or revised include a new Study Skills Workbook, a Diagnostic Pretest, Chapter Openers, Test Your Word Power, Focus on Real-Data Applications, and increased use of the authors' six-step problem solving process.
(Each Chapter ends with a Summary, Review Exercises and a Chapter Test. With the exception of Chapter 1, each Chapter also ends with a set of cumulative review exercises.). List of Applications. Preface. An Introduction to Scientific Calculators. To the Student. Diagnostic Pretest. 1. Review of the Real Number System.
The Square Root Property and Completing the Square. The Quadratic Formula. Equations Quadratic in Form. Formulas and Further Applications. Graphs of Quadratic Functions. More About Parabolas; Applications. Quadratic and Rational Inequalities.
Additional Graphs of Functions; Composition. The Circle and the Ellipse. The Hyperbola, and Other Functions Defined by Radicals. Nonlinear Systems of Equations. Second-Degree Inequalities; Systems of Inequalities.
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Elementary Linear Algebra / With CD-ROM - 5th edition
Summary: The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.
Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin.
Section 3.4, now named "Introduction...show more to Eigenvalues," has been
All real data in exercises and examples have been updated to reflect current statistics and information.
This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives.
Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM.
0352
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This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes:.:.; A modernized section on trigonometry.; An introduction to mathematical modeling.; Instruction in use of the graphing calculator.; 2,000 solved...Whether it's stuff in your kitchen or garden, stuff that powers your car or your body, stuff that helps you work, communicate or play, or stuff that you've never heard of you can bet that mathematics is there. MATH STUFF brings it all in the open in the Pappas style. Not many people think of mathematics as fascinating, exciting and invaluable. Yet... more...
Most people don?t think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive . Pappas explores mathematical ideas by looking behind... more...
What are the odds against winning the Lottery, making money in a casino, or backing the right horse? Every day, people make judgements on these matters and face other decisions that rest on their understanding of probability: buying insurance, following medical advice, carrying an umbrella. Yet many of us have a frightening ignorance of how probability... more...
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excel AS and A Level Modular Mathematics Core Mathematics 1 C1
Edexcel and A Level Modular Mathematics C1 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. ...Show synopsisEdexcel and A Level Modular Mathematics C1 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. *Sample exam papers for thorough exam preparation. *Regular review sections consolidate learning. *Opportunities for stretch and challenge presented throughout the course. *'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. *Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. *Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary
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MTH 98
Basic Mathematics
Course info & reviews
Topics include basic ideas of numbers, operations, and procedures to solve problems; representations of quantitative information; measurement and informal geometry; and the basics of logic. Required for education majors who fail the math portion of the PRAXIS I exam. INSTITUIONAL CREDIT ONLY. MAY NOT BE USED TO FULFILL ANY DEGREE REQUI...
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Delaney's Den of MaTThS
Learning & Succeeding in College Mathematics, Science and Writing
Series Circuits
This section is devoted to worksheets on Series Circuits. There is an Answer Key for every series circuit posted at the bottom of the page. If you have any questions or concerns about the worksheets, let me know. I will create more worksheets as time allows.
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Teaching Mathematics in the 21st Century. Responding to a Bigger World (page 2)
Even as the utilitarians were urging a reduced mathematics curriculum, others were calling for expansion. World War II had shown Americans a bigger world—a world where Swiss students studied calculus in high school, where scientific breakthroughs were needed, not just to win but to survive. The Commission on Post War Plans called for more, not less, mathematics in education. In 1947 the President's Commission on Higher Education proposed increasing college enrollments drastically for a minimum of 4.6 million by 1960—a change that would require a college-track mathematics curriculum for millions. By the time the Soviet Union launched Sputnik in 1957 and galvanized public opinion for the space race, educators were already experimenting with new mathematics curricula.
The "new math," as it was popularly called, emphasized mathematics structure. Students studied sets, number systems, different number bases, and number sentences. Teachers guided children to discover concepts rather than lecturing about them. While many ideas of the new math had merit, application may have been flawed. Textbooks were often hard to read and overly formal. Many parents complained that they could not understand their children's homework.
In the meantime, the social revolution of the 1960s and 1970s flooded colleges with students—many from backgrounds and groups that traditionally had not attended college. To what extent this new college population affected test scores remains unclear, but between 1963 and 1975 SAT scores declined, leading to several major concerns for the mathematics curriculum in the final decades of the century, including how to:
upgrade the curriculum to match the demands of an increasingly technological society,
balance student needs with the needs of society and of mathematics itself, and
teach the expanded curriculum to all of the students.
There were no easy answers. A back-to-the-basics movement called for a return to traditional mathematics—teacher lectures, drills, and tests. But many argued that traditional approaches had worked for no more than 5% to 15% of the students; what was needed was a challenging mathematics curriculum that prepared every student to think mathematically—to develop the foundations in mathematical reasoning, concepts, and tools needed for advanced mathematics education as well as enlightened living in the age of technology.
The National Council of Supervisors of Mathematics (NCSM) responded with a list of basic skills (1977) and later with "Essential Mathematics for the Twenty-first Century "(1989). NCTM did the same, producing an Agenda for Action in 1980, the first version of the Curriculum and Evaluation Standards in 1989, and now the Standards 2000 document, Principles and Standards for School Mathematics, compiled with the input of thousands of mathematics teachers responding over the World Wide Web. Some major points of consensus between the NCSM and the NCTM recommendations include the following:
that all students benefit from a challenging mathematics curriculum;
that mathematics reasoning and higher-order thinking skills should be integral to the curriculum;
that problem solving should be a priority;
that algebraic thinking, geometry, statistics and probability are essential rather than add-on skills;
that the emphasis in computation should be on meaning and patterns;
that communication of mathematical ideas in a variety of ways (oral, written, symbolic language, everyday language) is critical to the learning process;
that students need opportunities to explore and apply mathematics in hands-on and real-life activities.
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Peer Review
Ratings
Overall Rating:
This is a comprehensive resource to learn or refresh algebra skills and concepts. It includes step by step explanations as well as problem worksheets and quizzes. It does not demonstrate applications using these algebra techniques.
Learning Goals:
To learn elementary and intermediate algebra and to practice problem solving.
Target Student Population:
Students in beginning and intermediate algebra (and possibly college algebra).
Prerequisite Knowledge or Skills:
Pre-Algebra.
Type of Material:
Presentation, drill and practice, and quiz/test.
Recommended Uses:
Independent study or supplementary material to textbook and classroom.
Technical Requirements:
Any modern browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This site covers algebra described as Introductory (23 topics), Intermediate (72 topics) and Advanced (34 topics). The step by step explanations are excellent and include embedded links to terms used in the explanations as well as other resources such as mathematician biographies. The explanations include the general concept plus several sample problems. Also embedded in the site is the automated problem solver, Mathway that solves most algebra problems. The student types in the algebra problem and the computer provides the solution, the steps to the solution, and the accompanying graph if applicable. The site contains a comprehensive range of algebra material.
Concerns:
The one missing feature is applications or word problems – significant because this is an area where many students need additional resources and practice.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The visual effect of the graphics with color and occasional animation is effective. An algebra student can use this site to supplement his or her algebra class and use the math problem solver to check or get help with algorithmic oriented problems.
Concerns:
Some embedded links are not entirely effective – for example in adding algebra fractions the links for LCM and equivalent fractions lead to examples that show only numbers.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The site is simple to use with clear organization. The material is indexed both alphabetically and by course. Any student will have no difficulty finding a concept and reading through the explanation and examples. The math problem solver that is embedded in the site includes plenty of explanations on how to type in the problem to be solved and how to read the displayed solution.
Concerns:
None
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books.google.co.jp - This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional theory such as pseudoconvexity and holomorphic convexity, and leads up to complete proofs of fundamental... Functions and Integral Representations in Several Complex Variables
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About:
Systems of Linear Equations: Applications
Metadata
Name:
Systems of Linear Equations: Applications
ID:
m21983
Language:
English
(en)
Summary:
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
Beginning with the graphical solution of systems, this chapter includes an interpretation of independent, inconsistent, and dependent systems and examples to illustrate the applications for these systems. The substitution method and the addition method of solving a system by elimination are explained, noting when to use each method. The five-step method is again used to illustrate the solutions of value and rate problems (coin and mixture problems), using drawings that correspond to the actual situation.
Objectives of this module: become more familiar with the five-step method for solving applied problems, be able to solve number problems, be able to solve value and rate problems.
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Book Description
Publication Date: February 1, 1968 | Series: Schaum's OutlineEditorial Reviews
From the Back Cover
Students love Schaum's Outlines! Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use Schaum's!
If you don't have a lot of time but want to excel in class, this book helps you:
Brush up before tests
Find answers fast
Learn key formulas and tables
Study quickly and more effectively
Schaum's Outlines give you the information teachers expect you to know in a handy and succinct formatwithout overwhelming you with unnecessary detail. You get a complete overview of the subject, plus plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's let you study at your own pace and reminds you of all the important facts you need to rememberfast! And Schaum's are so complete, they're perfect for preparing for graduate or professionalexams!
Inside, you will find:
More than 2400 formulas and tables
Clear and concise explanations of all results
Formulas and tables for elementary to advanced topics
Complete index to all topics
If you want top grades and easy-to-use information for your math and science courses, this powerful study tool and reference is the best guide you can have!
--This text refers to an out of print or unavailable edition of this title.
About the Author
Murray Speigel, Ph.D., was Former Professor and Chairman of the Mathematics Department at Rensselaer Polytechnic Institute, Hartford Graduate Center.
--This text refers to an out of print or unavailable edition of this title.
As an undergraduate physics major, it is necessary to have some sort of mathematical handbook containing tables of integrals, trig identities, differentiation rules, vector identities, etc. As such, I cannot give this book higher praise! While does not contain as many features as the CRC Handbook of Tables and Formulae, or many of the other big famous hardcovers, it makes up for this in many ways. It is compact, lightweight and fits in most bookbags. It contains the tables and rules which will be most used in undergraduate homework problems. Most importantly, it is affordable on a student budget! I carry this with me to study groups and tutoring sessions.
As an undergrad in physics and math, one of the physics professors recommended this book as "the math reference you couldn't live without". Now as a grad student, I'm quickly discovering that she wasn't kidding. It has just about everything you could need. I don't know how much time I've saved from digging through a pile of textbooks to find the appropriate integral or function. Get it. You won't regret it.
PLEASE NOTE: The following review is for "Math Formulas and Tables: Algebra, Trigonometry, Geometry, Linear Algebra, Calculus, Statistics. Tables of Integrals, Identities, Transforms & more. FREE Derivatives in demo (Mobi Study Guides)." Amazon is erroneously cross-posting reviews to the Schaum's Outline book, which is unfortunate, because the Schaum's book is excellent.
MobileReference has awkwardly stitched this book together from Wikipedia content, but it costs nearly the same amount ($10) as the Kindle edition of the Schaum's outline. For the money, I find the Schaum's to be more comprehensive and easier to read.
This is a pretty helpful Schaum's outline, in that most of the mathematical tables and formulas that an undergraduate math student would need are included. Material from geometry, calculus, differential equations, numerical methods, special functions and transforms, and probability and statistics are included. Plus, there are some examples of how to perform some types of calculations. There is even a section on calculating compound interest and the value of an annuity for those students of financial mathematics. Also, it is much easier than lugging around the infamous 2600 page "CRC Handbook of Mathematics and Physics." Of course, there are tradeoffs. This book has mathematical tables and formulas only, there are no physics equations.
Generally, if you are an undergraduate student in math or science, your required textbook will have all of the equations and tables that your instructor would expect you to have committed to memory for exams. Thus I am not sure if it is worth the extra cost to buy this book too. I think this book would be most helpful for someone who is out of school who needs their undergraduate mathematics tables and formulas condensed and in one portable book that can be taken to work and stored at the office, rather than carrying around the dozen or so math texts you used during your undergraduate career. It would also be helpful for someone going to graduate school in math, physics, or engineering who is expected to already know this material and therefore needs a handy reference.
This handbook is a must have for any junior level or higher engineering major or any major that deals with advanced mathematics. It contains detailed and easy to understand charts and tables ranging from College Algebra and Trigonometry to Advanced Calculus and Differential Equations. It is also a must have reference book to anyone needing to access to advanced mathematics formulas.
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Shrinking Candles, Running Water, Folding Boxes
Lesson
Grade:
9-12
Periods:
4
Standards:
Author:
Unknown
Unknown
This activity allows students to look for functions within a given set
of data. After analyzing the data, the student should be able to
determine a type of function that represents the data. This lesson plan
is adapted from an article by Jill Stevens that originally appeared in
the September 1993 issue of the Mathematics Teacher.
translate among tabular, symbolic, and graphical representations of
functions;
recognize that a variety of problem situations can be modeled by the same
type of function;
analyze the effects of parameter changes on the graphs of functions. (NCTM
1989, 154)
The curriculum standards also stress the continued study of data analysis
and statistics so that all students can-
construct and draw inferences from charts, tables, and graphs that
summarize data from real-world situations;
use curve fitting to predict from data. (NCTM 1989, 167)
The following activities promote these objectives.
Prerequisites: Students should understand the relationships
between various functions and their graphs. Their knowledge should cover
linear, quadratic, higher-degree-polynomial, exponential, and trigonometric
functions. They should also be able to use a graphing calculator with
features that will allow them to edit data, create scatterplots, and draw
functions over those plots.
Directions: The activities will require three to five class
periods to complete with students working in groups of three to four. The
following problem will introduce the activities and allow time for any
necessary instruction on using a graphing calculator. One explanatory
example is usually sufficient for students successfully to use a graphing
calculator for these activities.
Allow time for students to explain why
they chose a particular function
As an example, our class discussed a unit called "How Does Corn Grow?" to
familiarize students with data and graphing. Students planted some
corn. After the seeds sprouted, they measured their growth each
day.
Analyze the collected data.
Day 1 is the first day that sprouts appeared. Each group chose a
sprout and measured its height for five days. The following results from
one group are shown.
Day
Height (cm)
1
2
3
4
5
1.50
2.59
3.91
6.02
7.11
Ask students to enter the data into a graphing calculator, make a
scatterplot of the data on the calculator, and analyze the results.
Before making the scatterplot, students must decide on an
appropriate domain and range so that all their points will appear on the
graph. In this example, we have chosen the day number as the independent
variable (x) and the height of the corn plant as the dependent variable
(y). We will let the x-axis go from -5 to 10 and the
y-axis go from -5 to 15. In so doing, all data will appear on the
screen so that both axes can be seen. After setting the appropriate
domain and range, students should use the calculator to produce a scatterplot
of the data and analyze the results.
Students can discuss how their equations
can predict future function values
Students should decide what type of function the data most
closely represents and write an equation to fit the data. In this
example, the data appear to be linear. The students can make an "eyeball"
fit of the
data by examining the scatterplot and determining a y-intercept and
slope. They might try a y-intercept of 0.05 and a slope of
1.3. The students should use the calculator to draw the equation y
= 1.3x + 0.05 over the scatterplot to check the accuracy of the fit,
which is shown in Figure 1.The
equation appears to
fit the data closely. In many examples, students will try several
equations before they find a close fit.
Allow time for students to explain why they chose a particular
type of function, how they derived their equation, and what restrictions the
problem situation places on the domain and range of the function. In our
example, x and y can be any real number in the algebraic
equation, but in the model, x must be a positive integer and y must be a
positive real number. Also, an upper bound will be necessary for x
and y, since the corn will not continue to grow indefinitely.
The students should also discuss how their equation could be used
to predict future function values. They could use their equation to
predict the height of a corn sprout on future days. If they had actually
grown the corn plants, they could test their predictions by later measuring the
specific sprouts.
The same general procedure that was outlined in the example
problem should be followed for the activity sheets. The student should
collect data, produce a scatterplot, analyze it, choose a function, and write
an
equation. Test the equations by drawing the function over the scatterplot
on the graphing calculator. Class discussion should include why a certain
function type was chosen, whether another function type might also work, how
equations were derived, what restrictions are placed on the domain and range by
the problem situation, and whether the model could be used to predict future
values. Although no one answer is correct for each problem, some
answers may be better than others. Some sample solutions are given.
" 'Weather' It's a Function" was calculated
from the normal high
temperature for the Dallas area and was obtained by writing to a local
television weather forecaster; see Figure
6. The average monthly temperature for many cities can be found
in
almanacs. This information reduces the domain to twelve values but still
yields a fairly smooth curve. Be sure the calculator is in the radian
mode to work this problem.
Discussion and extension activities: The
"EliM&Mination" problem serves as a model of decay. Have students
suggest real-life situations that this problem might model.
The "Flaming Function" is linear. It is interesting to
compare the equation the students obtain from the "eyeball" method with those
from the median-median-line and linear-least-square methods of curve
fitting. The Data Analysis software package from the National Council of
Teachers of Mathematics (1988) is a good source for information about these
methods.
"All Boxed In" presents a cubic model. This problem could
be extended by asking students to find the length plus girth and the surface
area of each box in addition to its volume. The problem would then
include a linear, quadratic, and cubic model. The post office uses the
concept of girth to limit the size of boxes sent in the mail (length + girth
<= 108
inches). Ask students to find the box with the greatest volume for the
least surface area that would meet postal regulations.
The problem " 'Weather' It's a Function"
produces a sine wave. The students can use this model to predict
temperatures and then check to see how close their predictions come to the
actual members.
The "Water Level" problem yields data for a quadratic
model. An interesting activity would be to have different groups use
different-sized jugs and compare the curves obtained from the data.
If computers are available, students may want to print their
graphs rather than draw them. The figures illustrated in this article
were created using The Mathematics Exploration Toolkit (IBM 1988).
Another
source of software is Data Analysis (NCTM 1988), which allows students to print
tables and graphs. The software also includes many algorithms to fit
curves to data sets.
|
Math Review for Physics
Get math review for physics and study guides here. Learn about geometry, trigonometry, and algebra for physics or brush up on your skills. Thorough explanations and practice examples will help you review math concepts require to understand physics.
Study Guides
Introduction
In physics, the numbers we work with are not always exact values. In fact, in experimental physics, numbers are rarely the neat, crisp, precise animals familiar to the mathematician. Usually, we must approximate. There are two ...
Introduction
When multiplication or division is done using power-of-10 notation, the number of significant figures in the result cannot legitimately be greater than the number of significant figures in the least-exact expression. You may ...
Introduction
Graphs are diagrams of the functions and relations that express phenomena in the physical world. There are all kinds of graphs; the simplest are two-dimensional drawings. The most sophisticated graphs cannot be envisioned even by the most astute human ...
The Polar Plane
The polar coordinate plane is an alternative way of expressing the positions of points and of graphing equations and relations in two dimensions. The independent variable is plotted as the distance or radius r ...
Introduction
Here are some other coordinate systems that you are likely to encounter in your journeys through the world of physics. Keep in mind that the technical details are simplified for this presentation. As you gain experience using ...
Fundamental Rules
The fundamental rules of geometry are used widely in physics and engineering. These go all the way back to the time of the ancient Egyptians and Greeks, who used geometry to calculate the diameter of the earth and the ...
Introduction
If it's been a while since you took a course in plane geometry, perhaps you think of triangles when the subject is brought up. Maybe you recall having to learn all kinds of theoretical proofs concerning triangles using ...
Introduction
A four-sided geometric figure that lies in a single plane is called a quadrilateral . There are several classifications and various formulas that apply to each. Here are some of the more common formulas that can be useful ...
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Differential Equations Teacher Resources
Find Differential Equations educational ideas and activities
Title
Resource Type
Views
Grade
Rating
Students solve differential equations. In this differential equations lesson, students use their TI-89 calculator to explore slope fields and find solutions to a differential equation. They graph their solutions.
Twelfth graders explore differential equations. In this calculus lesson, 12th graders explore Euler's Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler's Method of numeric solutions to a graphical solution.
Explore differential equations by using models representing growth and decline. Using calculus, learners will investigate exponential and logistic growth in the context of several models representing the growth or decline of a population. Most of the models have a closed-form solutions. Problems and solutions are included.
Learners use their TI-89 calculator to compute derivatives and anti-derivatives. In this differential equation lesson, students follow detailed directions to complete one table of derivative/anti-derivative values. They compute the anti-derivative of one equation and find the derivative of one equations.
Twelfth graders solve problems using differential equations. In this Calculus lesson, 12th graders analyze data regarding the spread of a flu virus. Students use the symbolic capacity of the TI-89 to develop a model and analyze the spread of the disease.
Students explore how to graph differential equations using a TI calculator. In this math instructional activity, students solve systems of equations using the calculator. Students explore graphing and use it to interpret experimental data.
In this differential equations worksheet, students solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
Twelfth graders investigate differential equations. In this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem. Students solve differential equations and application of differential equations.
In this atmospheric carbon dioxide worksheet, students use two diagrams to solve 6 problems about atmospheric carbon dioxide. One diagram shows the Keeling Curve and the other shows sources of carbon and the natural and anthropogenic flux. Students find sources and sinks of carbon dioxide, they write a differential equation describing the change in carbon dioxide in the atmosphere and they use the Keeling Curve to compare it to their equation for the rate of change.
Students identify and familiarize themself with the features and capabilities of the TI-92 Plus calculator. They also find symbolic solutions of differential
equations and general solutions or to find particular solutions of initial-value and boundary-value problems. Finally, students use TRACE to find numerical values for this phase-plane graph.
Students investigate differential equations and slope fields. In this differential equations and slope fields lesson, students determine how much time can pass before a cup of coffee is safe to drink. Students use a differential equation to solve the problem algebraically. Students create a slope field to represent the time at which it is safe to drink the coffee.
Twelfth graders investigate exponential decay. In this Calculus instructional activity, 12th graders explore Newton's Law of cooling which can be modeled by a differential equation. Students use the model to solve a murder as they examine the temperature of a body to determine time of death.
In this differential equations learning exercise, students solve and complete 3 different parts of a problem. First, they sketch a slope field for the given differential equation on the axes provided. Then, students write an equation for the line tangent to the graph of a given point.
Twelfth graders investigate differential equations. In this calculus lesson plan, 12th graders use the TI-89 to explore differential equations analytically, graphically, and numerically and examine the relationships between the three approaches.
In this calculus instructional activity, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
Learners follow detailed instructions for using their TI-86 graphing calculator to find solutions to differential equations. In this lesson plan, students learn to use their graphing calculator to solve 12 differential equations.
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Math 41 Autumn 2013
Problems from the textbook and other handouts will serve one of two purposes in Math 41: as uncollected Daily Discussion Problems
or as graded Weekly Homework.
Each is handled in a different way and has a different purpose.
About Daily Discussion Problems (Quick Jump to List):
Each time we cover a topic, we will list below the corresponding text section and also some "discussion problems" that will help direct the discussion in the upcoming Tuesday/Thursday section meetings. Some may be similar to problems from weekly homework assignments, and problems from prior years' exams will give you an idea of the level of exam questions. You should try working these discussion problems immediately after reading the book section(s) being covered in lecture. For complete understanding of the course material, be sure that you understand both the discussion problems and the weekly homework problems, in addition to all examples from the readings. (Work on daily discussion problems will not be collected.)
About Weekly Homework (Quick Jump to List):
Completing homework assignments is an essential part of this course. Problems are designed to reinforce concepts covered in lecture as well as to encourage students to explore implications of the results discussed in class. Very few students will be able to go through the entire course without struggling on many problems, so do not be discouraged if you do not immediately know how to solve a problem. In confronting difficult questions you should consider how the problem at hand connects to topics, definitions and/or theorems discussed in class.
When you have worked on a problem for a while and remain stuck, you are encouraged to ask for hints from your instructor or TA. Students may also discuss problems with one another, but must write solutions on their own. In particular if you have taken notes while discussing homework problems with friends or instructors, you must put these notes away when writing your solution. The Honor Code applies to this and all other written aspects of the course. Be warned: watching someone else solve a problem will not make homework a good preparation for tests. Don't get caught in the trap of relying on others to get through homework assignments.
Students are expected to take care in writing their assignments. For instance,
never forget to put your name, your section number and your TA's name on the top of your work;
assignments should be written neatly;
assignments should contain clear, complete solutions; and
completed assignments which contain multiple pages should be stapled for easy grading -- one point will be deducted for not doing this.
Partial progress toward solutions on problems will be awarded partial credit, but simply writing answers down without justification will receive zero credit. Please note that usually only a portion of each week's problems will be scored; the selection of problems chosen to be graded will not be announced in advance.
Logistics for Weekly Homework:
Assignments must be turned in to your TA (discussion section leader) -- you will not receive credit for work turned into another section leader.
(If you're unable to turn in your homework in section, slide it under your TA's office door; submission to TA mailboxes is not permissible.)
The deadline is 3:00 p.m. on the given due date, and no (or via electronic scan if absolutely necessary) If more than a week has passed since an assignment was returned in section, your CourseWork score entry for that assignment can no longer be changed.
Read the Section Assignments to determine which discussion section you should attend starting Tuesday. Note: you cannot use Axess to sign up for a discussion section, only a lecture. You must use CourseWork to make your discussion section choice -- and the chart on the page linked above will show you the options for times.
Look at the Course Schedule. Make sure you know when the three exams are (not during the lecture time
or in the regular classroom; locations TBA) and when the weekly homeworks are due. If you have a conflict with one of the two midterm exam times,
as soon as you know about it. (The final exam's date and time cannot be changed.)
Note: For full solutions to problems 11-14, click here -- but keep in mind there is no substitute for working these practice problems yourself before studying their solutions.
Section 4.2:
#1, 3, 11, 33, 35, 43, 47, 55
Section 4.3: (except for Mean Value Theorem, which we'll cover later)
#5, 7, 29, 33, 39
Section 4.6:
#3, 11, 19, 23, 25, 31, 45, 53, 57, 59a
Exercises Page 326: #63c, 65a
Notes: Recall that Chapter Review problems (like those on page 326) have full solutions available here [and also see Solutions to 11, 19, 23, plus comments] -- but you should be thinking carefully about all these problems on your own before consulting solutions.
Keep in mind that some topics on prior-year second midterms, such as l'Hospital's Rule, the Mean Value Theorem, Newton's Method, and Antidifferentiation, are not going to be covered on November 5th's midterm exam (they'll be on our final exam instead).
Additional Problem (required): It is a fact from trigonometry, which you do not have to prove, that $\sin x < x < \tan x$ for all $x$ in the interval $(0,\pi/2)$. Use this fact to determine the limit of $\frac{\sin x}{x}$ as $x$ approaches 0 from the right.
Note: This is the last homework due to turn in; during the last week of classes we'll post solutions to a brief "mock" assignment covering Section 5.6, which is the last topic covered on the course final exam.
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Course Listing
Math 6010 Systems of Numbers
Description: An introduction to the number systems of mathematics. Using an axiomatic approach and constructing models and examples, the number systems—natural, integer, rational, real, and complex are developed and studied. The course is designed to give a comprehensive understanding of number systems.
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Calculus 3 is considered by most to be a very difficult course to master in the realm of Calculus. This is because you will learn about many different topics, and each topic builds on the previous. If you dont understand something early on, the chances of catching up are drastically reduced as time goes on.
Most topics in calculus 3 are challenging because almost all of the problems are 3 dimenstional in nature. It takes time for the student to master how to visualize the problems in order to solve them. Once this is done, things are much easier. This DVD course teaches by example and you gain practice immediately with this visualization and problem solving techniques.
Our calculus video tutor lectures are based on a singular principle and that is the fact that if a student needs help with calculus, the task of learning becomes much easier when the calculus lectures are taught by someone who understands the frustration of a new student who is just starting out with this subject.
No matter if you are in business calculus, if you are a mathematics major, if you are a high school calculus student, a homeschooled calculus student, or an engineering student, our calculus video lectures will help you learn calculus. We back up this claim with a money back guarantee!
If you need calculus help, youll be interested to know that every single calculus video lecture features numerous solutions to calculus problems that you are likely to encounter in class. Furthermore, our lectures do not only deal with the easier calculus problems. Our calculus lectures feature calculus problems of all complexities ranging from the elementary problems all the way to the challenging problems that you will likely find on your exams.
You will also find that our calculus video lectures serve as a fantastic reference for calculus solutions as you work through homework problems. In many cases it is very helpful to see a similar problem worked out in detail as a guide to your own homework problems. When viewing a solution to a similar problem in calculus, it can in many cases help you turn the corner in discovering the solution to your homework problems
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Prealgebra - 5th edition
Summary: Prealgebra, 5/e, is a consumable worktext that helps students make the transition from the concrete world of arithmetic to the symbolic world of algebra. The Aufmann team achieves this by introducing variables in Chapter 1 and integrating them throughout the text. This text's strength lies in the Aufmann Interactive Method, which enables students to work with math concepts as they're being introduced. Each set of matched-pair examples is organized around an objective...show more and includes a worked example and a You Try It example for students. In addition, the program emphasizes AMATYC standards, with a special focus on real-sourced data. The Fifth Edition incorporates the hallmarks that make Aufmann developmental texts ideal for students and instructors: an interactive approach in an objective-based framework; a clear writing style; and an emphasis on problem solving strategies, offering guided learning for both lecture-based and self-paced courses. The authors introduce two new exercises designed to foster conceptual understanding: Interactive Exercises and Think About It95687.80 +$3.99 s/h
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Introduction to Discrete Mathematics
Experiments which are performed and measured according to the discrete values or continuous values both have different perceptions. Introduction to discrete mathematics is the branch of mathematics that refers to objects having only distinct and separate values or it can be said that this deals with the countable sets. Graph theory of hyper graphs, coding, the design of blocks, combinatorial and discrete geometry, matrices etc. fields are covered by discrete mathematics.
Basically, while giving discrete mathematics introduction, one cannot get the values on all the points as the function could be defined on some particular values only. But, continuous mathematics shows the combined result of smooth variation.
Congruence and recurrence relation are also a part of discrete mathematics.
To have a better understanding of these topics, the study of algorithms is must. The set of objects in discrete mathematics can have infinite of finite numbers. The removal of the errors is most significant in the discrete mathematics as compared with the continuous mathematics. In computer science, the areas of discrete mathematics are drawn on graph theory and logic. Besides that, in logic, combinatorics, probability, algebra, geometry and in all the sections, discrete mathematics concept is a must. Discrete is just the reverse process of continuous and the subject of engineering, digital signal processing and signal systems are totally based on this concept. Discrete mathematics is a contemporary field of mathematics that is
widely used in business and industry. It is sometimes called the mathematics
of computers.
Discrete Mathematics Definition
Discrete mathematics is the mathematics that deals with discrete objects as the discrete objects are separated from each other. Here, the data can only take certain values. Data is discrete, if there are only a finite number of values possible and occurs in a case where there are only a certain number of values, or when we are counting something.
For example, to obtain taxi license in Las Vegas, a person must pass a written exam regarding different locations in the city. Number of attempts a person takes to attempt the test is an example of discrete data. A person could take it once, twice, and so on. The possible values are 1, 2, 3, ......
Deviation: Difference between the value of an observation and the mean of the population.
Matrices: Rectangular arrays of numbers. Used in algebra, geometry, statistics, and probability, with many applications in science, business, and industry.
Permutation: A rearrangement of the elements in an ordered list S into a one-to-one correspondence with S itself.
Combinatorics: Branch of mathematics concerning the study of finite or countable discrete structures.
Graph: A graph that contains no cycles.
Graph Theory: The study of formal mathematical structures called graphs.
Ratio: A ratio is a relationship between two numbers of the same kind. Usually expressed as A : B.
Proportion: A name given to a statement, when the two ratios are equal. It can be written using a colon, a : b = c : d
Polar coordinates: This is the system of coordinates in which coordinates are defined with the help of angles.
Probability: Branch of mathematics that deals with the likelihood that a particular event will happen in the future. It is expressed as a number between 1 and 0 and can be expressed in fractions, ratios, percentage.
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Key Curriculum Releases IMP Year 4, 2nd Edition
IMP is four-year core mathematics curriculum and is aligned with Common Core State Standards. Adoption of the IMP curriculum includes implementation strategies, supplemental materials, blackline masters, calculator guides, and assessment tools.
Year 4 covers topics such as statistical sampling, computer graphics and animation, an introduction to accumulation and integrals, and an introduction to sophisticated algebra, including transformations and composition.
The second edition of Year 4 includes a new student textbook, 2 new unit books, and three updated unit books
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Mathematics
Welcome to the Westbury School District Mathematics Department
The mathematics program is designed to give students a useful and enjoyable experience. Our K – 12 program integrates technology and manipulatives in order to enhance learning. One of the major goals is to generate critical thinking skills and enable students to apply their knowledge of mathematics in order to analyze and solve unfamiliar problems in the real world. At the elementary level, students are learning mathematics through many modalities. Using a constructivist approach in a student centered learning environment, students use authentic situations to develop their own understanding of each mathematical concept. At the middle level, the focus is the Algebra Strand where the elementary concepts are extended and sustained. At the high school level, there is a rigorous range of courses which provide students with the opportunity to proceed at their own pace and achieve success. All of the math courses offered require the use of the graphing calculator and other forms of technology to enhance their study of mathematics.
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books.google.com - This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract... Mathematics with Applications
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A 10-question diagnostic quiz in every chapter to show readers where they need the most help.
Math from basic arithmetic to Algebra 2, broken down by subject and then building up from chapter to chapter so readers can group concepts together for easier learning.
A variety of practice exercises with detailed answer explanations for every topic.
A 15-20 question recognition and recall practice set that includes material from the entire chapter (and a few questions that cover material from the previous chapters), to once again reinforce what the reader has learned on a larger scale. Detailed answer explanations follow the practice set.
Description:
UNIQUE SELLING FEATURES AND BENEFITS Hundreds of practice questions, answers,
and explanations Complete review of the math topics covered by the three exams, with sample questions and explanations
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A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such...
see more
'A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.״According to the author, "I have written these pages for researchers and students in the sport and exercise sciences. I also...
see more
According to the author, "I have written these pages for researchers and students in the sport and exercise sciences. I also hope to get hits from students and researchers struggling to understand stats in other disciplines. If you're new to stats, most of what you read here will be a new view. But even if you have done some stats, there's plenty here that's new. For example, I've discarded most details of computation, in the hope that you will get a better understanding of the concepts. Let's leave the computations to the computers! You'll also find a new unified treatment of effect statistics and their magnitudes, a new emphasis and heaps of new stuff on validity and reliability, new valid methods to calculate reliability, a new exalted position for confidence intervals, a new attack on statistical significance and hypothesis testing, the first plain-language explanation of Bayesian analysis on the Web, a new way to understand all statistical models, a new simple treatment of non-parametric analyses, a new method of doing repeated measures with missing values (yes, it's true!), new simple ways to estimate sample sizes, and best of all, a highly ethical new way to reduce sample size. And as you may have noticed, I am blazing a trail with the use of plain language for a text of this sort.״
This is a free, online textbook that, according to the author, "is intended to suggest, it is as much an extended problem set...
see more
This is a free, online textbook that, according to the author, "is intended to suggest, it is as much an extended problem set as a textbook. The proofs of most of the major results are either exercise or problems. For instructors who prefer a lecture format, it shjould be easy to base a coherent series of lectures on the presentation of solutions to thoughtfully chosen problems.״ concerned
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More About
This Textbook
Overview
Based on the use of graphing calculators by students enrolled in calculus, there is enough material here to cover precalculus review, as well as first-year single variable calculus topics. Intended for use in workshop-centered calculus courses, and developed as part of the well-known NSF-sponsored project, the text is for use with students in a math laboratory, instead of a traditional lecture course. There are student-oriented activities, experiments and graphing calculator exercises throughout the text. The authors themselves are well-known teachers and constantly striving to improve undergraduate mathematics
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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This text aims to utilize all possible resources to help students understand calculus whilst integrating technology where appropriate. It introduces logarithms, exponetials and the trigonometric functions and places greater emphasis on problem solving. [via]
This modern calculus textbook places a strong emphasis on developing students' conceptual understanding and on building connections between key calculus topics and their relevance for the real world. It is written for the average student -- one who is mostly unfamiliar with the subject and who requires significant motivation. It follows a relatively standard order of presentation, with early coverage of transcendentals, and integrates thought-provoking applications, examples and exercises throughout. The text also provides balanced guidance on the appropriate role of technology in problem-solving, including its benefits and its potential pitfalls. Wherever practical, concepts are developed from graphical, numerical, algebraic and verbal perspectives (the "Rule of Four") to give students a complete understanding of calculusThe wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.
The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems. [via]
Help your students become effective users of technology for calculus problem-solving. These text-specific exploratory student workbooks present activities and instructions for the most popular graphing technologies
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Question:
I am a 13 year old math student who enjoys math. I know using a computer
will be important for me in my future. What computer programs should I be
learning right now? So far I am good at using word processing. We do not
use the computer in our math classes at all. What should I try to learn on
my own at home? My parents said they would help me! Thanks for any advice.
Replies:I am not a mathematician myself, I am a chemist. However, I would suggest
that you learn at least one programming language. In Chemistry or other
branches of science Fortran has been the traditional language though C is
becoming more common. You might want to start with Basic which is probably
available on your home PC (assuming you have one!).
gregory r bradburn While I would agree that learning the basics of programming is a good
educational experience, you might be interested in something with more
immediate utility. I would start by asking the teacher of the most advanced
math courses at the high school you will attend about the types of calcula-
tors that are used to support those classes. Usually, some type of graphing
calculator would be expected. I think the TI82 is a good example and it is
programmable, so you could learn quite a bit about programming basics with
this calculator, too. Eventually, you should get some experience with a
good general purpose math utility software product that also has symbolic
capability. My favorite for beginners in this category is MathCAD 5.0 which
is available in a student edition for windows. Before it will be of much
use you will have to study math a few more years. Good luck with your
studies.
tee If you have an interest in matrices, MATLAB is a valuable software package
to have available. Although the program has the capability of doing the
usual scalar operations, its primary strength lies in the area of calcula-
tions associated with matrices. MATLAB has an excellent "Help" facility and
the graphics are superb! It is available for both PC's and MAC's.
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2007 SUMMER MATHEMATICS INSTITUTE
PHILOSOPHY AND FACILITIES
The 2007 Summer Mathematics Institute at Oakland University will provide an
exciting mathematics program to stimulate the mathematical development of
bright students from Southeast Michigan. Students are selected based on
both exceptional talent and interest in mathematics. Those selected
will
generally have completed the tenth or eleventh grade, but very bright
students at the ninth grade level who have exceptional talent and have
accelerated their mathematical studies should also apply.
A major component of The Summer Mathematics Institute at Oakland
University
is the teaching of advanced undergraduate mathematical concepts from
probability theory, number theory, group theory, combinatorics, graph
theory, statistics, linear algebra, for college credit, in an creative
environment with a high level of mathematical activity. These are
interesting topics which can expand the horizons and confidence of
bright
students, and encourage them to work to their fullest potential. During
the program the students also participate in supervised computer lab
activity.
The Institute will have the use of a computer laboratory reserved for
the
participants. Students at the Institute will be given instruction on
the
use and ideas behind symbolic mathematical software (such as Maple or
Mathematica), which enable computers to answer sophisticated
mathematical
questions. Students will also be encouraged to explore self-directed
mathematical investigations independently.
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REA's Calculus Super ReviewGet all you need to know with Super Reviews!Updated 2nd Edition REA's Calculus Super Review contains an in-depth review that explains everything high school and college students need to know about the subject. Written in an easy-to-read format, this study guide is an excellent refresher and helps students grasp the important elements quickly and effectively.Our Calculus Super Review can be used as a companion to high school and college textbooks or as a study resource for anyone who wants to improve their math skills and needs a fast review.Presented in a straightforward style, our review covers the material taught in a beginning-level calculus course, including:More... functions, limits, basic derivatives, the definite integral, combinations, and permutations.The book contains questions and answers to help reinforce what students learned from the review. Quizzes on each topic help students increase their knowledge and understanding and target areas where they need extra review and practice
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5 other products in the same category:
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Wait, there's more! In the LIFEPAC Algebra I Set, each student worktext includes daily math instruction and review, as well as plenty of opportunity for assessment of student progress. In order to encourage individualized instruction, we have included a teacher's guide designed to help you guide your homeschooling student's learning according to his specific interests and needs. The helpful Alpha Omega curriculum teacher's guide includes detailed teaching notes and a complete answer key which includes solutions! Sound good? It is, so don't wait! Order the affordable LIFEPAC Algebra I Set for your high school student today!
LIFEPAC Scope and Sequence Download the LIFEPAC Scope and Sequence in PDF format.
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About the Teacher
Whether you're starting your first semester of calculus, or cramming for your final exam, integralCALC will help you quickly build skills with simple, step-by-step lessons.
Krista King (founder of integralCALC) worked as a calculus tutor while she was a student at the University of Notre Dame. After graduation, she started integralCALC.com to serve as a resource for calculus students. Since the beginning of 2010, Krista's calculus lessons have helped students around the world and she continues to publish lessons regularly.
17 Lessons
37
201
14K
1.1K
Table of Contents
1.
Lesson Intro
0:23
2.
Functions vs. Equations
0:23
3.
What are Functions?
1:06
4.
Domain and Range
1:32
5.
What Functions are Not
1:02
6.
Combinations and Compositions
0:54
Lesson Description
Lost in the world of calculus? Start at the beginning with integralCALC's online tutorials. The first in a series of eight, this lesson introduces the idea of functions - number 'machines' that describe a relationship between two or more variables (like 'x' and 'y'). Learn how functions differ from equations, what it means to find a function's domain and range, and how to use the vertical line test to check a function's validity.
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Professional Commentary: How many toothpicks does it take to make an n x n square composed of 1 x 1 squares? The lesson begins with a review of transformations of quadratic functions--vertical and horizontal shifts, and stretches and shrinks....
Professional Commentary: This tutorial begins with the definition of function and illustrates the graph, domain, and range of several nonlinear functions. These same functions are used to illustrate even (symmetric about the y-axis) and odd (symmetric about the origin) functions....
Professional Commentary: This conceptual understanding task requires students to evaluate three conjectures using their conceptual understanding of functions as well as a graphing calculator that can help students find the underlying structure in the changing parameters of the item. The Standards require students to express precise mathematical reasoning and this task assesses students' ability to reason well with...
Professional Commentary: Students use the innovative graphical interaction to experiment and create the image of the transformed function, providing a dynamic technological replacement for paper-and-pencil sketching. While the technology is not essential to solving the problem, it provides a support for students to interact with function transformations and has significant implications for future item development—a next iteration of...
Professional Commentary: This question asks students to identify the energy transformation that occurs in a hydroelectric plant from the turning turbine to electricity.? This is a multiple choice test item used in a past Ohio Achievement Test assessment (for more information, see IMS: Assessments). From this test item, a visitor may view the passages and stimuli, and information...
Professional Commentary: This question asks students to recognize the type of energy that makes a light bulb filament glow and produce light. This is a multiple choice test item used in a past Ohio Achievement Test assessment (for more information, see IMS: Assessments)....
Professional Commentary: Through text and diagrams, this tutorial reviews logarithms from several perspectives. Beginning with a short history of logarithms, the discussion covers rules of logarithms, graphs of logarithmic functions (including transformations of those functions), logarithmic equations, and applications of both exponential and logarithmic functions....
Professional Commentary: Students are asked to?perform a series of transformations on?a triangle drawn in the coordinate plane. This extended response question is a sample item used in the 2008 Ohio Graduation Test (see Overview of Ohio's Assessment System)....
Professional Commentary: This question asks students to identify under what conditions the energy being conducted through the circuit will cease. This is a multiple choice test item used in a past Ohio Graduation Test assessment (for more information, see IMS: Assessments)....
Professional Commentary: The task challenges a student to demonstrate an understanding of the graphical properties of a quadratic function given by its formula. A student must: make sense of and be able to identify and perform transformations on functions understand properties of functions identify, formulate, and confirm conjectures The task was developed by the Mathematics...
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College algebra lessons pdf software: Math games and Puzzles. Math Games, interactive math lessons, tests, MathProf is an easy to use maths program and moreBasic Algebra Shape-Up is interactive software that covers creating formulas; using ratios, proportions, and scale; working with integers, simple and multi-step equations. Students are able to track their individual progress. Student scores are kept in a management system that allows teachers and tutors to view and print reports
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12 Maths - Applications of the Integral
Applications of the Integrals: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between the two above said curves (the region should be clearly identifiable).
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...It is artificial to distinguish between the various subjects, such as elementary math, pre-algebra, algebra 1, algebra 2, etc. These are all just parts of the continuum of understanding that forms mathematics. Many people think that math is difficult; the big secret is that math is actually the easiest subject, because it all makes sense.
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Fourier Series and Transforms, a software and text package, complements standard textbooks and lecture courses by providing a solid overview of the topic. The software provides more extensive illustrations than a conventional text with interactive programs that have been designed to be open to...
A Data-Oriented Approach
Regression Analysis and Its Application: A Data-Oriented Approach answers the need for researchers and students who would like a better understanding of classical regression analysis. Useful either as a textbook or as a reference source, this book bridges the gap between the purely theoretical...
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"By the year 2000, American colleges and universities will be
lean and mean,
service oriented and science minded, multicultural and increasingly
diverse---if they
intend to survive their fiscal agony" ("Campus of the
Future," TIME,
April 13, 1992).
If our educational institutions are to remain competitive, it is
essential that our
students be prepared to enter a society that is increasingly dependent
on advanced
technology. Therefore, students must be exposed to advanced computer
tools in our science
and mathematics courses--even in introductory courses--to prepare them
for a world where
computers play an important role.
In the 10 years since Mathematica was introduced, it has
already had a significant
impact on the way physics is taught and how research is performed.
This presentation will
review our experiences during the last five years to integrate
Mathematica into the
physics curriculum at SMU, starting from the introductory-level
courses up to the graduate
level. By examining canonical problems from the undergraduate
curriculum and contrasting
the standard solution "before Mathematica" with the
modern standard
solution "after Mathematica," we will also examine
how Mathematica
allows the student to better focus on the underlying concepts. To be
specific, I will
consider two examples.
The double pendulum is a topic that is generally treated as an
"advanced" topic,
but with Mathematica the solution is elementary. Additionally,
using the animation
capability of Mathematica, it is trivial to animate the final
result, allowing
students to discover results on their own by varying the amplitudes of
the separate normal
modes.
Boundary value problems in electrostatics is a topic that beginning
students find
overwhelming. With the power of Mathematica, it is easy to show
these solutions are
quite straightforward--especially with the help of the different
coordinate systems built
into Mathematica. When students finish the problem with pen and
paper, they have
only a set of formulas that may mean very little. With
Mathematica's 2D and 3D
graphics, we can plot the final solution to verify visually that the
boundary conditions
are satisfied. This technique encourages the student to think about
the solution and not
simply grind out the math.
For the lower-level courses, it was the user-friendly interface and
the intuitive graphics
capabilities of Mathematica that encouraged and tempted the
student to experiment
with different methods of solving problems. The tedium of the algebra
or calculus no
longer was an impediment. For example, in 1993 we added
Mathematica as a component
of our calculus-based introductory physics course. The students were
given an initial
tutorial at the beginning of the semester and then assigned problems
from their text that
were particularly well suited to the capabilities of
Mathematica.
With intermediate-level courses, the students were able to delve
deeper into the
capabilities of the program in solving more complex problems.
It is said that there are only two problems in physics that can be
solved exactly: the
Kepler problem of an orbiting mass and the simple harmonic
oscillator--everything else is
perturbation theory.
With Mathematica we were not limited to analytic perturbation
theory, but could
easily devise numerical solutions to real-life problems that were not
solvable using
traditional analytic methods. Examples include projectile motion with
air resistance,
simple harmonic motion with a damping force, and chaotic double-well
systems.
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Let's Review : Math A - 2nd edition
Summary: This major revision prepares students to succeed on the New York State Math A Regents Exam as it is now given. The book places increased emphasis on mathematical modeling and the use of the graphing calculator. In line with New York State Regents core curriculum, it shows how given problems can be solved in several different ways. The author also includes new Regents question types dealing, for instance, with motion problems and mathematical systems defined by tables...show more. New contextualized word problems further enhance the presentation. The totally rewritten chapter on problem-solving offers students a core set of strategies that apply to a variety of curriculum-related exercises. In addition to subject review, demonstraton examples, and practice exercises with answers, the book includes several complete recent Math A Regents exams with answers ed.Good
boogieupbooks Bronx, NY
2003nationbooks Long Branch, NJ
Save some $$$. Perfectly Good Reading Copy. Owner inscription. Very few annotations
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You are here
A Student's Guide to Fourier Transforms with Applications in Physics and Engineering
Edition:
3
Publisher:
Cambridge University Press
Number of Pages:
146
Price:
29.99
ISBN:
9780521176835
This fall I will be teaching our senior seminar in Analysis, and I have decided to focus on Fourier Analysis. So I was delighted to receive a review copy of this little book: Fourier Analysis in 146 pages, including applications, sounded like something I could use to prepare.
It got more interesting when I read the introduction:
Showing a Fourier transform to a physics student generally produces the same reaction as showing a crucifix to Count Dracula. This may be because the subject tends to be taught by theorists who themselves use Fourier methods to solve otherwise intractable differential equations. The result is often a heavy load of mathematical analysis.
Hmm. I'm certainly a "theorist" but my interest in Fourier Analysis has more to do with representation theory than PDEs. It got a little stranger when, a few lines later, the author said that in practice "the transforms are done digitally and there is a minimum of mathematics involved." It seems that by "mathematics" and "mathematical analysis" what James means is computation. This is reinforced a little further on: "In spite of the forest of integration signs throughout the book there is in fact very little integration done and most of that is at high-school level." And here I always thought that it was the physicists who liked to compute things.
Anyway, despite the initial rhetoric this is a very nice book. The author focuses on the interpretation of Fourier transforms as finding the components of the initial function that correspond to oscillations at various frequencies. When the initial function is periodic, this yields Fourier series, since only a discrete set of frequencies is involved. When it is not periodic, one gets a continuous range of frequencies, sums turn into integrals, and we have the Fourier transform. All this is presented intuitively and without proofs, as is proper for a book of this kind.
In order to be able to include Fourier series as a special case of the Fourier transform, the author introduces Dirac's delta "function" and even "delta combs," which are infinite linear combinations of delta functions. No hint is given as to how to conceive of the delta function in a way that makes mathematical sense. In fact, the author even allows himself to give the delta function as an example of an unbounded function that nevertheless has a Fourier transform. Only occasionally is there a hint that there might be something to worry about, as when a footnote on page 31 cautions the reader not to apply the theorem about the Fourier transform of a derivative to the delta function.
A mathematician reading this book sometimes feels himself in the Twilight Zone, as the author assumes that arguments about signals and their detection are easier to understand than the underlying mathematics. Sometimes that is true even for me, but more often I have to read the mathematical result in order to understand the physical motivation!
Weird as this is, reading this book is a very useful discipline for anyone who is going to teach Fourier Analysis: it helps us understand how some of the users of the mathematics think about it, and includes several very nice applications. My students, most of whom are not physicists, would hate it.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.
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Introductory Algebra : An Integrated Approach - 99 edition
Summary: The second-level text in an innovative new workbook series, Introductory Algebra: An Integrated Approach is ideal for the first-year developmental arithmetic and pre-algebra instructor who seeks a flexible teaching tool that accommodates individual teaching and learning styles. Aufmann and Lockwood present math as a cohesive subject by weaving the themes of number sense, logic, geometry, statistics, and probability throughout the text at increasingly sophistic...show moreated levels. These themes are brought to life for students with applications from more than 100 disciplines. The text's interactive style encourages students to be active learners, quantitative thinkers, and true problem solvers.
A variety of analytic tools throughout include examples relevant to students' experiences; strategically placed questions that encourage students to be active learners; and an abundance of problems with complete solutions provided in an appendix.
Margin notes to guide students through the material include "Points of Interest," offering supplemental information; "Take Note," alerting students to challenging procedures; "Calculator Notes," demonstrating the functions of a calculator; and "Instructor Notes" (found only in the Instructor's Annotated Edition), offering teaching suggestions or related material.
A wide range of exercises includes "End-of Section" exercises providing practice in both concept and practice; "Critical Thinking" exercises requiring students to explore a concept in detail; "Writing Exercises," denoted by an icon; "Chapter Review" and "Cumulative Review" exercises, with all answers provided at the back of the book.
"Chapter Summaries" ensure that students have mastered material before being introduced to new concepts193
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Illiteracy, in both words and numbers, has become a national concern. While teaching, seasoned educator and mathematician Terence H. Murdock had to deal with students who lacked adequate knowledge of the fundamentals of mathematics. To help address this growing concern, Murdock publishes an effective and practical book that explains arithmetic processes to students, parents and teachers, titled Topics in Arithmetic.
Topics in Arithmetic is a collection of six studies in the fundamentals of arithmetic: (1) Simple Deductive Logic, (2) Number and Numeration, (3) The Basics of Arithmetic, (4) Understanding Arithmetic Algorithms, (5) Fractions and Decimals, and (6) Powers and Roots. Fundamentals are stressed. Murdock realizes that good mathematical thinking begins with elementary concepts and is developed from an early age.
This is not a textbook. There are no assignments; and no tests. It requires only a voluntary effort to read about topics in arithmetic that are interesting and enlightening. It is meant to augment, not replace, conventional textbooks. It is not a superficial treatment of elementary mathematics. It is directed at serious students, parents and teachers. It explains basic mathematics clearly and with insightful perspectives.
The education system is in trouble and there are scandalous numbers of school dropouts. With its simple, clear instructions, Topics in Arithmetic is a serious effort to make learning a rewarding experience for students from middle school through freshman college years, for parents who help them with their homework, for teachers who teach them, and for others who aspire to teach mathematics.
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This collection of activities is intended to provide middle and high school Algebra I students with a set of data collection investigations that integrate mathematics and science and promote mathematical understanding. The use of the TI-73 is an integral part of each activity. The activity book is available for purchase or each activity can be downloaded free in PDF format
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This is the Elementary Algebra textbook used by the Department of Mathematics in their Math 380 course at College of the Redwoods, Eureka, California.
Errata and Individual chapter and solutions are... More > available at:
Less
Ray's New Elementary Algebra. 241 pages. "In introducing Algebra to the student with Elementary Algebra, great care has been taken to make the student feel that he is not operating with... More > unmeaning symbols, by means of arbitrary rules; that Algebra is both a rational and practical subject, and that he can rely on his reasoning, and the results of his operations with the same confidence as in arithmetic. For this purpose, he is furnished, at almost every step, with the means of testing the accuracy of the principles on which the rules are founded, and of the results which they produce."
Ray's New Elementary Algebra focuses on the basic forms of Algebra. Algebraic Fractions, Simple Equations, Powers, Roots, Radicals, and finally Quadratic Equations are among the concepts explored. As always, after a concept has been taught, real-world applications for the process are given to the student.< Less
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Finite Mathematics, 1 or 2-semester or 2 3 quarter courses covering topics in college algebra and finite mathematics for students in business, economics, social sciences, or life sciences departments.This th... MOREe examples and exercises42% of the 452 examples are new or revised, and 31% of the 3,741 exercises are new or revised. The Table of Contents lends itself to tailoring the course to meet the specific needs of students and instructors. This the examples and exercises42% of the 452 examples are new or revised, and 31% of the 3,741 exercises are new or revised. Algebra and Equations; Graphs, Lines, and Inequalities; Functions and Graphs; Exponential and Logarithmic Functions; Mathematics of Finance; Systems of Linear Equations and Matrices; Linear Programming; Sets and Probability; Counting, Probability Distributions, and Further Topics in Probability; Introduction to Statistics. For all readers interested in finite mathematics with applications.
Chapter 9: Counting, Probability Distributions, and Further Topics in Probability
9.1 Probability Distributions and Expected Value
9.2 The Multiplication Principle, Permutations, and Combinations
9.3 Applications of Counting
9.4 Binomial Probability
9.5 Markov Chains
9.6 Decision Making
Chapter 9 Summary
Chapter 9 Review Exercises
Case Study 9: QuickDraw® from the New York State Lottery
Chapter 10: Introduction to Statistics
10.1 Frequency Distributions
10.2 Measures of Central Tendency
10.3 Measures of Variation
10.4 Normal Distributions
10.5 Normal Approximation to the Binomial Distribution
Chapter 10 Summary
Chapter 10 Review Exercises
Case Study 10: Statistics in the Law–The Castañeda Decision
Appendixes
Appendix A: Graphing Calculators
Appendix B: Tables
Table 1: Formulas from Geometry
Table 2: Areas under the Normal Curve
Table 3: Integrals
Answers to Selected Exercises
Index of Applications
Index
Marge Lial†has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
†
Thomas W. Hungerford received his bachelorís degree from Holy Cross and his Ph.D. from the University of Chicago. He taught for many years at the University of Washington (Seattle) before moving to Cleveland State University in 1980. He has been at St. Louis University since 2003. He has written a number of research articles in algebra and several in mathematics education. Dr. Hungerford is the author or coauthor of more than a dozen mathematics textbooks, ranging from high school to graduate level, several of which are published by Addison-Wesley. He is active in promoting the effective use of technology in mathematics instruction. Dr. Hungerford has also been a referee and reviewer for various mathematical journals and has served on National Science Foundation panels for selecting grant recipients.
†
John P. Holcomb, Jr.†received his bachelor's degree from St. Bonaventure University and his Ph.D. from the University at Albany, State University of New York. He taught for five years at Youngstown State University prior to arriving at Cleveland State University in Fall 2000. He is an associate professor and frequently collaborates with researchers in a variety of disciplines where he†provides statistical analysis. Dr. Holcomb has also authored several papers in statistical education and is very active in the†American Statistical Association and the Mathematical Association of America. He was named a Carnegie Scholar in 2000 by the Carnegie Foundation for the Advancement of Teaching and Learning and in 2003 received the Waller Award from the American Statistical Association for outstanding teaching of introductory statistics.
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098 Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra.
099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098.
109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099.
211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher.
220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above.
250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116.
290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor.
400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240.
490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor.
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Week 5: What do YOU think should be the kind of math competence we require students to learn? And, is it important for students to see the relevance of math to jobs and everyday life?
Sol Garfunkel
At COMAP (Consortium for Mathematics and Its Applications) we work with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world. In our 2009 paper, Math to Work we argued for offering curricular alternatives in math that would emphasize how discrete ideas taken from high school math courses apply to a variety of careers and your everyday lives. These alternatives would help students like you make connections between what they are learning and how you would use those skills in future jobs.
COMAP further argued that too many people have accepted a false argument that continuous mathematics is essential for all students. Continuous mathematics are highly technical subjects that teach a good deal of symbol manipulation (like using "x" and "y" in Algebra II) and typically lead up to calculus and analysis. This kind of math learning is necessary for future engineers and epidemiologists, but for the large majority of students it won't be needed. The false argument goes like this: All students need to learn mathematics (so far so good). We shouldn't discriminate against any group of students (still hard to argue). All students must be given the opportunity to reach some basic level of mathematical competence. That basic level of mathematical competence can be defined by the content of Algebra II (as exhibited on a particular test). Criminal!
In the name of giving everyone an equal chance to succeed, we merely give them an equal chance to fail. The simple truth is that there is an enormous choice of mathematical topics we could (and should) be teaching. If you read the short paper, you'll learn some examples of good, well-paying jobs where Algebra II is simply not required but other math concepts are used to some extent. In other words, we could say, as a nation, that the "basic level of math competence" is not about being well-along in the path toward calculus and more about having math skills for work and life. This would not mean that anyone who wants to pursue continuous mathematics necessary for their own future careers would be prevented from doing so (but even exposing such students to how what they're learning will apply to their careers and lives would be a good idea.)
My questions:
1. To what extent have you been told that continuous mathematics is important for all students? Have you heard varying ideas about this from different people? What do you think of the idea that every student must learn Algebra II to be successful at a well-paying job?
2. Do you think there is there a relationship between students' motivation to learn math and their understanding of how it will be useful in future jobs and in their everyday lives? (Generally? In their specific areas of interest?) How so?
3. Some have suggested: If teens don't see clear connections between school, work and jobs, they might see dropping out of college (or maybe even high school) as a rational choice--especially in today's economy where financing for four-year college is out of reach for many. The paper I just linked suggests that this is because other pathways to well-paying jobs aren't obvious (the "false argument" prevails). Would high school students benefit from increased guidance about the variety well-paying jobs available, whether you attend college or not? About what kind of math and other knowledge you'll need to do the jobs well? Do you think this could have an impact on dropout rates?
4. Your working question in this project is "What is Student Achievement?" Read the third paragraph above one more time for my opinion. What do YOU think should be the basic level of math competence we require students to learn? Need it be associated with "continuous mathematics"?
Failing to see the point of math--partiucalrly what Sol has termed continuous math-- is a longtime hobby of mine, so I've asked every math teacher I've had from seventh grade on to explain its relevance and justify its continued existence in secondary school curricula. They all open with a vague insistence that "we use math all the time, we just don't realize it." When I pressed them further, (Isn't it a problem that I don't realize the practical applications of what I'm learning? What are they, anyway?) one forced me to watch the CBS procedural Numb3rs (their spelling, not mine), one admitted that I would only need enough algebra to calculate interest and enough geometry to grasp basic measurements, and everything else wouldn't come up again unless I pursued a career in mathematics/engineering/hard sciences etc. All the others pointed out that the continuous math sequence was a college entrance requirement.
I find that last one bizarre. My teachers were right: most state universities explicitly require at least three years of math. (Colorado universities require four.) More often than not, they also mandate that those three years consist of Algebra I, Geometry, and Algebra II and specifically indicate that other math courses, such as finances and statistics, will not count towards the three year total. This seems backwards to me. Wouldn't those last two be more applicable to and useful in many more careers and fields of study, to say nothing of day-to-day life?
It appears to me that our obsession with teaching the calculus sequence has already hurt our nation. I realize, of course, that our current economic climate is the result of a perfect storm of any number of factors, but I would venture to say that at least one of those was consumers who didn't quite grasp the economic realities of exotic mortgages and predatory lending practices. Would so many have agreed to adjustable-rate mortgages and NINA loans had they received an education that empowered them to detect a too-good-to-be-true financial product?
To that end, I would be inclined to believe that proficieny standards should be geared less towards AP calculus and more towards financial independence. Can you do basic arithmetic? Can you balance a checkbook? Calculate interest? Keep a budget? These are the sorts of things that keep a person afloat in Grown-Up Land, not y=mx+b. Most of my teachers in subjects other than math , by their own admission, would have trouble breaking 400 on the math section of the SAT. But despite what some of my past math teachers would have me believe, they are all still happy, succesful people who can, to the best of my knowledge, put their pants on without bruising themselves.
As for the question of motivation, what I've just said more or less illustrates my interest in continuous math and my opinion of its worth, and I'd wager that my attitude is widespread. And it isn't just young people who are skeptical about the very idea of staying in school anymore. If I had a dollar for every op-ed I read that declared college degrees worthless, bemoaned the ever-shrinking job market, and urged would-be college students into vocational schools instead (to receive training in a job sector said to be "growing"), I'd be tempted to drop out of high school myself, in order to live full time on the island (Corsica) I bought with the money.
And only now do I notice my glaring typos. What a "succesful" demonstration of my "proficieny" in spelling. Sorry everyone..."partiucalrly" indeed.
I have certainly been told continous mathematics is a good idea for anyone possibly pursuing a career in an engineering, science, etc. field. However, for those not interested in a future with mathematics, I don't think it's very stressed. Honestly, I think Algebra II was an important class for me, and while every student will not directly benefit in their career from this class, I felt more confident in my algebra skills and thought it was a good basic class to have. As for students' motivation to learn math, I think if their not interested, they're not interested. Students understand why we take classes, and even if they realize it will benefit them later, I think its hard to get excited about math when that's not your passion. While clear connections between work/school might motivate many students to continue with their education, I think a lot of the motivation for a higher education comes from a love of learning. And while a guidance and knowledge of jobs that are possible with/without a college education would be helpful, I'm not sure how effective it would be in impacting dropout rates. For mathematical competence, I think Algebra II is sufficient right now. An integrated approach might be more effective though, combining Algebra I/Geometry/Algebra II. As I haven't taken anything beyond Algebra II yet, I do not yet see the advantages of taking a Calculus class.
I also agree with Miriam, having pre-calculus as the requirement could be beneficial because it gives students the option to pursue calculus in college, if during their junior/senior years in high school and freshmen year in college, they choose to go into a different career path. Why spend money taking pre calculus and more advanced classes when you can get it for free in high school?
In general, I don't like math much. But I feel like the thing I like the least about math (especially algebra) is that I struggle to find a real-world connection to the subject. I don't see how taking classes like Algebra I and II really apply to a wide variety of future professions. No one has really mentioned to me the need to take Algebra II to be successful later in life, but I have always somewhat assumed that I would have to take these classes no matter what, and not thought about the reasons why. Right now I am taking, Geometry, and I find I can enjoy it much more because I can find many more connections between the class and the real world. It's not that I don't consider algebra important, it's just that I think it needs to be taught in a way that students can connect with real-world issues. For me, there is definately a connection between my motivation to learn math and my understanding of how it connects to the real world. In Algebra I, I found that I didn't care about the work, didn't treat it with reverance, mostly because I couldn't see its importance. I also found it much harder to understand for this reason. In Geometry, I feel like I try much harder to do well because I can see more connections to how it might help me in the future.
i have almost been told by all my teachers that taking or learning mathematics is good for you because you use it everywhere and you will keep on using it in the future. They say its very imortant to learn and use mathematics. My mom says math is very important and my math teacher of course, and my science teacher because even though physics isnt math i still do problems in physics with math in it. I think every student should take Algebra II beacuse you never know that you are going to use it in your job. I dont think there is a relationship when students are motivated to learn math because if thats something they dont like they wont really care. But later on they will realize that math is important for all types of jobs and then they might be motivated.Yes giving more guidance to students about well-pay jobs and weather they have to attend college or not, will help their self awareness to choose their destiny. (hopefully not dropping out of school). I think it should be pre-caculus because their they have the choice to further study math but still stop while functioning in society.
Continuous mathematics at my public high school, Harry D. Jacobs, is recommended for most students however, some choose not to do so. Entering high school, all freshmen are required to take an Algebra I course. Depending on what track you take (general, advanced, or honors) determines the course length throughout the year. For example, a general class is all four terms and an honors class is only first and second term. As the year progresses, an honors student moves on to honors geometry for term three and four while a general student is still behind in algebra I. A general student would begin with geometry the following year as an honors student would advance to Algebra II. As you can see, a general student is hindered from the start and by their senior year may only reach Trigonometry, if they choose to do so. Many general students do not continue past Algebra II as it is the minimum math requirement to graduate at Jacobs. I am currently in the honors track and my honors friends agree continuous mathematics is beneficial to our future. The higher the math level course, the more it is likely for one to test out of math courses in college. My general class-level friends do not have the desire to continue math throughout their high school career and typically stop at algebra II. I think that every student should take algebra II and BEYOND in order to be successful in a well-paying job. The standards are being raised for this generation and students should take the courses offered to them, despite the challenge, in order to be prepared for their future.
I believe there is a correlation between a student's desire to learn math and their knowledge of how it will pertain to them in the future. If students aren't provided with the motivation to learn in high school, it's most likely they will not pursue higher level careers that require beyond algebra II math skills. I see how this may lead to the increase of drop-out rates. If motivation is not instilled in high school, it is likely this will carry on to the professional world.
I believe there should not be a basic level of math for students, I think math should be REQUIRED for all students, all four years of high school. This way students have the knowledge from the beginning of high school on the importance of math throughout their educational experience.
1. Math to me is the subject I find is most hotly debated on importance. I have heard equally throughout my life that math is one of the most important subjects and one of the least important. While I feel one would probably expect to mostly hear students say math is not important, I find I hear a fair amount of disregard for math from adults (even educators) as well as praise for math by a lot of students. I personally don't believe one needs to have taken courses in any particular subject to be succesful since often times success is not determine by skill but by luck, ( such as being born into an already "succesful" family).
2. I believe that it's the way math is taught in school that sways the way students feel about it I also feel there is this idea in society that being good at math makes one intelligent beyond all else and somehow more capable than anyone else. I' not sure I'm expressing it right here and if I need to explain again please ask.
3. Yes I do believe that high school students would benefit from understanding there is a wide range of career options, as for attending college, I am honestly unsure. I feel students dropout for all kinds of reasons, but mostly probably due to stress of college work and the feeling that pay-off my be minimal in comparison, at least this is a complaint I hear from fiends I have in college agree with the exerpt that college requirements would need to change before high schools would realistically change their requirements. But if colleges changed the requirements too it could be interesting.
Kumar- if math was taught in less straight out of the textbook and more tailored to how it can be useful in real life, do you think you would be more interested in math?
I think that if math were required only up to a certain level, I would certainly stop taking it. My problem with the math we learn in school is that there are no connections made to real life in the way it is taught. My intrest and the engagement of my mind on certain things really depends on how important I think it is. I am not questioning the importance of math, its just that I want to know what the importantce of certain kinds of math is.
Nora -- Thanks for clarifying your point. Did you see the quote Michael excerpted from Sol's work (I believe in his post last Sunday)? If you were given choices, but college's expectations didn't change, then what?
If I might, I would summarize the comments as "Continuous math must be good for us because people say so even though they can't explain why." My request to the students is to wonder to what extent this belief in math is a cutural artifact. That is, we believe certain things because everyone else around us believes it, not necessarily because it's true. The earth as the center of the universe, or the earth as flat come to mind as notable examples.
--What do Algebra II and calculus train us for? To think better? If so, are there other ways of accomplishing this? For jobs? According to Michael and Sol, not so much.
--If math weren't a college requirement, would you take it? (by the way, my son took Calculus III as a freshman in college; the professor read from the math text during lectures; my son dropped and never took another math class; he just graduated with Honors and Phi Beta Kappa from Madison)
--What kind of math do we need to succeed in life? (Marie, I like your answers on this). This is your life, and you want to be successful. What sorts of math abilities do you feel you really need?
I would like to make clear that many of the topics and subject matter in discrete mathematics is quite deep (and hard). If you want to prove this for yourself, just read Arrow's Theorem on the impossibility of a fair voting system. The proof is truly wonderful and very involved and in fact, Arrow won a Nobel Prize in Economics partly for this work. But it uses no algebra or calculus. Nor does most of current efforts in Behavioral Economics. I am simply arguing that there are choices and we act as if there is one and only one linear sequence of courses from birth to a PhD. And this is nonsense. Moreover, for most people continuous mathematics is not the mathematics that they will be called upon to use - in work or daily life.
Modeling the world through mathematics is in my opinion a life skill and we need to learn the mathematics behind those models. Modeling weather and the environment and epidemics certainly require the mathematics of differential equations and it would be lovely if everyone understood that mathematics. But learning how to hang pictures on a wall by a staircase so that they look straight is a much more likely everyday use of mathematics, which I doubt most calculus students could master.
But my basic argument is that we simply turn off too many students too soon. Our system is a filter, not a pump. Most students stop taking math courses with a bad taste in their mouths and no appreciation for the subject, its applications or its relevance to their lives. In the name of giving students an equal opportunity to go on in math and science, we in fact, give them an equal opportunity to fail.
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Product Details:
Comprehensive and easy-to use, this updated edition covers every type of practical math problem that automotive technicians will face on the job. The subject matter is organized in a knowledge-building format that progresses from the basics of whole number operations into percentages, linear measurements, ratios, and the use of more complex formulas. Complete coverage of fundamentals, as well as more advanced computations make this book suitable for both beginning and advanced technicians. With a special section on graphs, scales, test meters, estimation, and invoices used in the workplace, this book is tailor-made for any automotive course of study!
Description:
For pilots looking to improve their math skills in the
cockpit and easily perform math calculations in their heads, this book offers numerous tips and invaluable tricks to help in all areas of cockpit calculations. Pilots are guided through ...
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The O-Level Mathematics syllabus builds on the Standard Mathematics syllabus. The N(A)-Level Mathematics syllabus is a subset of O-Level Mathematics, except that it revisits some of the topics in - Standard Mathematics syllabus.
O Level Mathematics (syllabus D) (4024) Will students be given a formula sheet to help them in the exam or do they need to memorise this information? ... O levelMaths has a non-calculator paper whereas IGCSE Maths requires a calculator for both papers.
concepts; the inability to deliver the prescribed syllabusfor each class/grade level within the expected time frame; ... Maths/Problem-solving Infant Yr. 1 (Pre-number) zero to ten -Recognition of number names to 10 -Number value to 10
Maths 'A' level General Introduction Welcome to your 'A' level Mathematics course. ... The Specification (or Syllabus) This course has been designed to give you a full and thorough preparation for the AS level or Alevel Mathematics specifications,
GCE O'LEVELMATHS Lungsuri lelaman untuk melihat video ... Some questions may integrate ideas from more than one topic of the syllabus where applicable. Relevant mathematical formulae will be provided for candidates.
syllabus topics tested in this paper may be narrower than that tested in section A. Question type ... Level 2 cannot be achieved if the student only writes down mathematical computations without explanation.
TEACHING SYLLABUSFOR MATHEMATICS ( JUNIOR HIGH SCHOOL 1 – 3 ) Enquiries and comments on this syllabus should be addressed to: The Director ... in Ghana builds on the knowledge and competencies developed at the primary school level.
The Specification (or Syllabus) This course has been designed to give you a full and thorough preparation for the AS level or Alevel Mathematics specifications, ... OOL's 'A' levelMaths courses are divided into six separate modules.
Revised Mathematics Syllabusfor Elementary Level. Mathematics is a way of organizing our experience of the world. It enriches our understanding and enables us to communicate and make sense of our experiences.
There is a core A-levelsyllabus which all students completing a single mathsA-level ... Much of the material below is in the core A-Levelsyllabus but some is on the edges of the core and you may not be familiar with it especially those of you with a single mathematics A-level.
syllabus which is intended to be used simply as a guide. It is presumed that, as in all good practice, teachers will, where it is appropriate for their pupils, ... level 6 for lower-level candidates, (b) National Curriculum levels 5 and 6 with some
Mathematics Syllabus Grade 2 . Mathematics: Grade 2 /Desktop Files Returned by Experts, August 2008/ Grade 2 iii ... Another important point is that the teaching should be varied at this level. Try to find opportunities to include
Mathematics Teaching Syllabus, National Curriculum Development Centre. Ministry of Education and Sports The Republic of Uganda MATHEMATICS TEACHING ... The teaching syllabuses for O-Level subjects will go a long way in achieving the government aims and objectives of education for all.
In the last year students with amathsALevel from Wyke went on to Universities from Glasgow to Southampton, ... techniques in the GCSE syllabus are not well learned. Because of this we make pre-course work available on the web-site.
the ALevelsyllabus and additional specimen questions on Vectors, Complex Numbers and Continuous Random Variables; Past question papers will be available following each examination session. All the above are available from CIE Publications.
Project MathsA chara, As you are aware, students who commenced the Leaving Certificate course in September 2011, for ... syllabus at the corresponding level (2000 syllabus). Both Paper 1 and Paper 2 will be presented as a combined question-and-answer booklet. Sample
1 Changes and clarifications to the Higher LevelSyllabus. Changes to the IB Higher Level Mathematics Syllabus. First Examinations 2014. Big overall changes are that matrices (12 hours of teaching time) have been removed.
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Synopses & Reviews
Publisher Comments:
While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis.The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed - for example, rings, linear spaces, and metric spaces - and with many of the principal analytical concepts - convergence, connectedness, continuity, compactness and completeness. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics.Carefully crafted, clearly written and precise, and with numerous exercises and examples, Elements of Abstract Analysis is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics.
Synopsis:
"Synopsis"
by Springer,
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Basic Mathematical Skills with Geometry
Basic Mathematical Skills with Geometry, 9/e, by Baratto, Bergman, and Hutchison is part of the latest offerings in the successful Hutchison Series ...Show synopsisBasic Mathematical Skills with Geometry, 9/e, by Baratto, Bergman, and Hutchison is part of the latest offerings in the successful Hutchison Series in Mathematics. The book is designed for a one-semester course in basic math and is appropriate for lecture, learning center, laboratory, and self-paced settings. The ninth edition continues the series' hallmark approach of encouraging mastery of mathematics through careful practice. The text provides detailed, straightforward explanations and accessible pedagogy to help students grow their math skills from the ground up. The authors use a three-pronged approach of communication, pattern recognition, and problem solving to present concepts understandably, stimulate critical-thinking skills, and stress reading and communication skills in order to help students become effective problem-solvers. Features such as Tips for Student Success, Check Yourself exercises, and Activities underscore this approach and the underlying philosophy of mastering math through practice. Exercise sets have been significantly expanded and are now better-organized, and applications are now more thoroughly integrated throughout the text. The text is fully-integrated with McGraw-Hill's online learning system, Connect Math Hosted by ALEKS Corp, and is available with ALEKS 360
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Elementary Statistics-Text - 8th edition
Summary: ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for introductory statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing ...show moretechnologies commonly used in such32.11 +$3.99 s/h
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AQA Functional Mathematics Student Book
A complete one-stop solution for your Functional Mathematics course.
Written by senior examiners and authors of previous pilot schemes, our resources work both as a standalone course or integrated into your GCSE or KS3 teaching.
Covering both Levels 1 and 2, this Student Book comes packed with real-life scenarios, newspaper cuttings, timetables, maps and charts to bring maths into the real world. We've also organised our resources by mathematical topic so you can see at a glance how to integrate your Functional teaching with your GCSE teaching. Each topic covers the basic maths needed, also allowing you to teach Functional as a standalone course.
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At CRC Press, we believe that the future of our world as well as our company depends on preparing students to be tomorrow's leaders. We produce some of the world's best textbooks for the scientific and technical disciplines: textbooks that are as student and instructor friendly as they are authoritative. CRC textbooks are rich with pedagogic features designed to make instructors' jobs easier and students' learning experience richer.
Find the textbook you need by browsing by the disciplines listed on the left or using the Textbook Search box above.
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To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how
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Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think
…
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This book is a linear-algebraic
approach to the basic theory of
finite-dimensional algebras, written for readers who have prior knowledge
of undergraduate-level algebra. As such, the level of exposition
is suitable for senior undergraduate and first-year graduate students.
My aim
is to present a balance
of theory and example so that readers gain a firm understanding
of the fundamental results, the motivating examples, and some of
the important constructions. The study of finite-dimensional algebras
provides a useful
foundation for subsequent advanced work in
a number of areas of mathematics, but the subject in itself is rich,
elegant, and of classical importance.
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Success in your calculus course starts here! JamesStewart.
Success in your calculus course starts here! JamesStewartPR text.
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Achievement Levels
Mathematical Portfolios: Achievement Levels
Achievement Levels
Criterion A: Use of Notation and Terminology
Achievement level
0 The student does not use appropriate notation and terminology.
1 The student uses some appropriate notation and/or terminology.
2 The student uses appropriate notation and terminology in
a consistent manner and does so throughout the work.
Tasks will probably be set before students are aware of the notation and/or terminology to be used. Therefore the key idea behind this criterion is to assess how well the students' use of terminology describes the context.
Correct mathematical notation is required, but it can be accompanied by calculator notation, particularly when students are substantiating their use of technology. This criterion addresses appropriate use of mathematical symbols (for example, use of "≈" instead of "=", and proper vector notation).
Word processing a document does not increase the level of achievement for this criterion or for criterion B. Students should take care to write in appropriate mathematical symbols if the word processing software does not supply them. For example, using x^2 instead of x2 would be considered a lack of
proper usage and the candidate would not achieve a level 2.
This criterion also assesses how coherent the work is. The work can achieve a good mark if the reader does not need to refer to the wording used to set the task. In other words, the task can be marked independently. Level 2 cannot be achieved if the student only writes down mathematical computations without explanation. Graphs, tables and diagrams should accompany the work in the appropriate place and not be attached to the end of the document. Graphs must be correctly labelled and must be neatly drawn on graph paper. Graphs generated by a computer program or a calculator "screen dump" are acceptable providing that all items are correctly labelled, even if the labels are written in by hand. Colour keying the graphs can increase clarity of communication.
Criterion C: Mathematical Process
Type I — Mathematical Investigation: Searching for Patterns
Achievement level
0 The student does not attempt to use a mathematical strategy.
1 The student uses a mathematical strategy to produce data.
2 The student organizes the data generated.
3 The student attempts to analyse data to enable the formulation of a general
statement.
4 The student successfully analyses the correct data to enable the formulation
of a general statement.
5 The student tests the validity of the general statement by considering
further examples.
Students can only achieve a level 3 if the amount of data generated is sufficient to warrant an analysis.
Type II — Mathematical Modelling: Developing a Model
Achievement level
0 The student does not define variables, parameters or constraints of the task.
1 The student defines some variables, parameters or constraints of the task.
2 The student defines variables, parameters and constraints of the task
and attempts to create a mathematical model.
3 The student correctly analyses variables, parameters and constraints of
the task to enable the formulation of a mathematical model that is relevant
to the task and consistent with the level of the course.
4 The student considers how well the model fits the data.
5 The student applies the model to other situations.
At achievement level 5, applying the model to other situations could include, for example, a change of parameter or more data.
Criterion D: Results
Type I — Mathematical Investigation: Generalization
Achievement level
0 The student does not produce any general statement consistent with
the patterns and/or structures generated.
1 The student attempts to produce a general statement that is consistent with
the patterns and/or structures generated.
2 The student correctly produces a general statement that is consistent with
the patterns and/or structures generated.
3 The student expresses the correct general statement in appropriate
mathematical terminology.
4 The student correctly states the scope or limitations of the general statement.
5 The student gives a correct, formal proof of the general statement.
A student who gives a correct formal proof of the general statement that does not take into account scope or limitations would achieve level 4.
Type II — Mathematical Modelling: Interpretation
Achievement level
0 The student has not arrived at any results.
1 The student has arrived at some results.
2 The student has not interpreted the reasonableness of the results
of the model in the context of the task.
3 The student has attempted to interpret the reasonableness of the results
of the model in the context of the task, to the appropriate degree of accuracy.
4 The student has correctly interpreted the reasonableness of the results
of the model in the context of the task, to the appropriate degree of accuracy.
5 The student has correctly and critically interpreted the reasonableness
of the results of the model in the context of the task, to include possible
limitations and modifications of the results, to the appropriate degree of
accuracy.
Criterion E: Use of Technology
Achievement level
0 The student uses a calculator or computer for only routine calculations.
1 The student attempts to use a calculator or computer in a manner that
could enhance the development of the task.
2 The student makes limited use of a calculator or computer in a manner that
enhances the development of the task.
3 The student makes full and resourceful use of a calculator or computer
in a manner that significantly enhances the development of the task.
Using a computer and/or a GDC to generate graphs or tables may not significantly contribute to the development of the task.
Criterion F: Quality of Work
Achievement level
0 The student has shown a poor quality of work.
1 The student has shown a satisfactory quality of work.
2 The student has shown an outstanding quality of work.
Students who satisfy all the requirements correctly achieve level 1. For a student to achieve level 2, work must show precision, insight and a sophisticated level of mathematical understanding.
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"Were 'Algebra' to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics."—The Mathematical Intelligencer
This text, which is intended to supplement a high school algebra course, is a concise and remarkably clear treatment of algebra that delves into topics not covered in the standard high school curriculum. The numerous exercises are well-chosen and often quite challenging.
The text begins with the laws of arithmetic and algebra. The authors then cover polynomials, the binomial expansion, rational expressions, arithmetic and geometric progressions, sums of terms in arithmetic and geometric progressions, polynomial equations and inequalities, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means. The book closes with an elegant proof of the Cauchy-Schwarz inequality.
Topics are chosen with higher mathematics in mind. In addition to gaining facility with algebraic manipulation, the reader will also gain insights that will help her or him in more advanced courses.
The exercises, which are numerous, often involve searching for patterns that will enable the reader to tackle the problem at hand. Many of the exercises are quite challenging because they require some ingenuity. Some of the exercises are followed by complete solutions. These are instructive to read because the authors present alternate solutions that offer additional insights into the problem.
This book inspires even those with minimal interest in mathematics. If you are passionate about math, this is a must for you. The book is simply a refresher for high school algebra. It contains numerous gems that you could hardly find in a standard algebra text. If you are a teacher, you would have learned much to improve your teaching style and knows how to make your math classes more interesting...overall, a key source to keep on your bookshelf
Well, H. Wu on his page and N.F Taussig here have written quite good reviews, so I guess I can't really add anything new. Still, I feel the need to praise this book some more. Could it be used for a main text or should it be just a supplement? I don't know, but there is much more mathematics contained in these 149 pages than in any standard 500 page high school text on the market today. That's the unsurprising result of accomplished mathematicians writing a math book. Sure, some topics are missing. You won't find 3 or 4 chapters devoted to the several "different" ways to graph a line. There aren't fifty problems in a row that start with "suppose Sam rows upstream at 5 miles per hour and it takes her seven times as long as..." Unfortunately, there isn't even a treatment of complex numbers, the only omission that seems wrong.
You will find several interesting and serious topics that would be dangerous to bright students who insist they hate math, or rather what they've been told is math. Imagine their initial embarrassment when they find out that they can enjoy the subject! Maybe more importantly, imagine their relief when they realize that there IS a reason why we "FOIL", there IS a reason why negative times negative is positive, there IS a reason why we say a^(-1)=1/a, and it's not because "the teacher said so" or "that's just the rule" (ok, it is the rule, but now you'll see why). And there's no attempt to sneak anything by the reader. The authors are quick to acknowledge any gaps in their reasoning, and to assure the reader that in the future he or she will fill them.
It's this honesty and attention to rigor without being too formal or dry that give this book some extra charm. It moves smoothly from basic arithmetic (which everyone should still read if only to learn a different way of explaining it to a student/younger sibling/child) all the way to proofs, both algebraic and visual when possible, of some important inequalities. Cauchy's inductive proof, first for powers of two and then filling in the gaps, of the AM-GM inequality is here, as is the standard proof of Cauchy-Schwarz by the discriminant of a polynomial. Go to your local high school and look at its algebra book. I doubt that's in there.
I bought this book for my daughter (10 years old) and we read it together. We went very slow and I supplement it with a work book. She likes it. I was impressed by the beauty of this book. It might be a little too slim for a textbook but every kid who wants to learn algebra should read it. More than teaching algebra it shows what math should be: simple and beautiful.
My daughter's math textbook is 5 pounds and I can't even stand looking at it. I understand that not every is enthusiastic about math and not everyone can feel the beauty of math. But you don't have to make math so ugly.
Learning math with a 5 lb textbook is simply terrifying but if your kid goes to public school you probably have no choice. Let you kid read a good book like this one, as early as possible, before he(she) grows a life time aversion to math.
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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,
...more>>
Geometry in Motion - Daniel Scher
Direct interaction with geometric diagrams, courtesy of JavaSketchpad. The contents include a variety of curve-drawing devices (Intersecting Circles, Falling Ladder, Van Schooten's Parabola, and more); also other activities such as Constant Perimeter
...more>>
geometry-software-dynamic - Math Forum
A discussion group accessible as a Web-based discussion, a mailing list, or a Usenet newsgroup. This group focuses on discussion of such geometry software programs as The Geometer's Sketchpad and Cabri Geometry II. Read and search archived messages; and
...more>>
GoKnow! - GoKnow, Inc.
GoKnow, Inc. intends to be the leader in technology pervasive, standards-based, scientifically validated curriculum and educational tools. GoKnow offers tools for handheld devices' use in the classroom, professional development and consulting services.
...more>>
Helmer Aslaksen
A mathematics professor at the National University of Singapore. Research involves abstract algebra, including the trigonometry of symmetric spaces, and calculations for the Chinese, Islamic, and Indian calculators. Papers about these topics may be
...more>>
Janet Bowers - Janet Bowers
Current research projects, such as investigating multimedia case studies as a tool for preservice teacher development, the MEASURE project (SimCalc - San Diego), and reforming the preparation and professional development of elementary and middle school
...more>>
K-12 Multimedia Math Education - Sparkle Productions
Software and research: reports and articles are available, with print and web references and resources, in the Motivation and Learning Center, which provides suggestions for parents on increasing their child's intrinsic desire to learn. Their math materials
...more>>
Loci - Mathematical Association of America (MAA)
Loci is a peer-reviewed journal publishing articles, modules, applets, and reviews continuously as they are ready to be posted. Loci takes advantage of the World Wide Web as a publication medium for materials containing dynamic, full-color graphics;
...more>>
MaplePrimes User Community - Maplesoft
An online community for Maple users. Forums, blogs, and resource links. Quick answers to Maple user questions from experts in community and Maplesoft staff. Site is sponsored by Maplesoft but it maintains a very community-centric editorial policy.
...more>>
Math Apprentice - Colleen King
This rich, multimedia site provides students an opportunity to try various real-world professions that use math. Students can be scientists, engineers, computer animators, video game programmers, and more. Math Apprentice provides areas of free exploration
...more>>
Math Does Not Equal Calculating - Wolfram Research
This project aims to "build a completely new math curriculum with computer-based computation at its heart, alongside a campaign to refocus math education away from historical hand-calculating techniques and toward relevant and conceptually interesting
...more>>
Math Education Page - Henri Picciotto
Math education articles by the author, with an emphasis on algebra. A New Algebra: Tools, Themes, Concepts, an article that summarizes the pedagogical and curricular thinking behind ATTC; Early Mathematics: A Proposal for New Directions, a chapter in
...more>>
Mathematica in Higher Education - Wolfram Research
Lessons, resources, books, and classroom packs for making Mathematica software an integral part of math education in university and college classrooms. Also features Mathematica versions geared and priced for students, as well as flexible academic purchase
...more>>
A Mathematical Canvas - Kirby Urner
Urner's statements on his approach to curriculum writing and philosophy of education, as well as articles: "On Programming the Calculator," "Alien Curriculum," and "Python for Homeschoolers @ FreeGeek." Download 4D "Moodles" of courseware such as Geonumeracy - Centre for Educational Technology (CET)
A research and development center for math education. Read descriptions of CET's programs and workbooks, including One, Two and Three (Aahat, Shtayim, Ve Shalosh), for grades K-6; and Visualizing Mathematics, for grades 7-12. Learn about and download
...more>>
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Calculus is the basis of all advanced science and math. But it can be very intimidating, especially if you're learning it for the first time! If finding derivatives or understanding integrals has you stumped, this book can guide you through it. This indispensable resource offers hundreds of practice exercises and covers all the key concepts of calculus,... more...
An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background,... more...
The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis.
The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory... more...
Mathematical theory in basic courses usually involves deterministic phenomena; however, in practice, the input to a linear system may contain a "random" quantity that yields uncertainty about the output. Probability theory and random process theory have become indispensable tools when analyzing these systems. This SPIE Field Guide discusses basic probability... more...
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including... more...
This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial... more...
Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this... more...
This book contains survey papers based on the lectures presented at the 3rd International Winter School "Modern Problems of Mathematics and Mechanics" held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern... more...
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4.Do you use the logic or problem solving
skills learned in math class to work through situations in your professional or
personal life?
Please look over their responses.They are alphabetical by profession, with a
list of professions on the right hand side panel.
Alicia,Business and Chemistry
Math in current profession… I have used
math in every field I've worked in. When I worked in a lab, I used
everything up to and including calc 2 (integrals). In marketing I
actually used math MORE than when I worked in the lab! Lots of algebra,
probability, and statistics. Spreadsheet skills are KEY - use will use
spreadsheets in just about any career.
Skills that were useful or wish I had paid
more attention to… The single most important thing I learned in math (all
of school really) is CRITICAL THINKING. If you can develop good critical
thinking skills you will be MILES ahead of the competition when you are
applying for jobs. I wish I still had my stats book.
Math to maintain your home/personal life?...
All the time! Surface area and volume of simple and complex objects
(like say a wall or rectangular room vs molding with rounded parts and/or steps
or two level room. I do a lot of math keeping track of our
finances. Taking the time to do financial math can save you tens of
thousands of dollars over the life of a home loan, make you money with the best
possible saving vehicles, and save you from predatory lenders (who will laon
you way more than you can afford to pay back, then take your car/house/what
have you).
Logic or problem solving skills?... Constantly.
Everything from trying to repair things in the home to navigating workplace
politics to arguing with my husband.
Ryan, Engineer
The best math classes I ever took were physics 1 and 2, hands
down. The math instruction I've had (in real math classes) has mostly sucked.
The curriculum is probably to blame more than the instructors, but way too much
class time was spent on procedural rather
than "connective" work - in other words, that which fosters our
ability to connect what we were supposed to be learning with other things we
had learned before. If someone asks me why math is important, I tell
them one reason it's important is because it's the foundation upon which all
science education rests. Anyone who is considering a career that has anything
to do with science will have a much easier time of it if their math is solid.
Robley, English
Instructor
Math in current profession… I primarily use very basic math in my job - things like calculating
student grades, percentages, and weighing certain projects more heavily than
others.
Frequently I encounter students
who have no idea how to do this basic addition and averaging to determine their
current or final grades. This is actually really problematic for students
because they are unable to make decisions about their standing in class, their
participating in the class, and how to reach the desired grade in the
course.
Skills that were useful or wish I
had paid more attention to… Geometry. I
HATED geometry, it was surprisingly hard for me. But I find this is a tool I
used frequently when fixing my house. When I'm building a garden in my back
yard and need to calculate the supplies I need or what angle to cut the wood at
to create a certain shape (I have a six sided feature we created in our yard
that took FOREVER to figure out).
Logic or problem solving
skills?...Many of the courses that
are required in college (and high school) can seem pointless while we're in the
class. It's often difficult to understand the "use" of a certain
piece of history or set of skills. One thing that I'm frequently struck by,
however, is how much this knowledge does add value to my life. Even things I
don't "use" in my daily life (for example, understanding the history
of the Panama canal) add value to my life. I find this knowledge allows me to
be better engaged in the world around me. I'm more prepared to understand the
things I read (literature, news papers, blogs, FB status updates even); I'm
more able to engage in conversations with people that I meet about a variety of
subjects; I'm able to understand or question how current events (in my life and
in the world) will effect the future; in short I'm more prepared to participate
in the world. The knowledge, critical thinking skills and technical
skills (like math and writing) that you are learning while you are in college
serve not only to prepare you for a specific career, but to prepare you to be
engaged participants in the world. This gives you a level of control over the
things that are happening around you that you can't gain in any other way. My
experience has been that much of this knowledge developed a "purpose"
long after I left college and I am continually surprised at the variety of
purposes I find for this knowledge.
Tim, Finance
Math in current profession… We use calculus and
linear algebra every day as part of option value calculations and numerical
procedures we code up to calculate the fair value of a financial instrument.
Skills that were useful or wish I
had paid more attention to… Too often, math beyond algebra gets too
abstract. For example linear algebra is immensely useful, but most courses I've
seen don't drive home the real world applications. So I think I paid attention,
but the teaching was so math focused, it was hard to see how I would use it
until much later.
Math to maintain your
home/personal life?... I use math to calculate different
budget scenarios at home. For example, if I pay $50 more on my mortgage, how
much sooner will I pay off my mortgage?
Logic or problem solving
skills?...
I use stats every day at work, including probability theory to help make
decisions.
Travis, Chemist
Math in
current profession…calculate mole to mole
ratios for chemical synthesis.
Skills that were useful or wish I had paid
more attention to… quantitative data for chemical
analysis.
Angela, Chemistry,
B.S.
Math in current profession…For chemistry math problems I'll have to use math to
calculate concentration/molarity, volumes, and fractions of molecules included
in a square area for lattice structures. We use logs to calculate the pH, and
we use basic math to calculate total energy/entropy/enthalpy required in a
process.
Not to mention all the calculus we
use to calculate the probability of an electron's location at any given moment,
as well as the time-related Schrödinger equation for a wave function! YUCK.
Math to maintain your
home/personal life?...I use the "counting
money back" technique every time I purchase something to be sure I receive
the right amount of change. I use the 10% +half of the 10% to calculate tips!
Every time I explain to people that's how I do it, they're always like
"oh.. that's so easy".
Chris, Computational
Biologist
Math in
current profession… I'm a scientist who uses computers to help
understand why we get cancer and how we might treat it more effectively. I use
math every day, especially statistics. When we look at the DNA of a tumor, we
see thousands of mutations. Statistics helps us decide which ones are most
likely to be helping that cancer grow, and which ones might be good targets for
new drugs.
Skills that were useful or wish I had paid
more attention to… I was never a great math student in high school and
college. Because of that, I've had to go back to basics and teach myself a lot
of things later on. If I had really learned the fundamentals of Algebra
earlier, it would have made my life easier and really saved me a lot of time!
Math to maintain your home/personal life?...
We're saving up for a house and planning for our first kid. I need to
understand concepts like compound interest to understand where my money goes
and how much I need to save.
Logic or problem solving
skills?...Math and science have a lot in common. Both can be hard sometimes,
but by stepping through problems logically and trying different approaches, you
can usually figure out the answers.
Erin, Geologist
Math in
current profession… I do use math all the time. The main thing
that we try to do is find
where we think oil is accumulated below the earth's surface. Once we have
found an interesting area, we need to determine the volume of oil that could
potentially be in there. So we do volume calculations - There are a lot
of factors involved in that - but essentially we need to know the volume of the
entire rock body that would have the oil in it, then the porosity of the rock,
and how much oil would actually fit
in that pore space. All of the factors involved in determining the
volumes are imprecise, so we have to assign a range of the possibilities and
then simulate the range of volume outcomes for that
accumulation.
We interpret seismic data - which is like an ultrasound of the earth - sound
waves are sent down into the earth, and recording their reflections back to the
surface allow us to see the layers below the
earth's surface (up to 8 or so km!) So we have to know about wave theory
(maybe that is more physics...)
Skills that were useful or wish I had paid
more attention to… I wish I had paid more attention to the principles of
statistics. Or, more accurately, that I had taken a statistics
class...
Math to maintain your home/personal life?...
Yes! I use math in maintaining a budget and keeping track of where I
am financially. I report all my expenses and income and keep that up to
date monthly.
Logic or problem solving skills?...Right now I live in Denmark and
their currency is the Danish crown.
When I go shopping, I convert the price to US dollars so I can get a sense of
how expensive things are. I use logic in planning my projects and
managing my time throughout the day. For example, what time and other
resources do I have, what is my due date, what kind of product can I produce in
that amount of time? Also, when i read the news, my knowledge of statistics
helps me (I do have some....) to recognize sloppy reporting and know which news
articles to take seriously.
Skye, Greenhouse
Manager
Math in
current profession…I have to calculate man
hours for planting times at my greenhouse eg. 8 people planting for 3 hours is
24 hours of work.
Marilyn, Health
Insurance Agent
Math in current profession…I use math all the time in comparing
plans and their rates. It is mostly simple math, and some percentages etc. I
also use math in figuring tax savings etc.
Skills that were
useful or wish I had paid more attention to… I wish I had listened to my
Personal Finance teacher more. This class was all about math. Now that I
know how important it is to begin saving at a young age, I wish I had started
earlier. As I mentioned above, the financial calculations have been a
great skill to have over the years.
I use math in my personal life while shopping and figuring
out if I should refinance my home etc., but most importantly in budgeting.
It is mostly simple math. I use geometry and other math
occasionally when I am fixing things around the house. I often use a
financial calculator that allows me to see what the future value of my
investments will be given the amount and number of payments I make at a given
rate of return. (Everyone should know how to do this to inspire them to
save money!!!)
I use math all the time with my home budgeting and finances. I
calculate how much I need to save each month to pay taxes, or insurance
premiums that come once a year. I've even set up a very simple budget
that allows me to spend wisely and save money for the future. With math I
am also able to see how stupid it is to use credit cards/get into debt. I
recently used math to show my daughter the advantages of driving a 'paid for'
used car rather than leasing a new car. We figured that in just 9 years
she would be at least $25,000 ahead if she drove a used car.
Logic or problem
solving skills?...When
I solve problems I love to use math because it usually gives me a clear
cut answer. You've heard the saying "the numbers don't lie" and
that is the truth. Still, sometimes there is more than just the numbers
that need to be considered, for example, do we take the higher paying job if it
means more stress and sacrificing time with family? - etc. So you can't
rely just on the math, but it does help you weigh your options. I always
check the numbers.
I am really into SIMPLE budgeting. Budgeting seems to scare
a lot of people off, but it really does not have to be that hard and it is so
important. Without a money plan or a budget, people can get into major
financial problems, which in turn can lead to a lot of stress and pain.
Regardless of your career, budgeting and saving money are vital (math
intensive) skills to have. If I could give advice to young college
students I would encourage them to learn math and start budgeting and saving
now!!
Math in
current profession… I use math for both professions. At the
museum, we do a significant amount of measuring in taking care of our
objects. We use both metric and American measurement types, and so must
have a basic understanding of the comparison between the two. We also use
computer math functions, such as categorical numbering using our database as
well as Excel spreadsheet columns. And yes, we even use math to fill in
the correct hours on our timecards!
Skills that were useful or wish I had paid
more attention to… The most useful information from math classes is basic
math (addition, subtraction, multiplication, division) WITHOUT using a
calculator. I wish I had paid better attention so I could do all of that
in my head quickly!
Math to maintain your home/personal life?...
At home I use math every day. I am a mom of two, a 2-year-old and a
4-year-old. Meals are often mini fights about fair portions... I use
division and reasoning to make sure everyone gets their sandwich cut into 4
pieces. I use measurement and math when making recipes, even basic
macaroni and cheese! Budgeting and finances require addition and
subtraction all the time. Balancing the checkbook to make sure we haven't
overspent on our debit card and matching that against the bank's records is a
very important skill.
Logic or problem solving
skills?...Logic
and problem solving get used in my professional life at the museum when we are
trying to find the best places to store and display objects. Measurements
are crucial as well as logic: two big baskets probably won't fit on the
same shelf! At home, logic and problem solving are again crucial, as with
the even sandwiches. :)
Kyle, Lawyer
Math in current profession… I am self employed
and I use math with my bookkeeping, profit and loss, cost vs time
evaluation, interest calulations, etc. Also, I always have to
problem solve and have logical applications.
Nadya, Marketing
Math in current profession…Marketing
is actually full of math. I've used math to compute how much food to order for
an event or how many fun give-a-ways to order. How much money we have in the
budget and where it can be best used, how many visitors to the website actually
looked around, how many people read emails and responded, effectiveness of
promotions, how many extra newsletters to order to account for mailing run off
(basically the errors the mailhouse might make), how many bags of candy to buy
to hand out at Halloween in the branches and much, much more. Marketing
involves a lot more than just making things pretty or fun!
Math to maintain your
home/personal life?...Definitely used in
budgeting. Also used in figuring out which can of green beans is the best price
or other groceries (figuring per oz prices), estimating how much my grocery
bill should be while shopping so I can tell if an error is made when being rung
up.
Logic or problem
solving skills?... I do use logic quite a bit but I'm not sure if I learned it
in math class. Occasionally proofs have come in handy though when trying to
illustrate to other people that a process will work.
Danny, Neuroscience Researcher (Graduate
Student)
Math in current profession…I use algebra to make solutions needed
for my experiments. I must calculate the mass of the drug that I want in my
solution for a given volume of saline to reach the concentration that I need
for my experiment. I also use algebra/arithmetic to convert different
measures of the concentration of a solution to discuss the experiment with
other scientists. When administering drugs to live animals, dose of the drug is
described as mass of drug per mass of the animal (e.g. 5 mg/kg). However, if we
are doing experiments in brain slices, we express the dosage of a drug as its
molarity (20 µM).
I also do a lot of statistics on the results of the
experiments. I write matlab scripts to analyze my data, which could basically
be written as long, complicated, algebraic equations. I also use built-in
matlab functions to do a statistical multivariate, repeated measure analysis of
variance (ANOVA) to determine if the results for different experimental
conditions are different enough to be statistically significant, which we can
then report in scientific journals.
Skills that were useful or wish I had paid
more attention to…I paid pretty
good attention in my math classes, since I liked math. My problem has mostly
been forgetting certain concepts since I haven't been in a math class in
over 10 years. A solid understanding of algebra is probably the most important
for everyday life. Most problems can be solved with back-of-the-napkin type
math using algebra and simple arithmetic.
Math to maintain your
home/personal life?... Mostly I would say this consists of just some quick
mental arithmetic to make sure some company didn't make a mistake and charge me
too much or something.
Logic or problem solving
skills?...Logic
and problem solving are hugely helpful in my job as a research scientist.
Without them you cannot do science.
Janice, Nurse
(Medical Intensive Care Unit)
Math in current profession…I use math all the time in my job as a
nurse: estimate when the IV bag will be finished; basic adding and subtractding
for intake and out put totals (24 hr fluid balance); I use algebra to calculate
drug administration, setting IV pumps, etc. Everything is in metric system so
it is important to understand that.
Math to maintain your
home/personal life?... In my everyday life, I use it to do my
checkbook/bank statement, determine price of something I am buying (if it is a
good price or not) and how much I will save using coupons, 20% off, etc. I also
calculate if I am getting a good gas mileage with my car (miles/gallon of gas).
I use measurements in cooking and adjusting recipes i.e. making half the recipe
or doubling, etc. I use it when buying material for crafts/sewing. The list
goes on! I am sure I use it even more than that!
Jessica, Office Manager & Landscape Designer
Math in current profession…I surprisingly use
math a lot, which is a surprise for me because it was a real struggle for me
through school. I use it as an office manager entering the finances to the
theatre I work for and keeping the books up to date. I also use it as a
landscape designer; square footage, volume for things like compost or gravel,
dimensions, etc.
Kevin, Petroleum
Engineer
Math in current profession… I
use algebra for Multivariate statistics, I use geometry for wellbore
calculations, and I use calculus for finding the rate of change, inflection
points, and completed work (area under the curve).
Skills that were useful or wish I
had paid more attention to… I wish I paid
closer attention to statistics, the most important skill learned is
solving algebraic equations. Solutions to real world problems come about
by solving equations and have contributed to my project at Shell.
Christine, Statistician & Medical
Researcher (Graduate Student)
Math in
current profession…I do
research on statistical methods to infer biological networks. For example,
inside of each of our cells, there are reactions occurring constantly. In
a diseased state, this network of reactions is altered in ways that
lead to a loss of cellular function. Magnetic resonance
spectroscopy can be used to profile tissue samples, and from this we can
identify which molecules are present and estimate their concentrations. We can
then use statistical methods to infer the reaction network by looking
at the covariance of the concentrations of the molecules. This is a difficult
problem since the data is noisy (i.e. there is random variation in the
measurement), the networks are complex, and we often have small sample sizes.
We are developing statistical methods that allow us to incorporate prior
knowledge on the degree of connectivity of the network and known chemical reactions. These techniques can improve the
reliability of our inference. The resulting identification of the reactions
under diseased conditions can increase scientific understanding of the
mechanisms of disease and also guide the development of future treatments.
Skills that were useful or wish I had paid
more attention to…I still wish that
I could explain mathematical concepts better! It's really nice to be able to
help out other students, and you can feel sure that you understand
something once you are able to explain it someone else. Right now, I work a lot
with medical researchers, and I often have to explain statistical methods to
them. I am still trying to get better at how I communicate these ideas.
Erin, Swimming
Coach
Math in
current profession…add up the amount of
yardage that my swimmers are swimmingand calculate how much yardage is needed for a mile.
Math to maintain your home/personal life?...
balance a checkbook.
Ben, TV Production
Math in
current profession…I do base 60 Time math daily (e.g. adding and subtracting the
number of minutes in an hour),subtracting one time from another to find the difference between the
two.Also I use math in trying to
calculate time cues for production, which is tough since I have to do it
backwards in real time.
Alicia, Veterinarian
Math in
current profession…Yes, I use math everyday in my
profession.I use basic algebra and stoichiometry
for fluid rate calculation, drug dosage calculations, basic unit conversions,
etc.I love trigonometry and know I will
get to use some of it in when I go into my residency for sports
med/rehab and have to study/use biomechanics, basic trig is also used a lot in
orthopedic surgeries.
Skills that were useful or wish I had paid
more attention to… I wish I understood physics better which has a lot of
math in it because then I would understand ultrasounds better and be able to
use my machine better.The most useful
skill I learned in math class is basic math, like fractions.I am constantly surprised by how many people
can't understand that ¼ of a tablet is the same as 0.25 of a tablet…
Math to maintain your
home/personal life?... Yes, making a monthly budget and sticking to it has
been important given the amount of educational debt load I have.Also, calculating how much interest accrues
in my loans is important to know each year.
Andrea, Walmart Customer Service Manager
and Supervisor
Math in
current profession…I use it every day to calculate the ad
matching we do. For example say you are buying 10.29 pounds of oranges from
rancho market and their ad is 8 pounds for .99 cents you need to calculate how
their rates compare with Walmart's. At
Walmart we sell oranges by unit, so we have to figure out the price per orange
because not all our produce is by the pound.The reason I am giving you this example is I hear all day long from the
younger cashiers that they hate math and I don't know how to figure it out. I
show them all how to do this so they not only can handle the ad matches and so
they don't feel stupid. I sympathize with a lot of them because math was not my
best subject.I also use math in my
profession to figure out the difference I need to give customers as a credit if
they paid a higher rate of tax than in Utah.
Skills that were useful or wish I had paid
more attention to…Basic math, and
math that you need in the real world, and how to do this in your head without a
calculator.And that if you have
struggled in the past with math that you can get better, for example, I used to
struggle with arithmetic, but now I can do it in my head. Find someone to help
you break it down so that you can understand.I am very grateful that I had teachers throughout my schooling who took
time to do this for me.
Math to maintain your home/personal life?...
I use it to figure out how to cut fabric,to double check the machine on prices, and for gas mileage.The desire to learn and gain knowledge (being
able to solve the math problems like discounts, or being able to use the
computer, etc)has promoted me from a
temporary employee to a manager.
Jim, Web Developer
Math in
current profession… I definitely use math in programming.
Simple arithmetic is everywhere in programming, but also many of the concepts
of programming are based on math. For example, a key concept of
programming is understanding variables (assigning labels to data), which is the
basis for algebra. But most of the actual work of programming is more
like solving proofs in geometry, at least conceptually. The idea of tying
together a series of steps to produce a specific result is exactly the work
programmers do.
Skills that were useful or wish I had paid
more attention to… I wish I had taken a statistics class. I think
some of the concepts and algorithms would be useful, if for no other reason
than to have a clearer idea on how to express what sort of algorithm I am
looking for. The most useful thing from math for me was discovering that
I enjoyed doing geometry proofs. I think "math" is a huge field
and most people actually like certain parts of it, even if they "hate
math". You don't have to like everything, but I think everyone
should try to expose themselves to as many fields of mathematics as they can.
Math to maintain your home/personal life?...
I do use math for finances, but not in a straightforward way. I think
having a strong understanding of probabilities and percentages can be very
helpful for understanding things, such as the fact that if you buy a stock and
it loses 50% of its value, the stock will have to gain 100% to be worth its
original amount.
Logic or problem solving skills?...All the time. I think developing good
problem solving skills is useful in almost every aspect of life and business,
but the real key is being able to identify and translate real world problems
into solvable problems. I always hated solving word problems in math, but
I think that's an important skill to master.
Business and Chemistry
Engineer
English Instructor
Finance
Chemistry, B.S.
Chemist
Computational Biologist
Geologist
Greenhouse manager
Health Insurance Agent
Homemaker, Part-time curatorial assistant at Museum of
Natural History
|
General Objectives:
Besides developing your understanding of the topics
mentioned above, there are some particular skills you should improve upon along
the way in order to be able to apply what you learn in this course to future
courses of study. These include:
Šuse
of mathematical terminology and notation
Šmathematical
abstraction
Šmathematical
problem-solving techniques
Šwriting
skills – both formal and informal
Šappreciation
of the interplay between mathematics and the surrounding culture
WAC Objectives and Requirements:
This is aWriting Across the Curriculum (WAC) course. Like all
such courses, it emphasizes writing as a tool for both learning and
communication. Therefore the writing
assignments for this course are divided into two types according as the main
objective is either "writing to learn" (WTL) or "writing to communicate" (WTC).
The specific assignments are as follows. (See the attached schedule for exact
due dates):
WTL
ŠMath autobiography (1 to 2 pages) informal but neatly written story of
your own personal math history (from birth to present day.)
ŠFormal Paper (at least five-pages, type-written) on some aspect of
the historical developmentof a
specific mathematical topic. You will
submit this in three stages: (1) One-page description of the topic and the
references to be used (including at least one book other than our text.) (2) Rough draft. (3) Final draft. [Note: You may
choose the topic or take it from a list I will provide, but it must be approved
by me before you get too far into the research and writing stages of the
paper.]
ŠShort-answer exam
problems (two per exam, 1 paragraph
each.)
Evaluation Procedures:
Your understanding of
the subject material and your progress toward the aforementioned objectives
will be evaluated on the basis of your written work, as described above, your performances on
two written exams,
and your class participation (attendance, preparedness and contributions.)
Evaluation
Criteria: Grades on all work will be
based upon
Šaccuracy
of information (including calculations and use of mathematical notation and
terminology)
Šdepth
and breadth of solutions
Šlogic
and clarity of arguments
Šneatness
and clarity of presentation
Šcorrectness
of grammar and spelling
Šthoroughness
and timeliness of work
Šintellectual
honesty and creativity
Šachievement
of personal potential
Šdifficulty
of the assignment/test
Grades:My scale for converting
numerical grades (i.e., percentage points) to letter grades will be as follows:
89-100 A, 77-88 B, 65-76 C, 50-64 D, below 50 F
Your
final grade will be based on the following distribution of points:
Math autobiography3
%
Journal
entries (six installments)18
%
Problem
sets (six sets of four)24
%
Midterm
Exam score15
%
Final
Exam score15
%
Term
paper (topic report, rough draft and
final draft)15 %
Classparticipation *10
%
*Class participation
includes attendance: Missing more than one class meeting for any reason will result in a
deduction of 1 point per absence (beyond the first) from the 10 points
available.
Important
Reminders:
ŠAttendance
is important! However, should you find for some reason that you must miss a
class meeting, remember that you are still responsible for any and all material
you may have missed during your absence.
ŠAssignments
must be turned in at the prescribed times (see attached schedule) in order to
be eligible for any credit. All work on these assignments must be your own,
i.e., no help from anyone, without prior permission from the instructor.
Failure to abide by this policy will lead to serious consequences: automatic
zero on the assignment in question, possible expulsion from the class, etc.
ŠExams
must be taken at the prescribed times (see attached schedule), except by
prior permission from the instructor, which will only be given under the direst
of circumstances (serious illness, e.g.). In order for you to obtain such
permission, I must be notified of your "dire circumstances", by e-mail,
phone, or otherwise, before the test is given. Otherwise you will almost
certainly receive a score of zero for that test.
ŠIf
you find yourself falling behind in the course, do not delay in seeking out
appropriate help and advice from someone who is competent in the subject area
and who has your best interests at heart!
|
More About
This Textbook
Overview
The updated new edition of the classic and comprehensive guide to the history of mathematics
For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.
Distills thousands of years of mathematics into a single, approachable volume
Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present
Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.
Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
Editorial Reviews
Booknews
**** The first edition, 1968, is cited in BCL3. A classic history of mathematics, from its earliest origins to the present. This second edition features completely revised chapters on the 19th century, and far more material on Hilbert, Poincare, and 20th century mathematics. Contains a wealth of references (all in English), and exercises
|
GCSE Modular Mathematics Higher Unit 3
Edexcel GCSE Mathematics - The teacher's choice. We've worked closely with Edexcel for many years to provide resources that you know and trust, which ...Show synopsisEdexcel GCSE Mathematics - The teacher's choice. We've worked closely with Edexcel for many years to provide resources that you know and trust, which is why you can be confident our endorsed Edexcel GCSE Mathematics course is the best solution for the two-tier specification. Each Student Book is delivered in colour giving clarity to different concepts through artwork and diagrams. Worked examples, practice exercises and examiners tips ensure students are fully prepared for their exams. An experienced author team, including Senior Examiners, means you can trust that the specification is covered to ensure exam success Edexcel GCSE Mathematics for 2006.. Full
|
Calculus I (Math 210) 4 credit
hours
Functions and graphs, rational, trigonmetric, exponential
functions, composite and inverse functions, limits and
continuity, differentiation and its applications, integration
and its applications. Prerequisite: Four units of high school
mathematics including trigonometry, or Math 120, or Math 110 and
Math 125, or Math 202.
|
The Common Core standards consist of skills to be learned in each grade, though the curriculum details are left to schools to determine. Common Core standards do not mandate a particular curriculum: instead, they specify particular skills that children ...
By the end of the year, they'll be fluent in polynomials, quadratic equations and exponents, and will take the algebra I exam. Edgartown's program began last year in the seventh grade as a pilot; one that every school would learn from. It's an ...
Surely, the second hurdle is that for most students, myself included, what is the point of learning to factor a polynomial? The Graduate Record Exam required me to relearn factoring polynomials. Funny thing, throughout my Ph.D. programs, the call to ...
It shows different ways to factor polynomials. It explains how to correctly evaluate algebraic expression. It provides means to properly interpret the wording of algebra problems. It shows in detail how to work representative problems in algebra and ...
One set of ϕ-polynomials routinely used to fit deformations to optical surfaces in metrology is the Zernike polynomial set. To demonstrate the link between freeform surfaces and NAT, we consider a Zernike trefoil freeform overlay (see Figure 1), placed ...
Thus, I estimate time trends by using countries that have multiple DHS surveys, regressing polygamy on quartic polynomials in age and year of birth. I calculate the predicted probability that a woman aged 30 is polygamous as a function of her year of ...
Limit to books that you can completely read online
Include partial books (book previews)
|
Schaum's Outline of Vector Analysis
Synopses & Reviews
Publisher Comments:
The guide to vector analysis that helps students study faster, learn better, and get top grades
More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's is better than ever-with a new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study.
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
About the Author
Murray Speigel, Ph.D., was Former Professor and Chairman of the Mathematics Department at Rensselaer Polytechnic Institute, Hartford Graduate Center.Seymour Lipschutz, Ph.D. (Philadelphia, PA), is presently on the Mathematics faculty at Temple University. He has written more than 15 Schaum's Outlines
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Product Description
About the Author
Richard L. Scheaffer, Professor Emeritus of Statistics, University of Florida, received his Ph.D. in statistics from Florida State University. Accompanying a career of teaching, research and administration, Dr. Scheaffer has led efforts on the improvement of statistics education throughout the school and college curriculum. Co-author of five textbooks, he was one of the developers of the Quantitative Literacy Project that formed the basis of the data analysis strand in the curriculum standards of the National Council of Teachers of Mathematics. He also led the task force that developed the AP Statistics Program, for which he served as Chief Faculty Consultant. Dr. Scheaffer is a Fellow and past president of the American Statistical Association, a past chair of the Conference Board of the Mathematical Sciences, and an advisor on numerous statistics education projects product provides pretty good help for doing the problems from the textbook. It could, however, have gone into greater detail. We buy this book hoping for explanation as to why a calculation has been done the way it has, not just to see the calculation done. Which is why I give it a 3/5.
I've purchased quite a few solutions manuals and texts in the last few years, and this is by far the worst. The solutions cna be very vague and require a lot of intuition to figure out what exactly they're trying to do. Not to mention that there are a frequent amount of errors in the problem solving process. I would have given it 1 star, but it has helped me hand in more complete homework for my class (even if I don't fully understand what I did).
I would like to make a silly probability joke about the poor quality of this solutions manual, but I haven't learned enough to come up with anything that makes sense.
4 of 4 people found the following review helpful
1.0 out of 5 starsBig disappointmentMay 22 2012
By George - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
This manual gives solutions only to the odd-numbered problems, the answers for which are already in the textbook! So you would want this manual only if you think you'll have trouble figuring out how to get to those answers. The manual would have been a whole lot more helpful had it included answers to all the problems. Very disappointing.
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measure.
This book combines the history of mathematics with an explanation of mathematical procedures and principles.This book combines the history of mathematics with an explanation of mathematical procedures and principles.Hide synopsis
3.
Hardcover,
Houghton Mifflin
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This course will investigate in depth topics from differential and integral calculus, using the T183 graphing calculator (Regular, Plus or Silver edition). The following topics will be covered: limits, continuity, definition of the derivative, shortcuts to the derivative, product, quotient and chain rules, derivatives of the transcendental functions, applications of the derivative, integration, the fundamental theorem of calculus and applications of the integral. Students will analyze difficulties and misconceptions often experienced by secondary calculus teachers and will examine applications that connect theory with examples relevant to secondary students.
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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Review of a high school geometry course with Geometry: A Guided Inquiry book;
its Home Study Companion; and Geometer's Sketchpad software
I am reviewing here a "combo" package for high school geometry course, consisting of three different products: 1. Geometry: A Guided Inquiry textbook; 2. Home Study Companion to it, and 3. Geometer's Sketchpad software.
While these three will work together, I will describe each "part" separately in my review. Please use the quick links below to jump directly to the various sections, if you'd like. Naturally, the review about the book is the longest.
The book
Geometry: A Guided Inquiry is a problem-centered textbook. Each chapter starts with a central problem, which acts as a starting point for developing important concepts and theorems.
The text reads like a "worktext": many of the problems worked on are an inseparable part of the overall instruction, because they will lead the student in a step-by-step manner to important theorems and results. This lets students become familiar with the concepts little by little, and constantly keep building upon previous knowledge, just as is normally done in mathematics. (Naturally, the book also contains plenty of "exercises" that simply practice a concept just presented.)
In essence, the student is guided in his geometrical inquiries by the questions presented, as if a teacher was guiding him by hand. For this reason, I feel this text is an excellent choice for anyone who is studying geometry by themselves, or without a teacher.
Let's look at an example.
An example of guided exercises leading to a theorem
On page 197, the student first learns and proves that if a point P is equidistant from the endpoints of a line segment, then P is on the perpendicular bisector of the segment.
The very next exercise has a chord AB of a circle with center P, and asks why the perpendicular bisector of AB passes through P. The next part has a picture showing two chords of a circle, and asks where the perpendicular bisectors of the two cords intersect. Another picture with two chords, and a question, "Why must the perpendicular bisectors of the two chords intesect? The student fills in a sentence: The perpendicular bisector of a chord passes through the __________ of the circle.
Soon follows a problem with a triangle and the perpendicular bisectors of its two sides. Questions ask, "Why is PA = PC? Why is PB = PC? Deduce that PA = PB."
In such a manner, the student is gently led to deduce a statement: The perpendicular bisectors of the sides of any triangle all meet in a single point.
You can see all this for yourself in these two sample pages:
Page 197
page 198
The chapters in the book
The Shortest Path. The "central" or opening problem for this chapter presents a camper in forest who needs to return to his campsite but first fetch a bucket of water from the river. The problem is, "At what point P on the river should he fill his pail in order to make the shortest possible path to put out the fire?"
The opening problem in chapter 1: The Shortest Path
This single problem leads to the development of several important concepts: distance from a point to a line, perpendicular lines, and reflection of a point across a line. Finally the exact solution AND its proof are studied, along with applications.
Below you can preview the pages 6-9 of the first chapter, which show the development of concepts (such as reflection and triangle inequality) towards solving the "shortest path" problem.
Tiling the Plane deals with polygons and angles, and of course solve the question as to which regular polygons tile the plane.
Triangles deals specifically with the SSS, SAS, and ASA congruence properties of triangles. This chapter also has some practices in proving theorems.
What is a Proof? is about proofs and some common pitfalls in devising proofs. Along the way, the chapter also develops properties of quadrilaterals, especially of parallelograms.
Constructions with Straightedge and Compass covers basic constructions, the special points of a triangle, and also some impossible constructions.
Area and Volume is like the title suggests: areas and volume of basic figures.
The Pythagorean Theorem
Similar Figures
Perimeter, Area, and Volume of Similar Figures
Circles - this chapter has exceptionally many interesting projects.
Coordinates
Conic Sections - most of this chapter is devoted to the ellipse.
After each chapter's main worktext part (called Central), we find a Central Self Quiz, a review, a review self test, and projects, where the most interesting problems are found! There is also an algebra review at the end of chapters 1-7, and cumulative reviews at the end of chapters 3, 7, 9, and 12.
In the very end of each chapter you will find answers to the chapter's central self quiz, the review self test, algebra review, and most answers to the review.
The "projects" in the end of each chapter definitely have lots of interesting material. While they often deal with extensions of the main ideas of the chapter, you will also find explanations and explorations concerning mathematically important results, for example golden section, geometric mean, additional proofs of the Pythagorean theorem, the number of diagonals in a convex polygon, regular polyhedra, Gauss' theorem concerning which regular polygons can be constructed, and the problem about squaring the circle.
In a regular classroom instruction, these projects may get neglected or assigned only to the fastest students, but I would encourage anyone to really DELVE into them, as they often present the best and most fascinating parts of geometry -- all the while developing the student's reasoning skills.
How Geometry: A Guided Inquiry handles proof
Different geometry books handle the topic of proof in different manners, and teachers might prefer one approach over another, so I will now briefly describe how mathematical proof is approached in Geometry: A Guided Inquiry.
As explained above, this book often has a set of carefully crafted exercises leading to an important theorem, and these exercises build one upon another in logical succession, either preparing the student to understand the proof of the particular theorem or to build one for it.
Starting in chapter 2 (Tiling the Plane), students are often asked to complete parts of an argument. In some exercises students are also asked to give an argument or explain his answers using a certain fact. I find these bird-size steps towards more formal proof to be very well designed.
In chapter 3, after studying the SSS, SAS, and ASA properties of triangles, we encounter a section "Introduction to Proofs". In it, the student is again asked to fill in missing words or parts of sentences in paragraph-form proofs or supply reasons for a few two-column proofs. In othe problems the student is asked to write the proof with a hint, and finally without one.
The two pages below show an example of this.
Page 140
page 141
Chapter 4 is titled, "What is a Proof?" It explains such basics as "If...then" statements, converses, and axioms, and lets students practice filling in proofs or writing their own in the the context of properties of parallelograms. We also meet Alex and Danielle, who seem to manage to write flawed proofs all the time - so the reader can learn from their mistakes.
In the rest of the chapters, proof is not forgotten; quite the contrary: the students are often asked to write proofs, many times with a hint. On page 346 we find an example of circular reasoning. I also especially liked problems where you have to find what is wrong with each picture, with the pictures purposefully drawn distorted. This practices simple logical reasoning not based on the appearance of the figure.
An axiomatic vs. discovery based geometry text
Geometry: A Guided Inquiry is NOT written in a strict formal axiomatic style à la Euclid. It does not start out by presenting a set of axioms in the very beginning and then develop all theorems from those.
However, from chapter 2 on, it IS written as a system of geometry that is developed from axioms. This is just somewhat "hidden" from sight by the explorative exercises that precede the axioms and the theorems alike. Also, the few axioms are only introduced as they are needed. The emphasis is more on "local" proofs than on a "global" axiomatic system. Since the only difference is that the axioms are not proved, from a student's point of view it may all just seem to be material or knowledge to be learned.
Personally I feel that the problem-solving approach of Geometry: A Guided Inquiry is first of all more student-friendly and "gentle" than a strict or "pure" axiomatic text. Even more importantly, it truly focuses on the content of geometry rather than being merely a logic course with a geometric backdrop. It DOES contains plenty of rigorous arguments and proofs and practice in writing them, but it is all in a context of solving problems, blended in with the explorative and other kind of exercises.
This is likely a more natural way of learning stuff the first time around. Reading and following an axiomatically built mathematical work is easier once you have a good idea of the material it covers. Personally I would additionally try to introduce students to Euclid's work and to the strictly axiomatic system just a little -- not only for the sake of logic but also for its historical significance. Chandler's Home Study Companion (see below) contains some material to familiarize students with Euclid's work.
Research shows that students' geometrical understanding proceeds from reasoning about shapes based on their appearance gradually into logical and abstract reasoning. Studying high school geometry strictly as an axiomatic system is probably not the most productive way for the vast majority of students. (Please see the article
Geometry and Proof by Michael T. Battista and Douglas H. Clements for more information.)
Home Study Companion
Home Study Companion - Geometry (HSC) by David Chandler really makes this book a home run for homeschoolers, because it provides complete, worked out solutions (not just answers) to all problems in the Central (the main worktext) and Project sections of the Geometry: A Guided Inquiry textbook. The book itself contains answers to its various review and self-test sections. With the Home Study Companion, you will always have help available should you get stuck while doing the problems from the worktext or the "projects".
Not only that, but the Home Study Companion includes a collection of nearly 300 interactive demonstrations using The Geometer's Sketchpad. These demonstrations cover most of the main concepts and many additional explorations of the Central and Projects sections of each chapter.
How do these demonstrations work? For example, let's say you're asked to prove that the diagonals of a parallelogram bisect each other. A demonstration of that would have a parallelogram and its diagonals, and then measurements of the two parts of each diagonal (in centimeters or inches). You would then change the shape of the parallelogram in Sketchpad and see those measurements stay equal to each other. That is not a proof, but it is an interactive demo that helps you understand the matter.
Here are some example screenshots. Click to enlarge. Remember the screenshots are static; in reality the demonstrations are dynamic.
Attempting to speficy a triangle by SSA
An interactive pantograph
A theorem about the parts of intersecting chords in a circle
Chandler has used lots of color and animations in these demonstrations to show that certain angles add up to 180° or that certain areas are equal, etc. Many of these demonstrations actually go through a whole proof step-by-step, with explanations on the side, and you need to click on buttons to see the various steps. And each time, you can stretch the figure or change the lengths or whatever by dragging some points in the figure, and it still works. I was quite impressed!
For example, included are finding the value of Pi through inner/outer polygon approximation, several animated proofs of Pythagorean theorem. Or, some projects in the book in chapter 2 ask a student to draw and find out if certain figures tile the plane. The Sketchpad demonstrations provided in the HSC facilitate this task tremendously because you can just copy and paste the figure and move it on the computer workspace, instead of drawing copies of it on paper.
The interactive demonstrations add another dimension to the study of geometry by themselves, but your student can go even further: simply encourage him to learn Geometer's Sketchpad well enough to duplicate the demonstrations, including with color and animations. Computer-oriented kids will surely love such challenge.
In addition to the GSP demonstrations, the Home Study Companion also includes some additional lessons to supplement the main textbook. These extensions bring the content of
the text into alignment with the California State Standards. The extensions included are: Isometries and Symmetry, More on Proof, Surface Areas of Prisms and Pyramids; Introduction to Trigonometry;
Surface Areas of Cylinders, Cones, and Spheres; and More on Coordinate Geometry.
Geometer's Sketchpad
Geometer's Sketchpad (GSP) is a dynamic geometry software. This means that once you construct a drawing, you can dynamically move its parts and see what changes, and what does not. It also has the capabilities for animations, coordinate systems, fractals, graphing functions, and much more - it's a very versatile program.
Really the best way to understand how it works is to experience it. If you don't yet know what dynamic geometry software is all about, check some online dynamic geometry constructions real quick, and then come back here.
Prior to Sketchpad, I had used another dynamic geometry software while in university (about 12 years ago). So I had some knowledge of how things would work.
However, I decided to go through the GSP Learning Guide provided on the CD. It contains "tours" where you will construct certain things step-by-step. Doing these "tours" will teach you the basics of using Geometer's Sketchpad.
I found the guide vere well planned and enjoyable. It had me construct a square, learn a theorem about quadrilaterals, and even construct an animated kaleidoscope! Personally I would perhaps add an exercise where the student needs to construct two circles with identical radius, since those are so commonplace in many basic constructions that are studied in high school.
By the way, you shouldn't restrict the usage of Sketchpad for only viewing the demos in the Home Study Companion. Your student or child should definitely learn the simple basics of this software, and do SUITABLE construction/drawing exercises from the book with it.
To put myself to the test, I also tried doing a few of the exercises from the Geometry: A Guided Inquiry using Geometer's Sketchpad:
Review, p. 205. Problem 3: Construct a 6-leaved pattern. I did this first on paper, so I knew how to do it before I started Sketchpad. My paper construction wasn't very accurate; the lines didn't pass through the various points exactly, plus I had all kinds of auxiliary lines all over the place, some of which I tried erasing, but it sure looked messy. It hought maybe it'd look better with Sketchpad.
6-leaved pattern done in SketchPad. I could drag the points and see the pattern enlarge.
So here's a screenshot of my construction in Sketchpad. I had to do it twice; my original didn't stand the "drag test" because I had used a "copy and paste" of a line segment instead of making a longer line segment and finding its midpoint. But it was fun! And the result looks way neater than the pencil and paper version. Here's the GSP file if you'd like to download it.
In fact, I decided to try do it using a regular image editing program as well. These always have a circle drawing function. I drew the figure in a vector image program (Corel):
6-leaved pattern done in CorelDraw (click to enlarge)
I do such work all the time, but the fun part in working with Sketchpad is that your circles have a center point, you can "snap" objects to other objects, you can construct things by their relation to others, such as being perpendicular, and then "drag" the points and change it dynamically. In regular image editing programs you pretty much just "eyeball" many of the things or use a coordinate system and measurements - which of course works when you are not planning to dynamically change the figure in order to observe what changes and what doesn't. The two are for different purposes. (However, I'd say that learning the basic geometric constructions is a great help for anyone who plans to do extensive work with computer images or graphic design.)
Another one I tried was problem 1 on page 212. This one is about an alternative method for bisecting a line segment. At first I tried copying and pasting a certain circle in my construction, which worked for THAT particular situation, but then when I dragged my original point that defined the original line, the construction fell apart, because I needed the two circles to maintain the same radius (or as the problem states, "Using the same compass setting..."). I was able to do this right (so it stands the drag test) only after finding and using the construction "circle by center+radius". A lesson learned!
Your work with Sketchpad doesn't have to be limited to your geometry textbook, either. At the Geometer's Sketchpad resource website you can find tons of projects to do and sketch galleries to explore.
Conclusion
Overall, I feel this combo is very comprehensive, yet very suitable for a self-learning environment. You get a very logical and enjoyable textbook where exercises lead step by step to theorems or to proofs, solutions, interactive demonstrations, and a full-fledged geometry software to "play" with.
It is thus an excellent choice for doing high school geometry with a "guided inquiry" method. I especially applaud the problems of the book, which are very varied and make geometry enjoyable, and the quality of the demonstrations in the Home Study Companion.
One thing some people might find lacking in the text is that it won't work well as a reference book. You will not find all the main theorems on topic X clearly laid out in boxes with example pictures, followed by proofs. Instead, this is a "learn-by-doing" book. The important theorems and results are studied AND proven in a very natural surrounding: while doing problems.
However, I would venture to say that this type of learning is longer-lasting than the traditional "theorem-proof-exercises" model.
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Three hours per week throughout the year. Miss Decker, Miss Leigh.
Literary Interpretation.. This course gives opportunity to forge ahead and prepare onself for an instructor in reading and interpreting the best pieces of literature. It develops poise and presence in public speaking. Miss Decker.
MATHEMATICS.
Mr. Dalley.
Mr. Robb.
Mr. Gardner.
Mr. Wrigley.
Algebra a. This course affords a thorough and complete treatment of addition and substraction, parentheses, multiplication, division, simple equations, factoring, highest common factor, lowest common multiple, fractions, simultaneous equations, inequalities, involution, theory of exponents, radicals, quadratic equations, and equations solved like quadratics.
Wells's "The Essentials of Algebra" is the text book in use.
Five hours per week throughout the year.
Algebra b. This course treats simultaneous quadratic equations, theory of quadratic equations, ratio, proportion, and variation, arithmetical, geometrical, and harnomical progressions, imaginary numbers, and logarithms.
Two hours per week throughout the year.
Plane Geometry. This course covers the five books in plane geometry. It aims to familiarize the students a
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Basic TI-82 Tutorial
This tutorial starts from scratch with turning on the TI-82 calculator and takes you
through the basic steps needed to do arithmetic and function evaluation and to enter,
graph and tabulate functions. You use a TI-82 as you view the tutorial to do and check the
exercises scattered through the tutorial.
The downloadable version is in Microsoft PowerPoint and is available in both Macintosh
and PC formats. The on-line version is the identical PowerPoint presentation converted to
HTML. Choose the format that best suits you.
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I'm a rising sophomore interested in competing in some of the math competitions next year (AMC, hopefully AIME). I find questions on the SAT easy, but I always seem to hit my limit on questions 12-15 on the AMC 12 or about 3-5 on the AIME. Is it possible to raise these scores with practice? The Art of Problem Solving book seems interesting and may be able to help me, but is it worth it? Can the same resources be found online? Also, I'm a rising sophomore who has yet to take trigonometry/precalculus. Would knowledge of these fundamentals make a significant difference in my performance? I'm new to this whole process and excuse me if I'm oblivious to something very obvious. Thanks guys.
The Art of Problem Solving books are great! Well worth the money. I sponsor a math team, and all of the serious competitors have used these, including 3 USAMO qualifiers. There is nothing else comparable for preparing for contests. Their forums are well-worth hanging out on also.
Learning trig/precalc will definitely help a lot, especially on AIME. So i suggest taking such a class as soon as possible. I don't know about AOPS book though. My advice is to buy copies of old AMC and AIME tests. I hear they're pretty cheap.
I checked the Art of Problem Solving Website and it said there are two volumes available with one being more introductary than the other. I am going to be a senior so I have had a fair amount of math and have taken several contests already. Should I buy both volumes?
Try talking to your public librarian. I asked the library to look into the books (through a "book recommendation" form) and they bought 25 copies of each book (1 for each library location). Since few other people want the books, I can keep renewing my copies as long as I want.
Bianchi - I'd select based on where you are in terms of contests, rather than how many math courses you've had. The books don't really cover school-type subjects. It's strictly contest math. The first volume covers all but the hardest AMC problems. If you have never qualified for AIME, you should probably start there. The second volume would be approp for AIME and beginning USAMO type problems. If money was no object, I would say you should buy both (plus the solution books), and just figure you'll move pretty quickly thru the first one. Even if the problems are fairly easy for you, it would still take you a month or two and you could build up speed and pick up a few tricks. If money is an issue, does your school have a math team that could buy the books? Or do you have a younger friend who might want to buy them from you? That's what happens in my group. The older kids buy them and pass them down to the younger kids.
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The Sullivan/Struve/Mazzarella AlgebraSeries was written to motivate students to "do the math" outside of the classroom through a design and organization that models what you do inside the classroom. The left-to-right annotations in the examples provide a teacher's voice through every step of the problem-solving process. The Sullivan exercise sets, which begin with Quick Checks to reinforce each example, present problem types of every possible derivation with a gradual increase in difficulty level. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
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MTH 1000 College Math (Fall and Spring)
2 Credits
Students are placed in this course if they have a math SAT score of 480 or below. The course will address mathematic skills needed for elementary topics in algebra, basic statistics, and geometry. Emphasis will be placed on quantitative reasoning, problem solving, experiential learning and lab work.
This course is necessary for success in Algebraic Modeling, Statistics I, and Quantitative Literacy. In order to pass this course, the student must earn a raw score of 75% on their final exam, or they must take the course over again. Note: Required with a score of 480 or below on the Math SAT
MTH 1111 Quantitative Literacy (Fall and Spring)
In this course, mathematics will become a part of a larger set of skills called quantitative literacy or numeracy. This course will emphasize critical thinking, problem formulation, and written and oral communication. The topics will prepare students for careers and lives that will be filled with quantitative information and decisions. Students will be expected to possess strong critical and logical thinking skills so they can navigate the media and be informed citizens, have a strong number sense and be proficient at estimation, unit conversions and the uses of percentages, possess the mathematical tools needed to make basic financial decisions, and understand exponential growth, which describes everything from population growth to inflation to tumor growth and drug delivery. Additional topics of study include areas such as risk analysis, voting, mathematics and the arts, and graph theory. Note: A final grade of 80% or higher is required or student will repeat course before any other math course may be taken.
MTH 1180 Algebraic Modeling (Fall)
This course will cover linear, polynomial, and rational expressions and equations. More advanced topics will include functions, inequalities and linear programming, radical equations and rational exponents, quadratic equations and functions, and exponential and logarithmic functions. Emphasis will be on modeling real-life situations via traditional algebra. Note: This course does not count towards the Mathematics Major.
MTH 1250 Geometry (Spring)
4 Credits Prerequisite: MTH 1111 with a final grade of 80% or higher or permission of Department Chair
This course emphasizes the development of logical thinking through the study of geometric propositions and problems. The course content includes the study of triangles, perpendicular and parallel lines, quadrilaterals, area, and the Pythagorean Theorem. Note: Elective course/choice for Mathematics Majors
MTH 1401 Pre-Calculus I (Fall)
4 Credits Prerequisite: permission of department Chair or 80% or higher in MTH 1111 or MTH 1180 or permission of Department Chair.
MTH 1402 Pre-Calculus II (Spring)
This course is continues the study of functions and their graphs, particularly the fundamentals of trigonometry, analytic trigonometry, advanced topics in trigonometry, and complex numbers.
MTH 1500 Statistics for the Social Sciences (Spring and Fall)
4 Credits Prerequisites: MTH 1111 with a final grade of 80% or higher
This is a mathematics course strictly for non-mathematics and non-science majors. It will consist of brief introduction to descriptive statistics concentrating on levels of measurement, measures of central tendency, and measures of variation. In addition it will discuss the construction and various uses for contingency tables. The remainder of the course will consist in inferential statistics with emphasis on 1- and 2- Sample z- and t- Tests, One-way Analysis of Variance, Chi-square tests, and the basics of correlation and regression.
MTH 1501 Statistics I (Fall)
4 Credits Prerequisite: MTH 1111 with a final grade of 80% or higher or permission of Department Chair
This course will consist of tables, chart s and graphs, measures of central tendency, counting and probability theory, discrete and continuous distributions, the standard normal curve and table, the Central Limit Theorem, sampling distributions, confidence intervals for means and proportions, and hypothesis testing for mean and proportions.
MTH 1505 SPSS Lab
1 Credits
The MTH1505 lab will focus on the relationship between the course material learned from a statistics class or specifically from MTH 1500 Statistics for the Social and Behavioral Sciences and the application of SPSS. The SPSS program will be taught during this lab as students are introduced to the SPSS package and gain working knowledge of the software. The output of the data will be interpreted by the students during the one-hour period for the lab. MTH 1505 is design to be taken concurrently with MTH 1500, or may be taken as a stand-alone one-credit course for students who have already taken a statistics class and have no working knowledge of SPSS.
MTH 2151 Calculus I (Fall)
4 Credits Prerequisite: Placement by the Department or MTH 1402
This course is an introduction to the differentiation of functions of a single variable. Additional topics include limits, applications, integration and the Fundamental Theorem of Calculus.
MTH 2152 Calculus II (Spring)
4 Credits Prerequisite: MTH 2151
This course is an introduction to the integration of functions of a single variable. Topics include definite integrals, transcendental functions (including exponential and logarithmic functions) applications (including areas of regions and volumes of solids), and integration techniques such as L'Hopital's rule.
MTH 3030 Linear Algebra (Fall)
4 Credits Prerequisite: MTH2151
This course is an introduction to the basic structures and processes of linear algebra. Topics include systems of equations, matrices, determinants, vectors, inner product spaces, linear transformations, Gauss-Jordan elimination, eigenvalues and eigenvectors.
MTH 3040 Differential Equations (Spring)
4 Credits Prerequisite: MTH2152
This course will enable students to solve problems modeled by ordinary and partial differential equations, as well as systems of first- order and second-order differential equations with constant coefficients. Topics include a general introduction to differential equations, approximation methods, homogeneous linear differential equations, non-homogeneous differential equations, and Laplace transformations.
MTH 3070 History of Mathematics and the Natural Sciences (Spring)
4 Credits
This course will investigate important discoveries in their historical context and the lives and contributions of great mathematicians and scientists. Emphasis will be placed on the ancient civilizations of Egypt and Babylon, Greek mathematics, Fobonacci, the Renaissance, Pascal and probability theory, Gauss number theory, and 20th Century mathematics.
MTH 3161 Calculus III (Fall)
4 Credits Prerequisite: MTH 2152
Topics included in this course are a continuation of integration techniques, improper integrals, differential equations, infinite series, conics, parametric equations, and polar co-ordinates.
MTH 3162 Calculus IV (Multivariable Calculus) (Spring)
4 Credits Prerequisite: MTH 3161
This course continues the study of Calculus. Topics include vectors, vector-valued functions, functions or several variables, multiple integration, and vector analysis.
MTH 3200 Discrete Mathematics (Fall)
4 Credits
This course will introduce students to the basic concepts and problem-solving techniques of discrete mathematics, including algorithms, programming, predicate logic, and combinatorics.
MTH 3250 Probability Theory
4 Credits Prerequisite: MTH 2151 and 2152
This course is an introduction to the mathematical theory of probability for students who possess the prerequisite knowledge of elementary calculus. Topics include combinatorial analysis, axioms of probability, conditional probability and independence, discrete and continuous random variables, distribution and density functions, expectation and variance of a random variable, joint distributions, independent random variables, and Limit Theorems.
MTH 3350 Foundations of Advanced Mathematics (Spring)
4 Credits
This course is an introduction to the fundamental concepts and techniques of proof. Topics include reasoning, predicate logic set theory, mathematical induction, functions, and equivalence relations.
MTH 3740 Mathematical Modeling (Spring)
4 Credits Prerequisite: MTH2152
Students in this course will learn how to build suitable mathematical models for a variety of phenomena found outside the college classroom. Different equations, dynamical systems, proportionality, geometric similarity, model fitting, simulation and probabilistic and optimization modeling, dimensional analysis, differential equations, and simplex method are some topics covered.
MTH 4050 Advanced Geometry (Fall)
4 Credits
Topics discussed will include constructions and non-constructability, Greek astronomy, geometer's sketchpad, modern research, and the following geometries: Euclidean, hyperbolic, spherical, and projective.
MTH 4100 Modern/Abstract Algebra
4 Credits
This course will introduce students to the following modern/abstract algebraic structures and their accompanying theories: sets, groups and subgroups, ideals and rings, fields and homomorphisms. Pertinent algebraic properties will be discussed in relation to these structures.
MTH 4200 Advanced Calculus
4 Credits Prerequisite: MTH 2152 and 3350
In this course students will focus on the theoretical aspects of calculus, such as the concepts of limits, continuity, differentiation, and integration. Also, a variety of theorems (e.g., implicit function; inverse function) will be analyzed in relation to the fundamental issues within the calculus curricula.
MTH 2099, 3099, 4099 Special Topics in Mathematics
4 Credits
These courses focus on special topics in mathematics, and are designed to provide students with an opportunity for in-depth study of some topic having current professional or public interest that is not thoroughly addressed within the context of regular offerings. Topics may differ each time a course is offered. Students should consult the course offering schedule and their academic advisor each semester.
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Mathematics for Calculus
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling ...Show synopsisThis best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, this Custom edition for Wayne State University. Book is in...Good. Custom edition for Wayne State University. Book is in overall good condition! ! Cover shows some edge wear and corners are lightly worn. Pages have a minimal to moderate amount of markings. FAST SHIPPING W/USPS TRACKING! ! Precalculus: Mathematics for Calculus
Book is actually pretty good, I like the fact that its first chapter is a review of stuff from intermediate algebra...if you are using this book...and you have just finished intermediate/college algebra...get this book and do each section of ch. 1...this will set you up for a good foundation for the ...
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A beautiful presentation and treatment of all math required before studying calculus. Comprehensive, and a strong focus on theory. Lots of problems to test yourself. Get through this and then star in your calculus study, as you are now VERY well prepared.
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This book is one of the best out there in the current markets. Dr. Stewart explains this subject with geometrical shapes to better understand the subject. For example he explains and proves the the phytogorean theorem, laws of sines and cosines, and alot more. Highly recommend this book as well as
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Example links
About this module:Please visit to find out more about the Open Course Library.
Open Course Library Math 141: Precalculus 1
Also, these course packages do NOT include algorithmically generated online homework, and thus is NOT the complete course shell developed.
If you do not intend to use online homework, then you can continue to use the contents of the Angel or Common Cartridge shell.
If you wish to use graded online homework, you will need to request an account on wamap.org (or myopenmath.com if you're outside Washington State).
If you wish to give your students ungraded online exercises, refer to the "Letting students practice on their own" info later in this course guide.
There are a few other features of the full course shell which can only be used through wamap.org/myopenmath.com, including a diagnostic assessment, take-home portions of the exams, online projects.
If you wish to preview the full course shell, visit MyOpenMath.com and log in with username: OCL and password: OCL
Course Designers
David Lippman and Melonie Rasmussen, Pierce College Ft. Steilacoom. Bios are available in the preface to the textbook.
Intended Delivery
This course was designed for face-to-face delivery, but could potentially be used in a hybrid environment as well.
Prerequisites
The prerequisite for this course is Intermediate Algebra or equivalent. The student should be ready for college level math.
Textbook
Precalculus: An Investigation of Functions, by David Lippman and Melonie Rasmussen. This book is openly licensed (Creative Commons Attribution-ShareAlike) and is available through links in the course shell, or in Word and PDF formats at . Bound copies can be ordered from Lulu.com through the link above.
Other Materials/Resources Used.
These materials were utilized in the course design, but are optional depending on how the course is taught:
WAMAP/MyOpenMath. The course shell was built for use in WAMAP.org, a free online math assessment platform built on the open source IMathAS software. WAMAP provides
algorithmically generated online homework and practice problems with automated grading of numerical and algebraic answers. This provides immediate feedback to students, and gives opportunity for virtually unlimited practice. WAMAP also provides a full course management system, allowing worksheets and handouts to be easily shared, and provides a full gradebook. For faculty outside Washington State, the content will be mirrored on MyOpenMath.com, or can be made available for a local installation of the open source IMathAS software. This platform is entirely independent of WAOL Angel or other LMSs and does not exchange grades with Angel. If you choose to not use the algorithmically generated online homework, you can access the rest of the course package (Angel or Common Cartridge).
Graphing Calculator/Software. A student will need a graphing calculator or alternative. Links to online graphing software are provided if you choose to not require a graphing calculator.
About the Course Shell
Overview of Course Shell
In the course shell, you will find:
An instructor guide, including
A "How to use this course shell" guide
Bios of the course designers and the philosophy behind the textbook and course
A day-by-day course guide, showing how the included worksheets, handouts, and assessments fit in with the course material
A link to the whole textbook in multiple formats, including editable formats
A list of license details and attribution
A spreadsheet detailing the alignment between global, course, and unit outcomes with learning activities and assessments
Using the Course Shell
The course materials developed can be used in a variety of ways, and how you access them will depend on how you wish to use them:
Online graded homework. To take full advantage of the online homework, you can:
Option 1 (recommended): Since WAMAP.org provides the full course shell and learning management, Angel is not necessary.
Option 2: Use Angel or another LMS for document management, or however desired, and use WAMAP.org/MyOpenMath for online homework. Note that grades will have to be manually transferred back to Angel/your LMS from WAMAP.org/MyOpenMath.
Online practice. If you wish to make the online exercises available to students for practice, but are not interested in tracking their scores:
Option 1: The online homework can be set for practice only.
Option 2: Send students to have them Register as a new student, and select the "141 Precalculus 1 Self-Study" course to enroll in. This is an unmonitored course where students will be able to freely practice using the online homework.
No online homework. Import the Angel or Common Cartridge shells. Book homework can be substituted for the online homework.
There are a few other features of the full course shell which can only be used through WAMAP.org / MyOpenMath.com, including a diagnostic assessment, take-home portions of some exams, and online projects.
Student Outcomes
Course Objectives
Global Outcomes
Quantitative & Symbolic Reasoning
Students utilize mathematical, symbolic, logical, graphical, geometric or statistical analysis for the interpretation and solution of problems in the natural world and human society. Students will utilize both traditional and technological methods.
Critical, Creative and Reflective Thinking
Students will be able to question, search for answers and meaning, and develop ideas that lead to action.
Apply mathematical principles and techniques learned in this course to similar situations throughout the course.
Combine reason, experience, and information from this course, other courses, or earlier life experiences to: (a) critically interpret a problem using an appropriate mathematical model, (b) determine the methods of solution for problems, (c) then apply those methods, and finally (d) judge whether the calculated solutions are reasonable.
Citizenship
Student will be able to effectively communicate various topics and ideas while displaying respect and responsibility to other classmates continually striving to promote multiculturalism in the classroom to foster healthy working relationships.
Graph the elementary functions using a calculator and a variety of non-calculator methods that are appropriate for the function including, but not limited to, using table of values, slope-intercept, characteristic shape of the function, degree, maximum number of zeros, maximum number of turns, multiplicity of zeros, vertical asymptotes, horizontal asymptotes, and long-run behavior.
Determine the symmetries of a graph
Graph functions on a calculator and analyze them using various windows.
Solve and analyze application problems such as optimization or growth/decay, using the appropriate elementary functions
Determine an appropriate approach (verbal, algebraic, numeric, or graphic) to take in solving each particular problem.
Interpret the solution in the context of the problem and evaluate the reasonableness of the solution.
Solve applications of inequalities and clearly communicate the solution.
Interpret and analyze linear and non-linear data in numeric, graphic, and algebraic form to develop an appropriate model with and without a graphing calculator
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Cliffs Quick Review for Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies
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Functions and Their Graphs. Using Technology: Graphing a Function. The Algebra of Functions. Portfolio. Functions and Mathematical Models. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Summary of Principal Formulas and Terms. Review Exercises.
3. DIFFERENTIATION.
Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Portfolio. Using Technology: Finding the Differential of a Function. Summary of Principal Formulas and Terms. Review Exercises.
4. APPLICATIONS OF THE DERIVATIVE.
Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Function. Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Summary of Principal Terms. Review Exercises.
Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Consumers' Surplus and Producers' Surplus. Summary of Principal Formulas and Terms. Review Exercises.
Functions of Several Variables. Partial Derivatives. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of a Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Summary of Principal Terms. Review Exercises. Answers to Odd-Numbered Exercises0534419860249.00 +$3.99 s/h
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Relationship between two variable quantities - vary together. Relationship is ... 1.
To find the amount of change in Y per unit change in X. 2. To test for a cause-
effect relationship between X and Y.
13 Aug 2013 ... The critical areas, organized into units, deepen and extend ... Unit 1 –
Relationships Between Quantities ... Students may retake any major test for
which they would like to improve their ...
Modeling Unit 2. M2 Geometric Modeling 2. 1. Make sense of problems and
persevere in ... and test hypotheses, be systematic, and draw conclusions. ...
Using functions to describe relationships between quantities is a core idea in
high school.
Unit 1: Relationships between Quantities and Reasoning with Equations. 14-18
... After a review of these pathways, the superintendants of Maryland's LEA's
voted to adopt the pathway reflected in this ...
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Contents | Keyword: contents Holt McDougals United States Government: Principles in Practice is a secondary government ... all students an important lesson in ... Journal of Science and Mathematics ...
Holt Mathematics | Keyword: holt mathematics Name Date Class 1-6 LESSON 1. Athletes from 197 countries competed at the 1996 Summer Olympic Games held in Atlanta, Georgia. That is 25 more countries that competed ...
Family Letter CHAPTER Section A | Keyword: family letter chapter Copyright by Holt, Rinehart and Winston. 65 Holt Mathematics All rights reserved. Dear Family, When studying a group or a population, it is important to get
High School Algebra 2 Standards for Mathematics | Keyword: high school algebra Standards for Mathematical Practice ... Council of Teachers of Mathematics, 2010. Classzone has lesson resources for this standard from the Holt McDougal 2004 Algebra 2 ...
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Ratio & Proportion Dosage Calculations provides the ease of learning the ratio and proportion method of calculation with a building block approach of the basics. Its consistent focus on safety, accuracy, and professionalism make it a valuable reference for nurses and other allied health professionals. This book uses the Ratio and Proportion method for drug calculations; a time-tested approach based on simple mathematical concepts. It helps the reader develop a "number sense", and largely frees the healthcare professional from the need to memorize formulas.
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What is Mathematics? An elementary approach to ideas and methods by Richard Courant(
Book
) 68
editions published
between
1941
and
1996
in
3
languages
and held by
2,299
libraries
worldwide
Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world.
Methods of mathematical physics by Richard Courant(
Book
) 228
editions published
between
1924
and
2009
in
5
languages
and held by
1,893
libraries
worldwide present volume represents Richard Courant's final revision of 1961.
Differential and integral calculus by Richard Courant(
Book
) 295
editions published
between
1927
and
2010
in
5
languages
and held by
1,619
libraries
worldwide
The fundamental ideas of the integral and differential calculus; Differentiation and integration of the elementary functions; Further development of the integral calculus; Applications; Taylor's theorem and the approximate expression of functions by polynomials; Numerical mehtods; Infinite series and other limiting processes; Fourier series; A sketch of the theory of functions of several variables; The differential equations for the simplest types of vibration.
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A Practical Approach to Merchandising Mathematics Revised 1st Edition
Merchandising math is a multifaceted topic that involves many levels of the retail process,
including assortment planning; vendor analysis; markup and pricing; and terms of sale.
A Practical Approach to Merchandising Mathematics, Revised 1st Edition, brings each of these areas together into one comprehensive text to meet the needs of students who will be
involved with the activities of merchandising and buying at the retail level. Students will learn
how to use typical merchandising forms; become familiar with the application of computers
and computerized forms in retailing; and recognize the basic factors of buying and selling
that affect profit.
• Revised concepts introduced in each
chapter are followed by a practice
section entitles "Practicing What You
Have Learned," with answers to these
problems located at the back of the text
• Practical problems reinforce the
concepts covered in the text and
provide mini-case studies requiring the
application of multiple concepts in a
real-world situation
• Comprehensive review of basic math
concepts that are used daily in nearly
every decision a buyer makes
• Key terms are highlighted and defined
in the text and included in a glossary at
the back of the bookinda M. Cushman
is an Associate Professor of Retail Management in the Department of Marketing at Whitman School of Management, Syracuse University. She has taught a variety of courses including retail buying and electronic retailing and marketing courses and has been a member of the International Textile and Apparel Association (ITAA) for 13 years. She conducts research that examines the needs of retail industry employers and her research focuses on employee satisfaction and retention as well as preparing new college graduates for success in the industry. Her research appears in journals such as the Journal of Fashion Marketing and Management, Customer Relationship Management, and Journal of Shopping Center Research.
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Mathematics With Infotrac A Good Beginning
9780534529055
ISBN:
0534529054
Publisher: Thomson Learning
Summary: More than just a textbook, this is a complete instructional program that serves a multitude of curriculum needs. This edition is solidly grounded in the latest research on how children learn mathematics and how teachers develop attitudes, beliefs, and knowledge that promote successful teaching.
Troutman, Andria P. is the author of Mathematics With Infotrac A Good Beginning, published under ISBN 9780534529055... and 0534529054. One hundred twenty eight Mathematics With Infotrac A Good Beginning textbooks are available for sale on ValoreBooks.com, twenty two used from the cheapest price of $8.70, or buy new starting at $34
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This edition features the exact same content as the traditional book in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value–this format costs significantly less than a new textbook. TheTobey/Slater/Blair/Crawford seriesbuilds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the book. With this revision, the author team has added a new Math Coach featureMore... that provides This package contains:Books a la Carte for Beginning & Intermediate Algebra, Fourth Edition
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Item code: SAX-3214
Saxon Math 54 3rd edition offers proven results in these 4th grade homeschool lessons and teacher books. The 3rd edition Saxon Math 54 Tests and Worksheets offer new improved features. The tests provide review exercises to complete after every five or ten lessons in the student textbook. The new worksheets provide consumable problem solving exercises, investigations, facts practice, and activities for the entire course. Various recording forms are also provided for both teacher and student.
Saxon Math 54 student textbook presents 141 lessons with the same popular and effective Saxon methodology as previous editions. The textbook also includes problem exercises for each lesson. Step-by-step answers to problems in the student textbook are found only in the Solutions Manual, which is sold separately or as part of the kit
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GCSE
Mathematics A - J562 (from 2010)
Our GCSE Mathematics A specification's flexible structure supports your learners' growing understanding of mathematical concepts, giving you real choice to move your learners between routes - unitised, staged or linear - in response to their needs. Your learners will develop analytical and problem solving skills in a range of contexts, which they can take into employment or further study.
Community
Business
Apprenticeships and vocational qualifications in England, Wales, and Northern Ireland will soon benefit from new units in Business and Administration. We would like to get your feedback on them.
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Elementary Classical AnalysisThis was my favorite book as an undergraduate student and I've taught from it as a professor. It is an excellent geometric approach to analysis. It can even help students who have difficulty with epsilon delta proofs understand the geometric intuition behind them. The construction of the real line at the beginning is daunting for students who aren't clear about set theory and sequences already but a few supplementary materials can help the students out there (see my webpage notes on real analysis for example). The proofs are hidden which makes it a challenge for students to try prove everything themsleves before peeking at them, but they are available. Just remember to tell your students where they are!
As a student I loved the book because it allowed me to learn everything on the metric space level while allowing students who prefer to stay in Euclidean space to do that. Now I am a metric geometer.
15 of 16 people found the following review helpful
5.0 out of 5 starsvery helpful book31 May 2006
By Manhatã - Published on Amazon.com
Format:Hardcover
I am using this book to teach myself analysis. Because my mathematical background is limited, I cannot assess what the book is missing, or whether alternative methods of presentation would be more insightful. But in terms of clarity and comprehensibility, the book does very well. The authors write very carefully and are not cryptic; the proofs and examples are well-presented, and I rarely feel lost. The book is rigorous but not, let's say, snobbish. I am learning a lot from it.
14 of 15 people found the following review helpful
5.0 out of 5 starsAn excellent introduction to Real Analysis5 April 2004
By Chase Yarbrough - Published on Amazon.com
Format:Hardcover
Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:
"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."
Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.
A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view.
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The splitting extrapolation method is a newly developed technique for solving multidimensional mathematical problems. It overcomes the difficulties arising from Richardson's extrapolation when applied to these problems and obtains higher accuracy solutions with lower cost and a high degree of parallelism. The method is particularly suitable for... more...
Written in a friendly, Beginner's Guide format, showing the user how to use the digital media aspects of Matlab (image, video, sound) in a practical, tutorial-based style.This is great for novice programmers in any language who would like to use Matlab as a tool for their image and video processing needs, and also comes in handy for photographers or... more...
Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive... more...
Comput... more...
Master MATLAB(r) step-by-step The MATLAB-- "MATrix LABoratory"--computational environment offers a rich set of capabilities to efficiently solve a variety of complex analysis, simulation, and optimization problems. Flexible, powerful, and relatively easy to use, the MATLAB environment has become a standard cost-effective tool within the engineering,... more...
This is the first-ever book on smoothed particle hydrodynamics (SPH)
and its variations, covering the theoretical background, numerical
techniques, code implementation issues, and many novel and interesting
applications. more...
This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. more...
The essential guide to MATLAB as a problem solving tool This text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. Stressing the importance of a structured approach to problem solving, the text gives a step-by-step method for program design and algorithm... more...
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Basic Algebra II -- 22M:002
Spring 2004
This course covers the
material usually found in a second-year high school algebra course. Topics
include equations and inequalities, functions and graphs, exponential and
logarithmic functions, and systems of linear equations. Students who do not
have an adequate high school background may need to take this course before
going into higher-level mathematics or even other courses in other departments.
The course, together with 22M:005 (Trigonometry) provides the background
necessary to enter college level calculus sequences. Requirements included weekly quizzes,
two midterm exams, calculator projects, and a final exam.
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Edgenuity Geometry is a two-semester, hands-on and lecture-based course featuring an introduction to geometry, including reasoning and proof and basic constructions. Triangle relationships (similarity and congruency) and...
Edgenuity Algebra is a two-semester course that provides in-depth coverage of writing, solving and graphing a variety of equations and inequalities, as well as linear systems. Functions are a central theme of the course...
The purpose of this Algebra I course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics in a year long course. Topics included are real...
In this course students will use their prior knowledge to learn and apply Algebra II skills. This course includes topics such as functions, radical functions, rational functions, exponential and logarithmic functions,...
Trigonometry teaches students to use the trigonometric ratios and the unit circle to find and explore the relationship between the measure of angles and lengths of sides of triangles. Students learn how to solve directly...
Algebra II begins with a review of algebraic properties and equation and inequality solving. Students will study relations and functions, including linear, quadratic, and radical functions, and be able to graph these...
Probability and Statistics is a one-semester course that focuses on representations of statistical data, measures of central tendency, collecting and using data, and probabilities. Topics covered include construction and...
Each interactive lesson in this Algebra I course focuses on the skills needed to solve equations and perform manipulations with numbers, exponents, data sets, geometric figures, variables, equations, and inequalities...
Algebra 2 is an advanced course in mathematics, which completes the studies of high school algebra and prepares students to advance to trigonometry, pre-calculus, and beyond. It gives the opportunity to further skills in...
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