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Function Basics
Functions are mathematical ideas that take one or more variables and produce a variable. You can think of a function as a cook that takes one or more ingredients and cooks them up to make a dish. depending on what you put in, you can get very different things out. Moreover, not all functions are the same. If you give one cook peanut butter, jelly, and bread, he may make a sandwich, whereas another cook may start to sculpt a volcano with the peanut butter, and use the jelly for lava after discarding the bread.
In an abstract Mathematical sense, a function is a mapping of some domain onto some range. For each item in the domain, there is a corresponding item in the range of the function. Thus the domain is all of the possible inputs to the function and the range is all of the possible outputs. Each item in the domain corresponds to a specific item in the range. However, an item in the range may correspond to multiple items in the domain.
For example, let's describe a function for album titles. Our function will take as its domain, album titles. Our function, let's call it FL(album_title) will output the first letter of the first word in the title of the album. Thus the range of our function will be all of the letters in the alphabet. (I'm pretty sure that you can find an album for each letter of the alphabet, right?) Here are some examples of our function at work.
Album Title
FL(Album Title)
What's The Story, Morning Glory?
W
Achtung Baby
A
The Piano Rollls3
T
Piano Man
P
August and Everything After
A
Collective Soul
C
1812 Overture
???
For each album title (left) there is a corresponding FL(our album title) from the range of FL(album_title). As you can see, the function can get the same value in the range for two different inputs. But what about the good old 1812 Overture? Because the first word - "1812" - does not start with a letter, our function cannot handle it. Thus it is out of the domain of our function. Hence, the domain of FL(album title) is all album titles that begin with a letter.
Onto the math!
Higher Math Note!
For most of Algebra, functions are described as things that take a number and put out a number. In higher mathematics, this is described as R1 R1. This means that the real number line (R1) is being mapped to the real number line. If however, we have two inputs and one output, we have a function that is described as R2 R1, or the real plane(R2) is being mapped to the real number line. Generally, we can have a function described by any R
N R
M. We can even have functions in the complex plane, which is where much of Chaos comes from!
Let's start with an old favorite - the line.
f(x) = 2*x
Here, f is a function that is defined to take one variable - x. It takes that one variable and doubles it. We can plot this graph on a cartesian grid by taking x along one axis and f(x) along the other. Because f(x) is simply a constant, that is the number 2, multiplied by x, we know that f(x) is a line. Assuming that we are totally ignorant, let us proceed as though we know nothing at all. To draw a function that is new to us, here is what we normally will do (at least to begin with): We will construct a table. In one column, we will list various values for x that we would like to try to see what comes out. In the other column, we will list the values of f that we get when we stuff our values into the function. Next, on a piece of grid paper, we will plot the points, going over on the x-axis to the number we chose for x, and on the y-axis to what we got out for f(x). Finally, we will connect the dots for a rough view of what our function looks like. (More complex functions need lots of dots!) For f(x)=2*x, here's what we get:
x
f(x)
-2
-4
-1
-2
0
0
1
2
2
4
3
6
4
8
Let's move on to the parabola. A basic parabola formula is:
f(x) = x2. Let us try several values to plop into the function to see what comes out:
x
f(x)
-4
16
-3
9
-2
4
-1
1
0
0
1
1
2
4
3
9
4
16
Most of the time, functions come out with nice looking smooth curves. So, if instead of using straight lines to connect out dots, we use a smooth curve, we can get a better approximation of what the function looks like. Hence, the proper parabola looks like the following: | 677.169 | 1 |
5554650 / ISBN-13: 9780495554653
Calculus: Early Transcendentals
James Stewart's "Calculus: Early Transcendentals, 7e, International Metric" is widely renowned for their mathematical precision and accuracy, clarity ...Show synopsisJames Stewart's "Calculus: Early Transcendentals, 7e, International Metric" is "Calculus: Early Transcendentals, International Metric Edition", Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence 13 Calculus: Early Transcendentals
This is the book I learned Calculus from in college. I recently lost my copy from school, so decided to replace it. I've never used a different book, so I can't say it's the best, but it gets the job done. Never heard any complaints about it from fellow students either | 677.169 | 1 |
Summary: This text is designed for the sophomore/junior level introduction to discrete mathematics taken by students preparing for future coursework in areas such as math,computer science and engineering. Rosen has become a bestseller largely due to how effectively it addresses the main portion of the discrete market,which is typically characterized as the mid to upper level in rigor. The strength of Rosen's approach has been the effective balance of theory with relevant appl...show moreications,as well as the overall comprehensive nature of the topic coverage. ...show less
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MA231: Abstract Algebra I « The Saylor Foundation
Abstract Algebra I
Purpose of Course
The study of "abstract algebra" grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. For example, we are familiar with the notion that real numbers are closed under multiplication and division (that is, if we add or multiply a real number, we get a real number). But if we divide one integer by another integer, we may not get an integer as a result—meaning that integers are not closed under division. We also know that if we take any two integers and multiply them in either order, we get the same result—a principle known as the commutative principle of multiplication for integers. By contrast, matrix multiplication is not generally commutative. Students of abstract algebra are interested in these sorts of properties, as they want to determine which properties hold true for any set of mathematical objects under certain operations and which types of structures result when we perform certain operations. Abstract algebra has applications in a variety of diverse fields, including computation, physics, and economics and, as a result, is an important area in mathematics.
We will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. We then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. | 677.169 | 1 |
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An Adventurer's Guide to Number Theory by Richard Friedberg This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Number Theory and Its History by Oystein Ore A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Fascinating, accessible coverage of prime numbers, Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, and more.
Number Theory by George E. Andrews Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
Fundamentals of Number Theory by William J. LeVeque Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.
Continued Fractions by A. Ya. Khinchin Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, and more. 1964 | 677.169 | 1 |
Written by an experienced physicist who is active in applying computer algebra to relativistic astrophysics and education, this is the resource for mathematical methods in physics using MapleTM and MathematicaTM. Through in-depth problems from core courses in the physics curriculum, the author guides students to apply analytical and numerical techniques in mathematical physics, and present the results in interactive graphics. Around 180 simulating exercises are included to facilitate learning by examples. This book is a must-have for students of physics, electrical and mechanical engineering, materials scientists, lecturers in physics, and university libraries. * Free online MapleTM material at * Free online MathematicaTM material at * Solutions manual for lecturers available at | 677.169 | 1 |
Item code: SAX-1389
The unique approach of these 9th grade homeschool lessons and teacher books has helped make Saxon Math Algebra 1 a best seller. Saxon Math Algebra 1 homeschool curriculum books 3rd Edition Answer Key and Tests includes the Answer Key book and the Test Forms book. The Answer Key provides the final answers to every problem in the student textbook plus answers to the test questions. The Test Forms book provides tests to be completed after every ten lessons in the student textbook. Saxon's 3rd edition Algebra 1 covers topics typically treated in a first-year algebra course. Step by step solutions to the problems in the book can only be found in the Solutions Manual | 677.169 | 1 |
MATLAB or Introductory courses in Engineering and Computer Science.With a hands-on approach and focus on problem solving, this introduction to the powerful Matlab computing language is designed for students with only a basic college algebra background. Numerous examples are drawn from a range of engineering disciplines, demonstrating Matlab's applications to a broad variety of problems.Note: This book is included in Prentice Hall's ESource series. ESource allows professors to select the content appropriate for their freshman/first-year en... MOREgineering course. Professors can adopt the published manuals as is or use ESource's website to view and select the chapters they need, in the sequence they want. The option to add their own material or copyrighted material from other publishers also exists. With a hands-on approach and focus on problem solving, this introduction to Matlab uses examples drawn from a range of engineering disciplines to demonstrate Matlabrs"s applications to a broad variety of problems.Encourages readers to type in examples as they go for immediate application of techniques presented. Includes numerous broad-based examples embedded in the text, practice exercises with solutions, and hints related to commonly encountered problems. Introduces m-files early in the text to make it easier for readers to save their work and develop a consistent programming strategy.For those interested in learning Matlab. | 677.169 | 1 |
Download "Calculus" by Boundless for FREE. Read/write reviews, email this book to a friend and more...
CalComments for "Calculus"
We begin with function notation, a basic toolkit of functions, and the basic operation with functions: composition and transformation. Building from these basic functions, as each new family of functions is introduced we explore the important features of the function: its graph, domain and range, intercepts, and asymptotes. | 677.169 | 1 |
Master Sat Ii Math 1c And 2c 4th Ed (Mas...
(Paperback)
With detailed reviews and expert test-taking strategies, this guide helps prepare you for the exam. It includes extensive review of math subjects ranging from algebra and geometry to trigonometry and statistics. Additional resources include, review questions and full-length practice tests at the end of each chapter to reinforce what you have learned.
Feature and benefits include: - Four full-length practice tests - Diagnostic tests to help students identify the areas in which they need improvement - Detailed review of fundamental subject principles, followed by practice questions | 677.169 | 1 |
Algebra Word Problem: Problems Involving GeometryAlgebra Word Problem: Problems Involving Geometry Movie Description
This program teaches students how to solve word problems that involve geometry. Students are taught how to read the problem and what keywords to look for to gain clues on how to proceed and solve the problem. Students are then taught, for each proble how to set up the appropriate algebraic equation and solve for the unknown. All problem are fully worked with each step shown so that students learn how to proceed from the problem statement to the solution and every step in between.
Movie Details
EAN:
8901736032629
Studio / Distributor:
Excel Home Entertainment
Format:
DVD
Language(s):
English
Release Year:
2009
Category(s):
Educational Algebra Word Problem: Problems Involving Geometry DVD and all your favorite heroes and stars in the comfort of your own home. Buy English Movie DVD and watch great Educational | 677.169 | 1 |
The Best Math Books
Dear Students and fellow tutors,
There are so many resources out there to help you succeed in math. In fact, are there too many? If you do an internet search on a math topic (linear equations, for example) are you overwhelmed by the response? How many hours will you waste looking at bad
web sites?
OK, stop wasting time and go to the library to check out these books by mathematician and actress Danika McKeller: | 677.169 | 1 |
ODYSSEYWARE Middle and High School Math
ODYSSEYWARE gives middle school students a proven formula for math success and prepares them for pre-algebra. This interactive course reviews math fundamentals and gives students the digital tools to strengthen their skills in problem solving, number sense, and proportional reasoning. It also introduces them to new concepts including integers, equations, and geometry. Innovative and filled with learning games to increase retention, this curriculum is complete with multimedia clips and integrated audio files to make complex concepts comprehensible and promote academic achievement.
Solve the pre-algebra learning equation at your public or charter school with ODYSSEYWARE Pre-Algebra for middle and high school students. This interactive, web-based course lays the groundwork for higher-level math study through an examination of number relationships, variables, scientific notation, functions, integers, measurement, formula use, and data representation. Dynamic learning games, audio and video files, and multiple assessment opportunities help teachers to identify areas that need revisiting for individuals or the entire class. Take your students into the realm of digital learning with ODYSSEYWARE Pre-Algebra.
Increase the math success ratio of your public or charter high school with ODYSSEYWARE Algebra I. From variables and expressions to square roots and factoring, this interactive class covers the algebra basics and prepares students for higher level math instruction. Ongoing assessments and automatic data reporting help teachers keep track of student progress, allowing early intervention when challenges arise. With 24/7 access to content and interactive learning tools, ODYSSEYWARE's comprehensive curriculum allows students to conveniently practice new skills at a pace that enables mastery as students learn both in and out of the classroom.
Education intersects innovation with ODYSSEYWARE Algebra II. This inventive curriculum challenges students to take their math skills to the next level. Clickable videos enhance student understanding as they illustrate the analytical breakdown of complicated concepts. From combining terms in algebraic expressions to compound sentences, and from advanced polynomial functions to data analysis, this rigorous, standards-based course can be easily implemented and integrated into the high school curriculum in your school district. With ODYSSEYWARE, students have a digital choice.
Experience a new angle on learning with ODYSSEYWARE Geometry. This comprehensive, Internet-based curriculum guides students through interactive lessons that cover terminology, postulates and theorems, angles, shapes, and equations for determining area, circumference, volume, and area. Rigorous and standards-based, this course gives students a look at geometry from all sides from their computer screen at any time, facilitating self-directed learning.
Take your students beyond the limits of the traditional classroom and into the world of web-based learning with ODYSSEYWARE Pre-Calculus. This comprehensive course initiates study in mathematical analysis, the purpose of calculus. Lessons cover a wide range of materials including an observation of multiple mathematical functions, quadratic inequalities, logarithms, probabilities, and permutation. Multimedia activities give students additional tools to clarify key concepts in this exciting entrance into the sphere of calculus | 677.169 | 1 |
This is a book that every potential undergraduate student of mathematics should purchase. It has a very thorough description of what is involved with being an undergraduate in mathematics at university. Alcock has succeeded in writing a relevant, interesting and beneficial account of what it is like to be a maths undergraduate. She highlights the differences between pure and applicable mathematics and what skills are needed to flourish in these. However the emphasis is on pure mathematics throughout the book. Additionally the author does not shy away from doing some serious mathematics even though the book is written for the layman. The technical mathematics is described in simple… Read more
This is a popular mathematics book for the layman. The author has succeeded in writing interesting articles in mathematics which are laid out alphabetically. Dunham discusses the problems and personalities in the history of mathematics. If you want a student hooked into mathematics then this the book they should read. The technical mathematics in the book are excellently described in simple terms that the average layman can understand. Dunham really does bring mathematics to live in this book. Initially I was reluctant to purchase a book which is mapped out in alphabetic order. However Dunham managed to make the progression from one chapter to the next… Read more
The Story of Mathematics by Anne Rooney This book is full of interesting facts on the history of mathematics such as where our symbols + , - , = and originated from. There are also details of mathematics of the 20th Century such as fractals and fuzzy logic. In places the book is fascinating reading such as `Pascal's Triangle is called Khayyam's Triangle in Iran.' A student doing mathematics would find this book intriguing and learn some entertaining facts about the history of the subject. The author has made good use of colour in diagrams but the diagrams are not referenced. There is also no caption for tables. The layout of some details is rather peculiar. For example… Read more | 677.169 | 1 |
Groups
The Algebra One course begins with a fast-paced review of the previous year. The beauty, clarity, and utility of algebraic reasoning are explored through practical and not so practical challenges. We will conclude with a study of the quadratic formula, and introduce formal logical reasoning.
This section contains information for our Explorer Tournament El Toro Boat Building Project. Documents for this project are listed below. Not all documents are publicly available. For full access, login or create an account.
In eighth grade, students begin bulding functional furniture using
traditional tools and techniques. They often build a threee-legged stool, a
small table, or a bench. More complex use of mallots and gauges is required
in these projects, as well as a greatly expending set of other tools. Mortise
and tennon joints are used to join the legs to the top. | 677.169 | 1 |
realgebra, 2e, is a book for the student. The authors goal is to help build students' confidence, their understanding and appreciation of math, and their basic skills by presenting an extremely user-friendly text that models a framework in which students can succeed. Unfortunately, students who place into developmental math courses often struggle with math anxiety due to bad experiences in past math courses. Developmental math students often have never developed nor applied a study system in mathematics. To address these needs, the author has framed three goals for Prealgebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm. The author's writing style is extremely student-friendly. He talks to students in their own language and walks them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the monkey-see, monkey-do approach that some books take. The second edition has been revised to include an increase in mid-level examples and exercises. In addition, the explanations and annotations are now more concise, yet keep the ever-important thoroughness that is the Carson style. | 677.169 | 1 |
MATLAB: An Introduction with Applications
9780471439974
ISBN:
0471439975
Edition: 1 Pub Date: 2003 Publisher: Wiley & Sons, Incorporated, John
Summary: This practical guide offers a beginner2s introduction to understanding and using MATLAB®. Starting with basic features, the book covers everything needed to use the program effectively, from simple arithmetic operations with scalars to creating and using arrays to three-dimensional plots and solving differential equations. Detailed images of computer screens, tutorials, worked examples, and homework questions in math..., science, and engineering make mastering the program efficient and thorough. Users gain experience running MATLAN® with examples incorporated throughout the book. Topic explanations within framed boxes help users learn the program and its commands in an easy-to-use format. Sample programs, applications, and homework problems allows instructors to show how MATLAB® is used in science and engineering. Subject matter includes script files, 2-D and 3-D plotting, function files, programming (flow control), polynomials, curve fitting, interpolation, and applications in numerical analysis.
Gilat, Amos is the author of MATLAB: An Introduction with Applications, published 2003 under ISBN 9780471439974 and 0471439975. One hundred twenty eight MATLAB: An Introduction with Applications textbooks are available for sale on ValoreBooks.com, fifteen used from the cheapest price of $2.39, or buy new starting at $25.63 | 677.169 | 1 |
Wednesday, August 19, 2009
This book contains lOO problems for undergraduate students training for mathematics competitions, particularly the William Lowell Putnam Mathematical Competition. Along with the problems come useful hints, and in the end Oust like in the fairy tales) the solutions to the problems. Although the book is written especially for students training for competitions, it will also be useful to anyone interested in the posing and solving of challenging mathematical problems at the undergraduate level.
We make no claims that our solutions are the "best possible" solutions, but we trust you will find them elegant enough, and that The Green Book will be a practical tool in the training of young competitors. | 677.169 | 1 |
Calculus is traditionally divided in two areas, differential and integral. The area of differential calculus is mainly concern the concept of instantaneous rate of change, whereas integral calculus is about the concept of total change. These two areas blend perfectly in many fields of science, such as physics and engineering. If you can not explain things like that then you should find a way to do so. We generally judge a student's intelligence based on his skill and interest in mathematics. None of us is born intelligent and brainy. It depends on each one's interest to learn things quickly and easily. When it comes to mathematics also, the same thing matters. And now, if you are a math lover, then here is something you got to know about Calculus. Calculus is a branch of mathematics that deals with rate of change, area and volume. For example, if you are able to calculate the area of a rectangle with an algebraic formula, then using a calculus formula you can calculate the area under any curve.
Calculus problems might be a scary connotation to a lot of people, since it has long complicated equations and associations that makes it threatening for a lot of people to take the first class of the calculus sequence. Almost all modern physics, economics and other sciences use calculus as a foundation. Finally, calculus is abundant in everyday life. From designing a roller coaster to a baseball stadium, calculus proves its worth. Even meteorologists are required to take calculus in their studies. NASA uses calculus to send their spacecraft's into space, and to determine orbits for satellites. Oil companies use it to discover new sources of oil. Doctor's employ it into their most difficult diagnosis, and prosecutors use it to successfully prosecute their cases. Most of us thought we would never use calculus again.
1. Lower your thermostat at night and whenever the house is unoccupied. Close off and don't heat unoccupied rooms (unless you have a heat pump). If you consistently set your thermostat back at night 10 degrees Fahrenheit, you may reduce your heating bill by 10-20 percent. | 677.169 | 1 |
APPLIED MATHEMATICS
by PHAGAN
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Applied Mathematics provides easy-to-understand instruction in math skills. It makes use of numerous practical and realistic sample problems drawn from the building trades, the machining/ manufacturing and automotive industries, and other technical areas to provide students with real-world applications of math skills.
Learning new concepts is made easy by the structure of each chapter. Sample Problems accompany new concepts to show each step in the process involved. Practice Problems appear at the end of each major concept. Test Your Skills Problems cover all concepts taught throughout the chapter. Problem-Solving Activities allow students to relate concepts learned in the chapter to real-world problem solving with tools and materials. | 677.169 | 1 |
Excursions in Modern Mathematics -Std. Resource Gd - 7th edition
Summary: In addition to the worked-out solutions to odd-numbered exercises from the text, this guide contains selected hints that point the reader in one of many directions leading to a solution and keys to student success, including lists of skills that will help prepare for the chapter exams.
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Pre-Statistics Courses
A growing number of colleges have begun piloting alternatives to the traditional 3-4 semester developmental Math sequence. The new courses focus not on a review of Algebra concepts and skills, but instead on preparing students for college-level Statistics.
Pre-Statistics courses emerged from a widespread recognition that the traditional developmental Algebra sequence is not well-aligned with the study of Statistics. If a student is pursuing a major that includes Statistics rather than Calculus (e.g. fields outside of Science, Technology, Engineering, Math, and Business), the majority of what is covered in elementary and intermediate Algebra courses never comes into play in their college-level Math course. The content is not, in fact, pre-requisite knowledge for the study of Statistics.
This misalignment is especially problematic given how many students are lost in long remedial math pipelines. A nationwide study by the Community College Research Center found that among students who begin 3 or more levels below college Math, 90% disappear before ever completing the college-level course.
Los Medanos College was the first in the nation to pilot this kind of course with Path2Stats, a one-semester pathway to college Statistics with no minimum placement score. Rather than proceeding step-by-step though all the topics in the traditional math sequence, Path2Stats students engage in statistical analysis from day one. Basic skills remediation occurs in a "just-in-time" fashion, with students reviewing relevant arithmetic and algebraic skills — e.g. calculating percentages, converting ounces to grams — as they are needed for the statistical tasks at hand. Path2Stats students complete college Math at dramatically higher rates that students with comparable starting placements in the traditional sequence.
In 2011-12, 7 community colleges are working with the California Acceleration Project to offer redesigned pre-Statistics Courses. They include Diablo Valley College, Cuyamaca College, City College of San Francisco, College of the Canyons, Riverside City College, Moreno Valley College, and Berkeley City College (See video footage of CCSF students talking about their experience.) Some of these courses are open-access; others have arithmetic/pre-Algebra prerequisites.
Nationwide, an additional 19 community colleges and 3 state universities are part of the Statway initiative, led by the Carnegie Foundation for the Advancement of Teaching: "a one-year pathway that culminates in college-level statistics…with requisite arithmetic and algebraic concepts taught and applied in the context of statistics."
Classroom video: Los Medanos Developmental Math Students Discover an Error in a National Statistics Exam | 677.169 | 1 |
Retaining previously successful features, this edition exploits students' access to computers by including many new examples and problems that incorporate computer technology. Historical footnotes trace the development of the discipline. | 677.169 | 1 |
Differentiation Teacher Resources
Find Differentiation educational ideas and activities
Title
Resource Type
Views
Grade
RatingTwelfth 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.
In this Ares-V cargo rocket learning exercise, students read about this multi-purpose launch vehicle and its rocket boosters. Students are given an equation that relates the acceleration of the rocket to the time and mass of the rocket. They graph the thrust curve and mass curve, they graph the acceleration and they determine the rocket's absolute maximum in a given interval.
Twelfth graders investigate logarithm differentiation. In this calculus lesson, 12th graders explore situations in which one would use logarithmic differentiation as an appropriate method of solution. Students should have already studied the chain rule.
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, �Calculus Derivatives 2� and �Calculus Derivatives 2.5 (HD).� Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
This video is the 4th in a series of videos that explains derivatives. First, Sal shows another example of differentiating a polynomial and then shows two examples using the chain rule. Sal continues the chain rule in the next video.
This video continues with examples of differentiating functions using the chain rule including examples that use negative exponents and more complicated nested parenthesis. Note: Additional practice on using the chain rule is available.
In the first example, instead of actually using the quotient rule, Sal rewrites the denominator as a negative exponent and uses the product rule. In subsequent examples, Sal shows, but does not prove, the derivative of several interesting functions including ex, ln x, sin x, cos x, and tan x.
Continuing to use the chain rule, Sal shows more examples of finding the derivative, this time, by looking at composite functions. Note: The current set of practice problems titled �Chain rule 1� cannot be solved until one knows how to find the derivative of ex and trigonometric functions
In this circuits worksheet, students answer 25 questions about passive integrator circuits and passive differentiator circuits given schematics showing voltage. Students use calculus to solve the problems.
Students analyze implicit differentiation using technology. In this calculus lesson, students solve functions dealing with implicit differentiation on the TI using specific keys. They explore the correct form to solve these equations.
This lesson plan provides an introduction to integration by parts. It helps learners first recognize derivatives produced by the product rule and then continues with step-by-step instructions on computing these integrals. It also shows integrating special forms with e and trigonometric functions. This resource includes handouts and a practice worksheet.
Are your calculus pupils aware that they are standing on the shoulders of giants? This lessonIn this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key | 677.169 | 1 |
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Algebra II and ALGEBRA II/TRIG HONORS
The standards below outline the content for a one-year course in Algebra II. Students enrolled in Algebra II are assumed to have mastered those concepts outlined in the Algebra I standards. A thorough treatment of advanced algebraic concepts is provided through the study of functions, "families of functions," equations, inequalities, systems of equations and inequalities, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Emphasis will be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results also should permeate the course.
These standards include a transformational approach to graphing functions. Transformational graphing uses translation, reflection, dilation, and rotation to generate a "family of graphs" from a given graph and builds a strong connection between algebraic and graphic representations of functions. Students will vary the coefficients and constants of an equation, observe the changes in the graph of the equation, and make generalizations that can be applied to many graphs.
Graphing utilities (graphing calculators or computer graphing simulators), computers, spreadsheets, and other appropriate technology tools will be used to assist in teaching and learning. Graphing utilities enhance the understanding of realistic applications through mathematical modeling and aid in the investigation and study of functions. They also provide an effective tool for solving/verifying equations and inequalities. Any other available technology that will enhance student learning should be used.
AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices.
AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.
AII.3 The student will
a) add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; and
b) write radical expressions as expressions containing rational exponents and vice versa.
AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used as a primary method of solution and to verify algebraic solutions.
AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials.
AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and for confirming the algebraic solutions.
AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and for confirming the algebraic solutions.
AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators.
Algebra II and ALGEBRA II/TRIG HONORS (continued)
AII.9 The student will find the domain, range, zeros, and inverse of a function; the value of a function for a given element in its domain; and the composition of multiple functions. Functions will include exponential, logarithmic, and those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions.
AII.10 The student will investigate and describe through the use of graphs the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression.
AII.11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product.
AII.12 The student will represent problem situations with a system of linear equations and solve the system, using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations.
AII.13 The student will solve practical problems, using systems of linear inequalities and linear programming, and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems.
AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions.
AII.15 The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions.
AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include S№ №a n d a n .
A I I . 1 7 T h e s t u d e n t w i l l p e r f o r m o p e r a t i o n s o n c o m p l e x n u m b e r s a n d e x p r e s s t h e r e s u l t s i n s i m p l e s t f o r m . S i m p l i f y i n g r e s u l t s w i l l i n v o l v e u s i n g p a t t e r n s o f t h e p o w e r s o f i .
A I I . 1 8 T h e s t u d e n t w i l l i d e n t i f y c o n i c s e c t i o n s ( c i r c l e , e l l i p s e , p a r a b o la, and hyperbola) from
his/her equations. Given the equations in (h, k) form, the student will sketch graphs of conic sections, using transformations.
AII.19 The student will collect and analyze data to make predictions and solve practical problems. Graphing calculators will be used to investigate scatterplots and to determine the equation for a curve of best fit. Models will include linear, quadratic, exponential, and logarithmic functions.
( Ч Ш Б В Ÿ Ё Ї в г ј љ В Г Z [ o p r h j C I Т! , –, —, ќјюјузуќуЯЫСЫЖуЊујуЊуЊžууЊуvуЊуЊуtуe he7ю he7ю CJ OJ QJ aJ UhЩ#Ю hоg CJ aJ he7ю he7ю 6CJ H*aJ he7ю he7ю CJ OJ QJ aJ he7ю he7ю CJ H*aJ he7ю he7ю 6CJ aJ he7ю hЩ#Ю CJ aJ he7ю hЩ#Ю ;aJ hЩ#Ю he7ю CJ aJ he7ю he7ю 5CJ aJ he7ю he7ю CJ aJ he7ю he7ю ;aJ he7ю hоg & | 677.169 | 1 |
I've always wanted to excel in fractions with radicals sum, it seems like there's a lot that can be done with it that I can't do otherwise. I've searched the internet for some good learning resources, and consulted the local library for some books, but all the information seems to be directed to people who already know the subject. Is there any resource that can help new students as well?
What is your problem regarding fractions with radicals sum? Can you give me more details on the problems you encountered regarding fractions with radicals sum? I myself had experienced many troubles on my algebra tests. I tried getting a/an math tutor to teach me, but it was too costly. The most convenient way to help you figure out your math problems is by using a decent program. Among all algebra softwares I used, it's the Algebrator that really surpassed my expectations. Aside from giving errors-free answers, it also shows a step-by-step solution that led to the answer. It's really a fine software to learn from but remember to avoid copying answers from it because it would really not help you if you'd just copy the solutions. Use it just to understand how to solve certain algebra problems.
Algebrator is the perfect algebra tool to help you with projects. It covers everything you need to be familiar with in trinomials in an easy and comprehensive style. algebra had never been easy for me to grasp but this software made it very easy to understand. The logical and step-by–step approach to problem solving is really a plus and soon you will find that you love solving problems.
binomials, radical expressions and multiplying matrices were a nightmare for me until I found Algebrator, which is truly the best algebra program that I have ever come across. I have used it frequently through several math classes – Intermediate algebra, Pre Algebra and Algebra 2. Simply typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I really recommend the program. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This updated book is a self-teaching brush-up course for students who need more math background before taking calculus, or who are preparing for a standardized exam such as the GRE or GMAT. Set up as a workbook, Forgotten Algebra is divided into 31 units, starting with signed numbers, symbols, and first-degree equations, and progressing to include logarithms and right triangles. Each unit provides explanations and includes numerous examples, problems, and exercises with detailed solutions to facilitate self-study. Optional sections introduce the use of graphing calculators. Units conclude with exercises, their answers given at the back of the book. Systematic presentation of subject matter is easy to follow, but contains all the algebraic information learners need for mastery of this subject.
Synopsis:
back coverSynopsis:
This self-teaching brush-up course is designed for students who need more math background before taking calculus, or who are preparing for a standardized exam such as the GRE or GMAT."Synopsis"
by Libri,
This self-teaching brush-up course is designed for students who need more math background before taking calculus, or who are preparing for a standardized exam such as the GRE or GMAT | 677.169 | 1 |
For Algebra, Spreadsheets Beat Newer Teaching Tools
You already own better algebra-teaching software than any educational software developer is making.
I found in teaching elementary algebra to disadvantaged adult learners that the progression from table to graph and then to formula/function/equation might have been the most powerful tool for "selling" algebra I ever encountered. Anyone can see intuitively that for many problems, if you just make a table big enough, trying out all the possible values will lead to a solution. From there, it's a short step to, but what if there are millions of values? Then they're ready to graph it and the answers are right there at the intersections. From there it's just the step to, but what if you need an answer more exact than the line you can draw, or more dimensions than two? Well, by then, they're used to the idea of formula/function/equation as description, and if a point satisfies more than one description, it's a solution. And they've crossed over to doing algebra.
The spreadsheet provides a natural bridge from arithmetic procedure to formula/function. At first, students will just input numbers, as if the spreadsheet were a calculator. Then they see that if they input variables, they don't have to type nearly so much, and then that this means having not just this answer this time, but all the answers to all problems of this type, all the time.
It's a wide and easy-to-cross bridge from the specific to the general, and from procedure to concept.
One of the big changes in mathematics in the last 30 years has been the idea of experimental math, i.e., of exploring how numbers work by setting up numerical processes and looking at the results; it's at the heart of chaos research, for example. Just as the computer has become the equivalent of the telescope or microscope for mathematicians, Excel can be used as an amateur "scope" for exploring numbers, in a way very much analogous to the way countless students have gotten a handle on science by finding a planet in the sky or exploring the ecology of pond water. Among other things, I've used Excel to teach how every fraction is a division, and division is equivalent to multiplying by the inverse. It could easily be used for many other projects beginning even from a very early age in arithmetic.
Spreadsheet algebra is such an effective and intuitive idea that it has been re-invented several times in the last 20 years, and some Googling around will turn up immense amounts about it. (Caution: "spreadsheet algebra" is also a term used in advanced mathematics research for a kind of non-linear matrix algebra, so your Googling may very well turn up an article or two that's a bit beyond you. Don't worry, just keep looking!)
Although there still needs to be a human being there to guide the student in exploring and using the spreadsheet, as a teaching device for actual algebra (as opposed to a drilling device for standardized tests) the spreadsheet still beats out thousands of purpose-designed products.
re: For Algebra, Spreadsheets Beat Newer Teaching Tools They said that about calculators, graph paper, and probably the abacus. The funny thing is that although the spreadsheet does make it possible to avoid learning procedure, you can't use it effectively unless you learn concepts. So it's really a powerful tool for dragging people over the border from the "do your sums this way" to the real kingdom of mathematics | 677.169 | 1 |
1567506526
9781567506525
Learning and Teaching Number Theory:Number theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge.Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction.
Back to top
Rent Learning and Teaching Number Theory 1st edition today, or search our site for Stephen R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Ablex Publishing Corporation. | 677.169 | 1 |
Algebrainiac: Math Vocabulary
Description
Hangman and math vocabulary collide in this new app. Choose from three different categories, such as "Algebra", "Geometry" and "Linear Equations". Learn from over 60 different words, complete with it's definition! Fun for students of all ages, and for students who are either just learning, or refreshing their algebraic vocabulary words.
RELEASE INFO:
The second of our continuing math-based apps... | 677.169 | 1 |
Analysis of algorithms is really all math. How heavily do you want to get into the topic? The math is usually straight forward, but it uses calculus heavily. If you don't understand calculus, its going to appear opaque.
For years, Stanford University used Donald Knuth's Concrete Mathematics as a prerequisite for analysis of algorithms. Any university bookstore will have the textbook that their CS classes use for analysis of algorithms. Its a fairly advanced topic, typically junior or senior year for undergrads, or first year of grad school. | 677.169 | 1 |
Algebra and Trig.: Graphs and Models - Text - 5th edition
Summary: The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These books continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 explorations invite the reader to investigate research problems and related topics.
Book News Annotation:
Intended not as a text but to enrich the lives of young mathematicians-to-be who so love the field as to want to read independently in it, and to bring the pleasures of familiarity and fresh discovery into the relaxed hours of more mature mathematicians who can remember being young. Tours both the main elements and many interesting by-ways of an inexhaustible subject. Seven chapters, interrupted at frequent intervals with exercises, problems, invitations to exploration (relevant answers, solutions, hints provided at the end of the book); provides also much of historical and bibliographic interest. Written with sparkling clarity, and from manifestly affectionate seriousness of purpose. (NW) | 677.169 | 1 |
SJC Student Resources for Guidance on Careers and
Graduate Study in Mathematics
Career Guidance
Mathematics is of central importance to many
disciplines, including biological sciences, computer science, economics
and finance, statistics, and the social sciences. Hence a wide
variety of companies hire mathematicians, including companies in the computer
and communication, banks, insurance companies, consulting firms,
and all branches of government. Of course, there are career opportunities
in teaching mathematics at all levels.
On-line Employment Sites
The Internet offers one of the best ways to search for employment opportunities
for today's graduates. It is also helpful to have your own web page
and resume on-line for companies to review. A few of the Internet
career sites are linked below:
Professional Organizations
To find out more information about opportunities,
web sites of professional mathematical organizations can be very helpful:
The National Council of Teachers of Mathematics
The National Council
of Teachers of Mathematics is dedicated to improving the teaching and
learning of mathematics at all levels. NCTM is the largest nonprofit
professional association of mathematics educators in the world.
Association for Women in Mathematics
Actuarial Careers
Actuaries study the mathematics of risk. They employed by insurance
companies as well as consulting firms and are often involved in pension
planning. The two major professional societies for actuaries:
The Society of Actuaries (SOA)
and the Casualty Actuarial Society (CAS)
have jointly sponsored a web site containing important information about
preparing for an actuarial career.
Web site BeAnActuary.org
Peterson's
Guide To Graduate Programs This site will also be of interest to students
who are considering graduate school. You can search for information about
graduate programs based on a variety of key fields (geographical location,
discipline, etc.)
About the GRE GRE
Website The GRE General Test is primarily a multiple-choice
test that most graduate schools use for admission into their graduate
programs. You can study for this test and learn some of the
"tricks of the trade" that have been developed by educators who have helped
thousands of students prepare for this exam, and others similar to it.
The Graduate Record Examination Program, also
offers 16 Subject Tests (including mathematics), each of which measures achievements in specific
fields. Some graduate schools require the subject test. | 677.169 | 1 |
Homework & Quizzes
Homework will not be collected, but the problems on the weekly quizzes will either be chosen from among the homework problems or structured similarly.
Thus completing the homework on schedule is in the students' best interests. While working on the homework with classmates is both allowed and encouraged,
you need to be able to work out the material yourself, as homework is your best source of preparation for the quizzes and exams.
A short quiz will be given in your Tuesday discussion section every week that there is no exam. The two lowest quiz grades will be dropped.
Exams
There will be three 50 minute midterm exams held during discussion section. Midterms are tentatively scheduled for Tuesday, October 1st, Tuesday, October 29th, and Tuesday, November 26th. If you have a conflict with any of these dates, please contact your instructor immediately.
Each midterm will cover material up to the week of the exam. Use of calculators, phones, or any other electronic devices will not be allowed during quizzes or exams.
Lecture Notes
Slides from lecture will be made available later in the day after each lecture for which they exist.
On days when we review the midterms there may be no slides.
Important: Slides do not include examples (which are done on the blackboard), nor do they include the detailed explanations
of topics which are given during lecture. They are closer to an outline and general guide. They do not replace attending lecture,
but merely aid in reviewing the material later.
Extra Resources
This Trigonometry and Algebra reference card may be useful to students as you work through homework and prepare for exams:
Reference Card
Students may find the Khan Academy Calculus videos a handy supplement to lecture. Students are especially encouraged to watch the relevant
videos if they are unable to attend a lecture: Calculus Videos | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level.
To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics.
After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces.
Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Synopsis:
Synopsis: | 677.169 | 1 |
Extra Examples
shows you additional worked-out examples that mimic the ones
in your book. These requirements include the benchmarks from
the Sunshine State Standards that are most relevant to this
course. The benchmarks printed in regular type are required
for this course. The portions printed in italic type
are not required for this course.
understand that numbers
can be represented in a variety of equivalent forms,
including integers, fractions, decimals, percents,
scientific notation, exponents, radicals, absolute
value, and logarithms.
select and justify alternative
strategies, such as using properties of numbers,
including inverse, identity, distributive, associative,
and transitive, that allow operational shortcuts
for computational procedures in real world or mathematical
problems.
6.
Measure quantities in the real world and use the measures
to solve problems.
MA.B.1.4.1
use concrete and graphic
models to derive formulas for finding perimeter,
area, surface area, circumference, and volume of
two and three dimensional shapes, including rectangular
solids, cylinders, cones, and pyramids.
solve real world and mathematical
problems involving estimates of measurements, including
length, time, weight/mass, temperature, money, perimeter,
area, and volume and estimate the effects of measurement
errors on calculations.
9.
Visualize and illustrate ways in which shapes can be combined,
subdivided, and changed.
calculate measures of
central tendency (mean, median, and mode) and dispersion
(range, standard deviation and variance)
for complex sets of data and determine the most
meaningful measure to describe the data.
analyze real world data
and make predictions of larger populations by applying
formulas to calculate measures of central tendency
and dispersion using the sample population data
and using appropriate technology, including calculators
and computers. | 677.169 | 1 |
Sets for Mathematics
9780521010603
ISBN:
0521010608
Publisher: Cambridge University Press
Summary: In this textbook, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Lawvere, F. William is the author of Sets for Mathematics, published under ISBN 9780521010603 and 0521010608. Three hundred eighty six Sets for Mathematics textbooks are available for sale on ValoreBooks.com, one hundred two used from the cheapest price of $49.87, or buy new starting at $57.3...3 | 677.169 | 1 |
TI-Navigator
Robert Kowalczyk
Mathematics Department
TI-Navigator Activity
• Two-hour IMPULSE Calculus II class
• First-time user
• Goal — to investigate the potential use
of TI-Navigator as a teaching and
learning tool
Warm-up Activity
1. Plot the function f (x) x 3 25x 2 x 25 in
the
best viewing window that you can find?
Student Comments
• I liked the program, it was cool to see how the
class as a whole found answers, and I'm sure it
would help someone who didn't understand the
questions.
• This was a cool program to use and is a good way
to find out how other people do with the problem.
• Guaranteed everyone did work.
Lesson Plan
1. Revolve the region bounded by y = x, y = 0
and x = 1 about the x-axis.
• Poll: What does the solid of revolution look
like?
• Poll: Find the volume of the solid of revolution.
Give answer to 3 decimal places.
Lesson Plan (cont.)
2. Let m = your team number (1-12). Find
the volume of the solid generated by
revolving the region bounded by y = mx,
y = 0 and x = 1 about the x-axis.
• Enter your team number and volume
separated by a comma (e.g., 3, 1.234).
• Plot the list of points.
• Poll: What type of function do the plotted
points represent?
Lesson Plan (cont.)
3. Let m = your team number (1-12). Find
the volume of the solid generated by
revolving the region bounded by y = mx2,
y = 0 and x = 1 about the x-axis.
4. Find a formula for the solid generated by
revolving the region bounded by y = mxn,
y = 0 and x = 1 about the x-axis.
Student Comments
• The experiment involving TI Navigator was very
helpful in studying volumes of revolution. It gave
a visual aid that made interpreting the trends in
information easy and clear. The interactive
element also makes you feel more connected to
the class.
• I especially liked how it collectively can take the
students data and graph it to spot mathematical
trends.
Lesson Plan (cont.)
5. Let m = your team number (1-12).
• Poll: What is the x-value of the point of
intersection of the two linear functions y = x/m
and y = 5 – x/m.
Lesson Plan (cont.)
• Find the volume of the solid generated by
revolving the region bounded by y = x/m,
y = 5 – x/m and x = 0 about the x axis.
Student Comments
• I thought it was a good program. It made it so that
everybody could be involved. By making it so the
professor knew which group was giving the
answers, it lets the professor know who is actually
understanding the material. This program also
enables the professor to know what the class needs
improvement on and even what they should spend
more time focusing on.
• It was an interesting diversion from a normal
class. And added a break to relax and work with
less stress.
• Great teamwork project.
Student Comments
• I enjoyed the program. It allowed everyone to
workout the problem and respond anonymously
helping shy people to answer questions and learn
more about what they are doing.
• This was a fun way to work as a team to imply the
material learned in class. It was magical.
• It wasn't bad. It allowed everyone to participate in
class with less pressure than being called on.
While people were participating everyone had an
easier time paying attention because they had to
focus on getting the answer and inputting it. It
was also a little more fun. Something different
compared to a usual lecture.
Student Comments
• I think that the TI Navigator Eval went well. I
thought that this might become the future of math
classes all over the world. Now students can
compute answers and that professors can get
feedback on whether or not students get the
concepts of the lessons. It is interesting to see
what your classmates know compared to yourself.
• I thought this experience was priceless. I learned a
lot about a high tech calculator. It was a fun and
invaluable experience. I hope to do this many
times over. You are the man, keep on teaching!!
Student Comments —
Technical
• It was a good experience but definitely need one
calculator per person. Ends up being one person
does it & the other doesn't do anything.
• My only negative comment is that once you enter
an answer, it cannot be replaced without resetting
the question; it would be nice to have on record
what the first answer was, but be able to redo it,
Other than this the program is great!!
• I think that it took too much time to use, especially
when we had to enter words into a poll question.
Student Comments — Negative
• I thought it was a good experience, however I
don't see that ever being worked into actual
classes. I think it would just cause wasted time. It
isn't as practical as just having a teacher go over
the material. But other than practicality I think
every classroom should have some experience
with the TI Navigator.
• It seemed a little impractical for day-to-day use in
class. There was too much setup time.
• It was very easy to get off track like putting in
answers that make no sense as are just plain
wrong.
Student Comments — Negative
• Thoroughly enjoyable. Temptation to misbehave
is high, but as a teaching and a method for instant
reinforcement it was a success.
• The experience was fun, and very interactive. I
like it because it's a useful tool to measure
knowledge. However, it consumes more time from
learning a new concept in class.
• I thought the experience did a good job of
showing the ideas using technology. I don't think
it is practical for an everyday classroom
experience but it was a good change of pace.
Student Comments — Negative
• Old fashion (verbal) class participation
would have worked just as well. Probably
with less confusion and goofing off.
• It was interesting, but didn't help with
knowledge of the material being covered in
class.
• Nothing beats teaching on | 677.169 | 1 |
Common Errors
This is a set of errors that really doesn't fit into any of
the other topics so I included all them here.
Read the instructions!!!!!!
This is probably one of the biggest mistakes that students
make. You've got to read the
instructions and the problem statement carefully. Make sure you understand what you are being
asked to do BEFORE you start working the problem
Far too often students run with the assumption : "It's in
section X so they must want me to ____________." In many cases you simply can't assume
that. Do not just skim the instruction
or read the first few words and assume you know the rest.
Instructions will often contain information pertaining to
the steps that your instructor wants to see and the form the final answer must
be in. Also, many math problems can
proceed in several ways depending on one or two words in the problem
statement. If you miss those one or two
words, you may end up going down the wrong path and getting the problem
completely wrong.
Not reading the instructions is probably the biggest source
of point loss for my students.
Pay attention to restrictions on formulas
This is an error that is often compounded by instructors (me
included on occasion, I must admit) that don't give or make a big deal about
restrictions on formulas. In some cases
the instructors forget the restrictions, in others they seem to have the idea
that the restrictions are so obvious that they don't need to give them, and in
other cases the instructors just don't want to be bothered with explaining the
restrictions so they don't give them.
For instance, in an algebra class you should have run across
the following formula.
The problem is there is a restriction on this formula and
many instructors don't bother with it and so students aren't always aware of
it. Even if instructors do give the
restriction on this formula many students forget it as they are rarely faced
with a case where the formula doesn't work.
Take a look at the following example to see what happens
when the restriction is violated (I'll give the restriction at the end of
example.)
This is
certainly a true statement.
Since
and
.
Use the above
property on both roots.
Since
Just
a little simplification.
Since
.
So clearly we've got a problem here as we are well aware
that ! The problem arose in step 3. The property that I used has the restriction
that a and b can't both be negative. It
is okay if one or the other is negative, but they can't BOTH be negative!
Ignoring this kind of restriction can cause some real
problems as the above example shows.
There is also an example from calculus of this kind of
problem. If you haven't had calculus
then you can skip this one. One of the
more basic formulas that you'll get is
This is where most instructors leave it, despite the fact
that there is a fairly important restriction that needs to be given as
well. I suspect most instructors are so
used to using the formula that they just implicitly feel that everyone knows
the restriction and so don't have to give it.
I know that I've done this myself here!
In order to use this formula n MUST be a fixed
constant! In other words you can't use
the formula to find the derivative of since the exponent is not a fixed
constant. If you tried to use the rule
to find the derivative of you would arrive at
and the correct derivative is,
So, you can see that what we got be incorrectly using the
formula is not even close to the correct answer.
Changing your answer to match the known answer
Since I started writing my own homework problems I don't run
into this as often as I used to, but it annoyed me so much that I thought I'd
go ahead and include it.
In the past, I'd occasionally assign problems from the text
with answers given in the back. Early in
the semester I would get homework sets that had incorrect work but the correct
answer just blindly copied out of the back.
Rather than go back and find their mistake the students would just copy
the correct answer down in the hope that I'd miss it while grading. While on occasion I'm sure that I did miss it,
when I did catch it, it cost the students far more points than the original
mistake would have cost them.
So, if you do happen to know what the answer is ahead of
time and your answer doesn't match it GO BACK AND FIND YOUR MISTAKE!!!!! Do not just write the correct answer down and
hope. If you can't find your mistake
then write down the answer you get, not the known and (hopefully) correct
answer.
I can't speak for other instructors, but if I see the
correct answer that isn't supported by your work you will lose far more points
than the original mistake would have cost you had you just written down the
incorrect answer.
Don't assume you'll do the work correctly and just
write the answer down
This error is similar to the previous one in that it assumes
that you have the known answer ahead of time.
Occasionally there are problems for which you can get the
answer to intermediate step by looking at the known answer. In these cases do not just assume that your
initial work is correct and write down the intermediate answer from the known
answer without actually doing the work to get the answers to those intermediate
steps.
Do the work and check your answers against the known answer
to make sure you didn't make a mistake.
If your work doesn't match the known answer then you know you made a
mistake. Go back and find it.
There are certain problems in a differential equations class
in which if you know the answer ahead of time you can get the roots of a
quadratic equation that you must solve as well as the solution to a system of
equations that you must also solve. I
won't bore you with the details of these types of problems, but I once had a
student who was notorious for this kind of error.
There was one problem in particular in which he had written
down the quadratic equation and had made a very simple sign mistake, but he
assumed that he would be able to solve the quadratic equation without any
problems so just wrote down the roots of the equation that he got by looking at
the known answer. He then proceeded with
the problem, made a couple more very simple and easy to catch mistakes and
arrived at the system of equations that he needed to solve. Again, because of his mistakes it was the
incorrect system, but he simply assumed he would solve it correctly if he had
done the work and wrote down the answer he got by looking at the solution.
This student received almost no points on this problem
because he decided that in a differential equations class solving a quadratic
equation or a simple system of equations was beneath him and that he would do
it correctly every time if he were to do the work. Therefore, he would skip the work and write
down what he knew the answers to these intermediate steps to be by looking at
the known answer. If he had simply done
the work he would have realized he made a mistake and could have found the
mistakes as they were typically easy to catch mistakes.
So, the moral of the story is DO THE WORK. Don't just assume that if you were to do the
work you would get the correct answer.
Do the work and if it's the same as the known answer then you did
everything correctly, if not you made a mistake so go back and find it.
Does your answer make sense?
When you're done working problems go back and make sure that
your answer makes sense. Often the
problems are such that certain answers just won't make sense, so once you've
gotten an answer ask yourself if it makes sense. If it doesn't make sense then you've probably
made a mistake so go back and try to find it.
Here are a couple of examples that I've actually gotten from
students over the years.
In an algebra class we would occasionally work interest
problems where we would invest a certain amount of money in an account that
earned interest at a specific rate for a specific number of year/months/days
depending on the problem. First, if you
are earning interest then the amount of money should grow, so if you end up
with less than you started you've made a mistake. Likewise, if you only invest $2000 for a
couple of years at a small interest rate you shouldn't have a couple of billion
dollars in the account after two years!
Back in my graduate student days I was teaching a trig class
and we were going to try and determine the height of a very well known building
on campus given the length of the shadow and the angle of the sun in the
sky. I doubt that anyone in the class
knew the actual height of the building, but they had to know that it wasn't
over two miles tall! I actually got an
answer that was over two miles. It clearly
wasn't a correct answer, but instead of going back to find the mistake (a very
simple mistake was made) the student circled the obviously incorrect answer and
moved on to the next problem.
Often the mistake that gives an obviously incorrect answer
is an easy one to find. So, check your
answer and make sure that they make sense!
Check your work
I can not stress how important this one is! CHECK YOUR WORK! You will often catch simple mistakes by going
back over your work. The best way to do
this, although it's time consuming, is to put your work away then come back and
rework all the problems and check your new answers to those previously
gotten. This is time consuming and so
can't always be done, but it is the best way to check your work.
If you don't have that kind of time available to you, then
at least read through your work. You
won't catch all the mistakes this way, but you might catch some of the more
glaring mistakes.
Depending on your instructors beliefs about working groups
you might want to check your answer against other students. Some instructors frown on this and want you
to do all your work individually, but if your instructor doesn't mind this,
it's a nice way to catch mistakes.
Guilt by association
The title here doesn't do a good job of describing the kinds
of errors here, but once you see the kind of errors that I'm talking about you
will understand it.
Too often students make the following logic errors. Since the following formula is true
there must be a similar formula for . In
other words, if the formula works for one algebraic operation (i.e. addition,
subtraction, division, and/or multiplication) it must work for all. The problem is that this usually isn't true! In this case
Likewise, from calculus students make the mistake that
because
the same must be true for a product of functions. Again,
however, it doesn't work that way!
So, don't try to extend formulas that work for certain
algebraic operations to all algebraic operations. If you were given a formula for certain
algebraic operation, but not others there was a reason for that. In all likelihood it only works for those
operations in which you were given the formula!
Rounding Errors
For some reason students seem to develop the attitude that
everything must be rounded as much as possible.
This has gone so far that I've actually had students who refused to work
with decimals! Every answer was rounded
to the nearest integer, regardless of how wrong that made the answer.
There are simply some problems were rounding too much can
get you in trouble and seriously change the answer. The best example of this is interest problems. Here's a quick example.
Recall (provided you've seen this formula) that if you
invest P dollars at an interest rate
of r that is compounded m times per year, then after t years you will have A dollars where,
So, let's assume that we invest $10,000 at an interest rate
of 6.5% compounded monthly for 15 years.
So, here's what we've got
Remember that interest the interest rate is always divided
by 100! So, here's what we will have
after 15 years.
So, after 15 years we will have $26,442.01. You will notice that I didn't round until the
very last step and that was only because we were working with money which
usually only has two decimal places.
That is required in these problems.
Here are some examples of rounding to show you how much difference
rounding too much can make. At each step
I'll round each answer to the give number of decimal places.
First, I'll do the extreme case of no decimal places at all,
i.e. only integers. This is an extreme
case, but I've run across it occasionally.
It's extreme but it makes the point.
Now, I'll round to three decimal places.
Now, round to five decimal places.
Finally, round to seven decimal places.
I skipped a couple of possibilities in the
computations. Here is a table of all
possibilities from 0 decimal places to 8.
Decimal places
of rounding
Amount after
15 years
Error in
Answer
0
$10,000.00
$16,442.01 (Under)
1
$10,000.00
$16,442.01 (Under)
2
$60,000.00
$33,557.99 (Over)
3
$24,540.00
$1,902.01 (Under)
4
$26,363.00
$79.01 (Under)
5
$26,457.80
$15.79 (Over)
6
$26,443.59
$1.58 (Over)
7
$26,442.17
$0.16 (Over)
8
$26,442.02
$0.01 (Over)
So, notice that it takes at least 4 digits of rounding to
start getting "close" to the actual answer.
Note as well that in the world of business the answers we got with 4, 5,
6 and 7 decimal places of rounding would probably also be unacceptable. In a few cases (such as banks) where every
penny counts even the last answer would also be unacceptable!
So, the point here is that you must be careful with
rounding. There are some situations
where too much rounding can drastically change the answer!
Bad notation
These are not really errors, but bad notation that always
sets me on edge when I see it. Some
instructors, including me after a while, will take off points for these
things. This is just notational stuff
that you should get out of the habit of writing if you do it. You should reach a certain mathematical
"maturity" after awhile and not use this kind of notation.
First, I see the following all too often,
The just makes no sense! It combines into a negative SO WRITE IT LIKE
THAT! Here's the correct way,
This is the correct way to do it! I expect my students to do this as well.
Next, one (the number) times something is just the something,
there is no reason to continue to write the one. For instance,
Do not write this as ! The coefficient of one is not needed here
since ! Do not write the coefficient of 1!
This same thing holds for an exponent of one anything to the
first power is the anything so there is usually no reason to write the one
down!
In my classes, I will attempt to stop this behavior with
comments initially, but if that isn't enough to stop it, I will start taking
points off. | 677.169 | 1 |
Geometry Seeing, Doing, Understanding
9780716743613
ISBN:
0716743612
Edition: 3 Pub Date: 2003 Publisher: W H Freeman & Co
Summary: Jacobs innovative discussions, anecdotes, examples, and exercises to capture and hold students' interest. Although predominantly proof-based, more discovery based and informal material has been added to the text to help develop geometric intuition.
Jacobs, Harold R. is the author of Geometry Seeing, Doing, Understanding, published 2003 under ISBN 9780716743613 and 0716743612. One hundred nineteen Geometry Se...eing, Doing, Understanding textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $60.00, or buy new starting at $408.48 | 677.169 | 1 |
Next: Limits (An Intuitive Approach)
Previous: The Binomial Theorem
Chapter 8: Introduction to Calculus
Chapter Outline
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Chapter Summary
Image Attributions
Description
Students explore and learn about limits from an intuitive approach, computing limits, tangent lines and rates of change, derivatives, techniques of differentiation, conceptual basis for integration and The Fundamental Theorem of Calculus. | 677.169 | 1 |
Math for Elementary Teachers II
Welcome to Mth126: "Continued study of the mathematical
concepts and techniques that are fundamental to, and form the
basis for, elementary school mathematics. Topics include:
use of probability and statistics to explore real-world
problems; representation and analysis of discrete mathematical
problems using counting techniques, sequences, graph theory,
arrays and networks; use of functions, algebra and the basic
concepts underlying the calculus in real-world-applications."
News and Updates
See the Homework and Handouts table
below to download or print the syllabus, calendar, and all
homework sets and class notes.
Looking for the Mth126 page from a previous semester?
Here's a link to
mth126fa08.
Here's a link to the interactive
Normal Probability on Sketchpad document; you need
Geometer's Sketchpad to open it, which is available in
all GCA labs on campus. Right click and choose
"Save as" to download it to your desktop; then open it
from there.
Homework Solutions: Here are worked
solutions (see right) for some of the problems from Ch. 13.
There are solutions to problems I did not assign this
semester as well as problems I assigned that do not have a
solution listed here. Still, I hope these are helpful. If
there are others you have questions on, please stop by my
office or ask during class. | 677.169 | 1 |
Math Net
2001 Math Net is a valuable resource for anyone in any level math class. It provides students with detailed lessons in Algebra and Trigonometry, as well as a Glossary in which students can look up definitions. A Calculator page provides useful programs available for download to the TI-83 Calculator. Probably the most useful portion of the site is the Functions section. There are fifteen basic functions will detailed illustrations as to how they react to transformations. This is a valuable tool of reference, especially to students who have been away from math for some time. | 677.169 | 1 |
introductory book on optimization (mathematical programming) includes coverage on linear programming, nonlinear programming, integer programming and heuristic programming; as well as an emphasis on model building using Excel and Solver. The emphasis on model building (rather than algorithms) is one of the features that makes this book distinctive. Most books devote more space to algorithmic details than to formulation principles. These days, however, it is not necessary to know a great deal about algorithms in order to apply optimization tools, especially when relying on the spreadsheet as a solution platform. The emphasis on spreadsheets is another feature that makes this book distinctive. Few books devoted to optimization pay much attention to spreadsheet implementation of optimization principles, and most books that emphasize model building ignore spreadsheets entirely. Thus, someone looking for a spreadsheet-based treatment would otherwise need to use a book that was designed for some other purpose, like a survey of management science topics, rather than one devoted to optimization. The model building emphasis derives from an attempt to be realistic about what readers need most when learning about optimization. At an introductory level, the most practical and motivating theme is the wide applicability of optimization tools. To apply optimization effectively, readers needs more than a brief exposure to a series of numerical examples, which is the way that most mathematical programming books treat applications. With a systematic modeling emphasis, readers can begin to see the basic structures that appear in optimization models and as a result, develop an appreciation for potential applications well beyond the examples in the book. Formulating optimization models is both an art and a science, and this book pays attention to both. The art can be refined with practice, especially supervised practice, just the way a student would learn sculpture or painting. The science is reflected in the structure that organizes the topics in this book. For example, there are several distinct problem types that lend themselves to linear programming formulations, and it makes sense to study these types systematically. In that spirit, the book builds a library of templates against which new problems can be compared. Analogous structures are developed for the presentation of other topics as well.
Author Biography
Kenneth R. Baker, PHD, is Nathaniel Leverone Professor of Management at the Tuck School of Business and Adjunct Professor of Engineering at Dartmouth College. A Fellow of the Institute for Operations Research and the Management Sciences (INFORMS), Dr. Baker has published extensively in his areas of research interest, which include mathematical modeling, spreadsheet engineering, and scheduling. He is the coauthor of Principles of Sequencing and Scheduling and Management Science: The Art of Modeling with Spreadsheets, Third Edition, both published by Wiley. | 677.169 | 1 |
Hey Friends I really hope some math expert reads this. I am stuck on this assignment that I have to turn in in the coming couple of days and I can't seem to find a way to finish it. You see, my teacher has given us this test on convert radicals, converting fractions and relations and I just can't understand it. I am thinking of going to some private tutor to help me solve it. If someone can give me some suggestions, I will highly grateful.
Algebrator is a real treasure that can aid you with Algebra 1. Since I was imperfect in Remedial Algebra, one of my class instructors recommended me to try the Algebrator and based on his advice, I looked for it online, bought it and started using it. It was just extra ordinary. If you sincerely follow each and every lesson offered there on Pre Algebra, you would master the primary principles of equivalent fractions and graphing lines within hours.
Algebrator really is a great piece of algebra software. I remember having problems with graphing lines, adding matrices and exponential equations. By typing in the problem from homework and merely clicking Solve would give step by step solution to the math problem. It has been of great help through several Basic Math, College Algebra and Algebra 2. I seriously recommend the program.
graphing lines, inverse matrices and x-intercept were a nightmare for me until I found Algebrator, which is really the best math program that I have ever come across. I have used it through several algebra classes – Intermediate algebra, College Algebra and Intermediate algebra. Just typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I truly recommend the program. | 677.169 | 1 |
Part IV: 3-D Mathematics
Part IV: 3-D Mathematics
You've already done most of the work to enable you to move from two to three dimensions. The concepts of vectors, forces, energy, and momentum are the same in three dimensions as in two, and collision detection, while more complex, involves all the same techniques as before. In this fourth part of the book, you'll finish your exploration of mathematical and physical theory by taking this final step into 3-D.
You'll start by looking at the basics of 3-D space, and how it can be represented on a two-dimensional screen. Then you'll spend another chapter further extending the vector work you have done up to now, and I'll introduce the concept of a transform. Chapter 18 deals with collision detection for 3-D shapes, Chapter 19 looks at lighting and shading, and the final chapter covers various 3-D modeling techniques for creating complex objects and moving surfaces, such as waves on water.
3-D is a subject much more widely covered than the more general techniques in this book, and so you won't retread the ground of many other authors. Most of the topics are dealt with briefly. For a full mathematical treatment, along with much more information on the more obscure topics, it is helpful to consult the references given in the appendices of the book. | 677.169 | 1 |
83,"ASIN":"0199149364","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":24.83,"ASIN":"0199149879","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":15.41,"ASIN":"0199149380","isPreorder":0}],"shippingId":"0199149364::aU6M3Tmb55Sl8n0zkrvpFRE9cU3nPy4gAM70AMCDyBee1g%2B6YqNBKEpLun7hbD8r2ije3x8l3QnTzSVTD%2BJxh9A9Lh7QYcQh,0199149879::wIpy4LuiFkIFV96QniWyZRSJCwPAkTODPbzZFA9Xkw7sbPC5aITy0RtiSexTfSg3TK%2B%2BAAi9MuyxHe8Cp8gOLhSLtK2iHpAj,0199149380::YAZWdz7BfbeitRL1oNI4OVnwe7ogJ6Gr5imwa0RQKvIvIBgccveCCOBztIS%2BigzbABPXeAal0IMR1%2BoNoo5KlIDjzYxtCF learnt A-level Maths at home in my own time and followed the AQA sylabus. This book shows you everything you need to know to pass the exams MPC1 and MPC2 and nothing more. It's got good examples with normal and challenging questions.
It has revision excercises at the end of each section which are past exam questions.
Just don't use this book as your only resource if you're teaching yourself. The internet is brilliant and there's videos on there to help you.
The vast majority of A level Maths resources out there are tailored for Edexcel or for OCR, and AQA specific textbooks are very hard to come by - so this textbook was a godsend. It explains all the little bits of the syllabus, so it is great if you're a person who wants to learn things really thoroughly. There are also oodles of past exam questions, again all from AQA, so that you know exactly the type of questions you may get. The only downside is that some of the explanations are badly worded and hard to understand - but that is only occasional, and in those cases I just supplemented my studies by using other sources.
At the moment I i am using this book for As Maths and i think this book is excellent it has examples on how to do the questions so you wont be stuck, and it also has answers at the back so if you not in college you can do work on your own and then mark it yourself. | 677.169 | 1 |
Written to complement the explanations provided in Understanding Mathematics: From Counting to Calculus, the books may be used as a supplement or independent core curriculum. This textbook provides problem sets that are aligned with the sections explained in Understanding Mathematics: From Counting to Calculus. 305 pages, softcover.
Customer Reviews for Math Problems and Solutions Guide
This product has not yet been reviewed. Click here to continue to the product details page. | 677.169 | 1 |
Matrices, Geometry & Mathematica
Book Description: A computer-based course consisting of a complete interactive electronic text combined with a rich set of well chosen real life problems. The easy access to powerful technology allows experimentation. In the lab or lassroom the environment allows a partnership between teacher and student with emphasis on student responsibility. Independent study is also possible. Online tutoring is available. The courseware comes on a CD which contains all of the lessons, some extra tools, and Adobe PDF files for printing selected parts of the lessons: Lessons: Perp Frames and 2D Matrices, Higher Dimensions, Eigensystems, etc | 677.169 | 1 |
Linear Programming is a mathemematical techinque for choosing the best alternative form of a
set of feasible alternatives. In situations where the objective function as well as the restictions or...Linear Programming is a mathemematical techinque for choosing the best alternative form of a
set of feasible alternatives. In situations where the objective function as well as the restictions or
constraints can be expressed as linear mathematical functions.
Different appllications are of L.P.P are:
THE DIET PROBLEM:
To find the cheapest combinations of foods that will satisfy all your nutritional requirements.
Example:
Suppose the only foods available in your local store are potatoes and steak. The decision about
how much of each food to buy is to made entirely on dietary and economic considerations. We
have the nutritional and cost information in the following table:
Per unit
of potatoes
Units of
carbohydrates
Units of vitamins
Units of proteins
Unit cost
Per unit
of steak
Minimum
requirements
3
1
8
4
1
25
3
3
50
19
7
The problem is to find a diet (a choice of the numbers of units of the two foods) that meets all
minimum nutritional requirements at minimal cost.
a. Formulate the problem in terms of linear inequalities and an objective function.
b. Solve the problem geometrically.
a) We begin by setting the constraints for the problem. The first constraint represents the
minimum requirement for carbohydrates, which is 8 units per some unknown amount of time. 3
units can be consumed per unit of potatoes and 1 unit can be consumed per unit of steak. The
second constraint represents the minimum requirement for vitamins, which is 19 units. 4 units
can be consumed per unit of potatoes and 3 units can be consumed per unit of steak. The third
constraint represents the minimum requirement for proteins, which is 7 units. 1 unit can be
consumed per unit of potatoes and 3 units can be consumed per unit of steak. The fourth and fifth
constraints represent the fact that all feasible solutions must be nonnegative because we can't buy
negative quantities.
constraints:
{3X1 + X2
8, 4X1+ 3X2
19, X1+ 3X2
7, X1 0, X2
0};
Next we plot the solution set of the inequalities to produce a feasible region of possibilities.
PORTFOLIO OPTIMIZATION
To minimize the risk in your investment porttfolio subject to achieving a certain return.Many
investment companies are now using the optimiztion and linear programming extensively to
decide how to allocate assets.the increase in the speed of computers has enabled the solution of
far larger problems.
Example:
(Minimize the Risk)
minimize the variance xtV x
with a specified expected return r = atx subjected to linear and (or nonlinear)
constraints.
CREW SCHEDULING
An... View Full AttachmentShow more | 677.169 | 1 |
Study Guides
showing 1 - 10 of 711
1.
What is FOIL?
The FOIL Method — First Outer Inner Last — is the best system to use when multiplying two binomials. You can think of it as a slightly more advanced version of the distributive property of multiplication, which tells us that a(b + ...
Introduction to The Slope and Equation of a Line
The slope of a line and the meaning of the slope are important in calculus. In fact, the slope formula is the basis for differential calculus. The slope of a line measures its tilt. The sign of the slope tells us ...
Introduction to Functions and Their Graphs
The graph of a function can give us a great deal of information about the function. In this chapter we will use the graph of a function to evaluate the function, find the x- and y ...
Introduction to Combinations of Functions
Most of the functions studied in calculus are some combination of only a few families of functions, most of the combinations are arithmetic. We can add two functions, f + g(x), subtract them, ...
Introduction to Translations and Special Functions
Calculus students work with only a few families of functions—absolute value, n th root, cubic, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. Two or more of ... | 677.169 | 1 |
Category:Calculus
This category contains books on calculus: a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations.
Related categories
The following 5 related categories may be of interest, out of 5 total. | 677.169 | 1 |
Mathway Algebra Solver
Most of kids have a phobia of mathematic. That's why parents are worried about the mater. We should find out our kid's level then give him/her unique concept both of us and our child who accept it. The quantity we demand to reduce can change significantly one conception to the following. Our kid may be outstanding at finding area; only might be having it crude on angles. So we should it a gradation at one time. Such is how the mathematics conception as totally will be dominated, ...
Algebra is a division of mathematics regarding the study of quantity, relation, and. Structure. Together with analysis, geometry, number theory, and combinatorial, algebra is the major divisions of mathematics. Basic algebra is frequently fraction of the prospectus in secondary teachings. Most of the sites still give particular algebra software course recognized as my algebra solvers. This type of programs needs you to enter algebraic troubles along with suitable signs. | 677.169 | 1 |
049510941X
9780495109419
Mathematical Modeling with Maple:With an innovative approach that leverages the power of the Maple computer algebra system as an analytical tool, MATHEMATICAL MODELING WITH MAPLE offers an effective introduction to mathematical modeling of compelling real world applications. Intended for students with a background in calculus, the text shows how to formulate, build, solve, analyze, and critique models of applications in math, engineering, computer science, business, and the physical and life sciences. The book utilizes Maple for computations, plotting results graphically, and dynamically analyzing results within the modeling process. Easy-to-follow software instructions are provided, and Maple syntax in the book is also offered online as Maple workbooks allowing students to quickly and interactively work problems as they read. MATHEMATICAL MODELING WITH MAPLE helps students develop their analytical skills while harnessing the power of cutting-edge modern technology, allowing them to become competent, confident problem solvers for the 21st century.
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Rent Mathematical Modeling with Maple 1st edition today, or search our site for Fox textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. | 677.169 | 1 |
This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.
Examining the science behind everyday predictions—such as why the supermarket sends particular coupons to the appropriate people and how a bank can foretell if someone will default on a loan within a few minutes—this guide explains the basics of what data mining is, details a variety of data mining and techniques, and profiles the key figures behind the data-mining process. After first demonstrating fundamental approaches such as nearest neighbor and association rules, the resource goes on to analyze probabilistic techniques that use Bayes' theorem and artificial intelligence algorithms using neural networks. With chapters on a wide range of topics—from calculating similarity to dealing with uncertainty and modeling the brain—this comprehensive volume reveals how anyone with enough information can get an intimate view of someone's life and what to do about it.
WILEY-INTERSCIENCE PAPERBACK SERIES The " . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic." --London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking." --SIAM Review "Each chapter discusses a wealth of examples ranging from old standards . . . to novelty . . . each model is developed critically, analyzed critically, and assessed critically." --Mathematical Reviews A Concrete Approach to Mathematical Modelling provides in-depth and systematic coverage of the art and science of mathematical modelling. Dr. Mesterton-Gibbons shows how the modelling process works and includes fascinating examples from virtually every realm of human, machine, natural, and cosmic activity. Various models are found throughout the book, including how to determine how fast cars drive through a tunnel, how many workers industry should employ, the length of a supermarket checkout line, and more. With detailed explanations, exercises, and examples demonstrating real-life applications in diverse fields, this book is the ultimate guide for students and professionals in the social sciences, life sciences, engineering, statistics, economics, politics, business and management sciences, and every other discipline in which mathematical modelling plays a role.
How to apply statistical methods to survey data--a guide to effective analysis of health surveys. With large health surveys becoming increasingly available for public use, researchers with little experience in survey methods are often faced with analyzing data from surveys to address scientific and programmatic questions. This practical book provides statistical techniques for use in survey analysis, making health surveys accessible to statisticians, biostatisticians, epidemiologists, and health researchers. The authors clearly explain the theory and methods of survey analysis along with real-world applications. They draw on their work at the National Institutes of Health as well as up-to-date information from across the literature to present: The sampling background necessary to understand health surveys. The application of such techniques as t-tests, linear regression, logistic regression, and survival analysis to survey data. The use of sample weights in survey data analysis. Dealing with complications in variance estimation in large health surveys. Applications involving cross-sectional, longitudinal, and multiple cross-sectional surveys, and the use of surveys to perform population- based case-control analyses. Guidance on the correct use of statistical methods found in software packages. Extensive bibliography.
An accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-based search engine, processing with Daubechies' wavelets, and more. Among the special features of Discovering Wavelets are: Real-life, hands-on examples that involve actual wavelet applications A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book Challenging problems that reinforce and expand on the ideas being developed An appendix containing the linear algebra needed to understand wavelets as presented in the book
An insightful presentation of the key concepts, paradigms, and applications of modeling and simulation Modeling and simulation has become an integral part of research and development across many fields of study, having evolved from a tool to a discipline in less than two decades. Modeling and Simulation Fundamentals offers a comprehensive and authoritative treatment of the topic and includes definitions, paradigms, and applications to equip readers with the skills needed to work successfully as developers and users of modeling and simulation. Featuring contributions written by leading experts in the field, the book's fluid presentation builds from topic to topic and provides the foundation and theoretical underpinnings of modeling and simulation. First, an introduction to the topic is presented, including related terminology, examples of model development, and various domains of modeling and simulation. Subsequent chapters develop the necessary mathematical background needed to understand modeling and simulation topics, model types, and the importance of visualization. In addition, Monte Carlo simulation, continuous simulation, and discrete event simulation are thoroughly discussed, all of which are significant to a complete understanding of modeling and simulation. The book also features chapters that outline sophisticated methodologies, verification and validation, and the importance of interoperability. A related FTP site features color representations of the book's numerous figures. Modeling and Simulation Fundamentals encompasses a comprehensive study of the discipline and is an excellent book for modeling and simulation courses at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of computational statistics, engineering, and computer science who use statistical modeling techniques.
This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described. The author begins with basic characteristics of financial time series data before covering three main topics: Analysis and application of univariate financial time series The return series of multiple assets Bayesian inference in finance methods Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction—illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.—that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and eleme
This is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics.This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade.The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.
Guesstimation is a book that unlocks the power of approximation—it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet. Guesstimation enables anyone with basic math and science skills to estimate virtually anything—quickly—using plausible assumptions and elementary arithmetic. Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same. The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones—and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches, Guesstimation will delight popular-math enthusiasts and is ideal for the classroom. | 677.169 | 1 |
Algebra for College Students - Text Only - 04 edition
Summary: Miller/O'Neill's Algebra for College Students is an insightful text written by instructors who have first-hand experience with students of developmental mathematics. The authors introduce functions in Chapter 4 and do a very thorough treatment, devoting the entire chapter to the concept of functions. With such a solid foundation to build from, students will experience greater success when they encounter other function-related topics in later chapters, such as polynom...show moreial translating expressions Midchapter Reviews and classroom activities (classroom activities are worksheets that can be downloaded from the OLC). The classroom activities are of special value, in that through their use, students may begin to take greater ownership over their own learning. The classroom activities were designed to be quick activities students could perform in class (either individually, orcollaboratively in groups). In short, the Miller/O'Neill Algebra for College Students text offers enriching applications, a high level of readability, and excellent opportunities for students to become actively engaged in their exploration of mathematics | 677.169 | 1 |
Quantifying, using mathematics, is at the heart of much professional work done in the contemporary world. Math is essential for business, economics, technologies, natural sciences, social sciences, psychology, and any profession related to those fields. Most history departments now require quantitative reasoning courses such as demographics and other statistical methods. Arts and humanities courses are also making use of quantitative relationships in their studies of literature, art, and music. You can scarcely be educated in twenty-first century without mathematical skills and quantitative reasoning.
Take a moment to reflect on the many ways you encounter quantitative reasoning every day--do you see numbers, tables, graphs, diagrams in the newspaper? Think about your work environment, your volunteer work, or other daily life activities that deal in some way with quantitative information. For example:
What do those survey results, reported in opinion polls, really mean?
How can I use the nutritional information on the product label to analyze my diet or plan my family's meals?
How do I determine the budget for my department?
What pattern does that graph describe?
Math is a form of communication, just as writing is. It includes ways of representing precise relationships and of discovering or representing patterns. It's an important tool for inquiry as well as for problem solving, and it is a fundamental part of critical thinking. You need to examine your quantitative reasoning skills in order to determine what they are, how you use them,and whether they are appropriate to the type of critical inquiry and precise communication you will be doing in college and as an informed participant in modern life.
Do this self-assessment if:
you believe that quantitative reasoning means arithmetic and calculations
you generally just gloss over graphs, charts, statistics, or any mathematical information of this sort because you just don't know how to deal with it
you know that some level of math skill is expected for your profession and you don't know if your current learning is appropriate
you have "math anxiety"
The math self-assessment has many pieces. You may do one or many, depending on your individual needs. Go to the home page for this site, and click on "My Self-Assessments" in the upper left-hand corner. Under Academic Skills - Math, you'll find the following self-assessments: | 677.169 | 1 |
Intermediate INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The new edition has been thoroughly updated with a new interior design and other pedagogical features that make the user both easier to read and easier to use. Known for its clear writing and an engaging, accessible approach that makes algebra relevant, INTERMEDIATE ALGEBRA helps users to develop problem-solving skills and strategies that they can use in their everyday lives. The new edition welcomes two new co-authors Rosemary Karr and Marilyn Massey who along with David Gustafson have developed a learning plan to help users succeed in Intermediate Algebra and transition to the next level in their coursework. | 677.169 | 1 |
Video Text Math
This program uses new, interactive, video-based strategies to teach Algebra and Geometry from start to finish. The main components are the "videotext" (the video lessons), and a workbook. The video serves as the textbook. Each module is around $100 and there are multiple modules for each course in Algebra and Geometry. Entire courses can also be purchased.
Comments
Video Text Math Review by Rebecca Kovaly
November 6, 2010
Pros: Comprehensive Cons: None Grades Used: 8th & 10th
Where other Algebra programs have failed us, Video Text Interactive has excelled. We watch the video lesson together then students work the practice sets(odds or evens). Notes are already printed up and are very helpful while working the practice sets. After 2-3 problems, we check the answer book to make sure we are on the right track. The student finishes the practice sets. The next day before the next video lesson, the students take a quiz to make sure they remember the concept from the prior lesson. There is a seperate answer book for the quizes and end of unit test. Each lesson is presented to aid the student (and parent) in fully understanding the concept, the whys, as well as the parts of mathematical speech. The program may seem a bit expensive, but when compared to other math programs (especially the ones you bought only to find out they were not a good match), this program is a good value. We chose not to write in the workbooks, so the program can be used by multiple students for many years. Very please so far, we have just started Module B | 677.169 | 1 |
Instructor Class Description
Functions, Models, and Quantitative Reasoning
Explores the concept of a mathematical function and its applications. Explores real world examples and problems to enable students to create mathematical models that help them understand the world in which they live. Each idea will be represented symbolically, numerically, graphically, and verbally. Prerequisite: minimum grade of 2.5 in B CUSP 122, a score of 145-153 on the MPT-AS assessment test, or a score of 151 or higher on the MPT-GS assessment test. Offered: AWSp.
Class description
Students will explore in great detail the concept of a mathematical function and its applications. Functions are the key to how mathematical models are built. A large number of real-world examples and problems (including messy data sets) will be explored in an effort to enable students to creat mathematical models that will help them understand the world in which we live.
Student learning goals
General method of instruction
The class will be taught with a mixture of group activities and labs, as well as interactive lectures.
Recommended preparation
Score of 40% or higher on the UWB math placement test.
Class assignments and grading
Assignments will consist of homework problems, labs, some written assignments as well as reading from the textbook and other supplemental readings.
Grades will be assigned based on class participation and performance on labs, homework/quizzes, the midterm and the Nicole A Hoover
Date: 09/18/2006
Office of the Registrar
For problems and questions about this web page contact [email protected],
otherwise contact the instructor or department directly.
Modified:November 27, 2013 | 677.169 | 1 |
Professor Hutchinson's research lies within the general area of discrete mathematics, also known as combinatorial analysis. She specializes in graph theory, graph layouts, and graph algorithms, concentrating on chromatic and topological graph theory. | 677.169 | 1 |
Basic College worktext format for basic college math or arithmetic courses including lecture-based, self-paced, and modular classes.John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. The Tobey approach focuses on building skills one at a time by breaking math down into manageable pieces. This building block organization is a practical approach to basic math skill development that makes it easier for students to understand each topic, gaining confidence as they move through each section. Knowing students cra... MOREve feedback, Tobey has enhanced the new edition with a "How am I Doing?" guide to math success. The combination of continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the fifth edition of Tobey/Slater Basic College Mathematics even more practical and accessible. This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Chapter 7, Geometry, has been extensively revised and re-organized to include a new section 7.1 on angles and new section 7.4 devoted to triangles. Increased coverage of estimating with fractions and decimals with new ¿To Think About¿ exercises in Sections 2.5, 2.8, and 3.3 and a new lesson in Section 3.7. Coverage of fractions in Chapter 2 has been expanded as follows: Section 2.6 now begins with a discussion of least common multiples so that the subsequent coverage of least common denominators is more complete; a new lesson on order of operations in Section 2.8 offers readers additional review of these rules and practice applying them to fractions; and a new mid-chapter test on fractions appears after Section 2.5. Percent applications are now covered in two sections (Sections 5.4 and 5.5) to allow for a more patient presentation of this important topic. | 677.169 | 1 |
Recognize common errors that occur during dose calculation. ... Now that you
have learned basic math skills, ... Conversion factors are expressions that allow
you to switch from one ..... Available measuring device is marked in teaspoons.
c The Common Core Standards Writing Team. 26 December ... in daily life, such
as in cooking and in calculating tips, miles per gal- .... mathematical problems,
e.g., by reasoning about tables of equiv-.
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engineering disciplines, for ... use basic geometry and algebra to calculate ....
miologists, and medical scientists focus on.
The most common rate used is the Recordable Incident Rate. ... LOST
WORKDAY RATE – a mathematical calculation that describes the ... of medical
treatment or first-aid. ... experienced 2 recordable injuries, then the formula works
like this:.
validated by content experts in the Common Core State Standards in
mathematics ... A-CED.2 Create equations in two or more variables to represent
relationships ... Algebra II, Integrated Math II or III; Health Science or Medical
Terminology.
1.4 Systems of Linear Equations With Non-Unique Solutions . . 52. Systems ... We
will first review some basic material on functions. ..... goods, medical care, and
higher eduction, to name a few). That is ...
use of technology in mathematics education. ... Examinees will be expected to
know common mathematical formulae, but any ... Determine the equations of
lines, given sufficient ..... The number of students in medical schools increased by
.
Currently, Loretta is coordinator of the health information technology program at.
Hutchinson ... first edition of Basic Healthcare Statistics appeared in 1996. ... The
formula used to calculate each type.
such as from skin cancer and UV over-exposure, or medical X-rays, ... Space.
Technology makes it possible for students to experience the value of math, ...
Equations ..... Basic Unit Conversions: 1 Curie ...
Texas Tech University – HSC - School of Pharmacy is accredited by The
American ... MBA – Healthcare Administration, C.Ph.T. ... Use of proportions is
very common in dosage calculations, especially in ... of Y? The formula is as
follows:. | 677.169 | 1 |
Construct and Interpret Graphs (Resource Book Only) eBook
Grade 6|Grade 7|Grade 8 6+ provides six activity pages in which students construct & interpret graphs in order to find answers to riddles and other problems. The unit also includes an assessment page in test-prep format. (Find other units by searching 'Data Analysis/Probability 6') | 677.169 | 1 |
220 Engineering Mathematics
Course Description
An examination of the major mathematical tools for engineers and scientists.
Learning Outcomes
andlt;BRandgt;Upon successful completion of this course, students will be able to: andlt;ULandgt;andlt;LIandgt;Understand major features of the graphs, expressions, polynomial equations, and partial fractions.andlt;/LIandgt;andlt;LIandgt;Apply trigonometric techniques for solving engineering problems.andlt;/LIandgt;andlt;LIandgt;Demonstrate knowledge of differentiation techniques and its applications for particular engineering applications.andlt;/LIandgt;andlt;LIandgt;Contrast integration and differentiation applications. andlt;/LIandgt;andlt;LIandgt;Understand differential equations and their applications up to the second order.andlt;/LIandgt;andlt;/ULandgt;
Understand major features of the graphs, expressions, polynomial equations, and partial fractions.
Apply trigonometric techniques for solving engineering problems.
Demonstrate knowledge of differentiation techniques and its applications for particular engineering applications.
Contrast integration and differentiation applications.
Understand differential equations and their applications up to the second order. | 677.169 | 1 |
2010Acceptable This is a good book, and this is a great deal on it! I ship fast, because I know you need the book! Save your money, and buy from The Deal Factory! We cannot ...guarantRead moreShow Less
Acceptable 2ndThe author team of Dave Sobecki, Angela Matthews, and Allan Bluman have worked together to create the second edition of Mathematics in Our World, an engaging text catered to the needs of today's liberal arts mathematics students. This revision focuses strict attention to a clear and friendly writing style, integration of numerous relevant real-world examples and applications, and implementation of the step-by-step approach used for years in Bluman's Elementary Statistics: A Step by Step Approach. The result is an exceptionally engaging text that is able to both effectively and creatively convey the basic concepts fundamental to a liberal arts math curriculum for even the most hesitant student.
Related Subjects
Meet the Author
Dave Sobecki was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, he walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, he came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. Dave has won a number of teaching awards in his career, and more recently has turned his attention to writing textbooks. Dave is in a happy place where his love of teaching meshes perfectly with his childhood dream of writing. He lives in Fairfield, Ohio with his lovely wife Cat, and fuzzy dogs Macleod and Tessa. When not teaching or writing, Dave's passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement. | 677.169 | 1 |
Syllabus of SA-II CBSE 8th Class
1.Algebraic expressions and identities-What are expressions, Terms, Factors and coefficients, Monomials, Binomials and polynomials, Like and unlike terms, Addition and subtraction of algebraic expressions, Multiplication of algebraic expressions: introduction, Multiplying a monomial by a monomial, Multiplying a monomial by a polynomial, Multiplying a polynomial by a polynomial, what is an identity, Standard identities, Applying identities,
Dear Shrikrishna
Kindly register yourself for 8th CBSE on
After that you have to upgrade your package from demo to gamma.
For more information, you can call on +919872201234. | 677.169 | 1 |
My nephew is 8 years old and shows great promise as a student. Sadly, as most of you know most programs in secondary education don't offer any foundational courses for higher mathematics. What books/online resources/programs do you recommend?
My introduction was Modern Algebra: An Introduction which I found very comprehensible (although the last chapter on coding theory isn't very good IMHO). It's at a very basic level and assumes little yet eventually gives the reader some nice machinery, such as Lagrange's theorem, Sylow theorems and basic Galois theory.
–
Alex Becker♦Mar 28 '12 at 22:26
5
Enzensberger's The Number Devil: A Mathematical Adventure. Martin Gardner's various collections, and Ian Stewart's. Abbott's classic Flatland. Newman's 4-vol. The World of Mathematics. In other words, a wide variety of accessible and engaging topics. Let him decide what he wants to get serious about, and when.
–
Brian M. ScottMar 28 '12 at 22:51
1
I second Brian M. Scott, but I would also recommend Proofs from the Book which may be a bit too hard, but there are some elementary and beautiful proofs. It happened for my friend that he learned a bunch of complex stuff all by himself, just to understand more proofs from the book ;-)
–
dtldarekMar 28 '12 at 23:29
1
K\h oMaL is the Hungarian math journal for young problem solvers that has been given to generations of the best Hungarian mathematicians. Your nephew probably won't be able to solve too many problems at first, but learning to struggle is part of the journey. You can find it in English here:
komal.hu/info/bemutatkozas.e.shtml
If it's too difficult, perhaps some other source of competition problems might be a good introduction.
–
Brett FrankelMar 29 '12 at 2:01
1
@arete: Has your nephew learned any high school algebra? In my case, before I learned some algebra (using library books when I was in the 8th grade; my school didn't offer algebra until 9th grade), what I could usefully read and understand was WAY WAY less than what was the case after I learned some algebra. Also, you say that he's 8 years old but then mention secondary education. In the U.S. that's a gap of 6 to 7 years, which is sufficiently large that the Johns Hopkins program for children extremely gifted in math might be interested.
–
Dave L. RenfroMar 29 '12 at 14:40 | 677.169 | 1 |
Student Activities
Mathematics is everywhere—not just in classrooms, textbooks, and calculators. The St. Bonaventure Department of Mathematics offers numerous activities to explore mathematics beyond the classroom.
Awards for Seniors The Department of Mathematics recognizes excellence among St. Bonaventure mathematics students with two awards: The Mathematics Award and the Myra J. Reed Award. Learn more
Bona's Bonus Problems are special mathematical challenges for Bona's students. When a student solves a Bona's Bonus Problem, his or her name will appear in a nationally published mathematics journal as a solver of the problem. Learn more
Challenge 24 Competition
Integral Day
MATHCOUNTS Contest
Mathematical Association of America The Department of Mathematics sponsors a student chapter of the Mathematical Association of America (MAA). The MAA is the world's largest professional society that focuses on undergraduate mathematics education. Learn more
Mathematical Contest in Modeling
Pi Day On March 14 (3.14), the Department of Mathematics celebrates the important and mysterious number pi with pie, pi-ounce bags of m&m's, Pi Day songs, a giant Pi Day display, finding your birthday in the digits of pi, and pi costume contest. Learn more
William Lowell Putnam Mathematics Competition The Putnam Competition is an annual mathematics competition open to undergraduates in the United States and Canada. Administered by the Mathematical Association of America, the Putnam is widely regarded as the most challenging undergraduate mathematics examination given in America. Learn more | 677.169 | 1 |
Math
The Mathematics Department's goal is to prepare all students to be mathematically literate at a college preparatory level. It is the objective of the department that students be able to successfully solve problems and express mathematical ideas in a clear, concise, and logical manner. Students should be able to conjecture, reason, draw logical conclusions, and generalize their results. In examination of problem situations, students should apply their mathematics to model practical situations. It is the goal of the department to meet the National Council of Teachers of Mathematics Standards for college bound students. These include: Mathematics as Problem-solving, Mathematics as Communication, Mathematics as Reasoning and Proof, Mathematical Connections, Mathematical Representations, Numbers and Operations, Algebra, Geometry, Measurement, Data Analysis, and Probability.
Courses utilize lecture, discussion, investigations, guided discovery and numerous hands-on activities. Students interact through group activity to make concepts meaningful and concrete. Assignments to reinforce these concepts are given in connection with each lesson. The assigned problems are checked and group work or teacher demonstration is used to clarify difficult problems. Technology (computers and calculators) is utilized at age-appropriate levels in the mathematics program | 677.169 | 1 |
t... MOREheir This package contains: Books a la Carte for Beginning Algebra: Early Graphing, Third Edition MyMathLab/MyStatLab Student Access Kit This package consists of the textbook plus an access kit for MyMathLab/MyStatLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online4.2 Solving a System of Equations in Two Variables by the Substitution Method
4.3 Solving a System of Equations in Two Variables by the Addition Method
How Am I Doing? Sections 4.1–4.3
4.4 Review of Methods for Solving Systems
4.5 Solving Word Problems Using Systems of Equations
Use Math to Save Money
Chapter 4 Organizer
Chapter 4 Review Problems
How Am I Doing? Chapter 4 Test
Math Coach
5. Exponents and Polynomials
5.1 The Rules of Exponents
5.2 Negative Exponents and Scientific Notation
5.3 Fundamental Polynomial Operations
How Am I Doing? Sections 5.1–5.3
5.4 Multiplying Polynomials
5.5 Multiplication: Special Cases
5.6 Dividing Polynomials
Use Math to Save Money
Chapter 5 Organizer
Chapter 5 Review Problems
How Am I Doing? Chapter 5 Test
Math Coach
6. Factoring
6.1 Removing a Common Factor
6.2 Factoring by Grouping
6.3 Factoring Trinomials of the Form x2 + bx + c
6.4 Factoring Trinomials of the Form ax2 + bx + c
How Am I Doing? Sections 6.1–6.4
6.5 Special Cases of Factoring
6.6 A Brief Review of Factoring
6.7 Solving Quadratic Equations by Factoring
Use Math to Save Money
Chapter 6 Organizer
Chapter 6 Review Problems
How Am I Doing? Chapter 6 Test
Math Coach
Cumulative Test for Chapters 0–6
7. Rational Expressions and Equations
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions
How Am I Doing? Sections 7.1–7.3
7.4 Simplifying Complex Rational Expressions
7.5 Solving Equations Involving Rational Expressions
7.6 Ratio, Proportion, and Other Applied Problems
Use Math to Save Money
Chapter 7 Organizer
Chapter 7 Review Problems
How Am I Doing? Chapter 7 Test
Math Coach
8. Radicals
8.1 Square Roots
8.2 Simplifying Radical Expressions
8.3 Adding and Subtracting Radical Expressions
8.4 Multiplying Radical Expressions
How Am I Doing? Sections 8.1–8.4
8.5 Dividing Radical Expressions
8.6 The Pythagorean Theorem and Radical Equations
8.7 Word Problems Involving Radicals: Direct and Inverse Variation
Use Math to Save Money
Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach
9. Quadratic Equations
9.1 Introduction to Quadratic Equations
9.2 Using the Square Root Property and Completing the Square to Find Solutions
9.3 Using the Quadratic Formula to Find Solutions
How Am I Doing? Sections 9.1–9.3
9.4 Graphing Quadratic Equations
9.5 Formulas and Applied Problems
Use Math to Save Money
Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
Practice Final Examination
Appendix A: Table of Square Roots
Appendix B: Practice with Operations of Whole Numbers
Appendix C: The Point–Slope Form of a Line
Solutions to Practice Problems
Answers to Selected Exercises
Glossary
Subject Index
Photo Credits
Index of Applications (Available in MyMathLab) | 677.169 | 1 |
Algebra and Trigonometry - 2nd edition
Summary: Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors commun...show moreicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics | 677.169 | 1 |
A+ National Pre-traineeship Maths and Literacy for Retail book by Andrew Spencer
Pre-traineeship Maths and Literacy for Retail is a write-in workbook that helps to prepare students seeking to gain a Retail Traineeship. It combines practical, real-world scenarios and terminology specifically relevant to the Retail Industry, and provides students with the mathematical skills they need to confidently pursue a career in the Retail Trade. Mirroring the format of current apprenticeship entry assessments, Pre-traineeship Maths and Literacy for Retail includes hundreds of questions to improve students' potential of gaining a successful assessment outcome of 75-80% and above. This workbook will therefore help to increase students' eligibility to obtain a Retail Traineeship. Pre-traineeship Maths and Literacy for Retail also supports and consolidates concepts that students studying VET (Vocational Educational Training) may use, as a number of VCE VET programs are also approved pre-traineeships. This workbook is also a valuable resource for older students aiming to revisit basic literacy and maths in their preparation to re-enter the workforce at the apprenticeship level.
Buy A+ National Pre-traineeship Maths and Literacy for Retail book by Andrew Spencer from Australia's Online Bookstore, Boomerang Books.
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In Workbook 10: Promoting Safety, the retail sales associate will learn how to report safety problems in the store or department, how to follow emergency procedures, and how to maintain accurate safety records. By ensuring the store is a safe place to work and shop, the sales associate can become an even more valuable and successful employee.
This insider's guide shares the secrets of successful eBay listings, explaining how to use templates for a signature look, automate listings with sales generators, tweak photos to display an item at its best, shoot difficult items effectively (such as jewelry, coins, and cars), and fine-tune item descriptions.
From his striking window displays during the holidays to his glittering love affairs with the most beautiful women in Europe, this book reveals the secrets behind his success as a tycoon. Filled with revolutionary thoughts about business, leadership, and society, Selfridge will inspire you with powerful aphorisms
Suitable for people who have considered owning a retail store but just don't know where to start, how much it would cost, whether it would be profitable and, most importantly, whether they would really enjoy it. This title also includes information on small retailer trends, retailing software, and online selling.
Books By Author Andrew SpencerHelps learners' improve their Maths and English skills and help prepare for Level 1 and Level 2 Functional Skills exams. This title enables learners to improve their maths and English skills and real-life questions and scenarios are written with an automotive context to help learners find essential Maths and English theory understandable Hairdressing context beauty therapy context | 677.169 | 1 |
From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students demonstrates that the efficiency of a river can be measured using the hydraulic radius; this depends on the cross-sectional area of the river and the wetted perimeter of the cross-section. Topic…
From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity shows that derivatives can help to manage risk. The market in derivatives has grown enormously in recent years. On average, speculators break even. The mathematical ideas covered are:
• Comparing a model…
From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity shows that it is not possible to be certain what the market will do next. The mathematical ideas covered are:
• Time series
• Percentage change
• Random walks
• Geometric mean
• Normal…
From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students shows how regular sampling of a variety of prices is used to get a measure of inflation. There is more than one possible way to do this. A measure of inflation is used to update pensions and…
From the Integrating Mathematical Problem Solving project by Mathematics for Education and Industry (MEI), this activity for post-16 students shows how modelling helps decision making by allowing us to see what is likely to happen. The mathematical ideas covered are:
• Modelling cycle
• Binomial probability model
• Expected…
From the Integrating Mathematical Problem Solving project by Mathematics for Education and Industry (MEI), this activity for post-16 students shows how money which circulates has a greater effect than could be expected. The activity starts by students predicting on what they will spend their wages when they get a job and, from that,…
From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity shows how compound interest can be calculated over different intervals. As the intervals get smaller and smaller, the total value approaches a limit. Topic areas covered are:
• Use of different time intervals…
These supplementary materials for discussing data contain full colour versions of the graphs and diagrams for all the activities in the Discussing Data Activity Book. The graphs and diagrams are split into the six areas described in the book .
Handling Data Reference provides supports for students on each of the steps either activity from the Nuffield Foundation shows students how to use a recurrence relation to work out how long it takes to pay off a credit card loan and how much it costs. They can use a graphic calculator or spreadsheet to do the working.
After working through the given example, where a customer spends £1250 and repays…
This resource from the Nuffield Foundation allows students to investigate relationships between anthropometric variables and write a report on their findings, which may include the use of scatter diagrams, lines of best fit, regression lines, and correlation coefficients.
The spreadsheet contains anthropometric data from a sample…
The Nuffield Foundation provide this activity for students to consider the difficulties in using real data, from the Department of Trade and Industry, to identify which sport is the most dangerous to participate in. The data includes the age and gender of patients requiring treatment at a sample of hospitals after suffering sports…
The Nuffield Foundation provide this resource which can be used to introduce the shape and main features of proportional, linear, inverse proportional, and quadratic graphs. Different versions of Excel spreadsheets allow students to explore how the shape and the position of a graph changes when the constants in its equation are altered.
Students…
The Nuffield Foundation provide this resource which enables students to carry out significance tests on proportions and test hypotheses about successful applicants to higher education.
The data provided on information sheet A is simulated but similar to real data available on the UCAS website.
Information sheet B outlines…
The Nuffield Foundation provide this resource where students use simulated stature data for men and women in eight countries to draw histograms and look for general results, as manufacturers need to take these into account when they design products.
This is mainly intended as an introduction to the normal distribution, but the…
The Nuffield Foundation provides this resource which shows students how, given a set of measurements along an irregular coastline, it is possible to approximate the area of land which is lost to coastal erosion over a period of time.
Coastal erosion A - this activity uses the context of coastal erosion to introduce the trapezium…
The Nuffield Foundation provides this activity which students use to create spreadsheets that model what would happen to the temperature of the Earth if there were to be a sudden change in the amount of radiation entering or leaving the planet. Students then investigate polynomial and exponential functions to find the best model.
Before…
The Nuffield Foundation provide this resource where students are shown how to draw and format cumulative frequency graphs in Excel, showing the hourly earnings of men and women, and then interpret their graphs. Students need to know how to draw cumulative frequency graphs by hand before attempting to draw them using a spreadsheet.
There…
This resource from the Nuffield Foundation provides the opportunity for students to fit functions to linear and quadratic graphs. It is assumed that students will already have some knowledge of linear and quadratic functions and their graphs, which are used to compare models and comment on their suitability. A slide show is included,These datasets from stats4schools are compiled from the responses given by over 1500 people to a survey. They are intended to be used flexibly but some ideas are given to guide students in their interrogations.
There are three sheets in each set
1. Decoded data
2. An explanation of the questions that were asked in the survey
3.…
Using this resource from stats4schools, students investigate TV viewing habits by interpreting data and graphs, manipulating data to answer questions and draw conclusions.
The resource includes a lesson plan, datasheet, questions sheet and dataset. | 677.169 | 1 |
This course examines an important and interesting part of the history of mathematics, and more generally, the intellectual history of human kind: history of mathematics in the Islamic world. Some of the most fundamental notions in modern mathematics have their roots in this part of the history such as the modern number system, the fields of algebra and trigonometry, and the concept of algorithm among others. In addition to studying specific contributions of medieval Muslim mathematicians in the areas of arithmetic, algebra, geometry and trigonometry in some details, we will also examine the context in which Islamic science and mathematics flourished, and the role of religion this development. The rise of Islamic science and its interactions with other cultures (e.g. Greek, Indian and Renaissance Europe) tells us much about the larger issues of humanities. Thus, this course has both a substantial mathematical component (~60-65 %) and a significant history and social science component (~35-40%), bringing together three disciplines: Mathematics, History and Religion. It is part of the Islamic Civilization and Cultures program, and fulfills the QR requirement. No prerequisite is needed beyond high school algebra and geometry, but a solid knowledge in algebra and geometry is needed. | 677.169 | 1 |
emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. | 677.169 | 1 |
Math Word Problems Demystified trouble with word problems? No problem! Math Word Problems DeMYSTiFieD, Second Edition explains, in simple terms, how to solve mathematical word problems. No longer will you panic at the concept of a train traveling at 65 miles per hour! Based on mathematician George Polya'¬"s proven four-step process for solving word problems, this book helps you master the basic procedures and develop a plan of action that can be used to solve word problems found in all mathematics courses. Detailed examples, concise explanations, and worked-out proble... MOREms make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. Math Word Problems DeMYSTiFieDfeatures: Refresher sections on decimals, fractions, percents, equations, systems of equations, and quadratic equations Coverage of 10 different types of word problems, focused on numbers, digits, coins, age, distance, finance, and other topics Chapter-opening objectives offering insight into what you'¬"re going to learn in each step Questions at the end of every chapter to reinforce learning and pinpoint weaknesses '¬SStill Struggling?'¬ icons providing specific recommendations for those having difficulty with certain subtopics A final exam for overall self-assessment '¬SCurriculum Tree'¬ that shows how the topic covered in the book fits into a larger curriculum It'¬"s a no-brainer! You'¬"ll learn about: Solving decimal and fraction problems; Solving percent problems; Solving proportion and formula problems; Equations and algebra representation; Solving number and digit problems; Solving coin and age problems; Solving distance and mixture problems; Solving finance, lever, and work problems; Systems of equations; Quadratic equations; Solving geometry, probability, and statistics problems The second edition of one of the most successful math word problems books on the market is updated with all-new quizzes and test questions, clearer explanations of the material, and a completely refreshed interior design. Your solution to MATH word PROBLEMS! Find yourself stuck on the tracks when two trains are traveling at different speeds? Help has arrived! Math Word Problems Demystified, Second Edition is your ticket to problem-solving success. Based on mathematician George Polya's proven four-step process, this practical guide helps you master the basic procedures and develop a plan of action you can use to solve many different types of word problems. Tips for using systems of equations and quadratic equations are included. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll learn to solve: Decimal, fraction, and percent problems Proportion and formula problems Number and digit problems Distance and mixture problems Finance, lever, and work problems Geometry, probability, and statistics problems Simple enough for a beginner, but challenging enough for an advanced student, Math Word Problems Demystified, Second Edition helps you master this essential mathematics skill. | 677.169 | 1 |
Arithmetic/Introduction to Arithmetic/How This Textbook is Organized
This textbook is organized by parts and then into sections and subsections. The parts get more advanced as you work through the textbook and the sections build off of one another until the reader has a substantial working knowledge of the material for that part of the textbook. Skipping any part of this textbook is not advised. | 677.169 | 1 |
...
Show More center when you can have your own personal math tutor at a fraction of the cost. Master the skills that will ensure success in algebra and beyond. Algebra is the gateway to more advanced math, science, and technology classes, which means it is the key to success in the 21st century. Make sure that you are ready! SETS, INTEGERS, POSITIVE AND NEGATIVE FRACTIONS AND DECIMALS, EXPONENTS, SQUARE ROOTS, ORDER OF OPERATIONS, PROPERTIES OF NUMBERS, SCIENTIFIC NOTATION, RATIOS AND PROPORTIONS, PERCENTS, NUMBER THEORY, NUMBER LINES, COORDINATE SYSTEMS, SLOPE OF A LINE, EQUATIONS, GRAPHING LINEAR EQUATIONS, ALGEBRA WORD PROBLEMS, PROBABILITY, STATISTICS, AND MUCH MORE.Excellent for summer. TRY OUR FREE iphone app, MATH EXPERT, from Math Essentials.net | 677.169 | 1 |
MAD 2104 DISCRETE MATHEMATICS
credits: 3
Prerequisite: MAC 2311 or consent of instructor. This course is designed for those students who are majoring in computer science, engineering, mathematics and other highly technical fields. Topics include formal logic, set theory, combinatorics, mathematical induction, relations and functions, recursion, and graph theory. 47 contact hours.
MAD 3107 DISCRETE MATHEMATICAL STRUCTURES
credits: 3
Prerequisite: MAC 2311 with a minimum grade of C or MAC 2311H with a minimum grade of C. This course is designed to give mathematics education majors a thorough understanding of the nature and importance of mathematical proof as well as provide knowledge of a variety of discrete mathematics topics. Topics include proofs and proof techniques, direct proof, proof by cases, proof using the contrapositive, proof by contradiction, proof by counterexample, mathematical induction, logical arguments, sets and relations including equivalence relations and partial orders, functions and their inverses and compositions, recursion and recurrence relations, probability, counting principles, permutations, combinations, graph theory, and trees. Special emphasis will be placed on mathematical reasoning. 47 contact hours. (Credit is not also given for MAD 2104.) | 677.169 | 1 |
Accelerated Precalculus Semester One
Common Core State Standards for Mathematics
Accelerated Precalculus S1 V04
FIF0912.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 26, 27, 28
Domain: Building Functions (FBF)
Learning Standard: Build a function that models a relationship between two quantities.
Test Questions
FBF0912.01 Write a function that describes a relationship between two quantities.★
Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
13, 14, 15, 16, 17, 18, 25
Learning Standard: Build new functions from existing functions.
Test Questions
FBF0912.0322, 23, 24
FBF0912.04 Find inverse functions.
Verify by composition that one function is the inverse of another.
Read values of an inverse function from a graph or a table, given that the function has an inverse.
Produce an invertible function from a non-invertible function by restricting the domain.
11, 19, 20, 21
FBF0912.05. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
29, 30, 31, 32, 33, 34, 35, 36, 37, 38
Domain: Trigonometric Functions (FTF)
Learning Standard: Extend the domain of trigonometric functions using the unit code.
Test Questions
FTF0912.03ines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.
39, 40, 41, 51, 52, 53
FTF0912.04 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. | 677.169 | 1 |
handbook is unusual in that it combines in a single volume formulas and tables from both elementary and advanced mathematics. For example, topics treated range from those in algebra, geometry, trigonometry, analytic geometry and calculus to Fourier series, Laplace and Fourier transforms, Bessel and Legendre functions and many other advanced special functions. Such topics are needed by both students and research workers in the fields of engineering, physics, mathematics and other sciences. [via]
More editions of Schaum's Outline of Mathematical Handbook of Formulas and Tables:
This Schaum's Study Guide is the perfect tool for getting a handle on statistics. Fully stocked with solved problemsÑ508 of themÑit shows you how to work problems that may not have been fully explained in class. Plus you get 694 additional problems to use for practice, with answers at the back of the book. Ideal for independent study, brushup before exams, or preparation for professional tests, this Schaum's guide is clear, complete, and well-organized. It even prepares you for computer solutions of statistical problems, fully explaining the use of Minitab, the most popular statistical software. It's the perfect supplement for any course in statistics, and a super helper for the math-challenged. [via]
Designed with live formulae, tables and graphs which engage the student and enhance understanding, this CD-ROM contains 100 solved problems. Each chapter ends with several related examples which reinforce and extend the material found in the printed book packaged with the CD. [via]
More editions of Schaum's Outline of Theory and Problems of College Algebra (Schaum's Outlines):
This book gives theory and solved problems for a combined course in probability and mathematical statistics. A calculus background is employed. The first half of the book itself serves as a supplement to the study of probability. [via]
More editions of Schaum's Outline of Theory and Problems of Probability and Statistics:
" updated, this second edition includes vital new coverage of order statistics, best critical regions, likelihood ratio tests, and other key topics. [via] | 677.169 | 1 |
From the Publisher:Description:
Homework Helpers: Algebra is a straightforward and easy to read
review of arithmetic skills emphasizes the role that arithmetic plays in the development of algebra covering all of the topics in a typical Algebra I class, including: Solving linear ...
Description:
1001 Algebra Problems offers those with math anxiety and others
who need tutoring the hands on practice they need. This useful manual providers users the tools they need to master algebra. This title helps users to prepare for exams, ...
Description:
A comprehensive math review for the GRE, GMAT, and SAT.
This math refresher workbook is designed to clearly and concisely state the basic math rules and principles of arithmetic, algebra, and geometry which a student needs to master. This ... | 677.169 | 1 |
Bulk pricing discounts
A Report to the Nation on the Future of Mathematics Education (1989)
Overview
Table of Contents
Overview
Authors
Mathematical Sciences Education Board and the Board on Mathematical Sciences, National Research Council
Description
Mathematics is the key to opportunity. No longer only the language of science, mathematics is now essential to business, finance, health, and defense. Yet because of the lack of mathematical literacy, many students are not prepared for tomorrow's jobs. Everybody Counts suggests solutions. Written for everyone concerned about our children's education, this book discusses why students in this country do not perform well in mathematics and outlines a comprehensive plan for revitalizing mathematics education in America, from kindergarten through college. single copy, $8.95; 2-9 copies, $7.50 each; 10 or more copies, $6.95 each (no other discounts apply)
Hyman Bass, Zalman Usiskin, and Gail Burrill, Editors, U.S. National Commission on Mathematics Instruction, Board on International Scientific Organizations, Policy and Global Affairs Division, National Research Council | 677.169 | 1 |
Geometry to Go: A Mathematics Handbook
Book Description: Geometry to go is the Latest in the series of mathematics handbooks and is a must-have resource for any student of geometry. From coordinate geometry to non-Euclidean geometry, from congruence to constructions, Geometry to Go is packed with numerous examples, detailed explanations, east-to-follow charts and graphs, and easy-to-understand proofs and theorems to help students learn, reinforce, and review key concepts
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05218260 the Philosophy of Mathematics (Cambridge Introductions to Philosophy)
This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and 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).Scientific Calculator .NET was designed to be a more functional alternative to the Windows Calculator. It features a natural readout, advanced mathematical functions (including integration and differential), and it doesn't have a huge screen footprint | 677.169 | 1 |
respected text makes extensive use of applications and features items such as historical vignettes to make the material useful and interesting. The text is written for the one-term analytic geometry course, often taught in sequence with college algebra, and is designed for students with a reasonably sound background in algebra, geometry, and trigonometry. | 677.169 | 1 |
Scientific Notebook is The Easy Solution for Teaching and
Learning Mathematics!
Scientific Notebook is ideal for reports, homework, and exams. With Scientific
Notebook, creating attractive documents that contain text, mathematics, and graphics is
seamless and easy.
Scientific Notebook: Quick, Clean, and Easy
Scientific Notebook is simple to use, yet powerful enough to facilitate teaching,
communicating, learning, and exploring mathematics in the classroom. It
is based on an easy-to-use word processor that completely integrates
writing mathematics in natural notation.
Entering text and mathematics in Scientific Notebook is so straightforward there is
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The software comes with reference manuals and an extensive online help system for creating
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provides reliable, prompt, free technical support.
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Scientific Notebook is supplied with two built-in computer algebra systems-MuPAD
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point-and-click interface.
You don't have to master complex syntax to be able to evaluate, simplify, solve, or plot
mathematical expressions. Full computer algebra capabilities are available. You can compute
symbolically or numerically, integrate, differentiate, and solve algebraic and differential
equations. With menu commands, you can create 2-D and 3-D plots in many styles and
coordinate systems; import data from graphing calculators; and compute with over 150 units
of physical measure.
In addition, you can use the Exam Builder provided with Scientific Notebook to construct
exams algorithmically and to generate, grade, and record
quizzes on a web server.
Work with "Live" Mathematics Over the World Wide Web
If you have Internet access, you can open the file at any URL address from inside the
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A simulation course for high school students
Computer simulation presents a variety of opportunities for high school students to receive exposure to mathematics and engineering in the real world. We describe in a highlevel way a course that uses computer simulation to enhance students' general modeling skills in probability and statistics, queueing models, financial engineering, and programming. Our experience has been that students can easily handle the material, and certainly seem to enjoy the experience. | 677.169 | 1 |
Singapore Math's Primary Math, U.S. Edition series features the Concrete> Pictorial> Abstract approach. Students begin by learning through concrete and pictorial means before moving into abstract thought and development, which encourages an active thinking process, communication of mathematical ideas and problem solving. Lessons are designed for a mix of teacher instruction and independent work, and students are encouraged to discuss ideas and explore additional problem-solving methods.
This set of textbooks and workbooks is designed specifically for U.S. students. Names, terms in examples, measurement, spellings, currency and other such elements have been changed to reflect American names and stylistic preferences. Review included. 104 pgs, non-consumable and non-reproducible. Paperback.
Higher grade levels lack Instruction
Date:May 2, 2013
Jina
Quality:
3out of5
Value:
4out of5
Meets Expectations:
2out of5
I grew up in Japan and Korea as a kid and love their education systems. As a homeschool parent, I am always looking for affordable curriculum. We are in middle school math now and have had to switch from Singapore Math not because of aging out, but because the books lack the instructions for how to do the harder math it assigns. We use the Textbooks, Workbooks, and Tests books as supplements now, and are using Lifepac math now, but we are still looking for any other math curriculum, our goal for University is Engineering so we want to be prepared.
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Review 2 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Wonderful Product for Math-Oriented Student
Date:March 16, 2011
melissa745
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
We have used several other math programs before coming to Singapore. This program is just what my daughter needs. It's fast-moving, with little review. It has challenging word problems that keep her thinking about number and how to manipulate them to get the answer.
She found most of the other programs dreadfully boring, but is excited every day when we pull out her math book.
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0points
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Review 3 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Date:June 25, 2010
D. D.
Excellent resource. We would give all the Singapore Math books 5 stars! The books are visually clear and easy to understand. I recommend taking the placement test to make accurate book selection. We did and ended up starting in a lower book that I thought we would, but quickly gained speed. Now our child is faster than a calculator and loves math!
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0points
0of0voted this as helpful.
Review 4 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Date:November 10, 2009
Michelle Wheeler
I've been homeschooling my son for three years (this is our fourth) and for the first time, my son loves doing his math work! Singapore gets 5 stars from me, and my son!
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Review 5 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
4out of5
Date:February 8, 2008
Donna L. Hogue
My daughter, who struggles learning her math concepts, loves this book. The lessons are short and very easy. I am so grateful to have found this book. She will be testing next month so this has come at just the right time. | 677.169 | 1 |
Math Secondary School Curriculum
Starting this year, the Math department is using the International Baccalaureate textbooks for the Middle Years Programme (MYP), grades 7 through 11, and the Diploma Programme (DP), grades 11 and 12. The IB Math curriculum incorporates a multiplicity of cultural and historical perspectives on mathematics.
Math 8: IB-MYP Level 3: This is the third book in our new Middle Years series for international schools which is a continuation of the algebraic, geometric, statistics and probability topics.
Math 9: IB- MYP Level 4: IB- MYP Level 4: This is the fourth book in our new Middle Years series for international schools which is a continuation of the algebraic, geometric, statistics and probability topics.
Math 10: IB- MYP Level 5: This course prepares students for an 'Applications' type of Mathematics course. It is an integrated curriculum that covers various topics in algebra, geometry, trigonometry, Probability and statistics. After 10th grade, the students are offered two tracks: IB Mathematics Studies, or IB Mathematics SL.
Math 11:IB Mathematics Studies SL 1 & 2: Is a two year course that the students take in 11th and 12th grade. This course caters to students with varied backgrounds and abilities. It is designed for students who do not anticipate a need for mathematics in their future studies. The course teaches various topics such as probability, statistics, algebra, trigonometry and financial mathematics.
Math 12:IB Mathematics SL 1 & 2: Is a two year course that is offered for students with sound mathematical background and prepares them for future studies such as chemistry, economics, and business administration. This course focuses on advance algebraic concepts like functions and equations, matrices, vectors, circular functions and trigonometry, statistics and probability, and calculus and its applications.
Science Secondary School Curriculum
Science 7: Life Science: An overview of biology. Topics covered include life characteristics, the cell, classification of living things, and genetics.
Science 10: Chemistry: An introduction to the study of the properties and changes in matter. Topics include classification of matter, chemical shorthand, structure of atoms and compounds, the mole, chemical reactions, solids, liquids, and gases. A special section on nuclear chemistry is included.
IB Biology SL 1 & 2: Is a two year course that the students take in 11th and 12th grade. It covers the relationship of structure and function at all levels of complexity. Students learn about topics such as cell theory, the chemistry of living things, and genetics. Students become aware of scientific studies and applications in the world around us.
IB Biology HL 1 & 2: Is a two year course that the students take in 11th and 12th grade. It offers an extensive study of topics in biology and it is equivalent to a college course of general biology. It covers all the higher objectives identified for the HL biology curriculum. It consists of topics such as cells, genetics, ecology and evolution, and human health and physiology. Throughout this challenging course, students become aware of how scientists work and communicate with each other. Students enjoy multiple opportunities for scientific study and creative inquiry within global context.
IB Chemistry SL:: Is a one year course offered as an elective for students in 11th or 12th grade. This course builds on students knowledge of chemistry in 10th grade and offers them opportunities to appreciate chemistry and its applications. It covers topics of general chemistry such as acids and bases, chemical equilibrium, oxidation reduction, bonding, and organic chemistry.
English Secondary School Curriculum
English 7 Literary Genres and Composition (MYP English A Level 2): The study of various literary genres and themes develops analysis and composition skills. Vocabulary, spelling, and grammar are integrated into the literary themes discussed. Oral presentation and collaboration figure prominently in learning activities and project assignments. Students are introduced to the research process. The focus genre is non-fiction.
English 8 Elements of Literature and Composition I (MYP English A Level 3): Literary elements are studied through theme-based units. The study of writing conventions continues to develop composition skills. Vocabulary, spelling, and grammar continue to be integrated into class work, homework, activities, and discussions. Skills in oral presentation and collaboration are further developed. Students begin to apply knowledge of the research process to create a final product. The focus genre is drama.
English 9- Elements of Literature and Composition II (MYP English A Level 4): Good literature enriches the learning community through inquiry and reflection. The writer communicates a message to the reader, and the reader makes meaningful connections across disciplines. Throughout the genres, there is analysis of literary work, and students come to appreciate the writer's craft and the creative uses of elements and structures. Employing various reading skills and strategies, the reader grasps thematic understandings and responds both orally and in writing. With communication established, the reader becomes the writer; genre choices are made, and a portfolio of creative writing is built. The focus genre is the novel.
English 10- Elements of Literature and Composition III (MYP English A Level 5): Students refine their skills in annotation of texts, oral presentation, and essay writing as they prepare to enter the Diploma Programme. The focus genre is poetry.
IB English 11:This course comprises the first year (Parts 1 and 4) of the two-year International Baccalaureate Diploma Programme English A1 course. During the first semester, students study world literature texts (texts in translation), and examine a variety of features common to literary prose and the effects they have on readers' construction of meaning. Second- semester texts center on the theme of Race and Identity, and include the study of different genres. For second semester, students choose to take either the higher level (HL) or the standard level (SL) course.
IB English 12:This course comprises the second year (Parts 2 and 3) of the two-year International Baccalaureate Diploma Programme English A1 course. During the first semester, students study one (SL) or two (HL) Shakespeare plays, along with texts of other genres, and intensify their study of literary features to prepare for rigorous oral assessments (the Individual Oral Commentary). Second- semester texts center on the genre of the novel. Students take two final written IB examinations in May of their senior year.
Drama 7: This course introduces students to the elements of acting and theatrical production. Students explore the purpose of theater, and learn how to work collaboratively in writing, acting in, and designing skits that have a clear message. Students learn to use correct stage vocabulary and to respond appropriately to theatrical work.
Theater Arts: Students explore theatrical production more in depth by staging a full-length work. Focus is on character analysis and development, correct use of stage vocabulary, and design elements of a production. Students also explore play-writing techniques, with each student writing an original ten-minute play.
Social Studies Secondary School Curriculum
In grades 7 through 11, Social Studies is offered in both English and Arabic.
Social Studies 7: Civics and World Geography:Civics studies the U. S. Constitution and the duties, rights, and privileges of citizens. World Geography studies the world's physical characteristics and the impact of human activity on the environment.
Arabic Social Studies 7: Geography and History:Geography studies the world's physical characteristics; History studies Islamic history from the beginning of Islam until year 40 of the Islamic calendar.
Social Studies 8: Ancient World History: A chronological survey of the development of civilization from the appearance of man to the Renaissance.
Arabic Social Studies 8: Geography studies the physical and human geography of countries with Islamic populations around the world; History studies the Omayaad Empire and the Abassid Empire.
Social Studies 9: Modern World History:A chronological survey of the development of civilization from the time of the Renaissance to the present.
Arabic Social Studies 9Geography studies the physical and human geography of Saudi Arabia and the continents of the world as well as demographic issues such as population increase and migration; History studies the history of Saudi Arabia and its kings.
Social Studies 10: Global Studies: An in-depth geography course emphasizing development and encompassing demographics, population growth, resources, economics, political activity, and cultural and religious systems.
Arabic Social Studies 10/11 Geography and History: Global Studies: Geography studies the geography of the Arabic World, as well as the world superpowers, and Islamic and World Organizations; History studies the lives of the Major Prophets and the life of the Prophet Mohammed.
Social Studies: Grades 11 & 12
IB 20th Century World History—Hl & SL: This course is an in-depth study of specific topics in World History: Communism in Crisis 1976-89 (addresses the major challenges—social, political and economic—facing the regimes in the leading Communist states from 1976 to 1989, and the nature of the response of these regimes); the Origins and Development of authoritarian and single-party states (studies the origins, ideology, form of government organization, and the nature and impact of various 20th century authoritarian and single party states); and The Cold War (addresses the East-West relations from 1945 and aims to promote an international perspective and understanding of the origins, course, and effects of the Cold War).
IB History of Europe and The Islamic World-SL: This prescribed subject covers the Arabian peninsula from the pre-Islamic period to the end of the "Rightly Guided Caliphs". It focuses on the economic, social, political and religious environments into which Muhammad was born, and then examines central issues such as the challenges Muhammad faced in establishing the early Islamic state, questions of succession, the imposition of Islamic rule within the peninsula, and the Arab armies' conquests of Byzantine and Sassanian provinces beyond it.
IB Psychology: HL & SL This course consists of the systematic study of behavior and the mental processes and examines the interaction of biological, cognitive, and socio-influences on human behavior by using an integrative approach. No prior study of psychology is expected and the skills needed for this course are developed within the course itself. Since IB Psychology is a part of the Group 3 subjects, students are given the opportunity to explore the interactions between humans and their environment in time, space, and place.
Art Secondary School Curriculum
Art 7:Introduction to Visual Arts: Students are exposed to a variety of media and are given lessons in drawing, color, painting tempera, watercolors, sculpture, architecture, three dimensional design, crafts, appreciation and aesthetics. This is a ten-week program.
Art 8:Visual Arts: The eighth grade art program progresses from the seventh grade program. The content objectives are similar, but the skills are more refined and the projects are more challenging.
Art Elective:Studio Art: This course offers advanced study in drawing and painting. The class begins by developing a foundation of exploratory experiences in drawing and in painting. This introduces the student to a wide range of experiences before he selects a particular medium for concentrated effort.
Art Elective:Ceramics: This course introduces the basics of working with clay. It includes hand-building using pinch, slab, coil, and drape technique. The students learn methods for hand-building clay objects, glazing and firing them.
Art Elective:Graphics Arts: This course is designed for students who desire to take advanced work in the area of printmaking. Graphic design is primarily concerned with designing and printing the yearbook.
IB Visual Art SL/HL: The Visual Arts Course Higher Level and Standard Level at the Islamic Saudi Academy is designed to meet the needs of a multicultural student body whose ethnicity is a unique association of students from America, Middle Eastern, African and European countries. The aims of the visual arts course at HL and SL are to enable students to investigate past, present and emerging forms of visual arts and engage in producing, appreciating and evaluating these. Students will develop an understanding of visual arts from a local, national and international perspective. Through this practice and investigation they will build confidence in responding visually and creatively to personal and cultural experiences. Students of the Visual Arts Course HL and SL will develop skills in, and sensitivity to, the creation of works that reflect active and individual involvement. Students will take responsibility for the direction of their learning through the acquisition of effective working practices.
The World-Class Instructional Design Assessment (WIDA) is used to assess speaking, listening, reading, and writing levels. All new students take a screener test (W-APT) to determine if they need ESL and the appropriate level. At the end of the year, all students take a benchmark test (WIDA-ACCESS) to measure progress made throughout the year. Students advance to the next level based on their WIDA test results as well as their teacher's recommendation. Feedback from mainstream content area teachers is also considered.
English as a Second Language, Level I: Fundamentals of language and structures are emphasized at this level. Students learn basic vocabulary and grammar tenses. Students learn to form a simple sentence and eventually a paragraph with a topic sentence and supporting details. Capital letters and punctuation are emphasized. We introduce listening and speaking by having students participate in discussions and stating needs. Students receive at least two classes a day in order to move up to the next level.
English as a Second Language, Level II: We read fiction and nonfiction for comprehension and discussion. Here we also start introducing reading strategies, such as prediction, visual cues, inferences, and using references. Then we move into analysis and expressing opinions. In writing we focus on spelling, writing complete sentences, and then paragraphs, all correctly punctuated. Then we move on to complex sentences and paragraphs that distinguish between the general and the specific.
English as a Second Language, Level III: We introduce more advanced themes in reading and comprehension, and we use these as a basis for discussion. Writing is also more advanced. It includes writing essays with a variety of themes and structures. We also introduce the students to basic research and writing longer essays.
English as a Second Language, Level IVIB English B- Diploma Programme, 11th Grade : This course focuses on language acquisition and the development of reading, writing, listening, and speaking skills. Topics include attitudes and values in relationships; effects of modern living; social, political and cultural change; humans and animals; technical and scientific developments. The required IB criteria for both oral and written skills are: Language, Cultural Interaction, and Message. Students take internally moderated oral exams in the early spring and externally moderated written exams in May.
IB English B- Diploma Programme, 12th GradeComputer Science Grade 7: Computer 7 is offered in conjunction with Art 7 and PE. The course is 9 weeks in length, and is followed by or preceded by 9 weeks of Art. The goal for this course is to provide students with the computer knowledge necessary to competently function in other classes, where computer use is required. Topics include: Keyboarding, File Management and Windows, Word Processing, Spreadsheets, Graphics – Using Paint and Print-shop.
Computer Science Grade 8: Computer 8 is offered in conjunction with Art 8 and PE. The course is 9 weeks in length, and is followed by or preceded by 9 weeks of Art. Topics include: Keyboarding, File Management and Windows, Word Processing using Word, PowerPoint, Spreadsheets, and Internet, Graphics, and Designing Web pages using Word. **Students taking Computer 7 and 8 are encouraged to take more advanced computer courses in high school, such as programming.
Grade 10 &11 & 12 Courses :
Computer Applications : This course gives students an extensive overview of computers and computer applications. The main topics of the course are computer vocabulary, spreadsheets, creating multimedia documents, such as web pages, PowerPoint presentations and desktop publishing documents, with an introduction to Database, in addition to some advanced skills in Word processing.
Web Page Design : The Web Design course gives students a solid foundation in good web design techniques. The course has three major components: using and editing graphics, learning html code, and using Dreamweaver MX to create web sites.
Programming I : In this introductory course, students learn to write well-documented, logically structured programs. They learn how the computer can be programmed to perform specific tasks. The course teaches students to solve problems through the use of flowcharts and algorithms. It provides students a chance to hone their analytical skills.
Programming II : Students continue to learn to write original, well-structured programs in the second part to the programming course. The problems given become increasingly more complex and require a deeper knowledge of programming structures. At the close of the course, students will have an extensive background in computer programming concepts and will be able to apply their skills to other programming languages and computer courses
Arabic for Middle and High School
Grade 7: Introduces students to formal linguistic knowledge of Arabic through reading and writing about scientific, literary, and cultural topics. | 677.169 | 1 |
Video Description: There is more than one type of integral in multivariable calculus. In this lesson, Herb Gross defines and discusses line integrals. He reviews integration with respect to a curve (line) as distinguished from an integral as an area computation (double ...
Video Description: Herb Gross illustrates the equivalence of the Fundamental Theorem of the Calculus of one variable to the Fundamental Theorem of Calculus for several variables. Topics include: The anti-derivative and the value of a definite integral; Iterated integrals. Instructor/speaker: ...
Video Description: With our knowledge of matrix algebra to help, Herb Gross teaches how to find the local maxima and minima of functions of several real variables. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross defines the directional derivative and demonstrates how to calculate it, emphasizing the importance of this topic in the study of Calculus of Several Variables. He also covers the definition of a gradient vector. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross discusses the topic of equations of lines and planes in 3-dimensional space. Topics include: The normal vector to a plane; Parallel planes; Equation of a plane; Equation of a line in space. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross describes the "game" of matrices — the rules of matrix arithmetic and algebra. He also covers non-singularity and the inverse of a matrix. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross shows examples of the chain rule for several variables and develops a proof of the chain rule. He also explains how the chain rule works with higher order partial derivatives and mixed partial derivatives. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross show how the chain rule is involved in finding some integrals involving parameters. He computes the derivatives of integrals with constant limits, as well as derivatives of integrals with variable limits of integration (chain rule). ...
Video Description: Herb Gross reviews the definition of vectors — objects that have magnitude, direction, and sense. He also defines equality of vectors, their components, and rules of arithmetic. Vector arithmetic shares many structural properties with scalar arithmetic including a zero ...
Video Description: Herb Gross teaches us how to calculate infinite double (multiple) sums (for topics in calculus of several variables). This topic is analogous to the use of infinite sums in calculus of a single variable. Instructor/speaker: Prof. Herbert Gross | 677.169 | 1 |
This second edition of the Math Workbook for ISEE, SSAT, & HSPT Prep: Middle School and High School Entrance Exams has been overhauled from the first edition to reflect the most up-to-date knowledge of the private school admissions exams, as well as to incorporate new insights gleaned by our experts as they used the first edition to prepare students for these exams.Here are some new features you will find in the second edition:* A more logical progression of concepts and exercises* Over 60 new practice sets covering basic arithmetic, algebra, geometry, and advanced topics.* Expanded sections specific to the ISEE and HSPT* An assignment planner to help students track their practice sets andMore... measure scores* A formula sheet containing the most vital math rules and information* A thorough explanation of the major differences between the ISEE, SSAT, and HSPT* Updated answer key with easier navigationThe philosophy of this math workbook remains the same as in our first edition; rigor and drill. Because these are the first tests that actively try to trick students at every turn, those who sit for these exams need reflexive familiarity with mathematical computation , problem types, and strategy. The entrance exams are the first standardized tests for which budgeting time is a significant issue. Students need to spend the majority of time on analysis, rather than computation, to avoid getting tricked. By building skills, speed, and confidence, we hope to eliminate anxiety and give students a solid foundation on which to build excellent scores. This book is intended as a supplement for our highly trained staff, so it does not include strategies. However, motivated students can use it successfully with occasional help from a teacher or parent. Each chapter is comprised of units, with each unit comprised of problem sets with difficulty increasing in a logically progressive manner. Students should do as many of the problem sets for each unit as it takes to achieve a 90% accuracy rate. As a general rule, students taking lower level exams should complete chapters 1-8, and stick to "basic" questions in chapters 9-16. Students preparing for high school entrance exams should go through the entire book.While private school entrance exam preparation is the primary purpose of this book, we recognize that it may serve other purposes as well. This book would be useful for anyone looking for a workbook that encompasses all fundamental math concepts up through an 8th grade math program.For further information about the book and our test prep offerings, check out our website at Education (c) 2012 | 677.169 | 1 |
More About
This Textbook
Overview
Get a good grade in your precalculus course with PRECALCULUS, Seventh Edition. Written in a clear, student-friendly style, the book also provides a graphical perspective so you can develop a visual understanding of college algebra and trigonometry. With great examples, exercises, applications, and real-life data--and a range of online study resources--this book provides you with the tools you need to be successful in your course.
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Meet the Author
David Cohen, a senior lecturer at UCLA, was the original author of the successful, well-respected precalculus series--COLLEGE ALGEBRA, ALGEBRA AND TRIGONOMETRY, PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, and PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.
The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire.
Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
Synopsis: | 677.169 | 1 |
MATH Developmental CoursesMAT-098 Algebra I, 3 credits
Topics in this course include a review of the basic concepts of arithmetic
and algebra with real numbers, solving first degree equations and inequalities of one variable, graphs
and equations of lines in Cartesian co-ordinates, simplifying algebra expressions with exponent rules
and properties, and operations on polynomials.
Prerequisite: By Placement
MAT-099 Algebra & Applications, 3 credits
This course consists of selected topics that include simplifying and
operations on algebraic expressions and solving equations involving polynomials, rational expressions,
and roots and radicals; and solving systems of linear equations and inequalities.
Prerequisite: MAT-098 or placement
MATH 100-Level CoursesMAT-106 Math for the Liberal Arts , 3 credits
Math for the Liberal Arts is an introduction to non-technical applications of mathematics in the modern world. The course is designed to cultivate an appreciation of the significance of mathematics in daily life and develop students' mathematical reasoning. Subjects include Quantitative Information in Everyday Life, Financial Management, Statistics, and Probability. OLD
Prerequisite: MAT-098 or By Placement
MAT-107 Quantitative Reasoning , 3 credits
This course is an introduction to non-technical applications of mathematics in the modern world. The course is designed to cultivate an appreciation of the significance of mathematics in daily life and develop students' mathematical reasoning. Subjects include Statistics, Probability, Exponential Growth, and Geometry.
Prerequisite: MAT-098 or By Placement
MAT-110 College Algebra, 3 credits
This course contains algebraic techniques, functions, and graphs which are essential in
order to understand and use higher level mathematics. Topics include solving equations and inequalities,
graphing equations and functions, identifying types of functions and characteristics of graphs, and solving
application problems.
Prerequisite: MAT-099 or By Placement
MAT-111 Pre-Calculus, 3 credits
This course is an introduction to algebraic techniques, functions and graphs which are
essential in order to understand and use higher level mathematics in courses beginning with calculus. Topics
include exponential, logarithmic, trigonometric, and inverse trigonometric functions.
Prerequisite: MAT-110 or placement
MAT-114 Elementary Statistics I, 3 credits
This course is designed for students who need an elementary knowledge
of statistics. The basic ideas of descriptive statistical methods are considered, including frequency
distribution, measures of location and variation. It also includes permutation, combination and rules of
probability, together with well-known probability distributions such as binomial, poisson, geometric,
hyper geometric and multinomial.
Prerequisite: MAT-110
MAT-115 Elementary Statistics II, 3 credits
This course is a continuation of MAT 114. Among the topics covered are estimation, hypothesis
testing, design of experiments, chi-square, analysis of variance, regression analysis, covariance
analysis, and nonparametric approaches. Emphasis will be placed on interpretation and use of the
computer software packages. Prerequisite: MAT-114
MAT-117 Finite Mathematics, 3 credits
This course is designed for students in the Social Sciences, The goal of
the course is to give the student a working knowledge of the areas of mathematics that are most
applicable to his or her particular discipline. Among the topics studied will be elementary matrix
algebra, linear programming, logarithms, progressions, and the mathematics of finance.
Prerequisite: MAT-110
MAT-120 Calculus for Life Science and Social Science Majors, 4 credits
This course studies differential and integral calculus with a focus on its
applications to business and economics. Topics to be covered are increments and rates, limits, the
derivative, rules of differentiation, logarithmic differentiation, methods of integration, and applications
of the definite integral to business and economics.
Prerequisite: MAT-117
MAT-121 Calculus I, 4 credits
This is the first course in the calculus sequence designed for students intending to major in mathematics, the natural sciences, and engineering. The topics covered will include: limits and continuity; derivatives rules of algebraic, trigonometric and inverse trigonometric, exponential and logarithmic functions; extreme values and graphing of functions; and applications to optimization, related rate, and initial value problems.
Prerequisite: MAT-111
MAT-122 Calculus II, 4 credits
This is the second semester course in the Calculus sequence designed for students intending to major in mathematics, natural sciences, and engineering. The topics covered will include: integration, geometrical applications, integration techniques, and infinite series.
Prerequisite: MAT-121
MATH 200-Level CoursesMAT-210 Foundations and History of Mathematics ,120 or MAT-221
MAT-211 College Geometry,121 and MAT-213
MAT-212 Mathematical Modeling, 3 credits
This course is an introduction to the development and study of mathematical models. It is
designed in such a way that students from other disciplines will find it useful as a summary of
modern mathematical methods, and mathematics majors will benefit from applications of
mathematics to real life problems. Undergraduate students from the Natural and Social Sciences
will find most of the material accessible because the prerequisite is basic calculus. Prerequisite: MAT-120 or MAT-121
MAT-221 Calculus III, 4 credits
This is the third course in the Calculus sequence designed for students intending to major in mathematics, natural sciences, and engineering. The topics covered will include: power series, parametric equations, polar co-ordinates, vector calculus, partial derivatives, multiple integrals, and applications.
Prerequisite: MAT-122
MAT-222 Differential Equations, 3 credits
Topics include solution methods and applications of first order differential equations, solution of higher order differential equations using the characteristic equation, the undetermined coefficients and variation of parameters methods, existence and uniqueness theorems for initial value problems, and Laplace transforms.
Prerequisite: MAT-122
MAT-240 Combinatorics, 3 credits
Combinatorics is frequently described as the mathematics of "counting without counting." It has
a wide variety of applications in computer science, communications, transportation, genetics,
experimental design, scheduling, and so on. This course is designed to introduce the student to
the tools of Combinatorics from an applied point of view. Prerequisite: MAT-099 or MAT-110
MATH 300-Level CoursesMAT-310 Methods of Teaching Mathematics, 3 credits
This course is a study of strategies, techniques, materials, technology, and current research used in the teaching of mathematical concepts to high school students. Students will review the traditional and contemporary standards involved in teaching mathematics at the secondary school level; develop an awareness of the professional resources, materials, technology and information available for teachers; prepare unit and lesson plans with related assessment procedures on a variety of topics; and acquire teaching experience by taking part in individual tutoring, observation at a high school, and/or presenting lessons at the appropriate level.
Prerequisite: Junior Education MajorCo-requisite: MAT-211
MAT-313 Numerical Methods, 3 credits
Modern computational algorithms for the numerical solution of a variety of applied mathematics problems are considered. Topics include numerical solution of polynomial and transcendental equations, acceleration of convergence, Lagrangian interpolation and least-squares approximation, numerical differentiation and integration.
Prerequisite: MAT-122 and CSC-158
MAT-325 Modern Algebra I
This course covers the following topics: set theory, functions and mappings, permutations, theory of groups, rings and ideals, homomorphisms, integral domains and fields.
Prerequisite: MAT-213 and MAT-214
MAT-341 Mathematical Statistics I, 3 credits
This is a first course in a year-long sequence designed for Mathematics majors. The topics include the algebra of sets, probability in finite sample spaces, random variables and probability functions, including the mean, variance, and joint probability functions, the binomial distribution, and applications.
Corequisite: MAT-221
MAT-342 Mathematical Statistics II, 3 credits
This is the second course in a year-long sequence designed for Mathematics majors. The topics include distribution of random variables, conditional probability and stochastic independence, special distributions including the (t) and (F) distributions, moment generating techniques, limiting distributions, and the central limit theorem.
Prerequisite: MAT-341
MATH 400-Level CoursesMAT-400 & 401 Topics in Mathematics I & II, 3 credits each
These courses cover various topics chosen by the faculty as being of interest to current students in the Mathematics program.
.
Prerequisite: Permission of the instructor
MAT-421 Analysis I, 3 credits
This course is designed as an introduction to the rigorous development of the fundamentals of analysis. The following topics will be covered in this course: analytic and algebraic structure of the set of real numbers, sequences and series of real numbers, limits and continuity of functions.
Prerequisite: MAT-213 and MAT-221
MAT-422 Analysis II, 3 credits
This is the second semester course in a one-year sequence that is designed as a rigorous development of fundamentals of analysis for Mathematics majors. The following topics will be covered in this course: differentiation of functions, integration of functions, infinite series, and sequences and series of functions.
Prerequisite: MAT-421
MAT-423 Introductory Complex Variables I, 3 credits
Topics include complex numbers, analytic functions, contour integration, residues, and power series.
Prerequisite: MAT-221
MAT-475 Seminar I, 3 credits each
This course will focus on involving students in independent projects dealing with current topics or research interests in higher Mathematics. Students will be required to conduct a literature survey, carry out independent investigations projects, prepare a report, and defend their work in an oral presentation.
Prerequisite: Junior or Senior Math Major
CSC 100-Level CoursesCSC-151 Computer Applications, 3 credits
This course is designed to give the students an introduction to applications of computers in the area
of spreadsheets, database management, presentation, structured programming, and web programming.
Desktop software such as Microsoft office as well as a programming language compiler will be utilized
in this course.
Prerequisite: MAT-098 or placement
CSC-152 Introduction to Programming, 3 credits
This introductory programming course is designed for non-computer science majors.
This course introduces the student to principles of computer programming via a visual programming language.
The students will learn to create graphical user interface forms and apply visual programming to problem solving.
Topics will include basic control statements. Event-driven programming will be an integral part of the course.
Prerequisite: MAT-098 or placement
CSC-158 Computer Programming I, 3 credits
This course is the first course in a year- long sequence required for Computer Science majors. It
introduces the student to principles of computer programming via a structured programming
language. The students will write, test, and debug a wide variety of problems drawn from several
disciplines. The course will also address program design and program style. Prerequisite: MAT-110
CSC-159 Computer Programming II, 3 credits
This course is a continuation of CSC-158. The students will use a structured programming
language in problem solving. This course examines advanced features of programming
languages. Topics include file processing, and object oriented and event-driven programming.
As a preparation for CSC-254, this course will also include an introduction to data structures
such as queues and stacks. Prerequisite: CSC-158
CSC 200-Level CoursesCSC-201 Web Programming, 3 credits
This course is an introduction to web design with an emphasis on the scripting languages.
Both server-side and client-side scripting will be studied. HTML programming is an integral
part of the course. Topics include database processing for the web using SQL language and
Internet security.
Prerequisite: CSC-158
CSC-202 Introduction to Computer Animation, 3 credits
This is course is a study of the art and science of computer animation. Both programming and
utilization of animation software will be covered with an emphasis on the latter. The topics
include NURBS and Polygon modeling, rendering techniques, motion path, and introductory applications
of mathematics and algorithms in computer gaming.
Prerequisite: CSC-159
CSC-254 Data Structures, 3 credits
This course will focus on algorithms, analysis, and the use of basic and advanced data structures.
Among the specific data structures covered are strings, stacks, records, linked lists, trees and
graphs. Recursion will also be covered. Sequential and random files, hashing and indexed
sequential access methods for files will be discussed. Finally, some standard computer science
algorithms (sorting and searching) will be discussed. Prerequisite: CSC-159
CSC-290 Special Topics, 3 credits
Computer Scince department may occasionally offer special courses of interest such as COBOL. This course can count as a general elective course toward 120 crredits, but it may not count toward the CSC major curriculum requirements.
CSC 300-Level CoursesCSC-353 Computer Organization and Assembly Language, 3 credits
This course is intended as a first introduction to the ideas of computer architecture-both hardware
and software. Assembly language programming is the central theme of the course. The attributes
and operations of a macro assembler are discussed in some detail. Prerequisite: CSC-254
CSC-354 Database Management, 3 credits
This course will introduce students to the principles of single and multiple applications of database systems.
In addition, it will develop graphical and logical skills that are used to construct logical models of information
handling systems. Topics include normalization and removal of data redundancies, insertion, deletion, and update
anomalies; logical and physical views of data, the entity-relationship model, data description and data
manipulation languages, relational, hierarchal, and network approaches, as well as data security and integrity
and database processing for the web. Prerequisite:CSC-254
CSC-355 Operating Systems, 3 credits
An operating system is a program that acts as the link between the computer and its users. A well
written operating system makes it easy and fun to use a computer. This course will introduce the
student to the principles and concepts of operating systems design, discuss major issues of
importance in the design, and show how different widely used operating systems have
implemented the design ideas. In short, this course will teach what operating systems does, how
it may do it, and why there are different approaches. Prerequisite: CSC-254
CSC-357 Computer Architecture, 3 credits
This course is intended to explore the interface between a computer's hardware and its software.
The interface is often called computer architecture. Starting from the basic ideas of assembly
language programming, this course will give the students an idea of where the software stops and
the hardware begins, and what things can be done efficiently in hardware and how. Prerequisite: CSC-353
CSC-358 Artificial Intelligence, 3 credits
This course is intended to explore the ideas and developments in Artificial Intelligence. Artificial intelligence algorithms in pattern recognition, game playing, image analysis, and problem solving will be covered.
Also included among the topics are rule-based expert systems, fuzzy logic, neural networks, and learning systems. Prerequisite: CSC-254
CSC 400-Level CoursesCSC-451 Computer Simulations 3 credits
This course demonstrates to the student how computers may be used to represent selected
characteristics of real world systems by utilizing mathematical models. The simulation projects
will be done using a simulation software package and a structured programming language.
Statistical analyses are carried out. Prerequisite: CSC-254
CSC-452 Computer Graphics 3 credits
This course develops and applies the mathematical theory of computer graphics. The theory
includes rotation, translation, perspective projection, and curve and surface description. The
course will use a structured programming language. In addition, it will use available commercial
graphic packages. Prerequisite: CSC-254 and MAT-122 and MAT-213
CSC-454 Software Engineering 3 credits
This course will introduce the student to the principles and techniques involved in the generation
of production quality software items. The emphasis will be on the specification, organization,
implementation, testing and documentation of software products. Prerequisite: CSC-254
CSC-455 Mathematical and Statistical Software 3 credits
This course will introduce the student to the currently available mathematical and statistical
software on personal computers in particular, and mainframes in general. Hands-on activities
with software items will form a major part of the course. The student will be trained not only to
use the software items, but also interpret the results meaningfully as related to specific
applications situations. The course is designed primarily for students interested in scientific and
statistical computing and analysis. Report writing will be required on all projects. Prerequisite: CSC-159 and MAT-117
CSC-456 Operations Research 3 credits
Operations Research is a very important area of study which tracks its roots to business
applications. It combines the three broad disciplines of Mathematics, Computer Science, and
Business Applications. This course will formally develop the ideas of developing, analyzing, and
validating mathematical models for decision problems, and their systematic solution. The course
will involve programming and mathematical analysis. Prerequisite: CSC-151 and MAT-117
CSC-498 & 499 Topics in Computer Science I & II, 3 credits each
This course will focus on involving students in independent projects dealing with current topics
of current research interest in Computer Science. Students will be required to conduct a literature
survey, carry out independent investigations projects, prepare a report, and defend their work in
an oral presentation. Prerequisite: Senior Status in Computer Science
Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this site. Also, please forward suggestions about this page to [email protected]. | 677.169 | 1 |
Saxon Math 76: Third Edition
You have chosen the Dr. Aarsma's Saxon Math 76: Third Edition Checker. This Checker
is designed to be used with the following set of
three books.
1. Student Textbook
Saxon Math 76: Third Edition
Student Textbook
ISBN:1-56577-153-2
The Student Textbook is divided into 138 lessons, all of which are included in the
Checker. The textbook also contains 6 investigations, supplemental practice problems for remediation, an illustrated
glossary, and a comprehensive index.
2. Homeschool Packet
Saxon Math 76: Third Edition
Homeschool Packet
ISBN:1-56577-156-7
The Homeschool Packet contains step-by-step solutions for all test questions and answers
for textbook questions. This booklet also contains the answers for all supplemental materials.
3. Test Forms
Saxon Math 76: Third Edition
Test Forms
ISBN:1-56577-157-5
The Test Forms booklet provides all the worksheets and tests needed by one student to complete the program. There are 28 tests,
all included in the Checker. There are a large number of Facts Practice worksheets. We recommend use of Dr. Aardsma's Math Drill (see link in navigation bar at left) in place of these worksheets.
The booklet also contains optional student answer forms. | 677.169 | 1 |
Physics for High School Students
If you are look at this page now, you are probably a high school student looking for help in physics.
You probably studied other sciences before physics such as biology and chemistry but have never encountered any other science subject that was this math intensive.
Well have no fear!
This Fizzics Fizzle intermediate level physics guide will help you along with some of those difficult problems.
This section assumes that you have a basic background with algebra and trigonometry and that you have the basic knowledge covered in our beginner's guide.
So why is physics so math intensive anyway?
Biology describes life functions; chemistry describes the interaction of matter; but physics describes the fundamental mechanisms of the universe.
These mechanisms, such as why objects fall and why we have electricity, are based on mathematics.
In addition, these mechanisms are the same no matter where you are, whether on earth or on some distant planet across the universe.
Physics tries to descibe all interactions using pure mathematics. | 677.169 | 1 |
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