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Students should be familiar with algebraic manipulation, graphical representation of data (including logarithmic scales) and simple calculus. They should be able to use Microsoft Excel for data analysis (including some basic statistics, i.e., mean, mode, standard deviation). |
Classification
geometry lesson from Illuminations presents the Triangle Classification problem. Students will attempt to classify the triangles formed in a plane when a randomly selected point is connected to the endpoints of a given line segment. Students should have access to a computer with internet access for the lesson. The material is intended for grades 9-12 and should require 1 class period to complete.Wed, 29 Dec 2010 03:00:02 -0600Wallpaper Groups: The Discontinuous Groups of Rotation and Translation in the Plane
undergraduate tutorial on wallpaper groups, with illustrations of the 17 wallpapers groups and a wallpaper gallery. Technically, the derivation of all discontinuous groups of rotation and translation in the plane. Contents include: Some Theorems on Rotation and Translation; The Discontinuous Groups of Rotation and Translation in the Plane; Derivation and Classification of Groups; Appendix: The 17 Wallpaper Groups (with a Wallpaper gallery); and References and Related Web Sites. Hosted by the Math Forum.Thu, 4 Dec 2008 03:00:01 -0600Mathematics and Student Life Skills
course, designed for Miami Dade Community College, integrates arithmetic and beginning algebra for the undergraduate student. By applying math to real-life situations most students experience during college, the instructors attempt to make math both fun and applicable. The instructors specifically wish to dissipate the anxiety many college students feel when approaching math at an advanced level. Students can use the information provided on this website to help apply mathematical concepts to their own lives, while instructors can use the assignments, syllabus, and lecture notes to create their own relevant assignments in a mathematics course.Mon, 5 May 2008 03:00:13 -0500Episodes in the History of Geometry through Models in Dynamic Geometry
dynamic models to explain different aspects of geometry can be a powerful pedagogical tool. This is exactly what inspired Eduardo Veloso and Rita Bastos to write this classroom exercise for the Mathematical Association of America's "Convergence" site. In this exercise, mathematics educators will receive an introduction to several key aspects of the history of geometry through four examples. These examples include Albrecht D�rer's double projection and Piero della Francesca's perspective image. After reading the background essays on these projections, users can download the dynamic versions of these constructions for their own use and edification. It is worth noting that several of the constructions are available in French. Geometer's Sketchpad is required to view the files.Fri, 18 Jan 2008 03:00:02 -0600Geometry Formulas and Facts
and updated excerpts from the 30th Edition of the CRC Standard Mathematical Tables and Formulas. Covers all of geometry, minus differential geometry. Very complete collection of definitions, formulas, tables and diagrams, divided into two- and three- dimensional geometry, and further into 16 subdivisions such as transformations, polygons, coordinate systems, isometries, polyhedra and spheres.Fri, 7 Dec 2007 03:00:01 -0600BitArt - Spirolateral Series
on a spirolateral in one of these galleries to display a full-size version; see a self-running demonstration of a variety of spirolaterals, or generate one of your own and see all the reversals. "The Art of Spirolateral Reversals," a paper available in PDF format, "continues an investigation into spirolaterals as geometry to generate artistic forms of unexpected complexity and beauty... with two-dimensional representations of spirolaterals and its forms based on reversals of turns. Using mathematical and computer-based methods, issues of closure, variation, enumeration, and predictability are discussed. The overriding interest is to develop methods and procedures to investigate geometry for the purpose of inspiration for new architectural and sculptural forms."Fri, 30 Nov 2007 03:00:02 -0600Illusions of Depth (Elementary Art Lessons, Arts Wire)
3rd grade lesson plan on "Seeing Near and Far": students learn how overlapping and size differences show perspective, and that on a level surface, the lowest part of a near subject is lower in a picture than the lowest part of a farther subject, recognizing which objects in a picture are near and which are far. This is an introduction of the concept of the illusion of depth on a two-dimensional surface.Thu, 29 Nov 2007 03:00:02 -0600Maths Online Gallery
by the University of Vienna's futureMedia initiative, the Maths Online Gallery consists of a large collection of extremely useful interactive learning units that demonstrate mathematical concepts. A large number of interactive modules exist in such areas as analytic geometry, trigonometric functions, probability and statistics, integration, Fourier series, as well as model-building and simulation. The gallery was started in 1998 and new learning units are being continually added. This is an especially good resource for college and university teachers looking for in-class interactive illustrations of a large array of basic and advanced mathematical concepts.Wed, 14 Nov 2007 03:00:01 -0600 |
Differential Equations
9780495012658
ISBN:
0495012653
Edition: 3 Pub Date: 2005 Publisher: Thomson Learning
Summary: Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topi...cs that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.
Devaney, Robert L. is the author of Differential Equations, published 2005 under ISBN 9780495012658 and 0495012653. One hundred twenty one Differential Equations textbooks are available for sale on ValoreBooks.com, and twelve used from the cheapest price of $26.95.[read more |
0055720 / ISBN-13: 9780870055720
Mathematics for Retail Buying
The top-selling introductory retailing textbook/workbook, through four highly successful editions, has been revised. This popular classic text meets ...Show synopsisThe top-selling introductory retailing textbook/workbook, through four highly successful editions, has been revised. This popular classic text meets the needs of students who will be directly or indirectly involved in the activities of merchandising and buying at the retail level. Tepper continues to delineate the essential concepts, practices, procedures, calculations, and interpretations of figures that relate to the many factors that produce profit. She also describes the place of computers in retailing, updates MOR figures, and adds case studies. Clear instructions, multiple practice problems, and current terminology and data make this the best retail buying math book available. New to This edition: -- A chapter describing the impact of computer technology on the growth of retailing, the cardinal principles of successful merchandising, the role of computers in retailing, the functions of buying, the circular nature of the merchandising process, and the responsibilities of the buyer -- Provides a "road map" of the mathematical factors in the text -- Numerous work and practice problems test the understanding of fundamental principles -- Three-hole punched text pages allow students to interweave review problem answers with the text statement of the review problems -- Additional case studies utilizing practical retailing situations and difficulties in real-life merchandising -- Selected answers at the back of the book |
Description
A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.
The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.
What's New in the Second Edition: # Contains extra material concerning prime numbers, forming the basis for data encryption # Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics # Discusses Permutations and their importance in many topics in discrete mathematics
The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability Concise Introduction To Pure Mathematics |
Math books, math education
Discuss about math education in the U.S or in whatever your country is.
Let me start, my favorite math book is College Algebra by Murray R. Spiegel (from Schaum's outline series). It is the most complete book in terms of exercises and detailed solutions, I just love it.
About math education, I heard there is (or was recently) a crisis in the US, and that Danica Mckellar's books were a response to it, to help it, and also to diminish the gender gap in math. Here's her first book |
Roads to Geometry
9780130413963
0130413968
Summary: Clarifying, extending and unifying concepts discussed in basic high school geometry courses, this text gives readers a comprehensive introduction to plane geometry.
Wallace, Edward is the author of Roads to Geometry, published 2003 under ISBN 9780130413963 and 0130413968. Six hundred seventy Roads to Geometry textbooks are available for sale on ValoreBooks.com, one hundred twenty six used from the cheapest p...rice of $62.26, or buy new starting at $98.00Pages have significant wear and cover is damaged. May have writing and highlighting throughout. All pages are intact. This item contains a significant amount if highlighting. [more]
Pages have significant wear and cover is damaged. May have writing and highlighting throughout. All pages are intact. This item contains a significant amount if highlighting. The cover is creased on this item. This item has minimal damage that does NOT affect text. Please note: This item is the textbook ONLY. Any access codes and CDs are NOT guaranteed. We ship daily Monday-Friday![less]
This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a h [more]
This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a historical context. Chapter topics include axiomatic sy |
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Precalculus
Start off with a review of algebraic operations and linear and polynomial equations, then jump ahead into solving and graphing equations from linear and polynomial to exponential and logarithmic functions. Tackle trigonometric expressions and functions, learn how to model and solve applications using linear systems, and take on geometric sequences. By the time you're done, you'll be ready for the challenges of General Calculus I. |
Occidental CalculusThere will be an emphasis on having fun, so puzzles and games, and real-world problems, will be used as instruction tools. No homework will be assigned. Struggling students will improve their grades.
...Building confidence in the concepts introduced here and the ways to express them is critical. Understanding Precalculus and Trig concepts need not be daunting. They can be explained in simple terms and there are ways to remember key concepts |
Cheat Sheet
Calculus For Dummies
Calculus requires knowledge of other math disciplines. To make studying and working out problems in calculus easier, make sure you know basic formulas for geometry, trigonometry, integral calculus, and differential calculus.
Formulas You Need to Know for Calculus
When 'studying calculus, you should have a good understanding of the following tables of formulas so you can efficiently and correctly solve calculus problems:
Groovy geometry table
Use this geometry table to deal with shapes, lines, points, and planes.
Trippin' trig table
This trigonometry table will help you deal with triangles, finding their relationships between the sides and angles of right triangles, and make calculations based on these relationships.
Dandy derivative table
This table is helpful for finding things like velocity and acceleration, the slope of a curve, and finding maximum and minimum values (optimization), when you're dealing with differential calculus.
Handy-dandy integral table
If you're studying integral calculus, this integral table will help you to work out complex calculations involving area, volume, arc length, center of mass, work, and pressure. |
The Number System (Dover Books on Mathematics)
Book Description: The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant |
Subject: Mathematics (9 - 12) Title: Know Your Limits Description: The limit is the fundamental notion of calculus. This underlying concept is the thread that binds together virtually all of the calculus studied by the student. In this lesson, the student's knowledge of limits will be extended using some common language and illustrated ideas through simple examples. The concept of limits will be used to describe functions with specific properties. Additionally, the concept of a limit function is further developed, and theorems for limits are analyzed and applied. Students will refer to these rules as they work through exercises.
Thinkfinity Lesson Plans
Subject: Mathematics,Science Title: Northwestern Crows the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics,Science Title: Whelk-Come to MathematicsAdd Bookmark Description: In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea Students investigate the relationship between the height of the drop and the number of drops. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Limits Add Bookmark Description: This student interactive, from an Illuminations lesson, allows students to see a representation of three geometric series and the harmonic series. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics,Science Title: Conduct an Experiment whether the crows minimize their work by dropping whelks as they do. The amount of work depends upon the height of the drop and the number of times the crow has to fly to this height. To answer the question, students explore the relationship between the height of the drop and the number of drops needed. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
Abstract Algebra - 3rd edition
Summary: Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their ...show moreinterplay lead to powerful results and insights in a number of different settings45 +$3.99 s/h
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Payless Textbook Rowland Heights, CA
Brand new, hardcover. Isbn: 9780471433347, receive the book in 2-5 days
$88.29 +$3.99 s/h
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mermaidbookstore Cupertino, CA
0471433349 HARDCOVER. NEW. Never used. We do not ship to PO Box/APO/FPO addresses.
$94.50 |
This is a free mathematical calculator, which is able to add, subtract, multiply and divide numbers in binary format (used in computers).
Any number can be represented by any sequence of bits (binary digits), they are commonly written using the symbols 0 and 1.
Best math tool for school and college! If you are a student, it will helps you to learn arithmetics for computer science and electrical engineeringMay 19 2013 internet connection issue solved!!!!
IMPORTANT There is no virus on this app, what some programs are detecting as virus is just ads. You can confirm this using Kaspersky antivirus.
BinaryCC is a great simple app that allow you to convert from and to BIN, HEX, DEC, OCT. It's also a simple calculator.
Note: -The internet and network permission are for the Ads -The Ads supports the developers to keep this app free for you.
Features: -Instantly convert to BIN,HEX, DEC and OCT with just one input. -Automatically block the buttons acording to the base you are using (only in touchscreen phones). -Simple calculator (+, -, *, /) for all the basesThis free app is a math calculator, which calculates the values for the most important trigonometric functions, like: Sine, Cosine, Tangent, Arcsine, Arccosine, Arctangent.
Best math tool for school and college! If you are a student, it will helps you to learn geometry!
Note: Trigonometric functions are used for computing unknown lengths and angles in triangles (in navigation, engineering and physics). A common use in elementary physics is resolving a vector into Cartesian coordinates. The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillatorsThis free math app is a statistical calculator with various functions:
- Statistics: You are able to calculate the mean, median, variance, maximum and minimum for a set of numbers.
- Statistical Distributions: You are able to calculate the values of different Statistical Distributions. The following distributions are available: Binomial Distribution, Normal Distribution, Students t-Distribution, F-Distribution, Exponential Distribution, Poisson Distribution, Chi Squared Distribution
- Frequency Table: You are able to create a frequency table for a list of numbers. Just enter the numbers, separated by comma.
Best mathematical tool for school and college! If you are a student, it will helps you to learn statistics and probability theory.
Note: Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events.
This free app is an Electric Circuit Calculator. You are able to calculate: - the current in parallel circuits (both total and partial) - the voltage in series circuits (both total and partial) - the resistance in parallel and series circuits
The best tool for school and college! If you are a student it will helps you to learn electricity and electrical engineering which |
Friday, April 18, 2014
Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Extraordinary Book on Ordinary Differential Equations appears in the April/May 2014 issue.
Mathematics changes slowly; the mathematics curriculum
changes even more slowly. A few years ago, to celebrate the tercentenary of L'Hôpital's
Calculus, some colleagues and I read
it seminar-style. The most striking thing about the experience was that his table
of contents looked shockingly similar to our departmental calculus syllabus.
That being said, in the 30 years I've been teaching collegiate mathematics,
there is one course in the undergraduate math curriculum that has changed
dramatically–the course in ordinary differential equations (ODE).
These changes are rooted in the calculus reform movement of
the late 1980s and early 1990s, the easy access to powerful computing and
visualization, and the rise of dynamical systems theory and its accompanying qualitative
point of view.
The calc reform movement taught us to explain everything
from graphical, numerical, and symbolic perspectives. Computing, of course,
made it possible to do this in effective ways, especially the numerical and
graphical bits. Dynamical systems provided entirely new ways of thinking about
the evolution and bifurcation of systems.
The New on View
All these changes are fully on view in Virginia ("Anne")
Noonburg'sOrdinary Differential Equations from Calculus to Dynamical Systems, newly released by the MAA. Noonburg has a distinguished record of
research in dynamical systems, especially concentrating on equations that model
biological systems. You clearly see these intellectual interests in this book.
Biological science majors have replaced prospective engineers as the largest group of students taking regular Calculus I. From the MAA's Calculus Survey [2], just over 28% of all students in mainstream Calculus I intend to pursue a major in the biological sciences, the largest single group of majors in this course.
Friday, April 4, 2014
The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics have announced that the theme for Mathematics Awareness Month (MAM), April 2014, is Mathematics, Magic, and Mystery. The theme
This year the MAM Committee and volunteers have put together 30 theme-related activities. Each day in April one activity will be revealed that corresponds with an image on the theme poster. So stay tuned to mathaware.org to see some behind-the-scenes explanations and videos of Mathematics, Magic, and Mystery!
Martin Gardner in MAA Books
Gardner was perhaps best known as the author of the "Mathematical Games" column for Scientific American, which ran from 1956 to 1981. Throughout his career he wrote more than 70 books and collections of essays on topics ranging from Lewis Carroll and magic tricks to philosophy, religion, and scientific skepticism. Several of his most popular writings are available in the MAA Store.
The inaugural volume in Martin Gardner's New Mathematical Library. These mathematical recreations delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics.
The second volume in Gardner's New Mathematical Library, updated chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.
Friday, March 28, 2014
Bill Woods reviews Exploring Advanced Euclidean Geometry with GeoGebraby Gerard Venema as part of MAA Reviews. Exploring Advanced Euclidean Geometry with GeoGebra is written for an inquiry-based approach, with lots of exercises and just enough narrative and historical commentary to hold it all together. It is not the sort of book you read without some paper and probably a computer in front of you. What makes the book special is the inclusion of GeoGebra exercises (clearly identified with a *) to encourage experimentation. Exercises may ask students to construct a visualization of a theorem, verify results, and build examples and conjectures. Eventually the student gets to proving a theorem, but not before playing with the statement quite a bit.
The book focuses on "advanced" planar Euclidean geometry, which the author defines to mean anything developed after Euclid's Elements. This makes it an excellent candidate text for a second course in Euclidean geometry using inquiry-based methods that minimize lecture and maximize student discovery. There is also much value to be mined as a supplement to other Euclidean geometry texts. The author suggests a structure in which this text is used as something of a lab manual rather than a primary text.
Even if it does not fit for course adoption, this book is worth any geometry teacher's attention as way to reconnect with the learning experience they want for their students.
Friday, March 14, 2014
Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature.
— James Tattersall, Providence College
Steven S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him, some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Steve has strong, cogent and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Steve's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book. |
Author(s): LarsonCOLLEGE ALGEBRA: REAL MATHEMATICS, REAL PEOPLE, 6th Edition, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed. Retaining the series' emphasis on student support, selected examples throughout the text include notations directing students to previous sections to review concepts and skills needed to master the material at hand. The book also achieves accessibility through careful writing and design--including examples with detailed solutions that begin and end on the same page, which maximizes readability. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles. Reflecting its new subtitle, this significant revision focuses more than ever on showing students the relevance of mathematics in their lives and future careers. |
The Mathematical Association of America (MAA) continues to build on their already solid online presence with the addition of this lecture by noted mathematician and scholar Professor Ruth Charney. This particular...
The Mathematical Association of America (MAA) is creating a series of instructional materials for mathematics teachers, and they are drawing on the expertise of high-quality instructors from across the country. One such...
Published by Emory University, this site is a collection of ?inquiry-based lessons to engage K-12, undergraduate, and graduate students in exploring the science behind real-world problems.? Though most cases here are...
Many students arriving at college may find that they have forgotten some of the basic skills required to learn various mathematical concepts. Some educational researchers and mathematicians of note have commented that...
The American Mathematical Association of Two-Year Colleges was founded in 1974. It is the only organization exclusively devoted to providing a national forum for the improvement of mathematics instruction in the first... |
There are only three types of solutions: no solution, one solution, or infinitely MANY solutions. Mr. Defining Wizard will explain how to analyze and determine which type of solution you have for your problem (graphically and algebraically). Don't forget to check your answersgebra Geometry Formulae is an ideal free app for all students above 12th grade, college graduates, engineering graduates and students preparing for various exams. We have compiled all the algebra, geometry and statistics related formulas to cover all the Math's formulas. The maths topics covered in this free app are: ALGEBRA *Basic Properties and Facts *Factoring and Solving Formulas *Factoring and solving Methods (completing the squares methods etc...) *Functions and Graphs *Common Algebraic ErrorsA straight forward algebraic technique to solvingHow many times have you been told to "reduce or simplify fractions"? Calculating the GCF is a common routine to begin to reduce your fractions completely. Master this skill and you will not be afraid of fractions any more!
Prime Factorization is a technique used to find out what all numbers are made up of. This insight is a preliminary step for many math problems such as: add, subtract, reduce, or simplify fractions. Mastering this skill will definitely prepare you for more advanced problems. Give it a try, and have fun!
A nifty algebraic technique, so good it deserves two names. The Algebraic or Elimination method hints at both the process and result of the method. In this app, Mr. Defining Wizard explains how to take advantage of this method. Don't forget to check your answers. Solutions should be the same if you use the graphing, substitution, or matrices method.
When solving logarithm equations, we can only rely on our knowledge of the logarithm properties. Understanding what the properties mean will help you in the long run. Review with Mr. Defining Wizard all properties so you are prepared for any problem you face.
What values can x be? What values can y be? Practice with Mr. Defining Wizard and develop a good eye for determining domain and range for any equation which includes: fractions, square roots, and linear equations.
Simply put, math problems containing <, >, <=, and >= are called inequalities and math problems containing = is called an equation. Solutions to both inequalities and equalities are numbers that make the statements true. Practice these type of problems with Mr. Defining Wizard for additional tips
Did you know that all inverse equations are symmetric across the line y=x? Why is this? Mr. Defining Wizard explains the definition of inverse and reviews a simple problem for you to refer back to for future referencing. Horizontal Line Test and Vertical Line Test are not reviewed in this app.
Dealing with a system that involves 3 or more variables and/or 3 or more equations are best solved using matrices. Learn the rules to solving a system of equations using matrices as an alternate method to the substitution and elimination methods.
A graphical representation of a system may lead to your solution. In this app, Mr. Defining Wizard explains how to take advantage of this method. Don't forget to check your answers. Solutions should be the same if you use the substitution, addition, or matrices method.
Mr. Defining Wizard keeps it real brief and simple in this app. When solving a system of equations, what method should you use? This app will help you become familiar with your options when solving a system of equations: graphing, substitution, addition, and matrices method |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
algebra from the viewpoint of computergraphics. It covers most vector and matrix topics needed for college-level computer graphicstext books. Most graphics texts cover these subjects in an appendix, but it is often too short.This tutorial covers the same material at greater length, and with many examples.
of their appealing blood-and-gore covers, mass trade books on game programming require thesame understanding of vectors and matrices as more staid text books (and usually defer thesetopics to the same skimpy mathematical appendix).This tutorial is useful for more than computer graphics. Vectors and matrices are used in allscientific and engineering fields, and any other field that uses computers (are there any thatdon't?) In many fields, the vocabulary used for vectors and matrices does not match that usedin computer graphics. But the ideas are the same, and reading these notes will take only aslight mental adjustment.These notes assume that you have studied plane geometry and trigonometry sometime in thepast. Notions such as "point", "line", "plane", and "angle" should be familiar to you. Othernotions such as "sine", "cosine", "determinant", "real number", and the common trig identitiesshould at least be a distant memory.These pages were designed at 800 by 600 resolution with "web safe" colors. They have been(somewhat) tested with not-too-old versions of Netscape Navigator and Internet Explorer, using"Times Roman" font (the usual browser default font). Many pages require Javascript, and somepages require Java. If you lack these (or are behind a firewall that does not allow these inside)you will be able to read most pages, but the interactive features will be lost.Some sections are more than three years old and have been used in several lecture sections(and hence are "classroom tested" and likely to be technically correct and readable). Othersections have just been written and might fall short of both goals.This tutorial may be freely downloaded and used as long as copyright and authorshipinformation is not removed. (They are contained in HTML comments on each page.) Peoplewho wish to reward this effort may do so by going to their local public library and checking outany long neglected, lonely book from the stacks.
This chapter discusses the objects of computer graphics---vectors and points---and how they arerepresented in a computer---as column matrices. A column matrix is a mathematical object that hasmany uses besides its use in computer graphics. These notes discuss only the aspects that are used incomputer graphics.
Chapter Topics:
q
Computer graphics as modeling and viewing.
q
Geometrical points and vectors.
q
Column and row matrices.
q
Calculating displacements.
q
Equality of column matrices.
q
Names for column matrices.
q
Representing points with column matrices.
Computer graphics books use one of two ways to represent points and vectors. Some books use rowmatrices; other books use column matrices. The two methods are exactly equivalent (although someformulae have to be adjusted). These notes use column matrices.Some graphics books use the term "column vector" for the object that these notes call a "columnmatrix." This is just a variation in terminology and does not affect the concepts or formulae presentedhere. |
Find a Lone Tree, CO ACTCalculus generally begins with the concept of limits and then progressing into derivatives and integrals, along with their respective applications. The student will also learn about more advanced mathematical modeling, differential equations, infinite series, all of which will prepare them for m... |
Product Details:
From the Publisher: This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations. The presentation draws on geometrical intuition wherever appropriate and is supported by a large number of illustrations, exercises, and examples. |
Summary: - By Judith A. Penna - Contains keystroke level instruction for the Texas Instruments TI-83 Plus, TI-84 Plus, and TI-89 - Teaches students how to use a graphing calculator using actual examples and exercises from the main text - Mirrors the topic order to the main text to provide a just-in-time mode of instruction - Automatically ships with each new copy of the text1upbooks Columbia, MO
"Fast shipping! May contain notes, highlighting, and/or cover wear."
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2008 Paperback Good Most items ship same day from Michigan, USA!
$2.00 |
considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices - symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum-maximum characterization of characteristic roots, Kronecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools. |
9780321500052
ISBN:
0321500059
Edition: 2 Pub Date: 2008 Publisher: Addison Wesley
Summary: Gary Rockswold and Terry Krieger focus on teaching algebra in context, giving students realistic and convincing answers to the perennial question, When will I ever use this? The authors consistent use of real data, graphs, and tables throughout the examples and exercise sets gives meaning to the numbers and equations as students encounter them. This new edition further enhances Rockswold and Krieger s focus on math i...n the real world with new features and updated applications to engage today s students.
Rockswold, Gary K. is the author of Beginning and Intermediate Algebra with Applications & Visualization (Rockswold Developmental Mathematics Series), published 2008 under ISBN 9780321500052 and 0321500059. Two hundred forty four Beginning and Intermediate Algebra with Applications & Visualization (Rockswold Developmental Mathematics Series) textbooks are available for sale on ValoreBooks.com, one hundred one used from the cheapest price of $0.40, or buy new starting at $34
ISBN-13:9780321500052
ISBN:0321500059
Edition:2nd
Pub Date:2008 Publisher:Addison Wesley
is the #1 site for cheap Beginning and Intermediate Algebra with Applications & Visualization (Rockswold Developmental Mathematics Series) rentals, or used and new copies available to buy. |
The Canon F-604 can handle a total of 142 functions and comes with a large, high-contrast LCD that makes calculations easy and comfortable. This easy-to-use calculator includes Mathematics, Trigonometry, Computer math and Statistics and is designed with a removable hard cover case which protects your calculator against damage when you are on the move.Color: Black. Color Class: BlackThe two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Pink. Color Class: Pink
Advanced scientific calculator features a MultiView display and MathPrint capability. Enhanced math functionality makes this calculator ideal for computer science and engineering courses in which graphing technology may not be permitted. Easily input data, scroll through entries, make edits and investigate patterns as you would on a graphing calculator. The MultiView display shows multiple ...
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Orange |
Algebra can be a tricky subject to master but with the help of Hands-On Equations 1, equations like 4x+2=3x+9 and 2(x+4)+x=x+12 become child's play!
The app takes advantage of the iPad's and iPhoneSee a quick overview of this app at: Beginning with version 2.0, the app will keep track of the problems completed by several students.
To see a video of a 10-year old solving 4+3x-2x+x=x+5 on the app, go to
What's New in Version 3.4
Screenshots
Customer Reviews
REVIEW UNASKED FOR!
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I wasn't asked to review, but I just did Lesson 1 and feel that I simply must review this fine app. I'm in my 60's and have cognitive impairments from a head injury. This app gives me a fun way to exercise my neurons and also to learn something they didn't much teach girls 50 yrs ago. We were usually in sewing or cooking classes when the boys were in Algebra or Wood Shop. I love this app. Thank you very much.
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This is one of the best educational apps I have ever used. It really shows students how to grasp the complications of algebra by making it visual and concrete. Students will have so much fun as they learn algebra. They won't even know they are learning |
Synopses & Reviews
Publisher Comments:
Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's DEVELOPMENTAL MATHEMATICS FOR COLLEGE STUDENTS, Third Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, algebra is like a foreign language. They have difficulty translating the words, their meanings, and how they apply to problem solving. Emphasizing the "language of algebra," the text's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. It blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills.
Synopsis:
About the Author
: Alan Tussy teaches all levels of developmental mathematics at Citrus College in Glendora, CA. He has written nine math books-a paperback series and a hard-cover series. An extraordinary author, he is dedicated to his students' success, relentlessly meticulous, creative, and a visionary who maintains a keen focus on his students' greatest challenges. Alan received his Bachelor of Science degree in Mathematics from the University of Redlands and his Master of Science degree in Applied Mathematics from California State University, Los Angeles. He has taught up and down the curriculum from prealgebra to differential equations. He is currently focusing on the developmental math courses. Professor Tussy is a member of the American Mathematical Association of Two-Year Colleges. R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois University. Diane Koenig received a Bachelor of Science degree in Secondary Math Education from Illinois State University in 1980. She began her career at Rock Valley College in 1981, when she became the Math Supervisor for the newly formed Personalized Learning Center. Earning her Master's Degree in Applied Mathematics from Northern Illinois University, Ms. Koenig in 1984 had the distinction of becoming the first full-time woman mathematics faculty at Rock Valley College. In addition to being nominated for AMATYC's Excellence in Teaching Award, Diane Koenig was chosen as the Rock Valley College Faculty of the Year by her peers in 2005, and, in 2006, she was awarded the NISOD Teaching Excellence Award as well as the Illinois Mathematics Association of Community Colleges Award for Teaching Excellence. In addition to her teaching, Ms. Koenig has been an active member of the Illinois Mathematics Association of Community Colleges (IMACC). As a member, she has served on the board of directors, on a state-level task force rewriting the course outlines for the developmental mathematics courses, and as the association's newsletter editor.
"Synopsis"
by Netread, |
As an alternative option to lecture classes,
the Self-Paced Mathematics Program at Francis Marion University
is designed to give students majoring in the sciences
access to mathematics across a wide range of entry-level courses.
General Description of the Self-Paced Mathematics Program
Almost all of our admitted students
take at least two high-school algebra
courses, some more recently than others. Those not making top grades or
not held accountable for their mathematical maturity may find they
do not have the mathematical skills to pass courses satisfying the General
Education Requirement of 6 hours in mathematical communications or to enter
the program of study of their choice at the University.
The Self-Paced Mathematics Program offers four courses
every fall and spring semester:
Math 105-S
College Algebra with Analytic Geometry I
This course is designed for students
whose placement scores in mathematics are not strong.
Credit for this course counts toward graduation from the University,
but the core curriculum at Francis Marion University requires students
to pass six hours of mathematics at a level strictly higher
than Math 105.
Therefore, although this course does count three hours toward graduation,
it does not count towards the General Education Requirement in Mathematical Communications.
Students enrolled in this course must therefore take nine hours of mathematics
in order to satisfy the G.E.R. of the University.
Math 111-S
College Algebra with Analytic Geometry II
This course is designed for students
whose with moderate mathematics placement scores.
This course does count towards
the General Education Requirement in Mathematical Communications.
Math 132-S
College Trigonometry with Analytic Geometry II
This course is designed for students
with adequately strong mathematics placement scores.
This course counts towards
the General Education Requirement in Mathematical Communications.
Math 201-S
Calculus I
This course is designed for those students
who have passed Math 132 or Math 180 with a grade of C or higher
and those students entering college with very strong mathematics placement scores.
This course also counts towards
the General Education Requirement in Mathematical Communications.
Placement is initially done by SAT scores, but the misplacement of students
can be quickly noted and corrected, resulting in easy transfer into the correct
course within the Self-Paced setting.
Students work at their own pace,
plan their own test schedules, have planned
conferences, get assistance as needed from their instructor, peer tutor, video
tapes, and computer tutorials. The Program is a model in collaborative
learning. Each course requires that a student take and pass six tests. If the
student does not make a 70 or better on a test, he or she must re-study and
take the test again until a 70 or better is achieved. Scores of less than 70 do
not count against the student in any way.
All students are expected to finish the course
by passing all six tests in one
semester, but there is an option for those students whose progress is slower.
Students who complete tests 1 through 4 may receive a grade of CO (continuing).
Completion of fewer than four tests results in a grade of F.
Students with a grade of CO will complete the course the next semester by re-registering for it.
Upon completion, however, some students may get a head start by beginning the
next course in that same semester.
Experience with this program indicates
that students work many problems over
the course of the semester and become much more skilled in math and reading
than they were as high school students. The individual attention, the guided
tutors, and the high volume of student work, when combined with the faculty's
insistence on a minimum 70% mastery of each topic, yields students whose
mathemtical skills are sufficient to take them wherever they wish to go at
Francis Marion and in life.
Notes about the Self-Paced Mathematics Program
Our attendance policy is strongly adhered to.
Absences and tardies are discouraged.
You will be dropped from the course
if your attendance does not comply with this policy.
You should spend
approximately six to nine hours per week outside of class
studying required material.
The Self-Paced Mathematics Program has an Open Door Policy.
The facilities are open to all self-paced students every period
a class is offered.
Instructors are available outside of class
during office hours should you need extra help.
Student tutors are also available during the afternoon.
You need to know
your instructor's name, office number, and the section number of your class.
Make sure you have
your math book, a math notebook, and pencils for the first day of class. |
Explained: Matrices
Dec 06, 2013 by Larry Hardesty
Among the most common tools in electrical engineering and computer science are rectangular grids of numbers known as matrices. The numbers in a matrix can represent data, and they can also represent mathematical equations. In many time-sensitive engineering applications, multiplying matrices can give quick but good approximations of much more complicated calculations.
Matrices arose originally as a way to describe systems of linear equations, a type of problem familiar to anyone who took grade-school algebra. "Linear" just means that the variables in the equations don't have any exponents, so their graphs will always be straight lines.
The equation x - 2y = 0, for instance, has an infinite number of solutions for both x and y, which can be depicted as a straight line that passes through the points (0,0), (2,1), (4,2), and so on. But if you combine it with the equation x - y = 1, then there's only one solution: x = 2 and y = 1. The point (2,1) is also where the graphs of the two equations intersect.
The matrix that depicts those two equations would be a two-by-two grid of numbers: The top row would be [1 -2], and the bottom row would be [1 -1], to correspond to the coefficients of the variables in the two equations.
In a range of applications from image processing to genetic analysis, computers are often called upon to solve systems of linear equations—usually with many more than two variables. Even more frequently, they're called upon to multiply matrices.
Matrix multiplication can be thought of as solving linear equations for particular variables. Suppose, for instance, that the expressions t + 2p + 3h; 4t + 5p + 6h; and 7t + 8p + 9h describe three different mathematical operations involving temperature, pressure, and humidity measurements. They could be represented as a matrix with three rows: [1 2 3], [4 5 6], and [7 8 9].
Now suppose that, at two different times, you take temperature, pressure, and humidity readings outside your home. Those readings could be represented as a matrix as well, with the first set of readings in one column and the second in the other. Multiplying these matrices together means matching up rows from the first matrix—the one describing the equations—and columns from the second—the one representing the measurements—multiplying the corresponding terms, adding them all up, and entering the results in a new matrix. The numbers in the final matrix might, for instance, predict the trajectory of a low-pressure system.
Of course, reducing the complex dynamics of weather-system models to a system of linear equations is itself a difficult task. But that points to one of the reasons that matrices are so common in computer science: They allow computers to, in effect, do a lot of the computational heavy lifting in advance. Creating a matrix that yields useful computational results may be difficult, but performing matrix multiplication generally isn't.
One of the areas of computer science in which matrix multiplication is particularly useful is graphics, since a digital image is basically a matrix to begin with: The rows and columns of the matrix correspond to rows and columns of pixels, and the numerical entries correspond to the pixels' color values. Decoding digital video, for instance, requires matrix multiplication; earlier this year, MIT researchers were able to build one of the first chips to implement the new high-efficiency video-coding standard for ultrahigh-definition TVs, in part because of patterns they discerned in the matrices it employs.
In the same way that matrix multiplication can help process digital video, it can help process digital sound. A digital audio signal is basically a sequence of numbers, representing the variation over time of the air pressure of an acoustic audio signal. Many techniques for filtering or compressing digital audio signals, such as the Fourier transform, rely on matrix multiplication.
Another reason that matrices are so useful in computer science is that graphs are. In this context, a graph is a mathematical construct consisting of nodes, usually depicted as circles, and edges, usually depicted as lines between them. Network diagrams and family trees are familiar examples of graphs, but in computer science they're used to represent everything from operations performed during the execution of a computer program to the relationships characteristic of logistics problems.
Every graph can be represented as a matrix, however, where each column and each row represents a node, and the value at their intersection represents the strength of the connection between them (which might frequently be zero). Often, the most efficient way to analyze graphs is to convert them to matrices first, and the solutions to problems involving graphs are frequently solutions to systems of linear equations.It took only a few years for high-definition televisions to make the transition from high-priced novelty to ubiquitous commodity—and they now seem to be heading for obsolescence just as quickly. At site functionality, it is necessary to enable Javascript.
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books.google.ca - Wide... Algebra
Abstract Algebra
results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
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User Review - John Lee - Goodreads
My first algebra book, and definitely a good one. The exercises are a little too straightforward at times, and a little too tricky at times, but with a bit of guidance, all of them are very doable ...Read full review
Review: Abstract Algebra
User Review - Waffles - Goodreads
It's a math text, so I didn't enjoy reading it, but it is a good comprehensive overview of algebra. I'm glad this was the text for my algebra sequence.Read full review |
Shack's Math Problems - Michael Shackleford
Pages of math problems ranging from basic math to differential equations. Each problem comes with a difficulty rating from one to four stars, roughly a measure of how much time it took Shackleford to do the problem. Includes answers and, usually, solutions.Shelley Walsh
Syllabi and notes for math courses from arithmetic review to beginning calculus. Download MathHelp a tutorial program with problem sets for Mac or PC, or learn how to use MathHelp to create your own tutorials. Brief Mathematics Articles present concepts
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SIMMS IM LEVEL I - Research Project Help - T. DeBuff
High School freshman-level integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that willSkill in Algebra - Lawrence Spector
An introduction to algebra, with questions that, when moused over, reveal their answers: algebraic expressions, signed numbers, adding and subtracting signed numbers, multiplying and dividing signed numbers, reciprocals and zero, removing grouping symbols,
...more>>
Skydome Unit Plan - Ruth Carver, Margaret Sinclair
A unit suitable for grades 7-11 with the objectives: to review many different mathematical skills; to work on a unit that connects with the "real world"; to improve reading for information skills. Questions include: What is the lowest price for a seat
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SliderMath Equations - WhiteAcres Media
Windows software designed to introduce linear equations and basic algebra, bringing together many of the requirements of the grades 7-10 math curriculum or providing a review of fundamentals for adults. Levels 1-2 include addition, subtraction, multiplication,
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Smartkiddies Mathematics - Andy Hobeika
Free interactive lessons, number challenge exercises, worksheets -- and visual reporting for instant feedback. To begin, select a year (one through seven, corresponding to Australia's curriculum), then a module, ranging from whole number to position &
...more>>
Softmath - Neven Jurkovic
Developers of Algebrator, an automated tutor based on Maxima CAS that provides step-by-step solutions to algebra, trigonometry, and statistics problems, and exports answers to MathML. Demo and purchase Algebrator; use Softmath's free online software to
...more>>
Software for mathematics education - Piet van Blokland
Software for mathematical education that draws on David Tall's philosophy of teaching: use Graphic Calculus to visualize, explore, and conceptualize the graph of a linear function; analyze the data and simulations included with VUStat to learn statistics
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Solid Gold Gnarly Math
A Windows-compatible CD-ROM for kids, homeschoolers, parents, and teachers, designed to teach algebra, geometry, numbers, trigonometry, topology, and probability. It contains games, magic tricks, and other fun things, along with a Math Lab where kids
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Songs for Teaching - S. Ruth Harris, LLC
Lyrics to music that teaches or reinforces math facts and concepts, including addition, subtraction, multiplication, division, algebra, and geometry. Some songs have links to sound files as well.
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Stella's Stunners - Rudd Crawford
More than 600 non-routine mathematics problems named in honor of the Dutch baroness Ecaterina Elizabeth van Heemsvloet tot Schattenberg. Each collection in the Stella Library contains five subsets, one for each course of Pre-Algebra, Algebra I, Geometry,
...more>> |
In addition to developing a strong base of algebra skills,
this course is intended to help
you learn "how to learn" mathematics. It is intended to help relieve your
anxiety and
build your confidence in your mathematics skills. With the mathematics and study
skills
you will develop in MTH 03, you should be able to move to the next mathematics
course
with a higher expectation of success. |
Offering
8 subjects
including precalculus precalculus precalculus |
Pre-Algebra is a common name for a course in middle school mathematics. In the United States, pre-algebra is generally taught in the seventh grade. The objective of pre-algebra is to prepare the student for the study of algebra. |
Mathematics
Mathematics is a rich and varied subject, full of interesting and important applications to everyday life and distinguished by creativity and beauty at its higher levels.
At Johnson State College, we go beyond the numbers and formulas to give mathematics students greater context for what they learn. We also examine the relationships between mathematics and other disciplines, such as history, philosophy and music. Small upper-level courses focus on class participation rather than lectures and challenge students to think creatively.
Graduates of the mathematics program develop critical-thinking and analytical skills. Mathematics majors often go on to graduate school or careers in related fields such as finance or engineering. Many students earning teacher licensure (grades 7-12) in mathematics later work in Vermont public schools.
New Mathematics Scholarship!
Starting in fall 2014, a new scholarship is available from JSC for an incoming student from Vermont majoring in mathematics. The scholarship, generously funded by former JSC Mathematics Professor Stella Sargent, covers the full cost of unmet financial need for tuition over four years, up to a total of $40,000! |
Larson's TRIGONOMETRY is known for delivering sound, consistently structured explanations and exercises of mathematical concepts. With the ninth edition, the author continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.
Trigonometry: Search Results
Book Description:Cengage Learning. Hardcover. Book Condition: New. 1133954332 US Hardback copy. Identical to student edition except has publisher markings on cover and answers to the problems. Great opportunity to save on this book. WE SHIP DAILY!!!. Bookseller Inventory # SKU20225981133954330
Book Description:(B/C), 2014. Hardcover. Book Condition: new annotated teacher edition; 9e, ninth; HUGE, oversized, heavvy; book only; with all (odd and even) answers and with teacher intended annotations; you may learn more with this xtra information; check your work; heavy large book; we ship daily at 0900 CT IL USA; 500+pp all new all clean; "Not for Sale); Bookseller Inventory # 000759
Book Description:Cengage Learning1474
Book Description:Brooks/Cole, Cengage Learning, 2014. Hardcover. Book Condition: New. Ninth Edition. New ANNOTAED INSTRUCTOR EDITION, content same as the student Edition with All Answers Added in back of the book. Bookseller Inventory # 003540
Book Description:Cengage Learning. Book Condition: New. 1133954332. Bookseller Inventory # 19769
Book Description:Cengage Learning. Book Condition: New. 1133954332 INSTRUCTORS EDITION. Exact same content as the student version only may include all answers and/or teaching notes in margins. DOES NOT include supplements such as CDs or access codes. Orders ship within 1-2 business days w/ free tracking. Bookseller Inventory # 145 |
Available.
Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text... more
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Table of Contents Exponential and Logarithmic Series Complex Quantities. De Moivre-s Theorem Expansions of sin n, and cos n.Series for sin , and cos in Powers of Expansions of Sines and Cosines of Multiple Angles and of Powers of Sines and Cosines Exponential Series for Complex Quantities Circular Functions for... more
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Check your work-and your understanding-with this manual, which provides solutions for all of the odd-numbered exercises in the text. You will also find strategies for solving additional exercises and many helpful hints and warnings. The classic in the series of highly respected Swokowski/Cole mathematics texts retains the elements that have... more
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The goal of this book is to provide a solid mathematical foundation via visualization of real world data. This book uses technology as a tool to solve problems, motivate concepts, explore and preview mathematical concepts and to find curves of best fit to the data. Most mathematical concepts are developed... more
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This text uses the graphing utility to enhance the study of mathematics. Technology is used as a tool to solve problems, motivate concepts, and explore mathematical ideas. Sullivan's Series "Enhanced with Graphing Utilities" provides clear and focused coverage. Many of the problems are solved using both algebra and a graphing... more
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The Dugopolski Precalculus series for 1999 is technology optional. With this approach, teachers will be able to choose to offer either a strong technology-oriented course, or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility. College Algebra and... more
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Strong Algebra and Trig skills are crucial to success in calculus. This text is designed to bolster these skills while students study calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra or trigonometry topics and points out potential problem spots. The... more
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Over the years, the text has been shaped and adapted to meet the changing needs of both students and educators. As always, special care was taken to respond to the specific suggestions of users and reviewers through enhanced discussions, new and updated examples and exercises, helpful features, and an extensive... more
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Represents mathematics as it appears in life, providing understandable, realistic applications consistent with the abilities of any reader. This book develops trigonometric functions using a right triangle approach and progresses to the unit circle approach. Graphing techniques are emphasized, including a thorough discussion of polar coordinates, parametric equations, and conics... more
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This intermediate algebra text, based on standards in the AMATYC Crossroads document, motivates college math students to develop mathematical literacy and a solid foundation for future study in mathematics and other disciplines. This third book of a three-book series presents mathematical concepts and skills through relevant activities derived from real-life... more
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Primarily designed as a textbook, Trigonometry is a unique treatise on vectors, aiming at providing a fairly complete account of the basic concepts required to build a strong foundation for a student endeavouring to study this subject. The analytical approach to the major theories Inverse Circular Functions, De-Moivre s Theorem,... more
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Ideal for courses that require the use of a graphing calculator, ALGEBRA AND TRIGONOMETRY: REAL MATHEMATICS, REAL PEOPLE, 6th Edition, features quality exercises, interesting applications, and innovative resources to help you succeed. Retaining the book's emphasis on student support, selected examples include notations directing students to previous sections where they... more
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Available.
Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students t... more
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An unabridged printing to include all examples and over 180 highly detailed figures, with digitally enlarged text.... more |
23Kau mathematics courses in an easy-to-read format. TheTable of Contents
Basic Concepts And Properties
Sets, Real Numbers, and Numerical Expressions
Operations with Real Numbers
Properties of Real Numbers and the Use of Exponents
Algebraic Expressions
Summary
Review Problem Set
Test
Equations, Inequalities, And Problem Solving
Solving First-Degree Equations
Equations Involving Fractional Forms
Equations Involving Decimals and Problem Solving
Formulas
Inequalities
More on Inequalities and Problem Solving
Equations and Inequalities Involving Absolute Value
Summary
Review Problem Set
Test
Polynomials
Polynomials: Sums and Differences
Products and Quotients of Monomials
Multiplying Polynomials
Factoring: Use of the Distributive Property
Factoring: Difference of Two Squares and Sum or Difference of Two Cubes |
Numerical Analysis
Summary
Numerical Analysis, designed to be used in a one-year course in engineering, science and mathematics, helps the readers gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods. Fundamentals. Solving Equations. Systems of Equations. Interpolation. Least Square. Numerical Differentiation and Integration. Ordinary Differential Equations. Boundary Value Problems. Partial Differential Equations. Random Numbers and Applications. Trigonometric Interpolation and the FFT. Compression. Eigenvalues and Singular Values. Optimization. For all readers interested in numerical analysis.
Author Biography
Timothy Sauer earned the Ph.D. degree in mathematics at the University of California, Berkeley in 1982, and is currently a professor at George Mason University. He has published articles on a wide range of topics in applied mathematics, including dynamical systems, computational mathematics, and mathematical biology. |
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In:
TI-85 Graphing Calculator
The Texas Instruments TI-85 is a graphing calculator which can be used
in Algebra, Geometry, Trigonometry, Statistics, Calculus, Business/Accounting,
and Physics courses. The calculator has on-keypad functions such as SOLVER
(to solve equations of one variable), SIMULT (to solve equations of more
than one variable where specific values are inserted for those variables),
POLY (to solve polynomial equations of various degree), as well as menus
for matrices, vectors, and complex numbers. The calculator graphs functions
of one variable.
NOTE: This calculator is for LIBRARY USE ONLY and cannot be taken
out of the building.
The TI-85 comes with four AAA batteries.
The loan period for the TI-85 is two hours and cannot be renewed.
It can be picked up from and returned to the Circulation Desk. There is
one TI-85 available on a first come, first serve basis. |
Des Plaines Algebra math fits together. The more you know how it fits together, the easier it gets. I show a student a way to understand a math problem |
Betascript Publishing
Supplemental materials are not guaranteed for used textbooks or rentals (access codes, DVDs, workbooks).
ISBN:
9786132298874
/ 6132298878
Graphviz...
Show More mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges |
Mathematical Proofs: Transition To Advanced Mathematics - 2nd edition
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Algebra I – Unit 2
Ascension Parish Comprehensive Curriculum
Concept Correlation
Unit 2: Measurement
Time Frame: Regular – 12 days
Block – 6 days
Big Picture: (Taken from Unit Description and Student Understanding)
This unit is an advanced study of measurement.
It includes the topics of precision and accuracy and investigates the relationship and difference between the two.
The investigation of absolute and relative error and how they each relate to measurement is included.
Students should understand significant digits. Significant digits need to be studied along with the computations that can be performed using
them.
Students should be able to find the precision of an instrument and determine the accuracy of a given measurement.
Students should see error as the uncertainty approximated by an interval around the true measurement.
Activities Focus GLEs
Guiding Questions GLEs
17 - Distinguish between precision and accuracy (M-1-H)
Concept 1: 12 – What Does it mean to be
(Comprehension)
Measurement Accurate? (GQ 7) 4, 17
6. Can students 18 - Demonstrate and explain how the scale of a measuring
instrument determines the precision of that instrument (M-1-
determine the 13 – How Precise is Your
4, 17, H) (Application)
precision of a given Measurement Tool? (GQ 6)
18 19 - Use significant digits in computational problems (M-1-H) (N-
measurement
2-H) (Application)
instrument? 14 – Temperature – How
7. Can students 4, 17, 20 - Demonstrate and explain how relative measurement error is
Precise Can You Be? (GQ 6)
determine the 18 compounded when determining absolute error (M-1-H) (M-2-
H) (M-3-H) (Analysis)
accuracy of a 15 – Repeatability and
measurement? Precision (GQ 8, 9) 17 21 - Determine appropriate units and scales to use when solving
8. Can students measurement problems (M-2-H) (M-3-H) (M-1-H)
(Application)
differentiate between 16 –Precision vs. Accuracy
what it means to be 17
precise and what it 17 – Absolute Error (GQ 9) 18, 20
Algebra I – Unit 2 - Measurement
Algebra I – Unit 2
means to be
accurate? 18– Relative Error (GQ 9 ) 4, 5,
9. Can students discuss 20
the nature of 19 – What's the Cost of Those
precision and 4, 17,
Bananas? (GQ 6, 9) Reflections
accuracy in 18
measurement and 20 – What are Significant
note the differences Digits? (GQ 10) 4, 19
in final measurement
values that may
21 – Calculating with
result from error?
Significant Digits (GQ 10) 4, 19
10. Can students
perform basic
mathematical 22 – Measuring the Utilities
operations using You Use(GQ 10)
19
significant digits?
11. Can students
determine the most
appropriate units and
scales to use when 23 – Which Unit of
solving measurement 5, 21
Measurement? (GQ 11)
problems?
Algebra I – Unit 2 - Measurement
Algebra I – Unit 2
Unit 2 – Measurement (LCC Unit 6)
GLEs
*Bolded GLEs are assessed in this unit
4 Distinguish between an exact and an approximate answer, and recognize errors
introduced by the use of approximate numbers with technology (N-3-H) (N-4-H) (N-
7-H) (Application)
5 Demonstrate computational fluency with all rational numbers (e.g., estimation,
mental math, technology, paper/pencil) (N-5-H) (Application)
17 Distinguish between precision and accuracy (M-1-H) (Comprehension)
18 Demonstrate and explain how the scale of a measuring instrument determines
the precision of that instrument (M-1-H) (Application)
19 Use significant digits in computational problems (M-1-H) (N-2-H) (Application)
20 Demonstrate and explain how relative measurement error is compounded when
determining absolute error (M-1-H) (M-2-H) (M-3-H) (Analysis)
21 Determine appropriate units and scales to use when solving measurement
problems (M-2-H) (M-3-H) (M-1-H) (Application)
Purpose/Guiding Questions: Vocabulary:
Determine the precision of a given Accurate
measurement instrument Precision
Determine the accuracy of a Absolute Error
measurement Relative Error
Differentiate between what it Significant Digits
means to be precise and what it Computations with Significant Digits
means to be accurate Appropriate Unit of Measurement
Discuss the nature of precision
and accuracy in measurement and
note the differences in final
measurement values that many
result from error
Calculate using significant digits
Key Concepts (Math Across High School):
demonstrate an understanding of precision, accuracy, and significant digits
Assessment Ideas:
Portfolio Assessment: The student will create a portfolio divided into the following
sections:
1. Accuracy
2. Precision
3. Precision vs. Accuracy
4. Absolute error
Algebra I – Unit 2 - Measurement 13
Algebra I – Unit 2
5. Relative error
6. Significant digits
In each section of the portfolio, the student will include an explanation of each,
examples of each, artifacts that were used during the activity, sample questions given
during class, etc. The portfolio will be used as an opportunity for students to
demonstrate a true conceptual understanding of each concept.
The student will complete learning logs using such topics as:
o Darla measured the length of a book to be 11 1 inches with her ruler and 11 1
4 2
inches with her teacher's ruler. Can Darla tell which measurement is more
accurate? Why or why not? (She cannot tell unless she knows which ruler is
closer to the actual standard measure)
o What does it mean to be precise? Give examples to support your explanation.
o What is the difference between being precise and being accurate? Explain your
answer.
o Explain the following statement: The more significant digits there are in a
measurement, the more precise the measurement is.
o When would it be important to measure something to three or more significant
digits? Explain your answer.
Resources:
Video Clip – Drew Brees and Sports Science
Glencoe Geometry textbook - Ch. 1
Graphic Organizers:
organizers/printable/6293.html and
god3TaxVg
ABC Passing the GEE
ILEAP Practice workbook
Create your own organizers using:
and
Plato – Refer to end of Concept 1
Algebra I – Unit 2 - Measurement 14
Algebra I – Unit 2
Instructional Activities
Activity 12: What Does it Mean to be Accurate? (LCC Unit 6)
(GLEs: 4, 17)
Materials List: paper, pencil, three or more different types of scales from science
department, three or more different bathroom scales, student's watches, Internet access,
What Does It Mean To Be Accurate? BLM, sticky notes
This unit on measurement will have many new terms to which students have not
yet been exposed. Have students maintain a vocabulary self-awareness chart
(view literacy strategy descriptions) for this unit. Vocabulary self-awareness is
valuable because it highlights students' understanding of what they know, as well
as what they still need to learn, in order to fully comprehend the concept.
Students indicate their understanding of a term/concept, but then adjust or change
the marking to reflect their change in understanding. The objective is to have all
terms marked with a + at the end of the unit. A sample chart is shown below.
Word + - Example Definition
accuracy
precision
Relative error
Absolute error
Significant
digits
Be sure to allow students to revisit their self-awareness charts often to monitor
their developing knowledge about important concepts. Sample terms to use
include accuracy, precision, significant digits, absolute error, and relative error.
Have students use the What Does It Mean To Be Accurate? BLM to complete this
activity.
Talk with students about the meaning of ―accuracy‖ in measurement. During the
discussion, the following video may be used to supplement and encourage further
dialog regarding the meaning of accuracy in real life contexts.
( Accuracy indicates how
close a measurement is to the accepted ―true‖ value. For example, a scale is
expected to read 100 grams if a standard 100 gram weight is placed on it. If the
scale does not read 100 grams, then the scale is said to be inaccurate.
Algebra I – Unit 2 - Measurement 15
Algebra I – Unit 2
If possible, obtain a standard weight from one of the science teachers along with
several scales. With students, determine which scale is closest to the known value
and use this information to determine which scale is most accurate. Next, ask
students if they have ever weighed themselves on different scales—if possible,
provide different scales for students to weigh themselves. Depending on the scale
used, the weight measured for a person might vary according to the accuracy of
the instruments being used. Unless ―true‖ weight is known, it cannot be
determined which scale is most accurate (unless there is a known standard to
judge each scale).
Generally, when a scale or any other measuring device is used, the readout is
automatically accepted without really thinking about its validity. People do this
without knowing if the tool is giving an accurate measurement. Also, modern
digital instruments convey such an aura of accuracy and reliability (due to all the
digits it might display) that this basic rule is forgotten—there is no such thing as a
perfect measurement. Digital equipment does not guarantee 100% accuracy. Note:
If some students object to being weighed, students might weigh their book bags or
other fairly heavy items. Adjust the BLM if this is done.
Have all of the students who have watches to record the time (to the nearest
second) at the same moment and hand in their results. Post the results on the
board or overhead—there should be a wide range of answers. Ask students,
Which watch is the most accurate? Students should see that in order to make this
determination, the true time must be known. Official time in the United States is
kept by NIST and the United States Naval Observatory, which averages readings
from the 60 atomic clocks it owns. Both organizations also contribute to UTC, the
world universal time. The website has the official U.S. time,
but even its time is ―accurate to within .7 seconds.‖ Cite this time at the same time
the students are determining the time from their watches to see who has the most
accurate time.
Lead students in a discussion as to why their watches have different times (set to
home, work, and so on) and how their skill at taking a reading on command might
produce different readings on watches that may be set to the same time.
Ultimately, students need to understand that accuracy is really a measure of how
close a measurement is to the ―true‖ value. Unless the true value is known, the
accuracy of a measurement cannot be determined.
Activity-Specific Assessment
The student will write a paragraph explaining in his/her own words what it means to be
accurate. He/she will give an example of a real-life situation in which a measurement taken
may not be accurate.
Algebra I – Unit 2 - Measurement 16
Algebra I – Unit 2
Activity 13: How Precise is Your Measurement Tool? (LCC Unit 6)
(GLE: 4, 17, 18)
Materials List: paper, pencil, rulers with different subdivisions, four-sided meter sticks,
toothpicks, What is Precision? BLM, wall chart , blue masking tape
Discuss the term ―precision‖ with the class. Precision is generally referred to in one
of two ways. It can refer to the degree to which repeated readings on the same
quantity agree with each other. We will study this definition in Activity 15.
Have students use the What is Precision? BLM for this activity.
Precision can also be referred to in terms of the unit used to measure an object.
Precision depends on the refinement of the measuring tool. Help students to
understand that no measurement is perfect. When making a measurement, scientists
give their best estimate of the true value of a measurement, along with its uncertainty.
The precision of an instrument reflects the number of digits in a reading taken from
it—the degree of refinement of a measurement. Discuss with students the degree of
precision with which a measurement can be made using a particular measurement
tool. For example, have on hand different types of rulers (some measuring to the
1
nearest inch, nearest 1 inch, nearest 1 inch, nearest 1 inch, nearest 16 inch, nearest
2 4 8
centimeter, and nearest millimeter) and discuss with students which tool would give
the most precise measurement for the length of a particular item (such as the length of
a toothpick). Have students record measurements they obtain with each type of ruler
and discuss their findings.
Divide students into groups. Supply each group with a four-sided meter stick. (This
meter stick is prism-shaped with different divisions of a meter on each side. The
meter stick can be purchased at NASCO, and other suppliers.)
Cover the side of the meter stick that has no subdivisions with two strips of masking
tape and label it as side 1. (You need two layers of masking tape so the markings on
the meter stick will not show through the tape. The blue tape works better as the
darker color prevents markings from showing through better.) Repeat this with the
other sides of the stick such that side 2 has decimeter markings, side 3 has centimeter
markings, and side 4 has millimeter markings. Have students remove the tape from
side 1 and measure the length of a sheet of paper with that side and record their
answers. Repeat with the other sides of the meter stick in numerical order. Post a wall
chart similar to the one below and have each group record their measurements:
Algebra I – Unit 2 - Measurement 17
Algebra I – Unit 2
Length of Paper
Side 1 Side 2 Side 3 Side 4
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Average
Have students calculate the averages of each column. Lead students to discover
that the measurements become closer to the average with the increase in divisions
of the meter stick.
Help students understand that the ruler with the greatest number of subdivisions
per unit will provide the most precise measure.
Have students complete the following RAFT writing assignment (view literacy
strategy descriptions) in order to give students a creative format for demonstrating
their understanding of precise measurement.
Role- millimeter ruler
Audience-decimeter ruler
Format-advertisement
Topic-Buy my subdivisions
Once RAFT writing is completed, have students share with a partner, in small
groups, or with the whole class. Students should listen for accurate information
and sound logic in the RAFTs.
Activity-Specific Assessment
The student will keep a log of the various measurements that are taken at different
measurement stations. The student will record each measurement of each item and then
decide which measurement would be more precise. The student will be required to justify
each answer with a written explanation.
Activity 14: Temperature—How Precise Can You Be? (LCC Unit 6)
(GLEs: 4, 18, 17)
Algebra I – Unit 2 - Measurement 18
Algebra I – Unit 2
Materials List: paper, pencil, thermometers
Have students get in groups of three. Provide each team with a thermometer that is
calibrated in both Celsius and Fahrenheit. Have each team record the room
temperature in both oC and oF. Have students note the measurement increments of the
thermometer (whether it measures whole degrees, tenths of a degree, etc.) on both
scales. Make a class table of the temperatures read by each team. Ask students if it is
possible to have an answer in tenths of a degree using their thermometers and why or
why not?
It is important that students understand that the precision of the instrument depends
on the smallest division of a unit on a scale. If the thermometer only has whole
degree marks, then it can only be precise to one degree. If the thermometer has each
degree separated into tenths of a degree then the measurement is precise to the nearest
tenth of a degree. Regardless of the measurement tool being used, this idea of the
precision of the instrument holds true.
Activity 15: Repeatability and Precision (GLE: 17) (LCC Unit 6)
Materials List: paper, pencil
As stated in Activity 2, precision can also refer to the degree to which repeated readings
on the same quantity agree with each other.
Present students with the following situations:
Jamaal made five different measurements of the solubility of nickel (II)
chloride in grams per deciliter of water and obtained values of 35.11,
35.05, 34.98, 35.13, and 35.09 g/dL.
Juanita made five different measurements of the solubility of nickel (II)
chloride in grams per deciliter of water and obtained values of 34.89,
35.01, 35.20, 35.11, and 35.13 g/dL.
Have students work with a partner to discuss ways to determine which set of
measurements is more precise.
Have students come up with a method for determining which set of measurements is the
most precise. Lead students to the determination that the set that has the smallest range is
a more precise set of measurements.
Provide students with additional measurement situations so that they have the opportunity
to practice determining the more precise set of measurements when given a group of
measurements.
Algebra I – Unit 2 - Measurement 19
Algebra I – Unit 2
Activity 16: Precision vs. Accuracy (LCC Unit 6)
(GLE: 17)
Materials List: paper, pencil, Target BLM transparency, Precision vs. Accuracy BLM,
sticky notes
Student Questions for Purposeful Learning or SQPL (view literacy strategy
descriptions) is a strategy designed to gain and hold students' interest in the
material by having them ask and answer their own questions. Before beginning
the activity, place the following statement on the board:
Accuracy is telling the truth. Precision is telling the same story
over and over again.
Have students pair up and, based on the statement, generate two or three questions
they would like answered. Ask someone from each team to share questions with
the whole class and write those questions on the board. As the content is covered
in the activity, stop periodically and have students discuss with their partners
which questions could be answered, and have them share answers with the class.
Have them record the information in their notebooks.
Create a transparency of the Target BLM which includes the target examples
shown below and have students determine if the patterns are examples of
precision, accuracy, neither or both. Cover boxed descriptions with sticky notes
and remove as the lesson progresses. After the lesson provide students with
Target BLM to include in their notes.
If you were trying to hit a bull's eye (the center of the target) with each of five
darts, you might get results such as in the models below. Determine if the results
are precise, accurate, neither or both.
Neither Precise Nor Accurate
This is a random-like
pattern, neither precise
nor accurate. The darts
are not clustered together
and are not near the
bull's eye.
Algebra I – Unit 2 - Measurement 20
Algebra I – Unit 2
Precise, Not Accurate
This is a precise
pattern, but not
accurate. The darts are
clustered together but
did not hit the intended
mark.
Algebra I – Unit 2 - Measurement 21
Algebra I – Unit 2
Accurate, Not Precise
This is an accurate
pattern, but not precise.
The darts are not
clustered, but their
average position is the
center of the bull's eye.
Precise and Accurate
This pattern is both
precise and accurate.
The darts are tightly
clustered, and their
average position is the
center of the bull's eye.
Lead a class discussion reviewing the definitions of precision and accuracy and revisit the class-
generated questions.
Use the Precision vs. Accuracy BLM and present the examples to students. Lead a class
discussion using the questions on the BLM.
Provide students with more opportunities for practice in determining the precision and/or
accuracy of data sets.
Algebra I-Unit 2-Measurement 21
Algebra I – Unit 2
Activity-Specific Assessment
The student will be quizzed on the difference between being precise and being
accurate. Given examples similar to the ones in the activity, the student will answer
questions about the measurements.
Activity 17: Absolute Error (GLEs: 18, 20) (LCC Unit 6)
Materials List: paper, pencil, Absolute Error BLM, three different scales, 2 different beakers,
measuring cup, meter stick, 2 different rulers, calculator, cell phone, wrist watch
In any lab experiment, there will be a certain amount of error associated with the calculations.
For example, a student may conduct an experiment to find the specific heat capacity of a certain
metal. The difference between the experimental result and the actual (known) value of the
specific heat capacity is called absolute error. The formula for calculating absolute error is as
follows:
Absolute Error = Observed Value - Actual Value
Review absolute value with students and explain to them that since the absolute value of the
difference is taken, the order of the subtraction will not matter.
Present the following problems to students for a class discussion:
Luis measures his pencil and he gets a measurement of 12.8 cm but the actual measurement is
12.5 cm. What is the absolute error of his measurement?
( Absolute Error = 12.8 - 12.5 .3 .3 cm )
A student experimentally determines the specific heat of copper to be 0.3897 oC. Calculate the
student's absolute error if the accepted value for the specific heat of copper is 0.38452 oC.
( Absolute Error = .3897-.38452 0.00518 0.00518 )
Place students in groups and have them rotate through measurement stations. Have students use
the Absolute Error BLM to record the data. After students have completed collecting the
measurements, present them with information about the actual value of the measurement. Have
students calculate the absolute error of each of their measurements.
Examples of stations:
Station Measurement Instruments Actual Value
1 Mass 3 different scales 100 gram weight
2 Volume 2 different sized Teacher measured
beakers and a volume of water
measuring cup
Algebra I-Unit 2-Measurement 22
Algebra I – Unit 2
3 Length Meter stick, rulers Sheet of paper
with 2 different
intervals
4 Time Wrist watch,
calculator, cell
phone
Activity 18: Relative Error (GLEs: 4, 5, 20) (LCC Unit 6)
Materials List: paper, pencil
Although absolute error is a useful calculation to demonstrate the accuracy of a measurement,
another indication is called relative error. In some cases, a very tiny absolute error can be very
significant, while in others, a large absolute error can be relatively insignificant. It is often more
useful to report accuracy in terms of relative error. Relative error is a comparative measure. The
formula for relative error is as follows:
Absolute Error
Relative Error = 100
Actual value
To begin a discussion of absolute error, present the following problem to students:
Jeremy ordered a truckload of dirt to fill in some holes in his yard. The company
told him that one load of dirt is 5 tons. The company actually delivered 4.955
tons.
Chanelle wants to fill in a flowerbed in her yard. She buys a 50-lb bag of soil at a
gardening store. When she gets home she finds the contents of the bag actually
weigh 49.955 lbs.
Which error is bigger?
The relative error for Jeremy is 0.9%. The relative error for Chanelle is 0.09%.
This tells you that measurement error is more significant for Jeremy's purchase.
Use these examples to discuss with students the calculation of relative error and how it relates to
the absolute error and the actual value of measurement. Explain to students that the relative error
of a measurement increases depending on the absolute error and the actual value of the
measurement.
Provide students with an additional example:
In an experiment to measure the acceleration due to gravity, Ronald's group
calculated it to be 9.96 m/s2. The accepted value for the acceleration due to
gravity is 9.81 m/s2. Find the absolute error and the relative error of the group's
calculation. (Absolute error is .15 m/s2, relative error is 1.529%.)
Algebra I-Unit 2-Measurement 23
Algebra I – Unit 2
Provide students with more opportunity for practice with calculating absolute and relative error.
Activity-Specific Assessment
The student will solve sample test questions, such as:
Raoul measured the length of a wooden board that he wants to use to build a ramp. He
measured the length to be 4.2 m. The absolute error of his measurement is .1 m. His
friend, Cassandra, measured a piece of molding to decorate the ramp. Her measurement
was .25 m with an absolute error of .1 m. Find the relative error of each of their
measurements. Whose measurement was better? Explain your answer. (Raoul – 2%,
Cassandra – 40%, Raoul because his percentage of relative error was smaller.)
Activity 19: What's the Cost of Those Bananas? (LCC Unit 6)
(GLEs: 4, 17, 18)
Materials List: paper, pencil, pan scale, electronic scale, fruits or vegetables to weigh
The following activity can be completed as described below if the activity seems reasonable
for the students involved. If not, the same activity can be done if there is access to a pan scale
and an electronic balance. If done in the classroom, provide items for students to measure—
bunch of bananas, two or three potatoes, or other items that will not deteriorate too fast.
Have the students go to the local supermarket and select one item from the produce
department that is paid for by weight. Have them calculate the cost of the object using the
hanging pan scale present in the department. Record their data. At the checkout counter, have
the students record the weight given on the electronic balance used by the checker. Have
students record the cost of the item. How do the two measurements and costs compare? Have
students explain the significance of the number of digits (precision) of the scales.
Activity 20: What are Significant Digits? (LCC Unit 6)
(GLEs: 4, 19)
Materials List: paper, pencil
Discuss with students what significant digits are and how they are used in measurement.
Significant digits are defined as all the digits in a measurement one is certain of plus the first
uncertain digit. Significant digits are used because all instruments have limits, and there is a
limit to the number of digits with which results are reported. Demonstrate and discuss the
process of measuring using significant digits.
After students have an understanding of the definition of significant digits, discuss and
demonstrate the process of determining the number of significant digits in a number. Explain
Algebra I-Unit 2-Measurement 24
Algebra I – Unit 2
to students that it is necessary to know how to determine the significant digits so that when
performing calculations with numbers they will understand how to state the answer in the
correct number of significant digits.
Rules For Significant Digits
1. Digits from 1-9 are always significant.
2. Zeros between two other significant digits are always significant
3. One or more additional zeros to the right of both the decimal place and another
significant digit are significant.
4. Zeros used solely for spacing the decimal point (placeholders) are not significant.
Using a chemistry textbook as a resource, provide problems for students to practice in
determining the number of significant digits in a measurement.
In their math learning logs (view literacy strategy descriptions) have students respond to the
following prompt:
Explain the following statement:
The more significant digits there are in a measurement, the more precise the
measurement is.
Allow students to share their entries with the entire class. Have the class discuss the entries to
determine if the information given is correct.
Activity 21: Calculating with Significant Digits (GLEs: 4, 19) (LCC Unit 6)
Materials List: paper, pencil,
Discuss with students how to use significant digits when making calculations. There are different
rules for how to round calculations in measurement depending on whether the operations involve
addition/subtraction or multiplication/division. When adding, such as in finding the perimeter,
the answer can be no more PRECISE than the least precise measurement (i.e., the perimeter must
be rounded to the same decimal place as the least precise measurement). If one of the measures is
15 ft and another is 12.8 ft, then the perimeter of a rectangle (55.6 ft) would need to be rounded to
the nearest whole number (56 ft). We cannot assume that the 15 foot measure was also made to
the nearest tenth based on the information we have. The same rule applies should the difference
between the two measures be needed.
When multiplying, such as in finding the area of the rectangle, the answer must have the same
number of significant digits as the measurement with the fewest number of significant digits.
There are two significant digits in 15 so the area of 192 square feet, would be given as 190 square
feet. The same rule applies for division.
Algebra I-Unit 2-Measurement 25
Algebra I – Unit 2
Have students find the area and perimeter for another rectangle whose sides measure 9.7 cm and
4.2 cm. The calculated area is (9.7cm)(4.2cm) = 40.74 sq. cm, but should be rounded to 41 sq cm
(two significant digits). The perimeter of 27.8 cm would not need to be rounded because both
lengths are to the same precision (tenth of a cm).
After fully discussing calculating with significant figures, have students work computational
problems (finding area, perimeter, circumference of 2-D figures) dealing with the topic of
calculating with significant digits. A chemistry textbook is an excellent source for finding
problems of calculations using significant digits.
Activity 22: CC Activity 9: Measuring the Utilities You Use (LCC Unit 6)
(GLE: 19)
Materials List: paper, pencil, utility meters around students' households, utility bills
Have students find the various utility meters (water, electricity) for their households. Have
them to record the units and the number of places found on each meter. Have the class get a
copy of their family's last utility bill for each meter they checked. Have students answer the
following questions: What units and number of significant digits are shown on the bill? Are
they the same? Why or why not? Does your family pay the actual ―true value‖ of the utility
used or an estimate?
If students do not have access to such information, produce sample drawings of meters used
in the community and samples of utility bills so that the remainder of the activity can be
completed.
Activity 23: Which Unit of Measurement? (LCC Unit 6)
(GLEs: 5, 21)
Materials List: paper, pencil, centimeter ruler, meter stick, ounce scale, bathroom scale, quarter,
cup, gallon jug, bucket, water
Divide students into groups. Provide students with a centimeter ruler and have them measure
the classroom and calculate the area of the room in centimeters. Then provide them with a
meter stick and have them calculate the area of the room in meters. Discuss with students
which unit of measure was most appropriate to use in their calculations. Ask students if they
were asked to find the area of the school parking lot, which unit would they definitely want to
use. What about their entire town? In that case, kilometers would probably be better to use.
Provide opportunities for discussion and/or examples of measurements of weight (weigh a
quarter on a bathroom scale or a food scale) and mass (fill a large bucket with water using a
cup or a gallon jug) similar to the linear example of the area of the room. Use concrete
examples for students to visually explore the most appropriate units and scales to use when
solving measurement problems.
Algebra I-Unit 2-Measurement 26
Algebra I – Unit 2
Activity-Specific Assessment
The student will be able to determine the most appropriate unit and/or instrument to use
in both English and Metric units when given examples such as:
How much water a pan holds
Weight of a crate of apples
Distance from New Orleans to Baton Rouge
How long it takes to run a mile
Length of a room
Weight of a Boeing 727
Weight of a t-bone steak
Thickness of a pencil
Weight of a slice of bread
Algebra I-Unit 2-Measurement 27
Algebra I – Unit 2
PLATO Instructional Resources
GLE 17: Plato
o Applied Math – Estimating
o Chemistry I –Meas. & Calc.: Uncertainty…
GLE 18: Plato
o Applied Math – Using Linear Measurement Tools
o Chemistry I –Meas. & Calc.: Uncertainty..
GLE 19: Plato
o Chemistry I – Meas. & Calc.: Uncertainty…
GLE 20: Plato
o Chemistry I – Meas. & Calc.: Uncertainty…
GLE 21: Plato
o Applied Math-Using Linear Measurement Tools
o Chemistry I –Meas. & Calc.: Uncertainty
Algebra I-Unit 2-Measurement 28
Algebra I – Unit 2 changes
Number
* If you suggest an activity substitution, please attach a copy of the activity narrative formatted
like the activities in the APCC (i.e. GLEs, guiding questions, etc.).
Algebra I-Unit 2-Measurement |
Math 2423 (Honors Calculus II)
Fall 2010
Mississippi Kite (Ictinia mississippiensis).
These small birds of prey have, in recent years, been expanding their range northwards, and have learned to live in
urban areas. I first started noticing them in our neighborhood in East Norman about ten years ago. You can often see
them in the summer and fall soaring gracefully over the skies of O.U. They feed mainly on flying insects.
This image taken from the Ohio DNR website.
There is a Mathematics Help Center on the fourth floor of the Physical Sciences Center
(PHSC 425A) where math graduate students are available for free help with math classes up through Calculus II.
The Help Center is open Mondays, Wednesdays and Fridays from 9:30 am to 5:30 pm, and Tuesdays
and Thursdays from 9:00 am to 5:30 pm.
Final Exam: Friday, Dec. 17 at 4:30 pm
Links
Here is a nice online version of Euclid's "Elements". The Wikipedia article "Euclid's Elements" is also a good place to start learning about this work.
Newton's Principia is a physics book, not a calculus book. However, it represents the first appearance of the modern theory of calculus. It is more difficult to read than Euclid's Elements, and you
won't recognize any of the familiar formulas in your calculus text, but the calculus is there, present in a geometric guise.
You can find the Principia online by looking at the references in the Wikipedia article on "Philosophiae Naturalis Principia Mathematica". But maybe a better way to
approach it would be to first read the overview in the Stanford Encyclopedia of Philosophy, which is at |
Web Site Expressions and Equations The activities in each of the four categories are placed in the recommended order that they be taught in class: Simplifying Expressions, Informal or Intuitiv... Curriculum: Mathematics Grades: 8, 9, 10
43.
Web Site Learning about Rate of Change in Linear Functio... In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modificati... Curriculum: Mathematics Grades: 6, 7, 8
44.
Web Site Interactive Mathematics National Library of Virtual Manipulatives for Interactive Mathematics related to the NCTM standards for grades 6-8. Some of the tools include graphing and ex... Curriculum: Mathematics Grades: 6, 7, 8
45.
Web Site Order of Operations and Evaluating Expressions This site provides prep for Mathematics A so students are prepared on Order of Operations. (Keywords: Algebra, McDougall Littel, online tutorials, practice, ... Curriculum: Mathematics Grades: 6
Web Site A+ Math A plus math was designed to help students with their math skills interactively. This website has flashcards, math games, and you can even print worksheets so... Curriculum: Mathematics Grades: K, 1, 2, 3, 4, 5, 6, 7, 8, 9
49.
Web Site Online Calculus Tutorials From Algebra Review to Multi-Variable Calculus, this website provides step-by-step tutorials for high school and university students. Curriculum: Mathematics Grades: 10, 11, 12, Junior/Community College, University |
Summary: From the Core-Plus Mathematics ProjectMathematics That Makes Sense to More StudentsThis innovative program engages students in investigation-based, multi-day lessons organized around big ideas. Important mathematical concepts are developed in relevant contexts by students in ways that make sense to them. Students in ''Contemporary Mathematics in Context work collaboratively, often using graphing calculators, so more students than ever before are able to learn important and broadly us...show moreeful mathematics. Courses 1, 2, and 3 comprise a core curriculum that will upgrade the mathematics experience for all your students. Course 4 is designed for all college-bound students.Research-Based and Classroom-TestedDeveloped with funding from the National Science Foundation, each course in ''Contemporary Mathematics in Context is the product of a four-year research, development, and evaluation process involving thousands of students in schools across the country. The result is a program rich in modern content organized to make active student learning a daily occurrence in your classroomGood
Borgasorus Books, Inc. MO Wentzville, MO
Hardcover Good 0078275458 |
9780883139653
ISBN:
0883139650
Publisher: Hayes School Pub. Co
Summary: Frederick H Bell is the author of Know the essentials of pre-algebra mathematics: Problems, drills, tests, published under ISBN 9780883139653 and 0883139650. Four Know the essentials of pre-algebra mathematics: Problems, drills, tests textbooks are available for sale on ValoreBooks.com, three used from the cheapest price of $10.00, or buy new starting at $15.78. 1 [more] 1985, 1988. Text and pages are clean in all except First Year Algebra which has some pencil writing on one page.[less]
ISBN-13:9780883139653
ISBN:0883139650
Publisher:Hayes School Pub. Co
Valore Books has some of the lowest prices for cheap Know the essentials of pre-algebra mathematics: Problems, drills, tests rentals, or used and new condition books that can be mailed to you in no time. |
The mathematics program at St. Olaf is nationally recognized for innovative and effective teaching, for scholarship, and for service to the profession. We see mathematics as interesting, important, useful, and appropriate for students with a wide variety of interests. Welcome to our mathematical community.
It's summertime in MSCS!
It's quiet in Regents Hall of Mathematical Sciences, but we're working hard to get ready for the 2011-12 academic year, and to welcome the class of 2015 to campus. Incoming first year students might want to peruse our web pages (including some tidbits below) for some useful information.
Do I have to take a math class at St. Olaf?
The short answer is no, but the longer answer is that all B.A. students must satisfy the Abstract and Quantitative Reasoning (AQR) General Education requirement (B.M. students may choose to complete a general education requirement with an AQR course). Students complete the AQR requirement either by taking a designated course in Mathematics, Statistics, or Computer Science or through successful completion of an equivalent course prior to arriving at St. Olaf. Get started on the Math and AQR Placement Process by clicking here.
Do I have to complete the AQR requirement at St. Olaf?
Some students have taken the right kind of courses in high school or have had other academic experiences that give them credit for the AQR. Visit our AQR Placement page to see whether or not this includes you.
How do I satisfy the AQR requirement?
There are several different courses in mathematics, statistics, and computer science that satisfy the AQR requirement. Which kind of course you should take depends on your academic strengths and interests. Click here to get started on the Math and AQR Placement Process and you'll find your way to the information you need.
I know that I want to take a math course at St. Olaf, but which one should I take?
Excellent--we're glad you want to take a math course! In order to gather information and report it to your advisor you must go through the Math and AQR Placement Process. Click here to get started and you'll find your way to the information you need.
MSCS NEWS
Congratulations to two Ole grads for having their mathematics research papers published, both in the Electronic Journal of Combinatorics and even in the same issue. Cameron Marcott's paper is titled On the Relationship between Pipe Dreams and Permutation Words, and Vladimir Sotirov's paper is Involutions on Standard Young Tableaux and Divisors on Metric Graphs. Find both here. |
Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate levelThis is an introduction to predicate logic and how it is applied in computer science, electronic engineering, linguistics, mathematics and philosophy. Building on your knowledge of propositional logic, you will learn predicate logic—its language, interpretations and proofs, and apply it to solve problems in a wide range of disciplinesThis course on Division and Multiplication of Whole Numbers introduces a learning trajectory approach to students' multiplicative reasoning, exploring a stronger conceptual basis for multiplicative reasoning, so that, eventually, multiplication and division of fractions is an extension of multiplication and division of whole numbers, instead of a new and mystifying monster of its own. |
I only found Stretch math as a course offered by upenn. It is used as an introduction to Calculus type concepts to students who will be entering the university as freshman. This was offered as a summer course. It covers definitions of derivatives and integrals. The end of the course begins covering first derivatives.
Stretch math is some sort of the process where you stretch a graphical curve into different magnitudes. The curve would be moving further and further from the X-axis, increasing in magnitude or lowering of magnitude. It can lead to a narrowing or widening of the quadratic curve, but the vertex would not change. Vertical stretching is the reciprocal of the numerical coefficient of the y-value.
If coefficient is 2, then there would be a vertical stretching of 1/2. If it is 1/3, there would be a VS of 3. |
TI offers a wide range of graphing handhelds for multiple grade levels. The same tools that have become indispensable for math and science now can facilitate the study of Language Arts, Social Studies, History, World Languages and more by building interest, encouraging exploration and, ultimately, deepening understanding. And isn't that what the pursuit of knowledge is all about?
Summary
TI-73 Graphing technology designed for middle grades with a large screen to help students see patterns, analyze data and have fun while learning. Items included: TI-73 graphing handheld, unit to unit cable, 4 AAA batteries, English manual.
Abstract
The Explorer TI-73 ViewScreen Graphing Calculator joins our popular line of handheld technology, providing a larger screen alternative for teachers who feel limited by the two-line display of other fraction and scientific models. The Explorer TI-73 is completely compatible with existing TI-73 classroom accessories and related curricular materials for upper elementary through lower middle grades, from fractions through pre-algebra.
Product Specifications Compare with other products
Product Name
TI-73 Explorer Graphic Calculator - Blue
Product Type
Graphing Calculator
Product Family
ViewScreen
Power Source
Battery
Color
Blue
Functions
Fraction
Data Collection with CBR and CBL 2
Data Analysis and Plotting
Constants - Developing Number Patterns
Conversions
Stacked Fractions
English and Metric Conversions
4 xGraphs Functions Simultaneously
Interactive Equation Solver
Change Improper Fractions to Mixed Numbers
Simplifies Fractions
Fraction/Decimal Conversions
Combinations and Permutations
Random Number Generator
Trigonometry
Logs and Antilogs
Convert Angles From Degrees to Radians
%, x², 1/x, x, y², xy, and x
Fixed Decimal Capability
AOS: × and ÷ before + and -
Product Model
TI-73
Product Line
ViewScreen
Display Screen
8 Line x 16-digit - LCD
Batteries
4 x AAA Lithium
Calculator Features
Easy-to-read Display
Additional Information
13 x Zoom Features
14 x Digit Accuracy Displayed to 10-Digits with 2-Digit Exponent
7x Graph Styles: Thin, Thick, Animate, Animate with Path, and more
3 x Statistical Plot Set-Ups
Scrollable Home Screen
Four Constant Features
Function Evaluation Table
Programming Capabilities
Impact Resistant Slide Case
Large 64 × 96 Pixel Screen
Uses TI-82/83 ViewScreen LCD Panel
I/O Port for Linking and Data Collection
Upgradeable Operating System and Software
Display Indicates When Fraction Can be Simplified
Shows Common Factor Used During Simplification
Alphabetical CATALOG of All Calculator Operations in One Menu
2K Bytes RAM With 25K User-Available. 128K of Application Space
More Advanced Functions Accessed Through Pull Down Menus
Seven Statistical Plots: Pictographs, Pie Charts, Bar Charts and More
User-Defined List Names, Stores up to 999 Elements
Send and Receive Lists and Variables to and from the TI-82, TI-83, TI-83 Plus, TI-84 Plus |
Applied Mathematics - 4th edition
Summary: Applied Mathematics is a comprehensive text designed to benefit students in various fields of study. Text content emphasizes the application of mathematics to a variety of vocational and technical areas. The text uses realistic applications to develop problem-solving skills and provide an understanding of the importance of math in the real world. --This text refers to an alternate Hardcover edition.
1605252786 2010 Goodheart-Willcox. This hardcover copy has light shelf wear and scuffing to the cover. The text is unmarked and the binding is sturdy. "Applied Mathematics provides easy-to-understa...show morend 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." The sale of this item benefits the Hutchinson Public Library. 100% customer satisfaction guaranteed. We process and ship orders daily, securely and with delivery confirmation. ...show less
$18.00 +$3.99 s/h
LikeNew
Bookbyte-OR Salem, OR
Almost new condition. SKU:9781605252780-2-0
$39.20 |
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating... more...
This book has two main purposes. On the one hand, it provides a concise and systematic development of the theory of lower previsions, based on the concept of acceptability, in spirit of the work of Williams and Walley. On the other hand, it also extends this theory to deal with unbounded quantities, which abound in practical applications. Following |
Trigonometry Workbook: Teacher Guide [NOOK Book] ...
More About
This Book starters, students will actually like using them. Here's why: • Math is explained in simple language, in an easy-to-follow style • The workbooks allow students to learn at their own pace and master the subject • 15 lessons break down the material into the basics • Each lesson is fully devoted to a key math concept and includes many step-by-step examples • Paced instruction with drills and quizzes reinforces learning • The innovative "Math Flash" feature offers helpful tips and strategies in each lesson—including advice on common mistakes to avoid • Skill scorecard measures the student's progress and success • Every answer to every question, in every test, is explained in full detail • A final exam is included so students can test what they've learned When students apply the skills they've mastered in our workbooks, they can do better in class, raise their grades, and score higher on the all-important end-of-course, graduation, and exit exams. Some of the math topics covered in the Ready, Set, Go! Trigonometry Workbook include: • Trigonometric Ratios • Graphing Points and Angles • Special Angles • Inverse Trigonometric Values • Solving Triangles • Solving Four-Sided Figures • Solving Trigonometric Equations and more! Whether used in a classroom, for home or self study, or with a tutor, this workbook gets students ready for important math tests and exams, set to take on new challenges, and helps them go forward in their studies 4, 2014
Good book keep writeing
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Anonymous
Posted January 29, 2014
The story deserves it
I really loved the phone like thing idea but now i must read more! You finsh one part and are looking at all results for the next one you must find out that clif hanger!
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Anonymous
Posted January 29, 2014
Chapter 5- Light
The brightness of even a dim bulb would have been enough by now to blind Ana. So twenty or so super-high-watt bulbs was like pure agony after the last fifteen minutes or so. <br> Ana groaned. She wondered if this was some kind of defense mechanism. Leave the place ridiculously dark, then have extra-bright lighting blind th intruders. However, once she couod get both eyes to stay open without feeling like she was trying to look straight at the sun, she realized this place was all but abandoned. <br>The room she was in was not unlike her science classroom at school: lots of odd-looking bottles of who-knows-what, lab supplies strewn across a table in one end of the room. All it needed was her teacher, Mr. Speck. Had he been there, she would have easily believed herself to be in class. Waking up from a weird dream brought on by a longer than average lecture. Except it obviously wasn't a dream. Was it? <br> She decided to test the theory. If she was dreaming, she should be able to do whatever, right? So she should be able to teleport out. Ana closed her eyes, imagining herself appearing in her room. She stayed that way for about thirty seconds, concentrating. Then she opened her eyes again. <br> She was still in the mysterious room that resembled a science lab, standing there with her sock rope tied around her waist. Of course not. Either she was having a very strange dream, or this was real. Best she keep going with the latter assumption for now. A dream might not have much consequences, but if this was real...<br> She staggered over to the table to get a closer look at the contents. A bunch of vials of stuff she couldn't identify, a couple of unused petri dishes, and...a small grey box. <br> The box was about the size of her fist, with the thickness of about half an inch, and had a metallic sheen to it. She picked it up and turned it over in her good hand. A mark on the bottom caught her eye. <br> The mark looked familiar somehow...it took her a second to recognize it. It looked like the 'call' button on a cellphone. She wondered if she should press it or not. Then a loud buzz took her by surprise. It was coming from the box! She dropped it, startled, then saw how it had landed. <br>Button down. Meaning the button had just been pressed. Wonder what this one would trigger? 'Hopefully not another elevator...' she thought. <br>It wasn't an elevator, of course. It was something much stranger.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
I need to know soon how important math skill is to architecture?
I want to be an architect. I've wanted to do this since I was a little girl. I don't like math, and I've been stumbling through it all my life. Can someone tell me how much math will be used manually, and if I can do most of it on a computer or calculator. That is what I was counting on because my dad told me he uses computers and calculators for his construction business, and never needed all that heavy math. If I can pass courses, will I really rely on calculators and equipment mostly?
Asked By: - 12/7/2011
Best Answer - Chosen by Asker
There are different jobs in architecture, so it depends on what you wish to do. Most will require a basic background in math skills as you seem to already know. You'll need to understand geometry, algebra and trigonometry. If you're wanting to be involved with large projects and industry, you'll likely need calculus |
Survival Skills for
Quantitative Courses
These units will help you teach yourself the skills you need to
succeed in introductory science courses. Some of them will be very easy, some
you may never have seen before. Every person's preparation for these
courses is different and these units are designed to bring everyone to
the same level. Each unit has a series of associated problems.
Complete these problems to test your mastery of the material. |
Arithmetic and pre-algebra
The first math topic. Start here if you want to learn the basics (or just want to make sure you know these topics). After this, you should be ready for algebra. This topic includes videos from the former developmental math playlists. |
graph theory
Offering a comprehensive introduction to the fundamental topics of graph theory, this text is for undergraduate or graduate courses in Graph Theory. It includes basic algorithms and emphasizes the understanding and writing of proofs about graphs. It also contains examples and exercises to develop an understanding of the structure of graphs.Read more... |
Microsoft Mathematics 4.0 Can Help You Visualize Mathematical Concepts
Microsoft Math 4.0 is a free download and features a large collection of tools, tutorials, and instructions designed to help you tackle math and science problems quickly and easily. "With Microsoft Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus." |
Many students might know about one or two of these sites, the resourceful students know all of them. Whether if you do or don't could easily be the difference between a letter grade or two. Even if they cost money I'd highly recommend investing in these web resources.
Khan Academy
Cost: Free!!! What is it?: According to their website, "Khan Academy is a non-profit educational website created in 2006 by educator Salman Khan, a graduate of MIT and Harvard Business School. The stated mission is to provide 'a free world-class education for anyone anywhere.'" Salman Khan is a highly accomplished academic having three degrees from MIT (BS Math, BS Electrical Engineering & Computer Science, and a Masters in Electric Engineering & Computer Science) not to mention him going to Harvard for his MBA. Basically his website contains lectures from him and newly other experts in various fields of education (History, Mathematics, Physics, Organic Chemistry, etc. ). What can you gain from it?:Salman Khan's video lectures are perfect for when your class didn't cover the issue enough or if you're still having trouble understanding some concepts. He has a remarkable way of explaining things conceptually and often can explain things in a way that suddenly makes things click in your head. I would maybe use this for test review, but I would mostly use it to supplement in-class lectures. This is not a substitute for taking notes! Pros: Many different topics, not just STEM, and very thorough. Great for conceptual understanding. Cons: Very long winded, can talk a long time to explain a subject because he explains it in such detail, if you just need a little bit of help and not a lot, it wouldn't be my first choice. No specific advice for your homework problems.
PatrickJMT
Cost: Free
What is it: Patrickjmt.com is a lot like KhanAcademy except it focuses on Math and to a lesser extent physics. Rather than explaining to you all of the theoretical basis behind mathematics, Patrick simply does an example problem. His video's tend to be a lot shorter and more to the point than compared to Khanacademy, because he is not diving deep into the theories and intuition behind the solutions.
What can you gain from it?: This website is indispensable when you're just having trouble with a very specific problem, he tends to do many different examples so this can definitely speed up any homework problem or test review.
What is it: Chegg should be a name every college student knows for a number of reasons. First of all you can rent books as opposed to buying them saving you tons of money, you can even rent the etextbook saving you space and your back. But more importantly for $14.95 a month you can access the solutions manual for any textbook in the world. Step by step solutions to all the problems in your textbooks. If you don't know what a solutions manual is, you need to, especially if you're taking a STEM class. A solutions manual offers the step by step answer to every problem, rather than just the number. The homework help section is also amazing since there are tons of people on the website who will answer the questions you ask, or the question may have already been asked and you can look up the previous solutions. What can you gain from it?: Chegg's resources aren't great note supplements but in terms of homework help they're hard to beat. You can use this website to help you solve your homework and understand the solutions if you don't have a solutions manual.
Pros: Very specific to your HW, A large data base of answered questions. Can answer questions that are not straight forward. Sells and rents books.
Cons: Can have many wrong answers or solutions, can often be unhelpful. Still might be cheaper to get the solutions manual(s). Pretty specific but may not be extremely helpful with online homework due to the questions having different numbers.
WolframAlpha
Cost: Free – $2.99/Month for unlimited Access
What is it: WolframAlpha is a "computational knowledge engine" it can tell you thing from the "number of colon cancer deaths in japan" to . We are very lucky as math students that not only can it answer almost any math question you can type into it, but it also offers step by step solutions.
What can you gain from it?: It functions as an extremely powerful calculator, and can be used for doing your homework whenever you don't need a lesson and checking your answers.
Pros: Very specific, can answer almost any question you put into it, fast.
Cons: Very limited but still helpful free service, Can offer much theoretical or intuitive insight. |
Analysis - 04 edition
Summary: This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this cor...show moree material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.
--Self-contained coverage of basic analysis, from fundamentals to more advanced topics |
Too many students end their study of mathematics before ever taking an algebra course. Others attempt to study algebra, but are unprepared and cannot keep up. Key to Algebra was developed with the belief that anyone can learn basic algebra if the subject is presented in a friendly, non-threatening manner and someone is available to help when needed. Some teachers find that their students benefit by working through these book before enrolling in a regular algebra course; others use them as supplemental help and review. In books 1-4, students study multiplying, division, integers, area, perimeter, exponents, distributive principle, equations, polynomials, quadratic equations and more. This answer key provides brief notes to the teacher and gives the answers to the workbook problems. Student pages are reduced and overlaid with the correct answers. Accompanies Key to Algebra Book 1, Key to Algebra Book 2, Key to Algebra Book 3, and Key to Algebra Book 4. |
collection of downloadable software programs under the GNU freeware license that illustrate aspects of geometry and...
see more
A collection of downloadable software programs under the GNU freeware license that illustrate aspects of geometry and topology. From elementary to upper-level college; for both Mac and Windows machines.
Curved Spaces is a flight simulator for multiconnected universes. Such toy universes are the 3D analog of the torus and Klein...
see more
Curved Spaces is a flight simulator for multiconnected universes. Such toy universes are the 3D analog of the torus and Klein bottle on which the simpler 2D Torus Games are played. Because light itself wraps around such a space, inhabitants see their universe's contents repeating in a crystaline pattern, like a hall of mirrors but with no reflection. Curved Spaces is intended for undergraduates and graduate students studying 3-manifolds, and has also found use as a research tool in topology and cosmology.
Use principles of trigonometry to calculate the correct angle of decent for an aircraft during an emergency landing on an air...
see more
Use principles of trigonometry to calculate the correct angle of decent for an aircraft during an emergency landing on an air strip just long enough for the aircraft. Be careful, an incorrect calculation could put the aircraft in danger. |
More About
This Textbook
Overview
This book explores the impact of calculators on mathematics instruction in grades K-14. The authors examine underlying theoretical and research information which supports the use of calculators in the mathematics classroom. Chapters examine general issues related to calculator use. Successful calculator projects, while further discussing direction for the future utilization of calculators in mathematics. Many authors contributed articles to this original work, focusing on the benefits of calculators. Authors included are: George W. Bright, Hersholt C. Waxman, Susan E. Williams, Thomas A Romberg, Jane F. Schielack, Clarence J. Dockweiler, Gary C. Bitter, Mary M. Hatfield, Juanita V. Copley, Shwu-Yong L. Huang, Paul A. Kennedy, Bert K. Waits, Franklin Demana, Donald R. LaTorre, and John G. Harvey. Contents: Multiple Perspectives on the Impact of Calculators on the Mathematics Curriculum; Assessment and Technology; Calculator Inservice for Mathematics Teachers; Using the Calculator to Develop Number and Operation Sense, K-Grade 5; The Calculator Project; Assessing School-Wide Impact of Calculator Integration; Research on Calculator Use in Middle School Mathematics Classrooms; The Graphing Calculator in Pre-Algebra Courses; Research and Practice; The Calculator and Computer Precalculus Project (C2PC): What Have We Learned in Ten years?; Supercalculators in Undergraduate Mathematics; Teaching Mathematics with Calculators (TMC): A Local and National Inservice Teacher Education Project; Future Direction of the Study of Calculators in Mathematics Classrooms.
Author Biography: George W. Bright is Professor of Mathematics at the University of North Carolina atGreensboro.
Editorial Reviews
Booknews
From a May 1992 conference in Houston, 11 papers reflect on how calculators do and might influence the teaching of mathematics, and make recommendations for future efforts to integrate them into the curriculum. Among the topics are inservice training for teachers, the graphing calculator in pre-algebra courses, supercalculators in undergraduate mathematics, and surveys and assessments from various systems and levels. No index. Paper edition (unseen), $21 |
Chapters 1-3 focus on integers, rational numbers and real numbers in order to set the stage for equations, inequalities and functions. Real-World applications to the more abstract algebraic concepts are found throughout the text. More than 5 Activity Labs per chapter ensure students receive the visual and special instruction necessary to conceptualize these abstract concepts and prepare them for advanced math courses.There are many features built into the daily lessons of this text that will help you learn the important concepts and skills you will need to be successful in this course. There are numerous Exercises in each lesson to give you the practice you need to learn. Practice Multiple Choice exercises are included in the lesson to help you prepare for success on your state test. The text also contains Error Analysis, Test Prep exercises, Critical Thinking exercises, Challenge exercises |
Discrete Mathematics and Its Applications - 2nd edition
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 applications, as we...show morell as the overall comprehensive nature of the topic coverage. Copyright Libri GmbH. All rights reserved |
MATHEMATICS DEPARTMENT
The primary objective of the mathematics program
is to contribute to the total education of the student
with course offerings that present a strong preparation,
both in concepts and skills, for his or her future
needs. The following programs are subject to constant
study and review and revisions are made when necessary.
ALGEBRA I
This course introduces the student to the basic
structure of mathematics through a thorough study
of the real number system. An understanding of the
concepts and mastery of necessary skills is emphasized
throughout. The need for precision and exactness
in expression and thought is constantly stressed.
Other topics covered are equations, inequalities,
rational and irrational expressions.
GEOMETRY
In this course the aims begun in Algebra I are
continued and carried out to a greater degree.
This is accomplished
through the study of triangles, quadrilaterals,
polygons, circles, prisms, pyramids, cylinders,
cones and spheres. The students' power of
spatial visualization is developed through the
integration
of space geometry with plane geometry throughout
the course.
ALGEBRA II AND TRIGONOMETRY
This course is a continuation of Algebra I with
the repeated topics covered in greater depth than
in the first year. New topics include sequences,
logarithms, complex numbers, and the trigonometric
functions.
ANALYTICAL GEOMETRY / DIFFERENTIAL CALCULUS
In the Analytical Geometry course, material is presented
from the Vector and Cartesian viewpoints. This course
includes a thorough treatment of vectors, lines
and conic sections in a plane.
In the Elementary Functions course, the following
functions are covered in detail: polynomial, logarithmic,
and exponential. The basic concepts of calculus
are presented and used in the study of these functions.
PROBABILITY AND STATISTICS
This one semester course is primarily for students
whose college courses will not be in math-oriented
fields. Therefore, its goal is to give these students
a basic understanding of probability and statistics
to prepare them for college courses such as economics,
business, education and sociology.
A.P. CALCULUS/HONORS CALCULUS
These are college level courses which stress theory,
mechanics and applications in differential and integral
calculus. They prepare the student for future college
math courses and applications in related fields.
They cover the material which satisfies the agreement
with the University of Scranton
enabling students who successfully complete the
course to receive college credit without examination.
They also prepare students planning to attend other
colleges for the CEEB Advanced Placement examinations,
which they will take at the conclusion of this course.
The A.P. exam is mandatory for students in the A.P.
course and optional for those in the honors course.
MATH III AND IV - AN ALTERNATE PROGRAM
This program is designed primarily for the student
who, at the end of second year, is not strong in
mathematics. The material of the regular Math III
program - Algebra II and Trigonometry - is extended
over a three-semester period. A course in Probability
and Statistics in the second semester of fourth
year completes the program. This program gives the
student the necessary college preparatory mathematics
should his future interest be in some mathematically
oriented field.
ACCELERATED PROGRAM
There are two ways for students to qualify for the
accelerated math program. The first is for students
who have taken a course in Algebra I in eighth grade.
Based on the results of a qualifying examination
administered at Prep in May, students are given
the opportunity to begin their math program with
Algebra II in the first year, thus enabling them
to complete the pre-calculus program at the end
of their junior year.
Another group of students will qualify for this
programs based on their school record at the end
of freshman year.
All students in the accelerated program will take
Geometry in sophomore year followed by an integrated
course in Algebra II, Trigonometry, and Analytic
Geometry in junior year. These students will then
choose A.P. Calculus or Honors Calculus for senior
year.
To remain in the accelerated program, students must
maintain a sound academic record. |
Mu Alpha Theta (Math)
About Us
Mu Alpha Theta is a national honor society in mathematics for the junior college student. Its purpose is to stimulate interest in mathematics by providing public recognition of superior mathematical scholarship and by promoting various mathematical activities. Initiation is held in the spring.
The goal of the club is to promote interest in math and engineering among Blinn students. |
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems...
see more
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems regarding abstract algebra. Included is a Table of Contents that lists the topics such as Integers, Functions, Groups, Polynomials, Galois Theory, Unique Factorization, etc. There is also a link to an online study guide for the topic.
This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" ("...
see more
This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" (" target=״_blank״ as part of the MERLOT Classics Series on Elluminate. It is a good opportunity to explore the site from the authors' eyes and to gain insight into how they use it in classes.It would be good for a faculty development workshop or for individual enjoyment.
Here is a great site for statistical analysis. There are colorful presentations and explanations in "suggested learning...
see more
Here is a great site for statistical analysis. There are colorful presentations and explanations in "suggested learning order" from "Population" and "Histogram" to "Chi Square" and "ANOVA״. There are also alphabetical listings from "Alpha" to "Z-Score״. This is a great way to review material.
Hans Rosling says there's nothing boring about stats, and then goes on to prove it. A one-hour long documentary produced by...
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Hans Rosling says there's nothing boring about stats, and then goes on to prove it. A one-hour long documentary produced by Wingspan Productions and broadcast by BBC, 2010. Professor Rosling provides a very enthusiastic talk about the importance of statistics in the world.
This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever...
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This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever led you to believe was possible. Host Jason Marshall provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most mathphobic people looking forward to working out whatever math problem comes their way. If you're getting ready to take the SAT, GRE, or any of the other standardized tests; or if you're going back to school and need to brush up on the basics, the Math Dude's Quick and Dirty Tips to Make Math Easier will strengthen your fundamental skills, help you better understand the language of math, and succeed when it comes to taking a test. And if you just want to calculate the tip without using your iPhone and impress all your friends, his tips and tricks are for you too.'According to one user, 'I find this series very useful for students who need a different way to think about Math. The visual that is described and repetition of examples during the podcast are extremely helpful and go beyond memorization.'
This is a series of video lectures featuring a diverse group of speakers with a range of topics. The videos require Real...
see more
This is a series of video lectures featuring a diverse group of speakers with a range of topics. The videos require Real Player to run. Topics include Risk, Weather Forecasting, Stock Market Evaluation, Polls, etc. Don't miss the one on DNA Fingerprinting that discusses the statistics used in the O.J. Simpson case. At the end of the list are audio recordings from various NPR programs that discuss chance and include "Car Talk." |
Basic Mathematics
Description: Basic Mathematics: Revision and Practice is a popular textbook, widely used as a one-volume revision course for students aiming at grades B to E of GCSE and Standard Grade examinations. Key Points: · Exercises are preceded by notes and workedMore...
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Basic Mathematics: Revision and Practice is a popular textbook, widely used as a one-volume revision course for students aiming at grades B to E of GCSE and Standard Grade examinations. Key Points: · Exercises are preceded by notes and worked examples to provide students with clear models to follow · Makes students aware of the part that mathematics plays in everyday lives · Includes all numerical answers |
Atlanta ACT Math study cardiac dynamics and other complex dynamical systems, where differential equations play a key roll. The |
Quantitative Literacy
Drake students will learn to reason with the symbols and components of mathematical languages as well as effectively use the principles that underlie these operations. Courses that satisfy this requirement will have mathematical reasoning as their principal focus. They may also address questions that engage learners with the world around them and help them to analyze quantitative claims that arise from the study of civic, political, scientific, or social issues. Quantitative literacy courses may be focused on the mathematical needs of a specific discipline or on a specific interdisciplinary issue or problem. these courses will engage students to achieve these student learning outcomes. Students will be able to:
Analyze and present solutions to problems using symbols and components from mathematical languages and their underlying principles.
Identify and execute appropriate mathematical operations for a given question |
Find a Far Rockaway ACTWe also had another two semesters of a course called abstract algebra. Vector Spaces can be studied in a more general sense in abstract algebra as well. This area of math is concerned with abstract mathematical structures such as groups, rings, and fields. |
Algebra: Form and Function
9780471707080
ISBN:
0471707082
Edition: 1 Pub Date: 2009 Publisher: Wiley
Summary: This text offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging.
Connally, Eric is the author of Algebra: Form and Function, published 2009 under ISBN 9780471707080 and 0471707082. Five ...hundred seventy Algebra: Form and Function textbooks are available for sale on ValoreBooks.com, one hundred sixty seven used from the cheapest price of $19.73, or buy new starting at $153.89.[read more]
Ships From:Multiple LocationsShipping:Standard, ExpeditedComments:RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). 085 Item is intact, but may show shelf wear. Pages may include notes and highlighting. May or may... [more]RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). 085085 Item is intact, but may show shelf wear. Pages may include notes and highlighting. May or may... [more] |
Understanding Year 9 & 10 Advanced Maths
Important Note:
The Advanced book covers all the work in the Intermediate
books, plus many additional topics. There is more emphasis
on algebra, and the exercises at the end of each topic are
significantly more challenging.
This book covers two (2) years of work, and has been specially
developed for those students in NSW who are studying the ADVANCED
COURSE in Years 9 & 10. For States outside of NSW this book
is most suitable for talented students of above average mathematical
ability.
The topics shown in the left hand column tend to be covered by
most schools in Year 9, while the topics in the right hand column
are usually taught in Year 10. Schools can also choose certain Additional
Topics to study in more depth. We have only included the more popular
options which are extremely useful for Advanced Students who wish
to study 2 Unit Advanced Maths, or higher, in Year 11.
At the end of each Major Topic listed above, there are usually
two or more comprehensive review exercises. Some of the more important
topics have three review exercises. Because this book is aimed at
Advanced Students, the exercises are significantly more difficult
than the corresponding exercises in the Intermediate book. |
The treatise on conic sections by the Hellenistic mathematician Apollonius from Perga is regarded as a supreme achievement of Greek mathematics and maintained its authority right up to the 18th century. This new edition is the first to consider all Greek and Arabic sources, with the Arabic texts being presented in the first ever critical edition. Both... more...
Traditional methods for handling spatial data are encumbered by the assumption of separate origins for horizontal and vertical measurements. Modern measurement systems operate in a 3-D spatial environment. The 3-D Global Spatial Data Model: Foundation of the Spatial Data Infrastructure offers a new model for handling digital spatial data, the global... more...
This book is designed for grades K–2 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-10 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
This book is designed for grades 3–5 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-15 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was or what he proved, and what Fibonacci?s sequence or Pascal?s triangle are? The more you know about Maths, the less of a science it becomes. 30 Second Maths takes the top 50 most engaging mathematical theories, and explains... more... |
...Mathematics evolved over the past few thousand years as a way to answer questions about real-life. Algebra is the collection and categorization of many different rules, formulas and properties. A typical Algebra 1 course reinforces the very basics of solving, graphing, and writing linear equations and inequalities. |
Area Formulas - MAT-955 your students develop area formulas for parallelograms, triangles, and trapezoids. Using hands-on activities, video demonstrations, animations, and comics, your students will build a strong understanding of area formulas and how to use them in problem solving. This course is built around core propositions from the National Board for Professional Teaching Standards as well as national content standards.
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"The information that I have gathered while participating in various courses at Fresno Pacific University has impacted my classroom tremendously. The students are able to learn with a more hands-on approach which has improved their understanding of the material being presented." |
College Algebra : Graphs and Models - 3rd edition
ISBN13:978-0077221287 ISBN10: 0077221281 This edition has also been released as: ISBN13: 978-0073051956 ISBN10: 0073051950
Summary: TheBarnett Graphs & Modelsseries in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and proce...show moresses.A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful22128195 |
A Best Answer: An answer that clearly demonstrates how to solve the problem the student is facing. Remember, we're here to help students learn the material. Craft a solution as if you were sitting side-by-side with the student, explaining each step and your reason for doing so. This often means that you go back to the fundamental concepts behind the question in order to solve it, that you explain in words as well as mathematical symbols, and that you write clearly so someone at any level could understand how to solve the problem. Students come to Chegg with various levels of experience and expertise, so it's important that we offer them the support they need.
Some Key Components of a Winning Answer, in order of our experts' ranking of their importance:
Answer more questions to build up your reputation with the community. The higher your rating, the more reputable your answers appear.
Explain each step in words and equations. Write clearly, using proper grammar, punctuation, and spelling.
Upload a supporting diagram. This can be done using software and then saving as a .jpg or .png or just by simply drawing an illustrative diagram and then taking a photo with your camera phone.
Break big chunks of text up into paragraphs when you move on to a new idea.
Start the answer with a clear introduction to the problem-solving method you'll be using. This will help start things off on a clear foot.
Upload your profile with a photo of yourself and a headline. This will make your answers seem more human and easy to relate to.
Post as yourself, not anonymously. This communicates authenticity.
Software Suggestions for Creating Graphs and Diagrams:
Microsoft Excel for business, accounting, basic math, and tons of subjects in between. Creating graphs and tables is so easy in Excel that we always recommend you start here first. Then you can save them and import as jpegs. This is clearer than a hand-drawn table or diagram and looks super professional.
DrawPlus. This is a free drawing program you can download on the Serif website. It will help you create clear diagrams and figures for your answer.
Specialized software for certain subjects (this could include Avogadro for chemists, MATLAB for mathematics, PSPICE for engineering, etc.).
Pencil and paper. Take a photo of a graph or diagram you've drawn on paper (as long as it's super clear). Please note you can't currently rotate the image, so make sure you rotate it properly beforehand.
Here's an example:
Question: (x-2)^2 = 144
Solution:
This question requires familiarity with square roots and exponents.
Step 1) You need to remove the exponent from the left side of the equation to solve for x, so take the square root of both sides.
√[(x-2)^2)] = √144
Step 2) Solve for the square root. One the left side, the square root cancels out an equation that is squared. On the right side, the square root of 144 is 12 (i.e., 12^2 = 144).
(x-2) = 144
Step 3) Add 2 to each side of the equation to so that x is the only variable on the left side of the equation.
[...] I always include the required formulas and diagrams needed in the question. It is important for me to help students understand the concepts behind the problems, and including these is the best way to do this. I usually spend 2-3 minutes answering an average problem and maybe more than 15 minutes if the problem is complex. I make sure I answer each and every question with the utmost concentration, since my errors will have an impact on the student who asked the question. [...]
The probability that a customer would purchase a washing machine is 0.2. The probability that the customer would purchase a washing machine or a dryer is 0.30. The probability that the customer would purchase a dryer is 0.25. The probability that a customer would purchase a washing machine but not a dryer is |
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Starting at $0Intended for developmental math courses in intermediate immediate feedback, reinforcing the concept, identifying problem areas, and, overall, promoting student success. New!Interactive Exercisesappear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles. New!Think About ItEx. New!Important Pointshave been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently. New!Coverage of evaluating functions, graphing functions, and the vertical line test have been added to Section 3.2. New!An explanation that the x-coordinate of an x-intercept is a zero of a function can now be found in Section 3.3. New!Improved Introductions to exponential and logarithmic functions in Chapter 10 will lead to greater student understanding of and interest in these topics. New Media!Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool.
Table of Contents
Review of Real Numbers
Introduction to Real Numbers
Operations on Rational Numbers
Variable Expressions
Verbal Expressions and Variable Expressions
First-Degree Equations and Inequalities
Equations in One Variable
Coin, Stamp, and Integer Problems
Value Mixture and Motion Problems
Applications: Problems Involving Percent
Inequalities in One Variable
Absolute Value Equations and Inequalities
Linear Functions and Inequalities in Two Variables
The Rectangular Coordinate System
Introduction to Functions
Linear Functions
Slope of a Straight Line
Finding Equations of Lines
Parallel and Perpendicular Lines
Inequalities in Two Variables and by Using Matrices
Application Problems
Solving Systems of Linear Inequalities
Polynomials and Exponents
Exponential Expressions
Introduction to Polynomials
Multiplication of Polynomials
Division of Polynomials
Factoring Polynomials
Special Factoring
Solving Equations by Factoring
Rational Expressions
Introduction to Rational Functions
Operations on Rational Expressions
Complex Fractions
Rational Equations
Proportions and Variation
Literal Equations
Rational Exponents and Radicals
Rational Exponents and Radical Expressions
Operations on Radical Expressions
Radical Functions
Solving Equations Containing Radical Expressions
Complex Numbers
Quadratic Equations and Inequalities
Solving Quadratic Equations by Factoring or by Taking Square Roots
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula |
With this lesson, students will use tables of fees from a few different cell phone providers to create an algebraic expression that reflects billing for services. The example helps students apply algebraic functions to...
This lesson helps students further their understanding of linear functions by applying the material to a real-world example. The class will use data on an airline flight including travel time, ground speed, time...
This math lesson from Illuminations helps students understand rational functions. The material uses the real-world problem. Students will write rational functions that model problem situations and use rational functions...
This math unit from Illuminations includes 2 lessons on vectors and their properties. In the first lesson, students will learn the components of vectors. In the second lesson, the class will extend their knowledge to...
This course, authored by Denis Auroux of Massachusetts Institute of Technology, covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices... |
Precalculus : Concise Course - 07 edition
Summary: With the same design and feature sets as the market leading Precalculus, 7/e, this new concise text provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Precalculus A Concise Course is designed to offer a cost-effective, one-semester alternative to the traditional two-semester precalculus text. It contains the features that have made the Larson/Hostetler series a complete solution for both students and...show more instructors interesting applications, pedagogically effective design, and innovative technology combined with an abundance of carefully developed examples with worked-out solutions and exercises. In addition
Side-by-Side Example Solutions for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles.
Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, giving students the opportunity to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book.
Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts.
Exercise Sets are carefully developed to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications.
New! Make a Decision applications--presented throughout the text at the end of selected exercise sets--are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format.
Eduspace, powered by Blackboard, Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the Precalculus A Concise Course text. This content is paired with the recognized course management tools of Blackboard |
Art And Craft of Problem Solving
9780471789017
ISBN:
0471789011
Edition: 2 Pub Date: 2006 Publisher: John Wiley & Sons Inc
Summary: You' ve got a lot of problems. That's a good thing. Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What's the attraction? It's simple--solving mathematical problems is exhilarating! This new edition from a self-described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical p...roblem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no-holds-barred investigation of whatever mathematical problem you want to solve. You'll learn how to: get started and orient yourself in any problem. draw pictures and use other creative techniques to look at the problem in a new light. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more. tap into the knowledge gained from folklore problems (such as Conway's Checker problem). tackle problems in geometry, calculus, algebra, combinatorics, and number theory. Whether you're training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem-solver! About the Author Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He currently is an associate professor at the University of San Francisco. He won the USA Mathematical Olympiad (USAMO) and was a member of the first American team to participate in the International Mathematical Olympiad (IMO) in 1974. Since 1985, he has composed and edited problems for several national math contests, including the USAMO and helped train severalAmerican IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score. In 2003, he received the Deborah Tepper Haimo award, a national teaching award for college and university math, given by the Math Association of America.
Zeitz, Paul is the author of Art And Craft of Problem Solving, published 2006 under ISBN 9780471789017 and 0471789011. Six hundred twenty six Art And Craft of Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred thirty one used from the cheapest price of $59.32, or buy new starting at $59 |
covers the historical review of research and introductory mathematical concepts related to the structural dynamics of bridges. The e-book explains the theory behind engineering aspects such as 1) dynamic loadings, 2) mathematical concepts (calculus elements of variations, the d' Alembert principle, Lagrange's equation, the Hamilton principle, the equations of Heilig, and the δ and H functions), 3) moving loads, 4) bridge support mechanics (one, two and three span beams), 5) Static systems under dynamic loading 6) aero-elasticity, 7) space problems (2D and 3D) and 8) absorb systems (equations governing the behavior of the bridge-absorber system). The e-book is a useful introductory textbook for civil engineers interested in the theory of bridge structures. |
Algebra Fundamentals for Ultrasound Techs: A Student's Guide
Description: Anyone who wants to become an ultrasound technologist knows that understanding algebra and how it serves as a foundation for physics is a top priority. In this compact guidebook, a longtime teacher who has helped many students provides clearMore...
Anyone who wants to become an ultrasound technologist knows that understanding algebra and how it serves as a foundation for physics is a top priority. In this compact guidebook, a longtime teacher who has helped many students provides clear explanations and analysis to help you land your dream job. Even if you struggle with learning what everyone else seems to understand about math, don't despair. Take proactive steps to understand algebra fundamentals by referring to this guide, which offers answers to numerous questions and specific guidance, such as how exponents make multiplication easy;how to calculate in mathematics using scientific notation;how equations, relationships and graphics can help you;how fractions, decimals, and percentages work; andhow variables in equations can be solved. The guidebook includes practice problems, easy-to-follow explanations, answer keys, and a glossary defining key terms. Stop living in fear, and start seeking good employment. It begins with unraveling the mysteries of algebra |
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Many of the tools of today's technology--computer chips, lasers, and HDTV--were invented by people who are highly skilled in number sense and operations. As technology has become a major part of our everyday lives, these skills are in ever increasing demand.
Successful people apply the skills of problem solving in many areas of life. Mathematics helps you solve problems and think logically. Many times you need to assemble facts and use addition, subtraction, multiplication, or division to solve a particular problem.
Points, lines, and planes are the basic figures of geometry. In algebra, you used ordered pairs of numbers to locate points on a coordinate plane. You also used tables of ordered pairs and linear equations to locate and draw straight lines on a coordinate plane. Geometry on the coordinate plane is called coordinate geometry |
MATH36022 - Numerical Analysis 2
Requisites
Aims
To introduce students to theoretical and practical aspects of best approximation, quadrature, and the numerical solution of ordinary differential equations.
Brief Description
This module introduces numerical methods for approximating functions and data, evaluating integrals and solving ordinary differential equations. It continues the introduction to numerical analysis begun in MATH20602. It provides theoretical analysis of the problems along with algorithms for their solution. Insight into the algorithms will be given through MATLAB illustrations, but the course does not require any programming.
Learning Outcomes
On completion of the module, students will be familiar with
the theory of best approximation and how to compute best polynomial approximations in the 2- and -norms,
the theory and practice of numerical integration,
the theory and practice of numerical methods for solving ordinary differential equations.
They will also recognize some of the difficulties that can occur in the numerical solution of problems arising in science and engineering. |
Books
Mathematical Physics
"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)
"No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)
Reviews of the Second Edition:
"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)
R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:
- Unsurpassed coverage of path integrals and their relevance in contemporary physics
The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theoryVectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.
Revised and updated version of the leading text in mathematical physics
An insightful, revealing history of the magical mathematics that transformed our world.
At a summer tea party in Cambridge, England, a guest states that tea poured into milk tastes different from milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one man, Ronald Fisher, proposes to scientifically test the hypothesis. There is no better person to conduct such an experiment, for Fisher is a pioneer in the field of statistics.
The Lady Tasting Tea spotlights not only Fisher's theories but also the revolutionary ideas of dozens of men and women which affect our modern everyday lives. Writing with verve and wit, David Salsburg traces breakthroughs ranging from the rise and fall of Karl Pearson's theories to the methods of quality control that rebuilt postwar Japan's economy, including a pivotal early study on the capacity of a small beer cask at the Guinness brewing factory. Brimming with intriguing tidbits and colorful characters, The Lady Tasting Tea salutes the spirit of those who dared to look at the world in a new way.
Science is inextricably linked with mathematics. Statistician David Salsburg examines the development of ever-more-powerful statistical methods for determining scientific truth in The Lady Tasting Tea, a series of historical and biographical sketches that illuminate without alienating the mathematically timid. Salsburg, who has worked in academia and industry and has met many of the major players he writes about, shares his subjects' enthusiasm for problem solving and deep thinking. His sense of excitement drives the prose, but never at the expense of the reader; if anything, the author has taken pains to eliminate esoterica and ephemera from his stories. This might frustrate a few number-head readers, but the abundant notes and references should keep them happy in the library for weeks after reading the book.
Ultimately, the various tales herein are unified in a single theme: the conversion of science from observational natural history into rigorously defined statistical models of data collection and analysis. This process, usually only implicit in studies of scientific methods and history, is especially important now that we seem to be reaching the point of diminishing returns and are looking for new paradigms of scientific investigation. The Lady Tasting Tea will appeal to a broad audience of scientifically literate readers, reminding them of the humanity underlying the work. --Rob Lightner |
More About
This Textbook
Overview
Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding.
The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology.
This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes – "Special Relativity Review" and "The Chinese Connection" - and outline solutions to all exercises and problems, making it especially suitable for private study.
Editorial Reviews
From the Publisher
From the reviews of the third edition:
"This is the third edition of a book that is already familiar to those who teach an introductory course in general relativity. … Important concepts are introduced slowly and carefully, so that the resulting text is a comprehensible first introduction that is suitable for both physics and mathematics students. … its strength is that it is a short introduction to the subject that still covers all the essential material for a first course and provides a sound basis for further study." (J. B. Griffiths, Mathematical Reviews, Issue 2006 h)
"This book is a well-developed introduction to General Relativity. … the present third edition is really re-worked in many places in comparison with the previous ones. … Three appendices are quite helpful … . Solutions to the exercises, References and Index close this very readable book. … Every chapter ends with a list of problems … ." (Hans-Jürgen Schmidt, Zentralblatt MATH, Vol. 1089 (15), 2006)
Related Subjects
Meet the Author
J.D. Nightingale is Emeritus Professor of Physics at the State University of New York, College at New Paltz. J. Foster is recently retired Senior Lecturer in Mathematics at the University of Sussex. Both have extensive teaching experience in applied mathematics and theoretical physics. Prof. Nightingale's research interests tend towards the physical and cosmological consequences of general relativity, while Prof. Foster's tend towards the more mathematical aspects, such as exact solutions.
Table of Contents
Introduction
1 Vector and tensor fields.- 2 The spacetime of general relativity and paths of particles.- 3 Field equations and curvature.- 4 Physics in the vicinity of a massive object.- 5 Gravitational radiation.- 6 Elements of cosmology
Appendices
A Special relativity review.- B The Chinese connection.- C Tensors and Manifolds.- Solutions.- References.- |
Synopses & Reviews
Publisher Comments:
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Written by teachers and educational specialists
Polynomials
Polynomials: addition and subtraction
Polynomials: multiplication and division
Remainder Theorem
Rational Root Theorem
Equations and Functions
Factoring binomials
Greatest Common Factors
Exponential and logarithmic functions
Graphing functions
Systems of equations and inequalities
Systems of linear equations
System of equations and inequalities
Conic sections
Problem-Solving Tools
Clear, concise reviews of every topic
Practice problems in every chapter– with explanations and solutions
Diagnostic pretest to assess your current skills
Full-length exam– with answers– that adapts to your skill level
We take great notes– and make learning a snap
Synopsis:
"Synopsis"
by Libri, |
Select a content and you will automatically be redirected to the list of performance expectations.
7.1.
Core Content:
Rational numbers and linear equations
(Numbers, Operations, Algebra)
Students add, subtract, multiply, and divide rational numbers—fractions, decimals, and integers—including both positive and negative numbers. With the inclusion of negative numbers, students can move more deeply into algebraic content that involves the full set of rational numbers. They also approach problems that deal with a wider range of contexts than before. Using generalized algebraic skills and approaches, students can approach a wide range of problems involving any type of rational number, adapting strategies for solving one problem to different problems in different settings with underlying similarities.
7.2.
Core Content:
Proportionality and similarity
(Operations, Geometry/Measurement, Algebra)
Students extend their work with ratios to solve problems involving a variety of proportional relationships, such as making conversions between measurement units or finding the percent increase or decrease of an amount. They also solve problems involving the proportional relationships found in similar figures, and in so doing reinforce an important connection between numerical operations and geometric relationships. Students graph proportional relationships and identify the rate of change as the slope of the related line. The skills and concepts related to proportionality represent some of the most important connecting ideas across K—12 mathematics. With a good understanding of how things grow proportionally, students can understand the linear relationships that are the basis for much of high school mathematics. If learned well, proportionality can open the door for success in much of secondary mathematics.
7.3.
Core Content:
Surface area and volume
(Geometry/Measurement, Algebra)
Students extend their understanding of surface area and volume to include finding surface area and volume of cylinders and volume of cones and pyramids. They apply formulas and solve a range of problems involving three-dimensional objects, including problems people encounter in everyday life, in certain types of work, and in other school subjects. With a strong understanding of how to work with both two-dimensional and three-dimensional figures, students build an important foundation for the geometry they will study in high school.
7.4.
Core Content:
Probability and data
(Data/Statistics/Probability)
Students apply their understanding of rational numbers and proportionality to concepts of probability. They begin to understand how probability is determined, and they make related predictions. Students revisit how to interpret data, now using more sophisticated types of data graphs and thinking about the meaning of certain statistical measures. Statistics, including probability, is considered one of the most important and practical fields of study for making sense of quantitative information, and it plays an important part in secondary mathematics in the 21st century.
7.5.
Additional Key Content:
(Numbers, Algebra)
Students extend their coordinate graphing skills to plotting points with both positive and negative coordinates on the coordinate plane. Using pairs of numbers to locate points is a necessary skill for reading maps and tables and a critical foundation for high school mathematics. Students further prepare for algebra by learning how to use exponents to write numbers in terms of their most basic (prime) factors.
7.6.
Core Processes:
Reasoning, problem solving, and communication
Students refine their reasoning and problem-solving skills as they move more fully into the symbolic world of algebra and higher-level mathematics. They move easily among representations—numbers, words, pictures, or symbols—to understand and communicate mathematical ideas, to make generalizations, to draw logical conclusions, and to verify the reasonableness of solutions to problems. In grade seven, students solve problems that involve positive and negative numbers and often involve proportional relationships. As students solve these types of problems, they build a strong foundation for the study of linear functions that will come in grade eight. |
Life of Fred Mathematics
One day in Fred's life in which he . . .
• Falls in Love!
• Teaches you how to write an opera!
• Buys Hecks Kitchen!
• Does all of geometry up to the 14th dimension!
All of Geometry including...
Points and Lines
Angles
Triangles
Parallel Lines
Perpendicular Lines
Quadrilaterals
Area
Similar Triangles
Symbolic Logic
Right Triangles
Circles
Constructions
Non-Euclidean Geometry
Solid Geometry
Geometry in Four Dimensions
Coordinate Geometry
Flawless (Modern) Geometry
Unlike all other math programs, this one also has:
• The only verse of Fred's famous song, "Another Day, Another Ray"
• The difference between iambic, trochaic, anapestic and dactyllic in poetry
• How easy it is to confuse asinorum which is in the genitive plural in Latin with asinus which is in the nominative singular.
• A good use for Prof. Eldwood's Introduction to the Poetry of Armenia while on the deck of a pirate ship
Some answers are included in the textbook, the rest are included in a separate Answer Key.
Life of Fred Geometry is a hardcover textbook containing 542 pages. This book is not consumable. All answers are written on separate paper or in a notebook.
Number of Lessons: 2 Semesters. Expect to take anywhere from 9 to 14 months to complete. The amount of time required will be determined by the number of optional chapters (such as 5 1/2 and 7 1/2) you choose to cover and the academic ability of the student. Recommendation: Have the student look at the table of contents and plan out a schedule that will have the book completed in about a year. Taking responsibility for their own education is an important skill to learn. |
Teaching and Learning Guide 6: Non- Linear Equations
Section 2: The Concept of Quadratic Functions
1. The concept of quadratic functions
The difficulties in moving the focus away from linearity are perhaps two fold. First, as teachers we
have to undo the previous conception of a market or particular function and say that the real world
is very unlikely to be linear and thus we must alter how to try to model and represent real world
situations. Yet we need to do this in a way that does not lead the students to suddenly 'lose' all of
the economic understanding they have built up from this simplifying assumption. This is not easy
but is perhaps more straightforward than the second problem which is getting students to tackle
non-linearity in a mathematical setting when they have only just grasped the rudiments of linear
equations.
Clearly, the lecturer needs to build here on the assumption that linear equations have been taught
and the students have learned how to use them, interpret them in an economically sensible
manner and that they are comfortable when faced with problems that require solutions to linear
equation models. If you are uncertain about the students grasp of linearity, then please refer to
Teaching Guides 2 and 3 on this subject before reading any further.
In many respects, the difficulty with non-linearity is that students rarely encounter it in the early
years of their undergraduate degrees (if at all) and thus meaningful application is not always
forthcoming in parallel subject teaching. Again this reflects the more difficult application of non-
linear models within undergraduate teaching although that does not mean it is never done and nor
does it mean it has no value. This does not mean they do not realise that the assumption of
linearity is likely to be invalid, but that we do not do enough to show why it is useful, how
conclusions change and perhaps as importantly why assuming linearity is not always helpful.
2. Presenting the concept of quadratic functions
One approach is use a simple excel worksheet to demonstrate visually what happens when each
of the parameters of a quadratic equation are changed. Lecturers could plot the values of x and y
for a given quadratic equation (y = a + bx +cx2), perhaps one chosen by the students in a lecture
or small group and then illustrate this function. Values of a, b and c in the equation can be altered
and the equation re-plotted against the original graph.
Page 4 of 23
Teaching and Learning Guide 6: Non- Linear Equations
It is helpful to begin by switching between positive and negative versions of the same number
before altering the absolute value of the number. This demonstrates very quickly to students that
changing the value of a shifts the line up and down, it changes the value at which the line cuts the
y axis (x=0). Changing the value of b shifts the line left and right.
Finally and most importantly switching the value of c from positive or negative gives the line its 'u'
or 'n' shape, while increasing or decreasing the absolute value of c makes the slops steeper or
shallower. In the sample below we show the effect of a change in the c parameter from 1 to -1.
These worksheets could be mounted on the module website to allow students to work with in their
own time.
2
Function: y = a + bX + cX
Values a b c
old values 3 2 1
new values 3 2 -1
15000
X Old Series New Series
-100 9803 -10197
-99 9606 -9996 10000
-98 9411 -9797
-97 9218 -9600
-96 9027 -9405 5000
-95 8838 -9212
-94 8651 -9021 Old Series
-93 8466 -8832 0
New Series
-100
-84
-68
-52
-36
-20
-4
12
28
44
60
76
92
-92 8283 -8645
-91 8102 -8460
-90 7923 -8277
-5000
-89 7746 -8096
-88 7571 -7917 -10000
-87 7398 -7740
-86 7227 -7565
-85 7058 -7392 -15000
-84 6891 -7221
-83 6726 -7052
-82 6563 -6885
3. Delivering the concept of quadratic functions to small or larger groups
Students could benefit from a kinaesthetic and visual method of delivery. Lecturers could create a
range of laminated cards which cover the values 0 -1- inclusive, the variables x and y and the
power '2'. Students select cards and create their own quadratic in front of them and in pairs they
try to sketch what their quadratic might look like. Students could look at the quadratics and
sketches from other pairs.
The lecturer could select some or all of the quadratics and using Excel project what the functions
actually look like. This could be simple, effective and 'instant' way for students to develop a feeling
Page 5 of 23
Teaching and Learning Guide 6: Non- Linear Equations
for what a quadratic looks like and the function is constructed and behaves according to its
constituent coefficients.
Links with the online question bank
Questions on quadratic functions can be found on the METAL website at:
Lecturers might find it useful to refer to the questions on adding polynomials at
as a
precursor to the subsequent material or cubic and polynomial functions. These questions could
also be used to further differentiate teaching and learning.
Video clips
Although there are no clips which deal specifically with quadratics, lecturers might want to look at
the clip 1.09 at
which examines powers and indices in the context of gold mining and oil exploration.
4. Discussion Questions
Ask students to think of any relationships which are u-shaped. Could students who follow
geography courses make links e.g. mathematically modelling u-shaped valleys or river beds?
Obvious links to the natural world abound e.g. the wear on a step or the trajectory of a thrown
tennis ball. Students could see how many quadratic relationships they could identify and describe
within a week. Higher ability students might want to reflect on why the relationship is quadratic as
opposed to say a linear function.
5. Activities
Learning Objectives
LO1: Students learn to calculate values of y for different values of x using quadratic
functions
LO2: Students learn how to tabulate and plot quadratic functions
LO3: Students learn that many economic relationships are rarely linear and some can be
expressed using a quadratic expression.
Page 6 of 23
Teaching and Learning Guide 6: Non- Linear Equations
Task One
To begin with, let us assume that we are in a small group setting, such as a tutorial or problems
class, and we will show later how the activity can be adjusted for the large group (lecture theatre)
setting.
The first stage is to split the group into pairs or threes, which can be done with the people sitting
next to each other – there is no need to enforce randomness on this procedure as in fact that
might be threatening for some students and again create barriers to learning. The second stage is
to provide each group with a piece of graph paper with a relatively simple non-linear function
written onto it (e.g. y = 10 + 4 x 2 ).
Each group could have the same function or you could vary them so that there is exposure to a
number of equations. Another possibility is for the students to be given a series of equations and
they chose one of them to examine, which puts the element of control into their hands, again
helping to create a more positive atmosphere around the learning.
The exercise they are then set is to calculate the change in the dependent variable ( y ) for the
same (or possibly different) changes in the independent variable ( x ) . These can be written down
in tabular form on the sheet and then they can be plotted. Thus for example, for y = 10 + 4 x 2 it
might look like this:
(x ) (y)
0 10
1 14
2 26
3 46
Page 7 of 23
Teaching and Learning Guide 6: Non- Linear Equations
X=0
40
30
20
10
Y=0
0 1 2 3 4
The outcome of this exercise is that it should be apparent that for a given move from one value in
(x ) the change in ( y ) varies and thus the previously simple relationship between ( x ) and ( y ) found
in linear equations no longer holds. Crucially too the impact of changes in ( x ) on ( y ) depends on
where you start with ( x ) – a low value or a high value for instance.
Another issue here of course is how the lines are plotted. At first it is best to make explicit that you
simply want to plot the points as straight lines between two pairs of co-ordinates. Once this has
been done then, discussion of what happens to all the values in between the whole numbers we
have chosen and that can lead to plotting a smooth curve. This reinforces the staging process
from linear models to non-linear as the shape becomes exacerbated.
In essence, the exercise builds on prior learning as it requires manipulation of two variables to find
solutions to an equation and then plotting these on a graph, both of which they will have done
previously. In a large group setting the sheets can be handed out at the start of the session and
students can work on their own. Values for x are provided and they have to find y. They then offer
their answers to the lecturer who has a plot on the whiteboard or computer at the front of the
lecture theatre. As answers are plotted the non-linear nature of the relationship should become
Page 8 of 23
Teaching and Learning Guide 6: Non- Linear Equations
apparent quite readily. This can be done using Excel and plotting from the data therein which
could be pre-loaded with more data points than they provide in responses but which allow for the
curvature of equations to be emphasised.
An Example of an Excel chart with Data:
y= 10 + 4x2
x y
0 10
1 14
2 26
3 46
4 74
5 110
Task Two
Given the demand function QD = 75 – (1/4)P
a. Find the total revenue function written in terms of Q [TR = P(Q)]
b. Calculate the point at which total revenue is equal to zero
c. Calculate the point at which total revenue is maximised.
Task Three
A manufacturer faces two types of costs in its production process, fixed costs which are equal to
£1000 and variable costs which are equal to £2 for each tyre produced.
a. State the total cost function for this firm
b. Calculate average costs
c. Calculate total costs if 700 tyres are produced.
Page 9 of 23
Teaching and Learning Guide 6: Non- Linear Equations
Task Four
Using the total revenue function calculated from question 1 and the total cost function calculated
in question 2.
a. Derive the profit function for the firm
b. What is the value of profits when production equals 125 units?
Task Five
A company discovers the following economic information about its costs and demand function:
Demand Data Cost Data
1
Q = 33 − p Fixed costs are £200
2
Variable costs are £8 per unit
i) Derive the profits function for the firm
ii) What is the breakeven quantity?
iii) At what output level would profits be maximised?
ANSWERS
Task One
See Task
Task Two
1 2
a. TR = 75 p − P
4
b. TR=0, p=300
c. TR is maximised when P=150 (see diagram below)
Page 10 of 23
Teaching and Learning Guide 6: Non- Linear Equations
6000 TR
5000
4000
Total Revenue
3000
2000
1000
0
0 50 100 150 200 250 300
Price
Task Three
Let t denote the number of tyres produced
a. TC = 1000 + 2t
1000
b. AC = TC/t = +2
t
c. TC=£2400 when t=700
Task Four
1
a. Profit = TR-TC = 300Q − Q 2 − 1000 − 2Q
4
b. Profit = -£26,250 i.e. a loss
Page 11 of 23
Teaching and Learning Guide 6: Non- Linear Equations
Task Five
i)
1
Q = 33 − p
2
⇒ p = 66 − 2Q
TR = p × Q = 66Q − 2Q 2
π = TR − TC = 66Q − 2Q 2 − 200 − 8Q
π = −2Q 2 + 58Q − 200
ii) Breakeven occurs when π=0
π = −2Q 2 + 58Q − 200 =0
Factorising we get:
(−2Q + 50)(Q − 4) = 0
Q=4 or Q=25
So, the firm breaks even when output is 4 units and also when output is 25 units
∂π
iii) Profits maximised =0
∂Q
π = −2Q 2 + 58Q − 200
∂π
= −4Q + 58
∂Q
∂π
=0
∂Q
− 4Q + 58 = 0
58
Q= = 14.5units
4
Page 12 of 23
Teaching and Learning Guide 6: Non- Linear Equations
6. Top Tips
One of the best ways of keeping students engaged with non-linear ideas is to use as often as
possible graphical representations to illustrate points especially when dealing with more
complex equations. A visual cue often helps a more intuitive understanding of the ideas.
It often helps to approach quadratic equations in a structured way such as the following:
1. Determine the basic shape using the coefficient on the squared term.
2. Find the y intercept by substituting in x=0.
3. Find the x intercepts (if possible) using the formula.
7. Conclusion
Create opportunities for students to use both graphical and algebraic representations to help them
really acquire a solid sense of what a quadratic function looks like and how it is composed. This
would provide a good foundation for the next section.
Section 3: Cubic and other polynomial functions
1. The concept of cubic and other polynomial functions
Higher order polynomial functions, such as cubic, share some of the problems of quadratic
equations in that they are difficult to visualise and the equations look "messy". They do not
however, typically create problems and issues to the student that are distinct. It is also generally
the case that we actually offer very little in the way of mathematical tools to deal with them. We
rarely go beyond simply plotting them for different values of x. The mathematical tools applied to
them, such as differentiation, are covered in a later section of this guide.
Compared to linear and quadratic functions higher order functions have few properties that are
particularly useful in describing economic concepts, perhaps explaining why we often spend so
little time with them. This guide does not therefore spend a long time explaining why a cubic cost
function is of particular economic relevance for example.
Page 13 |
pre-algebra kk my teach told me to describe and draw things that are about pre-algebra and she told me to write what pre-algebra is... so can anyone help me??
Monday, August 25, 2008 at 9:03pm by damainmind
what does pre-algebra mean?? pre algebra is like a bunch of math that comes before algebra in middle school.
Monday, August 25, 2008 at 9:11pm by GraceHELP! pre-algebra What does this question have to do with pre-algebra? Using an online unscrambling tool, I came up with "proprietors"
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pre-Algebra Sorry, struggling through pre-Algebra .. :-( .. How do i figure out 5x = -20 ?
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Pre-Algebra I do not get this! me and my friend cannot get the "simplified" ecuation part of the homework! Pre-algebra...... tough work
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Tuesday, September 15, 2009 at 11:25pm by marinapre-algebra so the 15 - 9=4 okay thanks ms. sue for helping me with my 7th grade pre algebra hw I will probably need more help I will jut post my other questions too.
Sunday, September 16, 2012 at 4:23pm by emily
what does pre-algebra mean?? i have to draw things that have to do with pre algebra but...i dont understand the meaning of it
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algebra 2 thats part of algebra 2 thats easy were doing that now in pre algebra
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pre algebra my grade is 83.17 in pre algebra in college, but the final exam is worth 300 points. If I got a B or B- or a C on the final, what would my grade be overall?
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pre-algebra um as in for what is pre-algebra??
Monday, August 25, 2008 at 9:03pm by damainmind
Pre-Algebra its my pre-algebra homework
Tuesday, January 18, 2011 at 9:23pm by TiffanyJ
Pre Algebra random question: i have a pre-algebra unscramble and i need help to unscramble the word the word they gave me was: Seproropit can any of u help me?
Thursday, June 5, 2008 at 5:21pm by coco
Algebra 2 In Kentucky, where i am from, we do algebra and algebra two before pre-cal and calculus. I didnt realize that the problem could be solved in multiple ways and i apologise. But the solution should be done without calculus.
Thursday, February 24, 2011 at 10:33pm by Anon
Pre-Algebra ok well my pre algebra teacher copied some worksheets and its pg 40 and its about some friars in a floral shop buisness. for extra credit we do the joke which is also a way to find out if our answers were correct. there is no 3/8 in my answers and welll yeah thats it.
Tuesday, November 8, 2011 at 10:28pm by Emily
Pre-Algebra Evidently you haven't mastered pre-Algebra since your answer is WRONG. It takes him 4 hours to catch her. While she does ride for 5 hours, it only takes him 4 to catch her.
Wednesday, August 18, 2010 at 6:28pm by Joe Mama
Pre-Algebra: Help I have to do a webquest for pre-algebra and we have to make up a fundraiser thing, I need a list of things that one needs for a charity fundraiser, such as chairs, buffet tables, tables, tents, tablecloths. HELPP
Thursday, March 3, 2011 at 12:20pm by Cherylpre algebra You have to decide you're going to learn how to do algebra.
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pre-algebra write an inequality for the sentence. The total t is greater than five. Well your answer is going to be T and the sign for greater than is simply >. So the answer would be T > 5 ok again my name is above. i was just wondering what pre-algebra was? i mean i take the ...
Friday, March 9, 2007 at 8:50am by JoePre-Algebra Sorry, you are PRE-algebra, so you may not know how to solve for x. 8x = 10x - 10 Subtract 10x from both sides. -2x = -10 Divide both sides by -2. x = 5
Wednesday, August 18, 2010 at 6:28pm by PsyDAGtrig is this algebra or pre-algebra
Thursday, February 2, 2012 at 8:14pm by Brianna
Pre Algebra Thank you so much. I have another question :) In my Pre Algebra book, I have a question like this: Draw a line from one vertex to a point on another side to create a triangle. Cut along the line. What do they exactly mean by 'cut along the line'?
Thursday, March 20, 2008 at 6:36pm by Lilypre-Algebra How can you solve algebra equations? The idea is to find a way to isolate the unknown by itself. You can add, subtract, multiply, and divide both </s> sides of the equal signs to do that.
Friday, May 11, 2007 at 5:03pm by Cherlyn
Math oh no Vitaliy, this person is in 7th grade pre-agebra or 8th grade pre-algebra.
Thursday, February 5, 2009 at 6:58pm by haha
PRE-CALCULUS THIS IS FOR ALGEBRA/PRE-CALCULUS MATH. I POSTED IT JUST AS THE TEACHER WROTE IT.
Tuesday, September 13, 2011 at 10:41pm by aLVIN
pre-algebra i don't get them
Thursday, November 14, 2013 at 11:07am by pre-algbra-calc. Answers for Determine The Minimum Distance From The Point (18,20) To The Line 5x+8y=120 Include: Graph, Algebra Of Any Equations, Algebra Of System, Set-up & Steps Of Final Calculations.
Sunday, October 21, 2012 at 11:59pm by OkzyAlgebra II I first want to make it clear that I have only taken Geometry, Algebra I, and pre-Algebra. That seemed to clear things up last time. Question: Matt bought a car at the cost of 25,000 dollars. This car's value goes down 15% every year. 1. What is the decay factor? 2. Write the ...
Thursday, March 17, 2011 at 11:23pm by Anon
pre calculus Pre-Calculus? I wonder what the question is. In a basic algebra course, you would be looking for zeroes, and probably get those by factoring. 2x^2+11x-21=0 (2x-3)(x+7)=0 x= 1.5, or x=-7
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pre algebra what's pre-algebra about this? Sounds like 3rd-grade long division. Take a visit to and you can see all the steps involved with long division
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Pre-calc Pre calculus? This is stock Algebra II. put the equations in the form of ax^2+bx+c=0 then factor. for instance, c is already in that form. 2x^2+x-6=0 (2x-3)(x+2)=0 x= 3/2 x=-2 do the others the same method.
Monday, January 25, 2010 at 5:18pm by bobpursley
Math (Algebra/Pre-Algebra) After we took off 20%, doesn't the $15 represent 80% of what it used to cost? so .8x=15 x = 15/.8 = 18.75 test the answer by taking 20% of that, and subtracting it. Do we get $15 ?
Thursday, June 4, 2009 at 8:48pm by Reiny
pre-algebra Use algebra tiles to find the difference. Let one white tile equal +1 and one black tile equal –1.
Thursday, April 5, 2012 at 5:33pm by cakes
pre-algebra Simplify- (-2c+d)(-5)+3(-2c)(-8d) Solve the Equation- y/12= -3 -9+a=11 Here are rules that will help you. I hope it helps. Thanks for asking.
Wednesday, March 7, 2007 at 10:37pm by Janet
pre-algebra Simplify- 2(x+2y)-y 5a+2b+3b-7a 2(2r-2)-8(2r+2) Here are some rules that might be helpful: I hope this helps. Thanks for asking.
Wednesday, March 7, 2007 at 10:30pm by Jackie |
Math Formulas - Reference Guide
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Over 100 math formulas at high school level. The covered areas include algebra, geometry, calculus, trigonometry, probability and statistics. Most of the formulas come with examples for better understanding. Use the powerful search function to find what you are looking for and mark your favorites for easier access. A convenient tool for students and teachers and a handy reference for anyone interested in math |
Summary
The PRECALCULUS: FUNCTIONS AND GRAP
Table of Contents
List of Graphing Calculator Topics
vii
Preface
ix
Topics from Algebra
1
(134)
Real Numbers
2
(17)
Exponents and Radicals
19
(12)
Algebraic Expressions
31
(16)
Equations
47
(19)
Complex Numbers
66
(7)
Inequalities
73
(13)
Rectangular Coordinate Systems
86
(23)
Lines
109
(26)
Review Exercises
128
(4)
Discussion Exercises
132
(3)
Functions
135
(84)
Definition of Function
136
(17)
Graphs of Functions
153
(16)
Quadratic Functions
169
(15)
Operations on Functions
184
(11)
Inverse Functions
195
(10)
Variation
205
(14)
Review Exercises
212
(5)
Discussion Exercises
217
(2)
Polynomial and Rational Functions
219
(64)
Polynomial Functions of Degree Greater Than 2
220
(11)
Properties of Division
231
(8)
Zeros of Polynomials
239
(14)
Complex and Rational Zeros of Polynomials
253
(8)
Rational Functions
261
(22)
Review Exercises
279
(2)
Discussion Exercises
281
(2)
Exponential and Logarithmic Functions
283
(66)
Exponential Functions
284
(12)
The Natural Exponential Function
296
(10)
Logarithmic Functions
306
(16)
Properties of Logarithms
322
(8)
Exponential and Logarithmic Equations
330
(19)
Review Exercises
343
(3)
Discussion Exercises
346
(3)
The Trigonometric Functions
349
(102)
Angles
350
(11)
Trigonometric Functions of Angles
361
(18)
Trigonometric Functions of Real Numbers
379
(19)
Values of the Trigonometric Functions
398
(8)
Trigonometric Graphs
406
(15)
Additional Trigonometric Graphs
421
(8)
Applied Problems
429
(22)
Review Exercises
442
(7)
Discussion Exercises
449
(2)
Analytic Trigonometry
451
(68)
Verifying Trigonometric Identities
452
(6)
Trigonometric Equations
458
(15)
The Addition and Subtraction Formulas
473
(11)
Multiple-Angle Formulas
484
(10)
Product-to-Sum and Sum-to-Product Formulas
494
(5)
The Inverse Trigonometric Functions
499
(20)
Review Exercises
515
(3)
Discussion Exercises
518
(1)
Applications of Trigonometry
519
(64)
The Law of Sines
520
(10)
The Law of Cosines
530
(9)
Vectors
539
(15)
The Dot Product
554
(11)
Trigonometric Form for Complex Numbers
565
(7)
De Moivre's Theorem and nth Roots of Complex Numbers
572
(11)
Review Exercises
578
(4)
Discussion Exercises
582
(1)
Systems of Equations and Inequalities
583
(96)
Systems of Equations
584
(9)
Systems of Linear Equations in Two Variables
593
(9)
Systems of Inequalities
602
(9)
Linear Programming
611
(9)
Systems of Linear Equations in More Than Two Variables
620
(15)
The Algebra of Matrices
635
(10)
The Inverse of a Matrix
645
(7)
Determinants
652
(7)
Properties of Determinants
659
(8)
Partial Fractions
667
(12)
Review Exercises
673
(3)
Discussion Exercises
676
(3)
Sequences, Series, and Probability
679
(84)
Infinite Sequences and Summation Notation
680
(16)
Arithmetic Sequences
696
(7)
Geometric Sequences
703
(9)
Mathematical Induction
712
(7)
The Binomial Theorem
719
(9)
Permutations
728
(7)
Distinguishable Permutations and Combinations
735
(9)
Probability
744
(19)
Review Exercises
757
(3)
Discussion Exercises
760
(3)
Topics from Analytic Geometry
763
(78)
Parabolas
764
(10)
Ellipses
774
(14)
Hyperbolas
788
(12)
Plane Curves and Parametric Equations
800
(15)
Polar Coordinates
815
(16)
Polar Equations of Conics
831
(10)
Review Exercises
837
(2)
Discussion Exercises
839
(2)
Appendixes
841
I Common Graphs and Their Equations
842
II A Summary of Graph Transformations
844
III Graphs of Trigonometric Functions and Their Inverses
846
IV Values of the Trigonometric Functions of Special Angles on a Unit Circle |
Course Content and Outcome Guide for MTH 62
Course Number:
MTH 62
Course Title:
Introductory Algebra - Part II
Credit Hours:
3
Lecture Hours:
20
Lecture/Lab Hours:
20
Lab Hours:
0
Special Fee:
$6.00
Course Description
Introduces algebraic concepts and processes with a focus on linear equations in two variables, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended. Must take both MTH 61 and MTH 62 to satisfy MTH 60 requirements. Must take both MTH 62 and MTH 63 to satisfy MTH 65 requirements. Audit available.
Addendum to Course Description
Students will be evaluated not only on their ability to get correct answers and perform correct steps", but also on the accuracy of the presentation itself.
Application problems must be answered in complete sentences.
Intended Outcomes for the course
1. Use a variable to represent an unknown in a simple linear problem at home or in an academic or work environment, create a linear equation that represents the situation, and find the solution to the problem using algebra. 2. Recognize a linear pattern in ordered paired data collected or observed at home or in an academic or work environment, calculate and interpret the rate of change (slope) in the data,create a linear model using two data points, and use the observed pattern to make predictions. 3. Be prepared for future coursework that requires an understanding of the basic algebraic concepts covered in the course.
Outcome Assessment Strategies
The following must be assessed in a proctored, closed-book, no-note, and no-calculator setting: graphing lines; solving systems of linear equations; and simplifying expressions.
At least two proctored, closed-book, no-note examinations (one of which is the comprehensive final) must be given. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate.
Assessment must include evaluation of the student€™s ability to arrive at correct and appropriate conclusions using proper mathematical procedures and proper mathematical notation. Additionally", each student must be assessed on their ability to use appropriate organizational strategies and their ability to write conclusions appropriate to the problem.
Classify points by quadrant or as points on an axis; identify the origin
Label and scale axes on all graphs
Interpret graphs in the context of an application
Create a table of values from an equation
Plot points from a table
INTRODUCTION TO FUNCTION NOTATION,
Determine whether a given relation presented in graphical form represents a function
Evaluate functions using function notation from a set, graph or formula
Interpret function notation in a practical setting
Identify ordered pairs from function notation
LINEAR EQUATIONS IN TWO VARIABLES,
Identify a linear equation in two variables
Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
Find ordered pairs that satisfy a linear equation written in standard or slope-intercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs
Find the intercepts given a linear equation; express the intercepts as ordered pairs
Graph the line using intercepts and check with a third point
Find the slope of a line from a graph and from two points
Given the graph of a line identify the slope as positive", negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope
Graph a line with a known point and slope
Manipulate a linear equation into slope-intercept form; identify the slope and the vertical-intercept given a linear equation and graph the line using the slope and vertical-intercept and check with a third point
Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
Given the equation of two lines, classify them as parallel, perpendicular, or neither
Find the equation of a line using slope-intercept form
Find the equation of a line using point-slope form
Applications of linear equations in two variables,
Interpret intercepts and other points in the context of an application
Write and interpret a slope as a rate of change
Create and graph a linear model based on data and make predictions based upon the model
Create tables and graphs that fully communicate the context of an application problem
LINEAR INEQUALITIES IN TWO VARIABLES,
Identify a linear inequality in two variables
Graph the solution set to a linear inequality in two variables
Model application problems using an inequality in two variables
SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES,
Solve and check systems of equations graphically and using the substitution and addition methods
Create and solve real-world models involving systems of linear equations in two variables,
Properly define variables; include units in variable definitions
Apply dimensional analysis while solving problems
State contextual conclusions using complete sentences
Use estimation to determine reasonableness of solution
WORKING WITH ALGEBRAIC EXPRESSIONS,
Apply the rules for integer exponents
Work in scientific notation and demonstrate understanding of the magnitude of the quantities involved
Add, subtract, multiply, and square polynomials
Divide polynomials by a single term polynomial
ADDENDUM:
MTH 62 is the second term of a three term sequence in beginning algebra. One major problem experienced by beginning algebra students is difficulty conducting operations with fractions and negative numbers. It would be beneficial to incorporate these topics throughout the course, whenever possible, so that students have ample exposure. Encourage them throughout the course to get better at performing operations with fractions and negative numbers,, inverses, identities, the commutative property, the associative property, the distributive property, equations, expressions and equivalent equations.
The difference between expressions, equations, and inequalities needs to be emphasized throughout the course. A focus must be placed on helping students understand that evaluating an expression, simplifying an expression, and solving an equation or inequality13x+715x=55‹ 13x+17x=515x+715x=1215x=45x 62 course should consistently show appropriate steps using correct mathematical notation and appropriate forms of organization. All axes on graphs should include scales and labels. A portion of the grade for any free response problem should be based on mathematical syntax. |
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