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Authors:Laura Schmidt and Diane Christie, University of Wisconsin--Stout
Contact: Laura Schmidt, schmidtlaur@uwstout.edu
Discipline or Field: Mathematics
Course Name: Intermediate Algebra
Date: February 28, 2007
Course Description
This course develops basic algebraic skills: factoring, exponents, rational expressions, linear equations and inequalities, systems of equations, quadratic equations, and an introduction to functions. This course is not a terminal course for any of the majors on campus, but a prerequisite to the courses they need. Students lacking in high school mathematics skills from all majors across campus take this course to get into the math classes they need for their majors. Class sizes are 36 students maximum. They are conducted in a networked classroom, and all students have laptop computers. It is a hybrid class; the lecture/discussion is given for the first part of the 55 minute period, then students begin work on their homework assignment. All assignments, tests and quizzes are completed online. This lesson comes about 2 months into the course. By this time, students have learned to factor polynomials. In the previous lesson, students learned to multiply and divide rational expressions.
Executive Summary
Learning Goals. The overall learning goal is to have students be able to add and subtract rational expressions. Students will first combine expressions with common denominators, then find a common denominator to combine expressions with unlike denominators. Long-term goals not directly assessed by the lesson are to ease anxiety when dealing with fractions and to have students realize the connection between adding/subtracting rational numbers and adding/subtracting rational expressions.
Lesson Design. The lesson reviewed addition and subtraction of fractions, demonstrated addition and subtraction of simple rational expressions, and worked up to difficult examples. The lesson began with three examples of rational numbers, one with common denominators and two with un-like denominators, followed by rational expressions with common denominators. Examples of rational expressions with un-like denominators started out simple and increased in difficulty level. The number of expressions to be added increased along with the difficulty in the factorization of the denominators. The examples were chosen so that the answers could be rewritten in reduced forms at the end to remind students to check that final step in their answers. Due to the anxiety that this lesson has caused in the past, hard examples were presented by the end so that students could be exposed to more difficult problems.
Major findings about student learning. The findings showed that even though students were successful at the beginning problems in the homework, they were intimidated by the "difficult look" of the later homework problems and simply did not attempt them. This was evident in the analysis of the homework where the amount of incomplete problems drastically increased at a certain problem when the difficulty level was higher. In the revised lesson, more difficult examples were used, and it was stressed that the steps remain the same even though it looked much harder than previous examples. Several days later when the students had to use the lesson to solve equations involving rational expressions their confidence level was greater and the majority of students got the correct answers.
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The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems! So really, algebra 1 is a lot like the kinds of things you have already worked with - it just "looks" different.
...CheersPre-algebra is one of the most important sections in math. It is the basic fundamentals for all high-school and college math. The fundamentals include the following: Operations of real numbers, polynomials, rational expressions, radicals and exponents, equations/functions, area and volume...
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Math Department
NEW! Find your Math help with Math TV! View video explanations of common functions in a variety of ways. More than one person explains the function (you choose) so you can find the best explanation. Explanations are also available in Spanish. Login information is not required to play the Math videos. Create a login to make playlists or subscribe to certain types of videos. Students should be advised that advertisements for Math books and other materials exist in the top right of the site and should be avoided. Click here
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Covers points, functions, equations, and inequalities with number lines and coordinate planes
FEATURES
Play with the Basic Building Blocks of Algebra - You understand equations better when you can build them with VariaBlox. Manipulate the Blox to combine like terms, substitute or solve for a variable and multiply, and factor simple algebraic expressions. An alert warns you when your equation is out of balance!
Capture Satellites, Meteoroids and Unusual Outer-Space Treasures - Drag objects into the Cargo Bay to sort them and solve a mathematical problem. Use the special sorting bins for translating between fractions, decimals, and percents and identifying equivalent rational numbers or exponential expressions. The Proportion Tool can help you solve scale factor, equivalent ratio, proportion, and percent problems.
Represent Multiple Points and Graphs of Linear Equations and Inequalities - Use the Grapher Station to solve problems and complete missions by identifying slopes and intercepts and solving systems of equations and inequalities. In some missions, a Number Line replaces the coordinate grid and you can graph fractions, decimals, expressions, and inequalities.
Special Features! - The math fun in Astro Algebra takes place in two modes, On-Duty Mode and Off-Duty Mode. You begin the program in On-Duty Mode, where you are directed through missions. You can also go into Off-Duty Mode at any time in order to freely explore the tools and stations at your own pace, view trophies or play Equation of Mystery in the Cargo Bay. Surf the AstroNet, a simulated universe-wide Internet* that contains data on math topics and terms. Learn about important algebra concepts before or during a mission. Use the Calculator to evaluate functions, compute solutions, and create tables of values.
Astro Algebra's Grow Slide automatically records your progress and adjusts to guide your learning. The activities in Astro Algebra offer dozens of math topics and hundreds of problems in 7th, 8th and 9th grade algebra. As you learn and progress, the Grow Slide advances, offering more challenging problems. Students, parents, or teachers can also set the difficulty of each activity or choose a specific topic related to schoolwork.
Note: The AstroNet is contained wholly within the Astro Algebra CD-ROM and is not connected to the Internet or World Wide Web. The Internet cannot be accessed through the AstroNet.
Learning Opportunities
Solving for Variables
Expressions, Equations & Inequalities
Functions
Graphing on Number Line & Coordinate Grid
Ratios & Proportions
Slope & Intercept
Fractions, Decimals & Percents
Exponents
Problem Solving & Reasoning
Algebra Terminology & Notation
Universal Access
This product contains Universal Access features including TouchWindow and Single Switch compatibility to address a variety of learning styles and abilities.
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Program Details
TI-84 Plus and TI-83 Plus graphing calculator program for calculating the area under a curve and the area between 2 curves.
Program Keywords:
TI Programs, TI-83 Plus, TI-84 Plus, Graphing Calculators, Calculus, Integrals: Area Under a Curve, Area Between 2 Curves
Program Description:
This program finds the area under a curve and the area between curves. The program uses numerous methods of finding the area including left, right and middle, trapezoidal, solids of revolution and standard integration. The program can also find definite integrals, even when the equation is unknown, as long as co-ordinates are given. This program is great for any type of integral problems that might appear on homework, tests or final exams in calculus.
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Mathematics and Mechanics
What is Maths A level about?
Mathematics and Mechanics is comprised of two main areas: Pure Mathematics and Mechanics. Pure Mathematics is the study of the basic principles of Mathematics that underpin many real life processes. During this part of the course you will extend your knowledge of such topics as algebra, trigonometry and sequences. You will also learn new concepts such as calculus.
Mechanics is a practical application of Mathematics. It considers how we can use Mathematics to model real-life situations and how best to solve physical problems.
Is this course for me?
All students wishing to undertake an A level in Mathematics are required to achieve a grade B at GCSE with a minimum of 300 UMS marks. In addition to this, students will be required to pass the entry level algebra competency test.
This option complements Physics particularly well.
What else do I need to know?
There is the opportunity for Year 12 students to undertake community service. The Mathematics department also offer a weekly clinic on a Thursday. This is to support students with their studies. All pupils are welcome to come along and receive help from a variety of teachers.
What do other students say?
"Stimulating and challenging" "Maths is very challenging but we thoroughly enjoy it!"
Where could it lead?
Mathematics is a highly employable A level to have. Most students who study Mathematics go on to careers in Engineering, Computer Science and Finance.
How is this course structured?
All units are of equal weighting.
Unit Content
Unit Assessment
AS Unit 1: Core Maths 1
This extends your GCSE knowledge of Algebra, Indices and Co-ordinate systems. It also teaches you how to express your Mathematics correctly.
Module examination in January of Year 12.
AS Unit 2: Core Maths 2
This builds upon the work you did in Core 1. In this module you begin to look at such topics as Sequences and Series and Trigonometry. You are also introduced to Calculus.
Module examination in June of Year 12.
AS Unit 3: Mechanics 1
This looks at how to model situations involving velocity, distance and time. It also considers the motion of projectiles.
Module examination in June of Year 12.
A2 Unit 4: Core Maths 3
This module extends the calculus techniques that you learnt in Core 2. It also looks at functions and natural logarithms. You will be required to produce a piece of coursework on numerical methods.
20% coursework. 80% examination in January of Year 13.
A2 Unit 5: Core Maths 4
This module is called Applications of Advanced Mathematics. The module extends all the topics you have learnt thus far and asks you to apply them in more complex situations.
Module examination in June of Year 13.
A2 Unit 6: Mechanics 2
This builds on the work you learnt in Mechanics 1. It considers the forces in frameworks, centres of mass, friction and moments
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Second subject of two-term sequence on modeling, analysis and control of dynamic systems. Kinematics and dynamics of mechanical systems including rigid bodies in plane motion. Linear and angular momentum principles. Impact and collision problems. Linearization about equilibrium. Free and forced vibrations. Sensors and actuators. Control of mechanical systems. Integral and derivative action, lead and lag compensators. Root-locus design methods. Frequency-domain design methods. Applications to case-studies of multi-domain systems.
In Students learn that scientists need to shrink the Paean they engage in a hands-on activity where they find the maximum surface area of a computer component that must fit into a smaller PSA. Grades 6-8.
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Math 364 - Complex Analysis
Fall Semester, 1998-99
Calculus and real analysis are the study of real-valued functions of a
real variable. Not surprisingly then, complex analysis is the study of
complex-valued functions of a complex variable. The calculus of
complex-valued functions has some similarities to the calculus of
real-valued functions, but there are striking differences. In particular,
the amazing relationship between differentiation, integration, and
infinite series in complex calculus is much more intimate and complete
than it is in real calculus.
The above picture is a plot of the reciprocal of the absolute value of
the Riemann zeta function. The spikes correspond to the nontrivial zeros.
The Riemann Hypothesis, one of the most important unsolved problems in
mathematics, asserts that all the nontrivial zeros of the Riemann zeta
function lie along the line Re(z)=1/2. The Riemann Hypothesis is known to
be true for at least the first billion and a half zeros.
CLASS INFORMATION:
Meeting time: TTh 8:30-9:45
Meeting room: Glatfelter 203
OFFICE AND OFFICE HOURS:
Office: Glatfelter 215A
Office hours: MTWF 10:00-11:50 and by appointment
TELEPHONE NUMBER AND E-MAIL:
Telephone: 337-6630
E-mail: jfink@gettysburg.edu
WWW page:
Class e-mail alias: math-364-a@gettysburg.edu
EXAM DATES:
Exam 1: Tuesday, September 29
Exam 2: Tuesday, November 10
Final Exam: Saturday, December 12, 8:30-11:30 AM
PREREQUISITES:
Multivariable calculus (Math 211) with a C grade or better
TEXTBOOK:
Complex Variables with Applications by A. David Wunsch, second edition
class attendance and participation; attendance at three or more department colloquia and other designated special events (10%).
***There will be no make-up exams, and late work will not be accepted.***
DAILY READINGS:
Assigned readings should be done before class, and you should also attempt a problem or two from the textbook.
Working problems is essential for an understanding of the material, and there are plenty of problems in the textbook. A representative selection of problems is given on the course syllabus.
HOMEWORK:
Homework will be assigned, collected, and graded.
Assignments may include material that will not be discussed in class. You are expected to learn this material on your own and to make use of the resources available to you to complete the assignments.
Grading will be based both on mathematical content and on the quality of your write-up. NEATNESS COUNTS! Show all work necessary to justify your solutions. Answers alone are not sufficient.
You may work with other students on the homework; in fact, I encourage that. However, your write-up should be your own.
TEAM PROJECT:
The project will be a team effort on a topic of your own choice involving an application of complex analysis.
The project is not intended to take an unreasonable amount of time, but it is unlikely that you will complete a project in a single sitting. Thus, your team should begin work on the project well in advance of the due date. You will probably find that shorter work sessions spread over several days are the best way to attack the project.
To get you started early on the project, a written proposal is a required first step. The proposal is due on Tuesday, November 3.
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Books
Geometry & Topology
This edition includes the most recent Geometry Regents tests through August 2012. These ever popular guides contain study tips, test-taking strategies, score analysis charts, and other valuable features. They are an ideal source of practice and test preparation. The detailed answer explanations make each exam a practical learning experience. Topics reviewed include the language of geometry; parallel lines and quadrilaterals and coordinates; similarity; right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and an introduction to solid geometry.
This classroom text presents a detailed review of all topics prescribed as part of the high school curriculum. Separate chapters analyze and explain: the language of geometry; parallel lines and polygons; congruent triangles and inequalities; special quadrilaterals and coordinates; similarity (including ratio and proportion, and proving products equal); right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and working in space (an introduction to solid geometry). Each chapter includes practice exercises with answers provided at the back of the book
A bestselling math book author takes what appears to be a typical geometry workbook, full of solved problems, and makes notes in the margins adding missing steps and simplifying concepts so that otherwise baffling solutions are made perfectly clear. By learning how to interpret and solve problems as they are presented in courses, students become fully prepared to solve any obscure problem. No more solving by trial and error!
• Includes 1000 problems and solutions • Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other geometry workbook on the market • The previous two books in the series on calculus and algebra sell very well
The new and improved Tutor in a Book's Geometry. Designed to replicate the services of a skilled private tutor, TIB's Geometry, presents a teen tested visual presentation of the course and includes more than 500 well illustrated, carefully worked out proofs and problems with step by step explanations. Throughout the book, time tested solution and test taking strategies are demonstrated and emphasized. The recurring patterns that make proofs doable are explained and illustrated. Dozens of graphic organizers that help students understand, remember and recognize the connection between concepts are included. With the intent to level the playing field between students who have tutors and those that don't, long time successful private mathematics tutor and teacher, Jo Greig, packed 294 pages with every explanation, every drawing, every hint, every memory tool, examples of the right proofs and problems, and every bit of enthusiasm that good tutors impart to their private tutoring students. Ms. Greig holds a bachelors' degree in mathematics. Dr. J. Shiletto, the book's mathematics editor, holds a Ph.D in mathematicsFor seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.
In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.
Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can "do the math" in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.
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The study of differential equations is a wide field in both pure and applied mathematics. Pure mathematicians study the types and properties of differential equations, such as whether or not solutions exist, and should they exist, whether they are unique. Applied mathematicians, physicists and engineers are usually more interested in how to compute solutions to differential equations. These solutions are then used to simulate celestial motions, design bridges, automobiles, aircraft, sewers, etc. Often, these equations do not have closed form solutions and are solved using numerical methods.
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is a 3-credit course. Expect to spend at least two hours of study for each class hour. Study time should be spent:
a) Going over notes from previous class. Taking careful notes is important. Write down concepts or problems that you do not understand during class. Come in for help if you need it.
b) Doing assigned problems. The best way to learn mathematics is to do problems. Practice of homework assignments cannot be overemphasized. Suggestion - put an * next to problems which give you trouble and ask about them during the next class.
c) Watch the video lesson on the CD that corresponds to the topic covered in class. Read the text material paralleling the topics covered in class.
It is important to stay in touch on a regular basis. If you have problems or questions please contact me via email at fitte@bucks.edu. Please remember to include your full name, course and section number.
All tests will be proctored. There is a testing center at each of the three campuses: Newtown, Upper County, and Bristol. You may use any of them.
Questions about Online Learning? Contact the OL office
at 215-968-8052 or learning@bucks.edu
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The College Readiness Mathematics Standards
Connections
Comparisons involving process standards – reasoning/problem-solving, communication and connections – are not included at this time. Differences in how process standards are treated in these two sets of standards would make an alignment inaccurate.
The student extends mathematical thinking across mathematical content
3 areas, and to other disciplines and real life situations.
Component 3.1Use mathematical ideas and
strategies to analyze relationships
within mathematics and in other
disciplines and real life situations.
Evidence of Learning
College Readiness Standards
Footer information goes here
3.1a
Compare and contrast the different mathematical concepts and
procedures that could be used to complete a particular task.
3.1b
Recognize patterns and apply mathematical concepts and
procedures in other subject areas and real world situations.
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Polynomials: Operations The learner will be able to
add, subtract, multiply, and/or divide with polynomial expressions.
Strand
Scope
Source
Polynomials
Master
NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.17
Polynomials: Compare The learner will be able to
make comparisons and order polynomial expression by degree.
Strand
Scope
Source
Polynomials
Master
NM: Content Standards, 2002, Grade 9-12, pg 43: AFG.5
Polynomial Expressions: Study The learner will be able to
study the general shape of polynomial expressions and equations for various degree polynomials.
Strand
Scope
Source
Polynomials
Master
NM: Content Standards, 2002, Grade 9-12, pg 47: AFG.4
Radicals: Simplifying The learner will be able to
simplify square roots and cube roots that have monomial radicands which are perfect cubes or perfect squares.
Strand
Scope
Source
Radicals
Master
NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.11
Radical Equations: Solve The learner will be able to
obtain solutions to radical equations with one radical.
Strand
Scope
Source
Radicals
Master
NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.13
Factoring: Polynomials/Trinomials The learner will be able to
factor polynomials, difference of squares and perfect square trinomials, and the sum and difference of cubes.
Strand
Scope
Source
Factoring
Master
NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.14
Simplify Expressions: Simplify/Monomial The learner will be able to
simplify algebraic monomial expressions raised to a power and binomial expressions raised to a power.
Strand
Scope
Source
Simplify Expressions
Master
NM: Content Standards, 2002, Grade 9-12, pg 43: AFG.4
Quadratic Formula: Roots The learner will be able to
apply the quadratic formula (and/or factoring techniques) to find out if the graph of a quadratic function will intersect the x-axis in zero, one, or two places.
Strand
Scope
Source
Quadratic Equations/Formula
Master
NM: Content Standards, 2002, Grade 9-12, pg 45: AFG.12
Quadratic Equations: Represent The learner will be able to
represent real world problem situations using quadratic equations.
Strand
Scope
Source
Quadratic Equations/Formula
Master
NM: Content Standards, 2002, Grade 9-12, pg 46: AFG.1
Quadratic Equations: Apply The learner will be able to
use quadratic equations in the solution of physical problems of various types.
Strand
Scope
Source
Quadratic Equations/Formula
Master
NM: Content Standards, 2002, Grade 9-12, pg 45: AFG.13
Exponents: Comprehend/Rules The learner will be able to
comprehend the rules of exponents.
Strand
Scope
Source
Exponents
Master
NM: Content Standards, 2002, Grade 9-12, pg 46: AFG.11
Exponents: Apply Rules The learner will be able to
apply the rules of exponents.
Fractions: Simplify/Polynomial The learner will be able to
simplify fractions that are composed of polynomials in the numerator and denominator through factorization of both parts and reducing to lowest terms.
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Search Course Communities:
Course Communities
Lesson 36: Algebraic Fractions
The lesson begins with the definition of an algebraic fraction and then a quick review of the fundamental principle of fractions. Exercises in reducing fractions follow before a brief procedure for reducing algebraic fractions is provided. Opposites of binomials are reviewed before rational functions are defined and a motion application problem is discussed.
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McGraw-Hill's Math Grade 8
Synopsis
Now students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills!
McGraw-Hill's Math Grade 8 helps your middle-school student learn and practice basic math skills he or she will need in the classroom and on standardized NCLB tests. Its attractive four-color page design creates a student-friendly learning experience, and all pages are filled to the brim with activities for maximum educational value. All content aligned to state and national standards
"You Know It!" features reinforce mastery of learned skills before introducing new material
"Reality Check" features link skills to real-world applications
"Find Out About It" features lead students to explore other media
"World of Words" features promote language acquisition
Discover more inside:
A week-by-week summer study plan to be used as a "summer bridge" learning and reinforcement program
Each lesson ends with self-assessment that includes items reviewing concepts taught in previous lessons
McGraw-Hill's Math Grade 8
Found In
eBook Information
ISBN: 97800717486
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Saxon Geometry Homeschool Kit
A welcome addition to Saxon's curriculum line, Saxon Geometry is the
perfect solution for students and parents who prefer a dedicated
geometry course...yet want Saxon's proven methods!
Presented in the
familiar Saxon approach of incremental development and continual
review, topics are continually kept fresh in students' minds. Covering
triangle congruence, postulates and theorems, surface area and volume,
two-column proofs, vector addition, and slopes and equations of lines,
Saxon features all the topics covered in a standard high school
geometry course. Two-tone illustrations help students really "see" the
geometric concepts, while sidebars provide additional notes, hints, and
topics to think about. Parents will be able to easily help their
students with the solutions manual, which includes step-by-step
solutions to each problem in the student book; and quickly assess
performance with the test book (test answers included). Tests are
designed to be administered after every five lessons after the first
ten.
Key To Geometry Books 1-8
Key to Geometry offers a non-intimidating way to prepare students for
formal geometry as they do step-by-step constructions. Using only a
pencil, compass, and straightedge, students begin by drawing lines,
bisecting angles. Books are also sold separately.
Key To Geometry (KTG) Answers Notes, Books #1-3
The series of workbooks, Key to Geometry To Geometry (KTG) Answers Notes, Books #4-6
Key to
Geometry offers a non-intimidating way to prepare students for formal
geometry as they do step-by-step constructions. Using only a pencil,
compass, and straightedge, students begin by drawing lines, bisecting
angles
Book 4: Perpendiculars, Book 5: Squares and Rectangles, Book 6: Angles.
These are the answers and notes for Books 4-6 of the Key to Geometry
Series.
Key to Geometry (KTG) Answers Notes, Book #7
The series of workbooks, Key to Geometry, to Geometry (KTG) Answers Notes, Book #8
Key to Geometry
offers a non-intimidating way to prepare students for formal geometry
as they do step-by-step constructions. Using only a pencil, compass,
and straightedge, students begin by drawing lines, bisecting angles,
and reproducing segments. Later they do sophisticated constructions
involving over a dozen steps and are prompted to form their own
generalizations. When they finish, students have been introduced to 134
geometric terms and are ready to tackle formal proofs. Book 8:
Triangles, Parallel Lines, Similar Polygons This book contains the
answers and notes for Book 8 of the Key to Geometry Series.
The Complete Idiot's Guide to Geometry 2nd Ed.
See geometry from all the right angles.
Here is a
non-intimidating, easy-to-understand, and fun companion to the
textbooks required for high school and college geometry courses. Written
by a math professor who developed a geometry class for liberal arts
students, this book covers all standard curriculum concepts—from angles
and lines to tangents and topology.
Geometry, Level 2
Never waste a single minute, when you fill in down time with Daily
Warm-Ups. Give your students the skill to become confident at solving
problems, and helps prepare them for standardized tests. Contains 180
warm-ups, from converting distance to tesselations and everything in
between. Spice up your geometry class with this book and your kids will
thank you for it!
Geometry the Easy Way
This third edition of "Geometry the Easy Way" covers the "how" and
"why" of geometry with hundreds of examples and exercises with
solutions. More than 700 drawings, graphs, and tables help to
illustrate angles, parallel lines, proving triangles congruent, formal
and informal proofs, special quadrilaterals, inequalities, the right
triangle, ratio and proportion, circles, area and volume, locus,
coordinate geometry, and constructions.
Proofs Workbook
The concepts that are studied and applied in a geometry course fall
into two categories: theorems and postulates. This workbook will
provide an opportunity to develop specific skills used in proof
writing. Each strategy develops a particular technique that can be used
when writing a proof. Includes:
Informal presentations of theorems, postulates and definitions.
Perfect complement to any textbook.
Applications of ideas developed in clear explanations and practice exercises.
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Peer Review
Ratings
Overall Rating:
These online notes are intended for students who are working through the textbook Abstract Algebra by Beachy and Blair. The notes are focused on solved problems, and will help students learn how to do proofs as well as computations. There are also some "lab" questions on groups, based on a Java applet Groups15 written by John Wavrik of UCSD.
Learning Goals:
This site provides additional instruction in Abstract Algebra. Its examples and linked java-applet tools allow students to reinforce and refresh their understanding of the topics covered.
Target Student Population:
Abstract Algebra students.
Prerequisite Knowledge or Skills:
A course in Abstract Algebra is recommended.
Type of Material:
Reference and tutorial.
Recommended Uses:
This material can be used as an online textbook or as a reference guide.
Technical Requirements:
It requires a "Java-enabled" browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This site contains a study guide that is intended for students who are working through the Third Edition of the Abstract Algebra textbook by J. Beachy and D. Blair. The notes are focused on solved problems, and their main goal is to help students learn how to do proofs, as well as computations. The link to Java applet Groups15 written by John Wavrik of UCSD should be highly useful to students who actually attempt to practice exercises on their own
A sequence of topics makes it easy to use this interactive textbook in a "linear", not hyper-referenced way.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This online text provides major help in learning the concepts of Abstract Algebra and, in particular, in solving problems. The intent with the interactive examples and sections of problems is that the student should attempt to work the exercises presented in the sections before clicking on the solution button This reinforces the basic precept that the only effective way to learn mathematics is by doing mathematics. The Java-applet tool is well chosen to reinforce and supplement the topics covered.
The hyper-referenced definitions and theorems are extremely helpful if the site is used as a reference material.
Concerns:
At its current state the site is unlikely to be used as a textbook for a course in Abstract Algebra but certainly makes an excellent tutorial supplement.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This learning resource is easily navigable. The Java-applet tool is easy to use, and it seem to work flawlessly. The topics are well organized and all the key concepts are properly emphasized.
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Specification
Aims
The programme unit aims to provide an introduction to the basic elements of calculus.
Brief Description of the unit
This lecture course introduces the basic ideas of complex numbers relating them the standard transcendental functions of calculus. The basic ideas of the differential and integral calculus are revised and developed. Vectors in two and three dimensions are introduced and this leads on to the calculus of functions of more than one variable and the beginnings of vector calculus.
Learning Outcomes
On successful completion of this module students will have acquired an active knowledge and understanding of some basic concepts and results in calculus.
Future topics requiring this course unit
Almost all Mathematics course units will rely on material in this course unit.
More on Complex Numbers. Euler's Theorem and De Moivre's Theorem; polar form of complex numbers (polar representation of the plane); roots of unity; complex forms of sin and cos, relationship to trigonometric identities.
Functions of more than One Variable. Partial derivative, chain-rule, Taylor expansion; turning points (maxima, minima, saddle-points); grad, div and curl and some useful identities in vector calculus; integration in the plane, change of order of integration; Jacobians and change of variable; line integrals in the plane; path-dependence, path independence; Stokes' theorem and Green's theorem.
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Tensor analysis is an essential tool in any science (e.g. engineering,
physics, mathematical biology) that employs a continuum
description. This concise text offers a straightforward treatment of
the subject suitable for the student or practicing engineer. The final
chapter introduces the reader to differential geometry, including the
elementary theory of curves and surfaces. A well-organized formula
list, provided in an appendix, makes the book a very useful
reference. A second appendix contains full hints and solutions for the
exercises.
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Introduction to Calculus
The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications, and integrals and their applications. This guide is an indispensable aid to helping make the complex theories of calculus understandable. Completely revised and updated by Dr. Joan Van Glabek, this book includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, illustrations, and examples.
The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.
Elementary Algebra...
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MA THEME TICS
Mathematics reveals hidden patterns that help us under-
stand the world around us. Now much more than arithmetic
and geometry, mathematics today is a diverse discipline that
deals with data, measurements, and observations from sci-
ence; with inference, deduction, and proof; and with math-
ematical models of natural phenomena, of human behavior,
and of social systems.
The cycle from data to deduction to application recurs
everywhere mathematics is used, from everyday household
tasks such as planning a long automobile trip to major man-
agement problems such as scheduling airline traffic or man-
aging investment portfolios. The process of "doing" math-
ematics is far more than just calculation or deduction; it
involves observation of patterns, testing of conjectures, and
estimation of results.
As a practical matter, mathematics is a science of pattern
and order. its domain is not molecules or cells, but num-
bers, chance, form, algorithms, and change. AS a science
of abstract objects, mathematics relies on logic rather than
on observation as its standard of truth, yet employs obser-
vation, simulation, and even experimentation as means of
discovering truth.
M:
~ ~ ~ athematics is a science of pattern and
order.
The special role of mathematics in education is a con-
sequence of its universal applicability. The results of
mathematics theorems and theories-are both significant
and useful; the best results are also elegant and deep.
Through its theorems, mathematics offers science both a
foundation of truth and a standard of certainty.
In addition to theorems and theories, mathematics of-
fers distinctive modes of thought which are both versatile
and powerful, including modeling, abstraction, optimiza-
tion, logical analysis, inference from data, and use of sym-
bols. Experience with mathematical modes of thought builds
searching for patterns
Mathematical Modes of Thought
Modeling Representing worldly
phenomena by mental constructs,
often visual or symbolic, that
capture important and useful fea
tures.
Optimization Finding the best
solution (least expensive or most
efficient) by asking "what if' and
exploring all possibilities.
Symbolism- Extending natural
language to symbolic represen-
tation of abstract concepts in an
economical form that makes pos-
sible both communication and
computation.
Inference Reasoning from data,
from premises, from graphs,
from incomplete and inconsistent
sources.
Logical Analysis Seeking impli-
cations of premises and searching
for first principles to explain ob-
served phenomena.
Abstraction Singling out for spe-
cial study certain properties com-
mon to many different phenom-
ena.
31
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Mathematics
Back to School
Design a dog house that can be
made from a single 4 ft. by ~
ft. sheet of plywood. Make the
dog house as large as possible and
show how the pieces can be laid
out on the plywood before cut-
ting.
32
mathematical power a capacity of mind of increasing value
in this technological age that enables one to read critically,
to identify fallacies, to detect bias, to assess risk, and to sug-
gest alternatives. Mathematics empowers us to understand
better the information-laden world in which we live.
Our Invisible Culture
Mathematics is the invisible culture of our age. Although
frequently hidden from public view, mathematical and sta-
tistical ideas are embedded in the environment of technology
that permeates our lives as citizens. The ideas of mathemat-
ics influence the way we live and the way we work on many
different levels:
· Practical knowledge that can be put to immediate use in
improving basic living standards. The ability to compare
loans, to calculate risks, to figure unit prices, to understand
scale drawings, and to appreciate the effects of various
rates of inflation brings immediate real benefit. This kind
of basic applied mathematics is one objective of universal
elementary education.
· Civic concepts that enhance understanding of public pol-
icy issues. Major public debates on nuclear deterrence,
tax rates, and public health frequently center on scien-
tific issues expressed in numeric terms. Inferences drawn
from data about crime, projections concerning population
growth, and interactions among factors affecting interest
rates involve issues with essentially mathematical content.
A public afraid or unable to reason with figures is unable to
discriminate between rational and reckless claims in pub-
lic policy. Ideally, secondary school mathematics should
help create the "enlightened citizenry" that Thomas lef-
ferson called the only proper foundation for democracy.
· Professional skill and power necessary to use mathemat-
ics as a tool. Science and industry depend increasingly
on mathematics as a language of communication and as a
methodology of investigation, in applications ranging from
theoretical physics to business management. The principal
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...searchi1lg for patterns
M athematics is a profound and powerful
part of human culture.
goal of most college mathematics courses is to provide stu-
dents with the mathematical prerequisites for their future
careers.
· Leisure- disposition to enjoy mathematical and logical
challenges. The popularity of games of strategy, puzzles,
lotteries, and sport wagers reveals a deep vein of amateur
mathematics lying just beneath the public's surface indif-
ference. Although few seem eager to admit it, for a lot of
people mathematics is really fun.
· Cultural the role of mathematics as a major intellectual
tradition, as a subject appreciated as much for its beauty
as for its power. The enduring qualities of such abstract
concepts as symmetry, proof, and change have been devel-
oped through 3,000 years of intellectual effort. They can
be understood best as part of the legacy of human culture
which we must pass on to future generations. indeed, it
is only when mathematics is viewed as part of the human
quest that lay persons can appreciate the esoteric research
of twentieth-century mathematics. Like language, religion,
and music, mathematics is a universal part of human cul-
ture.
These layers of mathematical experience form a matrix of
mathematical literacy for the economic and political fabric
of society. Although this matrix is generally hidden from
public view, it changes regularly in response to challenges
arising in science and society. We are now in one of the
periods of most active change.
From Abstraction to Application
During the first half of the twentieth century, mathe-
matical growth was stimulated primarily by the power of
l
``Ifyou want to under-
stand nature, you must be
conversant with the lan-
guage in which nature
speaks to users
- Richard Feynman
33
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Mathematics
Strictly Speaking
MATHEMATICAL SCIENCES is a
term that refers to disciplines
that are inherently mathematical
(for example, statistics, logic, ac-
tuarial science), not to the many
natural sciences (for example,
physics) that employ mathemat-
ics extensively. For economy of
language, the word "mathemat-
ics" is often used these days as a
synonym for "mathematical sci-
ences," as the term "science" is
often used as a summary term for
mathematics, science, engineer-
ing, and technology.
34
abstraction and deduction, climaxing more than two cen-
turies of effort to extract full benefit from the mathematical
principles of physical science formulated by Isaac Newton.
Now, as the century closes, the historic alliances of mathe-
matics with science are expanding rapidly; the highly devel-
oped legacy of classical mathematical theory is being put to
broad and often stunning use in a vast mathematical land-
scape.
Several particular events triggered periods of explosive
growth. The Second World War forced development of
many new and powerful methods of applied mathematics.
Postwar government investment in mathematics, fueled by
Sputnik, accelerated growth in both education and research
Then the development of electronic computing moved math-
ematics toward an algorithmic perspective even as it pro-
vided mathematicians with a powerful too! for exploring
patterns and testing conjectures.
At the end of the nineteenth century, the axiomatization
of mathematics on a foundation of logic and sets made pos-
sible grand theories of algebra, analysis, and topology whose
synthesis dominated mathematics research and teaching for
the first two thirds of the twentieth century.
. · . ~. ~
These tradi-
onal areas nave now oeen supplemented oy major develop-
ments in other mathematical sciences in number theory,
logic, statistics, operations research, probability, computa-
tion, geometry, and combinatorics.
In each of these subdiscinTines~
__ 7 applications parallel
theory. Even the most esoteric and abstract parts of
mathematics number theory and Tocic. for example are
now used routinely in applications (for example, in com-
puter science and cryptography). Fifty years ago, the leading
British mathematician G. H. Hardy could boast that number
theory was the most pure and least useful part of mathemat-
ics. Today, Hardy's mathematics is studied as an essential
prerequisite to many applications, including control of au-
tomated systems, data transmission from remote satellites,
protection of financial records, and efficient algorithms for
computation.
., .
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...searching for patterns
Mathematics is the foundation of
science and technology. Without strong
mathematics, there can be no strong science.
in 1960, at a time when theoretical physics was the central
jewel in the crown of applied mathematics, Eugene Wigner
wrote about the "unreasonable effectiveness" of mathematics
in the natural sciences: "The miracle of the appropriateness
of the language of mathematics for the formulation of the
laws of physics is a wonderful gift which we neither under-
stand nor deserve." Theoretical physics has continued to
adopt (and occasionally invent) increasingly abstract math-
ematical models as the foundation for current theories. For
example, Lie groups and gauge theories exotic expressions
of symmetry are fundamental tools in the nhv~icist's search
for a unified theory of forces.
~, _ ~
,
During this same period, however, striking applications
of mathematics have emerged across the entire landscape
of natural, behavioral, and social sciences. All advances in
design, control, and efficiency of modern airliners depend
on sophisticated mathematical models that simulate perfor-
mance before prototypes are built. From medical technology
(CAT scanners) to economic planning (input/output models
of economic behavior), from genetics (decoding of DNA)
to geology (locating of! reserves), mathematics has made an
indelible imprint on every part of modern science, even as
science itself has stimulated the growth of many branches of
mathematics.
Applications of one part of mathematics to another of
geometry to analysis, of probability to number theory-
provide renewed evidence of the fundamental unity of math-
ematics. Despite frequent connections among problems in
science and mathematics, the constant discovery of new al-
liances retains a surprising degree of unpredictability and
serendipity. Whether planned or unplanned, the cross-
fertilization between science and mathematics in problems,
"Equations are just
the boring par' of
mathematics. reattempt
to see thi1'gs it' terms of
geometry."
- Stephen Hawking
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Mathematics
Myth: As computers become
more powerful, the need for
mathematics will decline.
Reality: Far from diminishing the
importance of mathematics, the
pervasive role of computers in
science and society contributes to
a greatly increased role for math-
ematical ideas, both in research
and in civic responsibility. Be-
cause of computers, mathematical
ideas play central roles in impor-
tant decisions on the job, in the
home, and in the voting booth.
36
theories, and concepts has rarely been greater than it is now,
in this last quarter of the twentieth century.
Computers
Alongside the growing power of applications of mathemat-
ics has been the phenomenal impact of computers. Even
mathematicians who never use computers may devote their
entire research careers to problems arising from use of com-
puters. Across all parts of mathematics, computers have
posed new problems for research, supplied new tools to solve
old problems, and introduced new research strategies.
Although the public often views computers as a replace-
ment for mathematics, each is in reality an important too}
for the other. Indeed, just as computers afford new opportu-
nities for mathematics, so also it is mathematics that makes
computers incredibly elective. Mathematics provides ab-
stract models for natural phenomena as well as algorithms
for implementing these models in computer languages. Ap-
plications, computers, and mathematics form a tightly cou-
pled system producing results never before possible and ideas
never before imagined.
Computers influence mathematics both directly- through
stimulation of mathematical research and indirectly by
their effect on scientific and engineering practice. Comput-
ers are now an essential too} in many parts of science and
engineering, from weather prediction to protein engineer-
ing, from aircraft design to analysis of DNA. In every case,
a mathematical mode! mediates between phenomena of sci-
ence and simulation provided by the computer.
Scientific computation has become so much a part of the
everyday experience of scientific and engineering practice
that it can be considered a third fundamental methodology
of science-parallel to the more established paradigms of
experimental and theoretical science. Computer models of
natural, technological, or social systems employ mathemati-
cally expressed principles to unfold scenarios under diverse
conditions scenarios that formerly could be studied only
through lengthy (and often risky) experiments or prototypes.
The methodology of scientific computation embeds mathe
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...searchi1'g for patterns
matical ideas in scientific models of reality as surely as do
axiomatic theories or differential equations.
Computer models enable scientists and engineers to reach
quickly the mathematical limits permitted by their models.
Robotics design, for instance, often encounters limits im-
posed not by engineering details, but by incomplete under-
standing of how geometry controls the degrees of freedom of
robot motions. Models of weather forecasting consistently
reveal uncertainties that suggest intrinsically chaotic behav-
ior. These models also reveal our severely limited knowledge
of the mathematical theory of turbulence. Whenever a sci-
entist or engineer uses a computer mode! to explore the fron-
tiers of knowledge, a new mathematical problem is likely to
appear.
Computer models have extended the
mathematical sciences into every corner of
· . ~ . · · .
sclentl~c anc . engineering practice.
Whereas, traditionally, scientists and engineers who were
engaged primarily in experimental research could get along
with a small subset of mathematical skills uniquely suited to
their field, now even experimentalists need to know a wide
range of mathematical methods. Small errors of approxi-
mation that are intrinsic to all computer models compound,
like interest, with subtle and often devastating results. Only
a person who comprehends the mathematics on which com-
puter models are based can use these models effectively and
efficiently. Moreover, as a consequence of current limits on
computer models, further advances in many areas of sci-
entific and engineering knowledge now depend in essential
ways on advances in mathematical research.
The Mathematical Community
Because of its enormous applicability, mathematics is-
apart from English the most widely studied subject in
37
OCR for page 38
Mathematics
Back to School
Two banks are offering car loans
with monthly payments of $100.
One has an interest rate of 16
percent; the other has a higher
rate of 18 percent together with
a premium of a free color televi-
sion (worth $400~. If you need a
$5,000 loan and would really like
the color TV, which bank should
you choose?
38
school and college. Present educational practice for mathe-
matics requires approximately 1,500,000 elementary school
teachers, 200,000 high school teachers, and 40,000 college
and university teachers. Mathematics education takes place
in each of 16,000 public school districts, in another 25,000
private schools, in 1,300 community colleges, 1,500 colleges,
400 comprehensive universities, and 200 research universi-
ties. Roughly 5,000 mathematicians, principally those on the
faculties of the research universities, are engaged in research.
Only half of the nation's students take more than two
years of high school-level mathematics; only one quarter take
more than three years. That remaining quarter roughly one
million enter colleges and universities with four years of
mathematics. Four years later, about ~ 5,000 students emerge
with majors in mathematics. One quarter of these students
go on to a master's degree, but only 3 percent (about 400)
complete a doctoral degree in the mathematical sciences.
M
athematics is the nation's second-
largest academic discipline.
Just to replace normal retirements and resignations of high
school teachers will require about 7,000 to 8,000 new teach-
ers a year, which is half of the expected pool of ~ 5,000 math-
ematics graduates. Elementary school teachers, in contrast,
are drawn primarily from the three quarters of the popula-
tion who dropped mathematics after two or three courses in
high school. For many prospective elementary school teach-
ers, their high school experiences with mathematics were
probably not positive. Subsequently, teachers' ambivalent
feelings about mathematics are often communicated to chil-
dren they teach.
In sharp contrast to the eroding conditions of mathemat-
ics teaching, one finds enormous vitality and diversity in the
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...searching for patterns
breadth of the mathematics profession. Over 25 different or-
ganizations in the United States support some facet of pro-
fessional work in the mathematical sciences. Approximately
50,000 research papers 20,000 by U.S. mathematicians-
are published each year in 2,000 mathematics journals
around the world. At the school and college level alone,
there are over 25 U.S. publications devoted to students and
teachers of mathematics. Students and faculty participate
in problem-solving activities sponsored by these journals as
well as learn about the ways in which current research can
relate to curricular change.
This massive system of mathematics education has had no
national standards, no global management, and no planned
structure despite the facts that each step in the mathemat-
ics curriculum depends in vital ways on what has been ac-
complished at all earlier stages and that scores of professions
depend on skills acquired by students during their study of
mathematics. Both because it is so massive and because it is
so unstructured, mathematics education in the United States
resists change in spite of the many forces that are revolution-
izing the nature and role of mathematics.
Undergraduate Mathematics
Undergraduate mathematics is the linchpin for revitaliza-
tion of mathematics education. Not only do all the sciences
depend on strong undergraduate mathematics, but also all
students who prepare to teach mathematics acquire attitudes
about mathematics, styles of teaching, and knowledge of
content from their undergraduate experience. No reform of
mathematics education is possible unless it begins with revi-
talization of undergraduate mathematics in both curriculum
and teaching style.
During the last two decades, as undergraduate mathemat-
ics enrollments have doubled, the size of the mathematics
faculty has increased by less than 30 percent. Workloads
are now over 50 percent higher than they were in the post-
Sputnik years and are typically among the highest on many
campuses. Resources generated by the vigorous demand for
undergraduate mathematics are rarely used to improve un
"Between now aids the
year 2000, for the firs t
time in history, a ma-
jority of all new jobs will
require postsecond~ary
education."
Workforce 2000
39
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Mathematics
"Too many teachers over
mathematics on a take
it-or-leave-it basis in the
universities. The result is
that some of the brightest
mathematical minds elect
to lea ye it."
Edward E. David, Jr.
A Pipeline to Science
The undergraduate mathematics
major not only prepares students
for graduate study in mathemat-
ics, but also for many other sci-
ences. Indeed, nearly twice as
many mathematics majors go on
to receive a Ph.D. in another sci-
entific field rather than in the
mathematical sciences them-
selves.
40
dergraduate mathematics teaching. To administrators wor-
ried about tight budgets, mathematics departments are often
the best bargains on campus, but to students seeking stimu-
lation and opportunity, mathematics departments are often
the Rip Van Winkle of the academic community.
R· · · . . . . . . . . . . . .
form of undergraduate mathematics is
the key to revitalizing mathematics education.
During these same two decades, both the opportunity and
the need for vital innovative mathematics instruction have
increased substantially. The subject moves on, yet the cur-
riculum is stagnant. Only a minority of the nation's colle-
giate faculty maintains a program of significant professional
activity. Even fewer are regularly engaged in mathematical
research, but these few sustain a research enterprise that is
the best in the world. Unfortunately, those who are most
professionally active rarely teach any undergraduate course
related to their scholarly work as mathematicians. Mathe-
maticians seldom teach what they think about and rarely
think deeply about what they teach.
Departments of mathematics in colleges and universities
serve several different constituencies: general education,
teacher education, client departments, and future mathe-
maticians. Very few departments have the intellectual and
financial resources to meet well the needs of all these fre-
quently conflicting groups. Worse still, most departments
fait to meet the needs of any of these constituencies with
energy, effectiveness, or distinction.
Since almost everyone who teaches mathematics is edu-
cated in our colleges and universities, many issues facing
mathematics education hinge on revitalization of undergrad-
uate mathematics. But critical curricular review and revital-
ization take time, energy, and commitment essential in-
gredients that have been stripped from the mathematics fac-
ulLty by two decades of continuous deficits. Rewards of pro-
motion and tenure follow research, not curricular reform;
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...searching for patterns
neither institutions of higher education nor the professional
community of mathematicians encourages faculty to devote
time and energy to revitalization of undergraduate mathe-
matics.
To improve mathematics education, we must restore in-
tegrity to undergraduate mathematics. This challenge pro-
vides a great opportunity. With approximately 50 percent
of school teachers leaving every seven years, it is feasible to
make significant changes in the way school mathematics is
taught simply by transforming undergraduate mathematics
to reflect the new expectations for mathematics. Undergrad-
uate mathematics is the bridge between research and schools
and holds the power of reform in mathematics education.
41
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The MILE:
The Mathematics Interactive Learning Environment
The MILE, located in 301 Urban Life Building, was created to support the
redesign of the delivery of Math 1111(College Algebra) and Math
1113(Precalculus). This state-of-the-art computer lab contains 82 computers for
general student use and 1 ADA compliant computer. The lab also contains 2
printers for student use through their Panther Id account. One-on-one assistance
is provided by peer tutors, graduate research assistants, as well as
departmental faculty. Use of the lab is a required element for all sections of
these MATH 1111 and 1113 beginning fall 2005. The MILE provides students with an
array of interactive materials and activities through mathematical software(MyMathLab). This software
is designed to engage the student in their learning process.
Multimedia learning aids for students:MyMathLab includes a
variety of multimedia resources – such as video lectures, animations, and audio
clips – to help students improve their understanding of key concepts. Videos and
animations are also accessible from individual online homework and practice
exercises.
Student study plan for self-paced
learning:MyMathLab generates
personalized study plans for students based on their test results. The Study
Plan links directly to tutorial exercises for topics a student still needs to
work on, and these exercises regenerate algorithmically to provide unlimited
practice. The Study Plan is updated each time a student takes a test, so
students can continually monitor their progress throughout the course.
Free tutoring for students from the Math Tutor
Center : Students using MyMathLab can use their
instructor's Course ID to sign up for free math tutoring from the Math Tutor
Center . The Tutor Center is staffed by qualified mathematics instructors who
provide one-on-one tutoring via toll-free phone, email, and real-time Internet
sessions.
Students get immediate feedback
while doing their homework assignments. If unsuccessful, they received
help online through four different modes of learning.
Free response questions help build students' use of
mathematical notation.
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Excursions In Modern Mathematics -with Excursions - 6th edition
Summary: For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. NEW: Now with ''Mini-Excursions'' Included! These are enrichment topics that have been added at the end of each part and require an understanding of the core material covered in one or more of the chapters. Shorter than a full chapter but much more substantive than an appendix. Each mini-excursion includes its own exercise set. This very successful liberal arts mathemat...show moreics textbook is a collection of ''excursions'' into the real-world applications of modern mathematics. The excursions are organized into four independent parts: 1) The Mathematics of Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts mathematics
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Mathematics of Chance utilizes simple, real-world problems-some of which have only recently been solved-to explain fundamental probability theorems, methods, and statistical reasoning. Jiri Andel begins with a basic introduction to probability theory and its important points before moving on to more specific sections on vital aspects of probability,... more...
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Science
Issue 28 / October - December 1999
Cybermath : Using The Internet As A Math Tool
Ercan Demiroz
Over the last decade, the Internet has impacted every aspect of our lives. It is now easy to perform very complicated tasks from your computer desktop by clicking buttons on the appropriate Web pages. For example, you can serve as your own travel agent by arranging your flight, car, or hotel reservations, and by searching for the lowest price by choosing the FareBeater option.1 You can do your shopping via computer, there by saving yourself a trip to a store or a mall.2 Since these Internet features make our lives easier and faster, they will continue to be a hot topic in the years to come.
While almost everybody who has access to a computer is somehow involved with the Internet for a variety of personal reasons, scientists and the academic community also use it for their own purposes. Examples are sharing data and information, browsing technical papers, searching for related documents, and posting their research activities to colleagues and other interested parties. Recent developments have proven to researchers and academia, both of which publish large amounts of technical literature, that the day of electronic publishing is close at hand.
The easiest way to publish electronically is to post documents on the Internet by generating Web pages. In this case, however, the user remains a passive recipient of information, for the Internet's interactive communication ability is not being used. This particular capability of the Web allows a scientist or researcher to generate Web pages with which the user can interact. One example of such interaction is performing mathematical operations over the Internet. This is very useful and powerful, for it allows the user to become an active receiver by gathering the needed information from that particular home page.
For instance, if you visit Rice University's home page for its Department of Mathematics, you will find several interactive math tools designed to help students taking the Ordinary Differential Equations course.3 These tools are activated by using Java or MATLAB programming language. For example, Figure 1 shows a tool called PPLANE, which draws the magnitude and direction of a differential vector in an x-y plane. PPLANE also graphs the linearization about equilibrium points, and displays eigenvalues, eigenvectors, nullclines, and stable and unstable orbits. The user can change the differential equation's variables and then run the associated MATLAB code over the Internet. A licensed MATLAB copy in the user's personal computer is not required, for the MATLAB routine is run on the server and displays the output on the user's browser. This makes it easy for the student to understand how the changes made alter the equation's features.
This technique is very efficient and powerful for a student who is still in the learning process. It also suggests that the Internet's interactive feature will affect the education system and the way courses are taught in the future.
Another home page that contains a wide variety of interactive math tools is found at the Web site for Dartmouth College's mathematics department.4 Professor Richard Williamson has written about 30 interactive math programs for common scientific problems. These vary from differential equations to heat equation solvers, from Newton's method of calculating the root of an equation to simulating a swing's motion. All of these programs are activated by the user's input parameters, and display the answer in the same manner.
Another interesting and very useful Web site is (see Figure 2). This interactive site allows the user to take any symbolic integral over the Internet. It is provided by Wolfram Research, which also produces the well-known and widely used Mathematics tool MATHEMATICA. After the user enters an expression, the integrator automatically runs MATHEMATICA on the server, integrates the expression, and sends the result back to the user's browser.5 This site is already helping many calculus students with their homework, and is quite handy for researchers who deal with complex integrals in their everyday research.
Another useful interactive math Web site can be found at the Geometry Center Web page of the University of Minnesota, Science and Technology Center.6 This site offers such interactive math tools as hyperbolic triangles, Lorenz simulation, and interactive proofs of popular theorems. There is also a tool for taking numeric integrals. If you get tried of doing mathematics, you can take a break and play some Tetris games at the same site. In fact, interactive games on the Internet are also a particular type of interactive math tool. A better graphical version of Tetris can be found at 7/tetris.htm.
All of the above Web pages show that cybermath has found its way onto the Internet, thanks to the Web's interactive communication capability. It is not difficult to imagine that students in other majors will apply this useful and efficient tool to their own field, thus making the Web even more interactive
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Assessing Modeling Projects In Calculus and Precalculus: Two Approaches
Once you've assigned a writing project and collected the papers, how are you going to grade it
without spending the rest of the semester on that one set? This article outlines two grading scales which
can make this more efficient.
Background and Purpose
Projects that require students to model a real-life
situation, solve the resulting mathematical problem and interpret
the results, are important both in enabling students to use
the mathematics they learn and in making the
mathematics relevant to their lives. However, assessing modeling
projects can be challenging and time-consuming. The holistic
and analytic scales discussed here make the task easier.
They provide the students with a set of guidelines to use
when writing the final reports. They also provide me with
a structured, consistent way to assess student reports in
a relatively short period of time.
Currently I use these scales to assess projects given
in precalculus and calculus classes taught at a two-year
branch of a university. I have used these scales over the last
seven years to assess projects given in undergraduate as well
as graduate-level mathematics courses. The scales have
worked well at both levels.
Method
I provide each student with a copy of the assessment scales
the first class meeting. The scales are briefly discussed with
the students and care is taken to point out that a numeric
solution without the other components will result in a failing grade.
I review the scale when the first group project is assigned.
This helps the students to understand what is expected of them.
The analytic scale (p. 117, adapted from [1]) lends
itself well to situations where a somewhat detailed assessment
of student solutions is desired. When the analytic scale is
used, a separate score is recorded for each section:
understanding, plan, solution, and presentation. This allows the students
to see the specific strengths and weaknesses of the final
report and provides guidance for improvement on future reports.
The holistic scale (p. 119, adapted from [2]) seems
better suited to situations where a less detailed assessment
is required. It often requires less time to apply to each
student report and can be used as is or adjusted to meet your
individual needs and preferences. For some problems it might be
useful to develop a scale that has a total of five or six points
possible. This will require rewriting the criteria for each level of score.
Findings
One of the easiest ways to demonstrate how the scales
work is to actually apply them. Figure 1 contains a proposed
solution to the problem given below. The solution has been
evaluated using the analytic scale.
The Problem: You want to surprise your little
brother with a water balloon when he comes home, but
want to make it look "accidental." To make it look
accidental you will call, "Watch out below!" as you release
the balloon, but you really don't want him to have time
to move. You time the warning call and find that it
takes 1 second. You have noticed that it takes your
brother
about 0.75 seconds to respond to warning calls and you know sound travels about 1100 feet per
second. If your brother is 5 feet tall, what is the greatest
height you could drop the balloon from and still be certain
of dousing him?
Using the holistic scale on p. 119 to assess this
proposed solution results in a score of "3a." The "a" is included
to provide the students with guidance regarding
the shortcoming(s) of the report.
Use of these scales, especially the analytic scale, has
led to reports that are much more consistent in organization
and usually of a higher quality. Students have repeatedly
made two comments regarding the use of the scales. First
they appreciate the structure. They know exactly what is
expected of them. Second they are much more comfortable with
the grade they receive. On more than one occasion students
have expressed concern regarding the consistency of
assessment in another class(es) and confidence in the assessment
based on these scales.
Use of Findings
One issue I focus on is how well the students are
interpreting what is being asked of them. After reading many reports
where the students are first asked to restate the problem, it
has become clear that I need to spend time in class teaching
the students how to read and interpret problems. They may
be literate, but they often lack the necessary experience
to understand what is being described physically.
I also focus on the students' mathematical reasoning.
In the problem presented above, a number of students run
into difficulty developing an equation for the brother's
reaction time. They will add the times for the warning call and
the reaction while completely ignoring the time for sound
to travel. Although it does not significantly alter the solution
in this problem, it is important for the students to realize
that sound requires time to travel. Prior to giving this
assignment, we now spend time in class looking at situations where
the time needed for sound to travel affects the solution.
Success Factors
When using the holistic scale, I include a letter (the "a"
of "3a" above) to indicate which criterion was lacking.
Students appreciate this information.
When new scales are developed it is well worth remembering that as the number of points increases so
does the difficulty in developing and applying the scale. In
the case of the holistic scale, it is often best to start with
four points. As you gain experience, you may decide to
develop more detailed scales. I have always found five or at most
six points sufficient for holistic scales.
To avoid problems with one or two students in a
group doing all of the work, I have them log the hours spent on
the project. I warn the class that if a student in a group spends
20 minutes on the project while each of the other
members averages four hours, that person will receive one-twelfth
of the total grade. There has only been one case in seven
years where this type of action was necessary.
A final note about using these scales. It often seems a
huge task to evaluate the reports, but they go rather quickly
once started. First, there is only one report per group so the
number of papers is reduced to one-third of the normal load.
Second, having clearly described qualities for each score reduces
the time spent determining the score for most situations.
An analytic scale for assessing project reports
(Portions of this are adapted from [1]. See Figure 1 for
a sample.)
Understanding
3 Pts The student(s) demonstrates a complete
understanding of the problem in the problem statement section
as well as in the development of the plan and interpretation of the solution.
2 Pts The student(s) demonstrates a good understanding
of the problem in the problem statement section.
Some minor point(s) of the problem may be overlooked
in the problem statement, the development of the
plan, or the interpretation of the solution.
1 Pt The student(s) demonstrates minimal
understanding of the problem. The problem statement may be
unclear to the reader. The plan and/or interpretation of
the solution overlooks significant parts of the problem.
0 Pt The student(s) demonstrates no understanding of
the problem. The problem statement section does
not address the problem or may even be missing. The
plan and discussion of the solution have nothing to do
with the problem.
Plan
3 Pts The plan is clearly articulated AND will lead to
a correct solution.
2 Pts The plan is articulated reasonably well and correct
OR may contain a minor flaw based on a correct interpretation of the problem.
1 Pt The plan is not clearly presented OR only
partially correct based on a correct/partially
correct understanding of the problem.
0 Pt There is no plan OR the plan is completely incorrect.
Solution
3 Pts The solution is correct AND clearly labeled OR
though the solution is incorrect it is the expected outcome
of a slightly flawed plan that is correctly implemented.
Figure 1. A proposed solution evaluated using the analytic scale.
2 Pts Solution is incorrect due to a minor error
in implementation of either a correct or incorrect plan
OR solution is not clearly labeled.
1 Pt Solution is incorrect due to a significant error
in implementation of either a correct or incorrect plan.
0 Pt No solution is given.
Presentation
1 Pt Overall appearance of the paper is neat and easy
to read. All pertinent information can be readily found.
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Linear Algebra with Applications, CourseSmart eTextbook, 8th Edition
Description
This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.
This thorough and accessible text–from one of the leading figures in the use of technology in linear algebra–gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides, which also come with the package. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Preface
What's New in the Eighth Edition?
Computer Exercises
Overview of Text
Suggested Course Outlines
Supplementary Materials
Acknowledgments
1. Matrices and Systems of Equations
1.1 Systems of Linear Equations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 Elementary Matrices
1.6 Partitioned Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
2. Determinants
2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 Additional Topics and Applications
Matlab Exercises
Chapter Test A
Chapter Test B
3. Vector Spaces
3.1 Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
Matlab Exercises
Chapter Test A
Chapter Test B
4. Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
Matlab Exercises
Chapter Test A
Chapter Test B
5. Orthogonality
5.1 The Scalar Product in Rn
5.2 Orthogonal Subspaces
5.3 Least Squares Problems
5.4 Inner Product Spaces
5.5 Orthonormal Sets
5.6 The Gram—Schmidt Orthogonalization Process
5.7 Orthogonal Polynomials
Matlab Exercises
Chapter Test A
Chapter Test B
6. Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Systems of Linear Differential Equations
6.3 Diagonalization
6.4 Hermitian Matrices
6.5 The Singular Value Decomposition
6.6 Quadratic Forms
6.7 Positive Definite Matrices
6.8 Nonnegative Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
7. Numerical Linear Algebra
7.1 Floating-Point Numbers
7.2 Gaussian Elimination
7.3 Pivoting Strategies
7.4 Matrix Norms and Condition Numbers
7.5 Orthogonal Transformations
7.6 The Eigenvalue Problem
7.7 Least Squares Problems
Matlab Exercises
Chapter Test A
Chapter Test B
Appendix: MATLAB
The MATLAB Desktop Display
Basic Data Elements
Submatrices
Generating Matrices
Matrix Arithmetic
MATLAB Functions
Programming Features
M-files
Relational and Logical Operators
Columnwise Array Operators
Graphics
Symbolic Toolbox
Help Facility
Conclusions
Bibliography
A. Linear Algebra and Matrix Theory
B. Applied and Numerical Linear Algebra
C. Books of Related Interest
Answers
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Elementary Number Theory And Its Application - 6th edition
Summary: Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps students explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of professor feedback, this edition offers new examples, exercises, and applications, while incorporating advancements and di...show morescoveries in number theory made in the past few
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This manual includes resources designed to help both new and experienced instructors with course preparation and classroom management. This includes mini-lectures for each section of the text, chapter by chapter teaching tips, sample syllabi, support for media supplements, and more.
Using MyMathTest as a Student
You can use MyMathTest to practice for and take placement tests, or to do a refresher course to improve your maths skills. MyMathTest helps you build your skills by taking practice tests and working through a personalised Study Plan based on those results.
Whe...
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This course is the second half of a two-quarter precalculus sequence. The focus of this courseis the development of trigonometry from the unit circle point of view. Exponentialand logarithmic functions and their applications to constant percentage rate growthproblems will be a second focus. Other topics include polar graphs, conic section equations(for the parabola, ellipse, and hyperbola), using augmented matrices to solve linearsystems, arithmetic and geometric sequences, mathematical induction, and the binomialtheorem.
This course will make more sense if you can read or at least browse through the relevant sectionsof the book before each class. Generally we'll cover a section of the book in one to twodays.
Keeping up with the new concepts through homework exercises is essential to success in thecourse. I will frequently collect homework exercises handed out in class, but will not usually collecthomework exercises from the book. We will spend class time discussing the the book exercises, andyou need to do the book exercises to learn the material well. There will be occasional quizzes aswell.
I'm planning to give three tests and a final exam. Some of the tests may have a take-home part.There will be an opportunity to make-up one test by the way I score the final exam. I look at eachsection of the comprehensive final (a test one part , a test two part , etc. ) and look to see onwhich section you have improved the most. If you have, for example, improved the most on thetest two part of the final exam, then the score on the test two portion of the final replaces youroriginal test two score. Of course, if the final exam scores are all lower, your original test scores areleft unchanged.
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Information
Required Materials:
A pencil
A scientific calculator.Calculators may be borrowed.A note signed by a parent/guardian must
be filled out prior to receiving the calculator.Students who do not bring a calculator to class will not be
provided with a loaner.
An organized notebook.Each student will need a separate
three-ring binder used solely for Algebra class.It can be on the small side, 1" to 1 ½".Notebook will be assessed throughout
the year.The notebook should be
divided into five sections:Syllabus/Reference,Warm-ups, Notes, Homework,
Tests/Quizzes.
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4. Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare "accurate to the nearest foot" when measuring the height of a person versus when measuring the height of a mountain.
9. Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable.
2. Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.
2. Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.
8. Differentiate and explain the relationship between the probability of an event and the odds of an event, and compute one given the other
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About Standard Deviants: Recommended by teachers and professors across the country, the
Standard Deviants approach to teaching is anything but standard. By
simplifying complex subjects and presenting the material with humorous
skits, computer graphics and a fun, approachable format, the Standard
Deviants make even the most difficult subjects enjoyable!
The Standard Deviants DVDs are the perfect way to learn and
review at your own pace with real-time, immediate feedback – all at the
touch of a button! The Standard Deviants combine cutting-edge
technology, interactive quizzes, award-winning educational material and a
troupe of young actors and comedians. Everything you need to learn is
at your fingertips. Recommended for junior high, high school, college
and beyond!
Standard Deviants - Algebra Introduction 2 Pack: Required study by high schools and colleges, algebra has been a notorious stumbling block for students. Without a solid foundation in algebra, however, you cannot expect to do well in more advanced math and science courses, such as calculus, physics and chemistry. Suitable for students of all ages, this DVD presents the three basic principles of pre-algebra and algebra in a clear, fun and approachable manner: functions, algebraic properties and linear equations.
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MAA Review
[Reviewed by Charles Ashbacher, on 11/08/2012]
Nearly every teaching mathematician has heard some form of the question "What is math good for?" This book starts with the work of George Boole and his "Laws of Thought" that are quite abstract and takes the implementation of those ideas by Alan Turing and Claude Shannon to the development and structure of the modern computer. Through the treatment, which includes some basic digital logic design and probabilistic computations, the reader is taken on a journey from the development of some abstract mathematical ideas through a nearly ubiquitous application of those ideas within the modern world with so many embedded digital computers.
While most of the treatment is understandable, readers who are unfamiliar with Turing machines will likely struggle a bit when reading the section that covers them. While simple in structure, Turing machines are an abstraction that is best understood by seeing some examples, which is not done well here. The sections on digital devices such as logic gates and flip-flops may also prove challenging.
I enjoyed the discussion of Claude Shannon. In the history of the computer and development of the internet and World Wide Web, his ideas and contributions are too often overlooked. He is one of my heroes and I believe that everyone that reads this book will come to the same conclusion. If you read this book and hear the question, "What good is algebra?" you will have a ready and irrefutable answer, "Boolean algebra is the basis for describing and designing the circuits of computers."
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.
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My Advice to a New Math 175 Student:
Always go to class!!! If you skip a day, you will get very far behind.
Everything in Calc builds off of something you learned earlier, even if
you don't see the connection at first. Do not be afraid to ask
questions in class. Don't worry about looking like an idiot for asking
a question, someone else probably wanted to ask that question too, but
was afraid to. One question can be the difference between
understanding
and not understanding something. See someone at the first sign of
trouble, don't wait until the problem is too big to handle. Five
minutes with a tutor when you first get confused is better than two
hours later on down the road. Keep up on the assignments. I have
found
that when I skipped an assignment or didn't put a lot of time into it,
I
did bad on that part of the test. Try all of the assigned problems,
even if you are sure you understand something, try them anyway,
practice
can only make you better, and may uncover something that you really
don't understand. Take good notes!! At night when you are doing your
assignment, they are your best friend and help to get it done. To see
if you really understand a concept, try explaining it to someone else.
This is one of the best tests to see how well you understand what you
are studying.
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Congratulations to Folena DeGeus for winning a Certificate of Merit in the UVM Mathematics Prize Exam and for winning Best in School in the UVM Math Prize Exam.
Congratulations to Kevin Keene for winning a Certificate of Merit in the UVM Mathematics Prize Exam.
Mathematics
The Mathematics Department has developed a curriculum that is designed to meet the needs of every student. We offer courses at many different levels of difficulty, so that each student can take courses that are appropriate for his or her mathematical development. The courses are planned in a sequence that provides reinforcement of previously learned concepts and the sequential development of new material. Each course has prerequisites that are designed to ensure that every student will have a high probability of success.
The Mathematics Department also recognizes that appropriate study skills are important to academic success. Therefore, each student is required to maintain a comprehensive notebook. Regular attendance, participation in class, and completion of daily assignments are also considered minimum requirements.
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Description:For
students who need review of the fundamentals of arithmetic, a thorough
introduction to signed numbers, and a presentation of the basic concepts of
algebra.Topics include proportion and
percent, polynomials, factoring, inequalities in one
variable, linear equations, systems, graphing, integer exponents and quadratic
equations.Applications are
included throughout the course.This
self-paced course has no lecture and incorporates independent computer use; in
order to advance through course topics, students must achieve required level of
mastery.Students scoring below 46 on
the Accuplacer Algebra Placement Test are expected to
complete the course in two semesters; students scoring 46 or higher are
expected to complete in one semester.Assessment level:RD 099/103.For computation of tuition, this course is equivalent to three semester
hours.
II.Class Format:
This course incorporates independent computer use and requires a level
of mastery in order to advance through the course topics.
III. Software,
Textbook, and Other Supplies:
Required:
MyLabsPlus access code which includes an electronic
form of the textbook
Customized Workbook - available in bookstore, bundled
with the access code
Homework:You are required to use the online software, MyLabsPlusto complete homework
assignments at your own pace. Once you achieve 100% on each homework
assignment, you will be allowed to progress to the next one, and so on, until
you reach the test on that unit.TWO
personal notebooks are required… one notebook to show all work on homework
assignments and a SEPARATE notebook to take notes from media assignments. It is
expected that students watch all media in their entirety AND take notes just as
if they are in an on-campus class. Not doing so is equivalent to skipping
class.
In order to move forward in the course, you must
achieve 80% on each test.Retakes will
be allowed after the appropriate correction assignment is completed at a 100%
level.Scoring at least 60% on the Final
Test is a requirement for completion of MA094.Students may not receive help during testing and may only use
calculators on Tests 5-10.Sanctions
given in response to violations will be governed by the Student Code of
Conduct.
Course Grade:
A student
has completed Math 094 when the Final Test (Test 10) is completed with at least a score of 60%.The MyLabsPlus
(MLP) Overall Score, which can be found in the MLP grade book, is a weighted
average computed as follows:
A grade of A, B, or C is awarded when the MA094
Final Test (Test 10) is completed with
at least a score of 60%, and the MLP Overall Score is:
90% – 100%:Grade of A80% – 89.99%: Grade of
B70% – 79.99%: Grade of C
Students who have not
completed Test 10 with at least a score of 60% will need to register for Math 094 again in a
subsequent term.If the student has passed
at least 6 tests, their grade for this semester will be an H, indicating that
the students has done at least a semester's worth of work.Students who do not qualify for an A, B, C,
or H will be assigned a grade of U for the semester. Students
are encouraged to complete their math requirements in consecutive semesters.
Students continuing in Math 094 within a year
of their last attempt will
begin at thesection following the last test they successfully
completed. Students continuing after a year or more will be placed by
their instructor.
2.You will be asked to input a username and password.Your username is the first part of your MC
ID.
Your
password is the word: password.
You
will have a chance to select a more secure password later.
3.MLP will take you to a screen where you should see your course
listed in blue hyperlink.You will see your
instructor's name, day of the week, and time.Click on this hyperlink.
4.You will be prompted with the License Agreement and Privacy Policy
page.Click "I Accept" once you have read the terms of
use.
5.MLP will take you to a screen that will give you the option of
selecting one of two options:
- Access Code
- Buy Now
If
you have already purchased your MLP Access code, select the first option,'Access Code'.Tear off the thin strip inside your access
code folder and enter that code now.
If
you have a credit card and want to buy the access code online, select the
option 'Buy now' and follow the instructions on the screen.
If
you are not able to purchase an access code now, MLP will allow you to use a
Temporary Access Code, which expires within a short period of time. It is important that you purchase a
regular code soon, however, because MLP will not let you continue in the course
after the expiration date.You must
enter the new code on that day, when the system prompts you to do so. The temporary code is found by selecting 'Temporary Access' in the blue
left-hand margin of your screen.Copy
the code onto a sheet of paper, or by using your mouse, and then click on any
item in the left margin to get back to the previous page.Select the 'Access Code' option, and then
enter your code.
6.Click the orange box that says NEXT.
7.MLP will take you to a screen that has a yellow box that says:
Return to course.
Click that box.
8.You are now in your course. You must complete the orientation
assignment.
9.Lastly, it is important that you email your instructor to let him/her know that youhave
logged into MLP.He/she will let you
know whether you should continue working in MyLabsPlus
at assignment 1.2 (Part 1) or at assignment 9.1 (Part 2).
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Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each of the 120 lesson concepts and 12 investigations in Saxon Math's Geometry textbook is taught step-by-step on a digital whiteboard, averaging about 10-20 TThis course covers all topics in a high school geometry course, including perspective, space, and dimension associated with practical and axiomatic geometry. Students learn how to apply and calculate measurements of lengths, heights, circumference, areas, and volumes, and will be introduced trigonometry and transformations. Students will use logic to create proofs and constructions, work with key geometry theorems and proofs, and use technology such as spreadsheets, graphing calculators, and geometry software.
DIVE CD's
I have purchased the DIVE CD's for all the high school math my children have done. It is an excellent teaching tool.
Share this review:
0points
0of0voted this as helpful.
Review 2 for Saxon Geometry 1st Edition DIVE CD-Rom
Overall Rating:
4out of5
Date:September 12, 2011
hsbbmom
Location:Tennessee
Age:45-54
Gender:female
Quality:
4out of5
Value:
5out of5
Meets Expectations:
4out of5
I was very hesitant to buy this, but I am pleased with it. I do not remember much of geometry so this has helped. I have my son watch it before each lesson.
Share this review:
0points
1of2voted this as helpful.
Review 3 for Saxon Geometry 1st Edition DIVE CD-Rom
Overall Rating:
5out of5
DVD is a must for explaining new material
Date:January 7, 2011
mother of eight
Location:ohio
Age:35-44
Gender:female
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
This DVD made our Saxon purchase complete and now our daughter who hated Saxon math understands the new concepts for each lesson in this well-structured product.
Share this review:
+1point
1of1voted this as helpful.
Review 4 for Saxon Geometry 1st Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:April 13, 2010
Vesta Williams
Great, understandable lectures; professional and personable professor. We were happy to find fine quality assistance with geometry lessons!
Share this review:
+1point
1of1voted this as helpful.
Review 5 for Saxon Geometry 1st Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:April 13, 2010
Donna Makley
My children and I love all the Saxon DIVE CD-ROM's. I purchase them with each Saxon Math course I purchase. I am the mother of nine homeschooled children and it is wonderful to have a excellent resource to help me teach Math to my children. It gives me peace of mind to know we are doing Math right. I love that a child can be taught a lesson as much as a child may need, until they understand 100%. I recommomend the Saxon Geometry Dive CD ROM 100%!
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The curriculum in mathematics is designed to serve students of varying abilities and interests. Its purpose is to enable students to develop their thinking and problem-solving capacities, as well as to provide them with basic mathematical skills and positive attitudes about their use of mathematics.
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Pre-Calculus (SparkCharts)
9781586636227
ISBN:
1586636227
Pub Date: 2002 Publisher: Spark Publishing Group
Summary: SparkChartsTM--created by Harvard students for students everywhere--serve as study companions and reference tools that cover a wide range of college and graduate school subjects, including Business, Computer Programming, Medicine, Law, Foreign Language, Humanities, and Science. Titles like How to Study, Microsoft Word for Windows, Microsoft Powerpoint for Windows, and HTML give you what it takes to find success in sc...hool and beyond. Outlines and summaries cover key points, while diagrams and tables make difficult concepts easier to digest. This four-page chart reviews: Definition of a function Exponential and logarithmic functions Changing a function Polynomial functions Rational functions Polar coordinates Complex numbers Trigonometric functions[
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Basic Multivariable Calculus - 93 edition
Summary: Basic Multivariable Calculus helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.
Only first year calculus required--all necessary linear al...show moregebra is explained
Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises
Volume and Cavalieri's Principle The Double Integral over a Rectangle The Double Integral over Regions The Triple Integral Change of a Variable, Cylindrical and Spherical Coordinates Applications of Multiple Integrals
6. Integrals over Curves and Surfaces
Line Integrals Parametrized Surfaces Area of a Surface Surface Integrals
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Long description International MetricProduct details
Publisher:
Brooks/Cole
ISBN:
9780495383628
Publication date:
February 2008
Length:
254mm
Width:
224mm
Thickness:
48mm
Weight:
2421g
Edition:
6th international ed
Pages:
1344
Table of contents
1. Functions and Models. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Principles of Problem Solving. 2. Limits. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. 3. Derivatives. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent?. Imlicit Differentiation. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. 4. Applications of Differentiation. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity
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Solving Equations DVD Sample Track
The ability to solve equations is a foundation of algebraic instruction and algebraic thinking. The student who is able to demonstrate a mastery of this skill is well on the way to success in understanding algebra and achieving success in higher mathematics courses. In this video, Brad and I will show you how we have presented this concept successfully in our own middle and high school classes. Our students have exhibited a high level of mastery of this concept both in their conceptual understanding and their computational expertise.
Brad and I begin our instruction in solving equations by establishing a solid foundation for understanding how the equal sign functions in mathematics in general and in algebraic equations in particular. You will see us initiate our lesson by asking students to solve equations that are presented in parallel conjunction with a visual model of a balance scale.
As a teacher and an expert in the needs of your specific students, you will decide how much of a foundation already exists in your class and how much still needs to be developed. Thus you may leave the visual model sooner or later depending upon your students' conceptual development of equation solving.
This foundation is not only necessary for your students' understanding of equations, it will also provide invaluable assistance to their teachers in future higher mathematics courses who build upon the foundation we establish. Often students demonstrate some success in mathematics until they reach the secondary level. This can be attributed to the fact that some of them do not really understand mathematics at the elementary level but are simply mimicking our models and processes without conceptual fluency. As these mathematical processes become more involved in middle and high school, their lack of understanding leaves them with skills that are little more than trying to master algebra by rote procedures. While this worked on simpler or shorter problems in the past, it leaves them wandering without a compass in the rugged algebraic landscape.
One of the components of teaching mathematics using Conceptual Layering is the presentation of concepts using positive whole numbers. Only when students have demonstrated an understanding of the concept are fractions and negative integers introduced. During the course of this training video, we will focus on equations that utilize positive whole numbers to develop the concept. Many of the worksheets in the accompanying PDF handout provide students with opportunities to practice these same concepts with more challenging numbers." The vocabulary of additive inverses, multiplicative inverses, subtraction, division property of equality, and combining like terms are all covered in this video.
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GCSE Maths: Simplifying logarithmic expressions
Activities to enable learners of secondary mathematics to develop their understanding, and practise using, the laws of logarithms to simplify numerical expressions involving logarithms. This standards unit is part of the 'Mostly algebra' set of materials.
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Authors:
Year Published:
ISBN-13:
Extent:
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About the book
This book offers you a succinct summary of skills and concepts necessary for
success in the Year 12 Specialist Mathematics examination.
There are three sections:
The first section 'Key Facts and Concepts' presents concise
definitions and summaries. Important terminology is clearly explained,
definitions are given and helpful tips about what you need to know –
all in a clear and accessible format.
The second section helps you to practise in the 'write-on'
format of the new examinations. Five trial examination papers are given: A,
B, C, D and E. The first four trial examination papers are based on recent
Maths 2 examination papers (A – 1999, B – 2000, C – 2001, D
– 2002) but questions have been modified in line with the new syllabus
and many have been replaced by completely new questions. Trial examination E
is similar to the exemplar paper on the SSABSA website.
The third section shows you the fully worked solutions for all five trial
examinations. Correct answers can sometimes be obtained by different methods.
In this book, where applicable, each worked solution is modelled on the
worked example in the textbook.
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McGillFaculty of EngineeringMIME 310 Engineering EconomyChapter 2 Principles of Accounting Accounting, the source of all financial information to the business world OutlineSection 1: How businesses keep financial records Basic Principles in
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MATH191: Problem Sheet 5Due Thursday 6th November1. Dierentiate the following functions. This is a no mercy question: you will get no marks for an incorrect answer, no matter how minor the mistake. There is no need to simplify your answers and if
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M101 Tutorial Problem Sheet 4 - Solutions sin x for x < 1. To make f ( x ) = differentiable at x = , we first arrange for it to be mx + c for x continuous. The left limit at x = is sin = 0 ; the right limit and the value are m + c . So we ne
MATH101 January 2008 Note: there is no bookworkin this paper. All questions are similar to ones set in homework, class tests and past papers. SECTION A1. Sketch the function in each interval, noting which end points are open and which are closed: [
MATH101 - Foundation Module I - CalculusModule NotesWe hope you enjoy this mathematics module. It is the first of three `Foundation Modules' which are taken by all year one students following any of our Mathematics-based degree programmes. This one
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MATH101 Tutorial Problem Sheet 6 - 2008 These are for discussion during the weekly problems class. (1) Phoebe and Monica are on Staten Island, but have promised to meet Rachel in Bloomingdales. They can take a boat to any point on the shore and then
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MATH101 Tutorial Problem Sheet 7 - 2008 These are for discussion during the weekly problems class. (1) Show that the equation of the tangent to the curve y = cos x at the point (a, cos a) can be written y = cos a (x a) sin a. Hence derive a linear
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Provides an introductory text to statistics, emphasizing inference, with extensive coverage of data collection and analysis as needed to evaluate the reported results of statistical studies and act ...
The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic-visual side-by-sides, the authors show students the ...
Appropriate for a one-term course in intermediate algebra, this text is intended for those students who have completed a first course in algebra. By requiring the use of the graphing calculator, this ...
This book offers the sound presentation of mathematics, useful pedagogy, clear and well-constructed writing style, superb problem-solving strategies, and other qualities that have made the Martin-Gay ...
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Topic 6: Quantitative Skills
Basic Math Tutorial
The Basic Math Refresher provides a review of math concepts which with all SPP students are expected to be familiar. This familiarity is particularly important for those students who are required to take Statistical Analysis for Public Policy (PUBP 704) or Methods of Analysis for International Commerce and Policy (ITRN 501). The math refresher will help you to be better prepared for these courses.
Math for Economics Tutorials
In addition to the general quantitative skills you will need for many SPP courses, "Microeconomics for Policy Analysis (PUBP 720)" uses more specific mathematical concepts and principles. Many of these concepts are introduced in our general quantitative skills tutorial and reviewed in a special "math camp" offered to students in the weeks prior to the semester they take the microeconomics course.
While the quantitative requirements for microeconomics can vary by instructor, all students should be very familiar with certain topics related to graphs and functions. We have found that once students build a strong base in a discrete number of quantitative topics, they are able to better enjoy and understand the models presented in PUBP 720. This enables instructors to focus the course on applications rather than elementary quantitative requirements.
The video tutorials below review the key mathematical concepts used in SPP's microeconomics courses. These topics are generally covered in pre-algebra, algebra and pre-calculus math courses in high school and college; students that want additional resources in any of these topics should refer to the appropriate math (not economics) textbooks and/or discuss the issue with their professors. Knowledge of the material presented in the video tutorials is generally assumed in PUBP 720, and may not be reviewed in detail during the course.
Math Camp
Each semester, SPP offers a two-day math camp (PUBP 555) designed to review fundamental mathematical concepts associated with microeconomics (PUBP 720) - particularly basic algebraic and calculus principles. All students taking PUBP 720 should plan to enroll in the math camp the semester in which they are taking PUPB 720. The free workshop is open to all SPP students. Students taking PUBP 720 will receive instructions for registering for the workshop
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Mathematics
Introduction
Mathematics is a science that involves abstract concepts and language. Students develop their mathematical thinking gradually through personal experiences and exchanges with peers. Their learning is based on situations that are often drawn from everyday life. In elementary school, students take part in learning situations that allow them to use objects, manipulatives, references and various tools and instruments. The activities and tasks suggested encourage them to reflect, manipulate, explore, construct, simulate, discuss, structure and practise, thereby allowing them to assimilate concepts, processes and strategies1 that are useful in mathematics. Students must also call on their intuition, sense of observation, manual skills as well as their ability to express themselves, reflect and analyze. By making connections, visualizing mathematical objects in different ways and organizing these objects in their minds, students gradually develop their understanding of abstract mathematical concepts. With time, they acquire mathematical knowledge and skills, which they learn to use effectively in order to function in society.
In secondary school, learning continues in the same vein. It is centred on the fundamental aims of mathematical activity: interpreting reality, generalizing, predicting and making decisions. These aims reflect the major questions that have led human beings to construct mathematical culture and knowledge through the ages. They are therefore meaningful and make it possible for students to build a set of tools that will allow them to communicate appropriately using mathematical language, to reason effectively by making connections between mathematical concepts and processes, and to solve situational problems. Emphasis is placed on technological tools, as these not only foster the emergence and understanding of mathematical concepts and processes, but also enable students to deal more effectively with various situations. Using a variety of mathematical concepts and strategies appropriately provides keys to understanding everyday reality. Combined with learning activities, everyday situations promote the development of mathematical skills and attitudes that allow students to mobilize, consolidate and broaden their mathematical knowledge. In Cycle Two, students continue to develop their mathematical thinking, which is essential in pursuing more advanced studies.
This document provides additional information on the knowledge and skills students must acquire in each year of secondary school with respect to arithmetic, algebra, geometry, statistics and probability. It is designed to help teachers with their lesson planning and to facilitate the transition between elementary and secondary school and from one secondary cycle to another. A separate section has been designed for each of the above-mentioned branches, as well as for discrete mathematics and analytic geometry. Each section consists of an introduction that provides an overview of the learning that was acquired in elementary school and that is to be acquired in the two cycles of secondary school, as well as content tables that outline, for every year of secondary school, the knowledge to be developed and actions to be carried out in order for students to fully assimilate the concepts presented. A column is devoted specifically to learning acquired in elementary school.2 Where applicable, the cells corresponding to Secondary IV and V have been subdivided to present the knowledge and actions associated with each of the options that students may choose based on their interests, aptitudes and training needs: Cultural, Social and Technical option (CST), Technical and Scientific option (TS) and Science option (S).
Information concerning learning acquired in elementary school was taken from the Mathematics program and the document Progression of Learning in Elementary School - Mathematics, to indicate its relevance as a prerequisite and to define the limits of the elementary school program. Please note that there are no sections on vocabulary or symbols for at the secondary level, these are introduced gradually as needed.
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E-mail Abstract
You are about to send the following abstract: Simonsen, L.M. & Dick, T.P. (1997). Teachers' Perceptions of the Impact of Graphing Calculators in the Mathematics Classroom. Journal of Computers in Mathematics and Science Teaching, 16(2), 239-368
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The Common Sense of Teaching Mathematics (Digital Edition)
"Since knowing produces knowledge, and not the other way around, this book shows how everyone can be a producer rather than a consumer of mathematical knowledge. Mathematics can be owned as a means of mathematizing the universe, just as the power of verbalizing molds itself to all the manifold demands of experience."
-Caleb Gattegno
This edition is in the ePub file format. For more info on ePub, select the "Other Info" tab.
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Program Goals and Objectives
Department of Mathematics
Mathematics Major
2010-11 Goals and Objectives
Below are the goals and objectives for the mathematics major. You will also see how the department assesses the program to be sure students (and the department itself) are meeting these goals and objectives. The assessment results help the department to know what it is doing well (so it can keep doing that well) and where it has weaknesses (so it can develop strategies to strengthen these areas and then to know if these changes were effective). If you look at other math programs, they will have similar goals and objectives and similar methods of assessing. There is a link to the left "Why SBU?" that details three aspects of our program that we feel are important to consider as students select a college.
Goal 1: All mathematics majors will become familiar with the standard tools and structure of mathematics.
Objectives:
The student will be able to:
Assessment Method:
Use the techniques of statistics to describe data sets.
Major Field Test
Praxis Exam
Student work on Final Exam in MAT 3343
Compute correctly the derivative and integral for standard functions.
Major Field Test
Praxis Exam
Student work in MAT 1195, 2255, 2263
Perform standard matrix computations
Major Field Test
Praxis Exam
Student work in MAT 3323
Goal 2: All mathematics majors will become able to apply the tools and structure of mathematical systems.
Objectives:
The student will be able to:
Assessment Method:
Perform complex mathematical tasks to solve multi-step problems
Major Field Test
Praxis Exam
Student work in all courses
Compare similarities and contrast differences in number systems,
Major Field Test
Praxis Exam
Student work in MAT 3313, 3333, 4663
Compare similarities and contrast differences in axiomatic systems.
Major Field Test
Praxis Exam
Student work in MAT 3313, 3333, 4483, 4663
Goal 3: All mathematics majors will become able to creatively solve mathematical problems.
Objectives:
The student will:
Assessment Method:
Be able to contribute effectively to group efforts to solve mathematical problems.
Student work on collaborative papers in MAT 3313, 3363, 4663
Graduate Survey
Be able to design and implement and to locate and evaluate different strategies for solving mathematical problems.
Major Field Exam
Praxis Exam
Student work in MAT 3313, 3373, 4483, 4663, EDU 4513
Be prepared for career success and/or further study in mathematics.
Graduate Survey
Be able to adapt to changing employment demands.
Graduate Survey
Goal 4: All mathematical majors will become able to communicate mathematical results to others in written and oral work.
Objectives:
The student will be able to:
Assessment Method:
Use proofs as an effective tool for communicating results.
Student work on proof in MAT 3313, 3333, 4663, 4483
Design graphs to accurately convey information.
Major Field Exam
Praxis Exam
Student work in MAT 1195, 3343, 3373
Restate and explain the definitions for common mathematical terms.
Major Field Exam
Praxis Exam
Student work in MAT 3313, 4663, and EDU 4513
Evaluate which is the appropriate tool to use for solving a given problem.
Major Field Exam
Praxis Exam
Student work in MAT 3353 and 3373
Evaluate the effectiveness of a mathematical process as applied to a particular situation.
Major Field Exam
Praxis Exam
Communicate effectively in their career.
Graduate Survey
Explain how differences in life assumptions produce differences in life, just as differences in axiomatic systems produce differences in mathematical structure.
Student work in MAT 3313, 4483, 4663
Graduate Survey
Assessment Results
We graduate 5-10 students per year, but this is not enough for us to feel comfortable releasing group results on the Major Field Test (which are taken during a student's senior year, typically). The MFT is taken by students at a variety of types of schools (such as those preparing most of their majors for graduate school) and has some topics we do not have room for in our program at SBU.
This does not fit all of our majors, so we have looked for another external test to use.
However it is the only external test of this type that we know of.
The Praxis is a test taken by all students seeking math certification in Missouri.
Since 2006, we have been able to get information on how our students have performed on the secondary Praxis and middle school mathematics Praxis. These results are available here.
The method of sampling student work in courses was begun in 2002 and we are still analyzing the trend data to see if there are strengths and weaknesses we can identify. The data we have from this is available here.
Some information from our last graduate survey, taken in 2006, is given below.
Graduate Survey
A graduate survey is sent out every five years. In 2006, we sent it to graduates of the past ten years. We sent out the survey to 102 graduates in early-April (later than we had hoped to send it out).We had about 15 returned for lack of a current address (some of these we were able to track down and most were glad we had taken the time to track them down).We had 25 surveys completed (following an extension of the deadline a couple of times).
Strengths
On the graduate survey, the faculty is consistently identified as strength of the department, combined with small class sizes which allows for personalized attention.Nearly all returned surveys (22 of 25) had some written comment on strength of the department.Items having over 80% responding as agree or strongly agree were:
My mathematics degree from SouthwestBaptistUniversity prepared me well for my current job.
I am very satisfied with my mathematics degree from SouthwestBaptistUniversity (at 92%).
I am very satisfied with my current job (at 92%).
I was able to find employment in a reasonable time.
In the past year I have often looked for further information to help me in my present occupation.
While at SouthwestBaptistUniversity, I thought a lot about how one recognizes the problems of integrating life's assumptions, absolute truth, and personal faith.
While at SBU, I was challenged to examine the complexity and order of the number systems and the effect that changes in assumptions have on outcomes.
While at SBU I was challenged to examine the professional values and attitudes necessary for my occupation.
Only one item, "Knowing what I do now about my major and the employment opportunities it allows, I would choose to major in math at SBU again," had a disagree/strongly disagree response of 20% or more and it was just 20% disagree. This is five students and only one of them has ever been employed in the field of mathematics to use their SBU degree. There are only 11 of the 25 currently working in the field of mathematics (and only 14 of the 25 ever having been employed in the field of mathematics). This is lower than anticipated, but some may narrowly define the field of mathematics as they provided negative responses. Even with lower responses on choosing to major in math at SBU again and employment within mathematics, our graduates are very satisfied with their math degree, with how it prepared them for their current job, and with their current job.
Weaknesses
On the graduate survey, comments about specific weaknesses seemed to follow the themes of:
limited course offerings
Need for additional rigor
Comments on Weaknesses
With a student population of 40-50 majors, it is difficult to offer as wide a variety of courses as students might desire. Student population contributes to the rigor issue as we have a wide variety of ability levels in our math classes. It is a difficult balancing act between teaching with enough rigor to prepare a few students for further mathematical study (which is what the MFT measures) and not overwhelming some students (who have no intention of further mathematical study, but have chosen the difficult field to major in as an undergraduate). In some sense this is a weakness, but in another sense it is a strength. We care about all of our students and work hard to enable them all to succeed. Some schools intentionally use some beginning math classes (such as Calculus) to "weed out" weaker students from their program.
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easy for the beginner to do and understand algebra. It also has a "Einstein" level that even algebra experts will find fun and challenging. You can choose from a ten problem, a time trial, or a two-player game. High scores are saved and you are given a rank according to your score. The ranks are Novice, Learner, Veteran, Calculator, Math Pro, Math Whiz, Math Genius, and Einstein.
The practice menu lets you practice each function individually. The game menu lets you choose one function, two functions, and so on up to 21 functions. You can choose from calculate value (1 x and 1y value and the equation to solve), choose formula (you figure out the equation using the given x, y, and z values), or figure formula and calculate (you figure out the equation and solve for the missing z value).
If you get stuck trying to figure out what the function (equation) is a hint will be displayed. If you choose the wrong answer it will help you figure out the right one. The calculate option combined with the practice game enables students to practice solving the problems in the area they are having trouble with.
Algebra - One On One
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Maths a subject that tests your Problem-solving approach, it uses different numbers,
variables, functions and theorems to reach to the solution of any problem.
BITS
iText in ActionWriting a book forManning Publications Co.What is iText?• First PDF library: rugPdf (1998)– One Christmas holiday of study– Developed in six weeks time– Not user-friendly: for PDF experts only• 2000: I want my own project!– Rebuild a PDF library from scratch– For people who don't know anything about PDF– iText hosted at lowagie.comorialee tutFr2004: First contact• November 2004: offer to write a book forO'Reilly• April 2005: offer to write a book forManningPreparing a book• First contact: Publisher's Assistant• After evaluation: Acquisition Manager:helps writing the Book Proposal– Short Summary– Detailed Table of Contents– Marketing Overview• Industry reviewBook contract• 5 deadlines– Chapter 1– 1/3 of the manuscript– 2/3 of the manuscript– 3/3 of the manuscript– Final manuscript• "Author Launch"Writing a book• Development Manager assigns:– Developmental Editor• Helps the writer "developing" his book• Obey the Manning Style Guide!• Review Manager• Coordinates the review processProduction• Production Manager assigns:– Copy Editor– Technical Editor– Lay-out– Proof Reader• Cover Designer• Marketing Manager: go or no-go• Back cover: written by the Publisher himselfTimingFirst Edition:• May – July 2005: preparing the book• September 2005 – February 2006: writing• March – November 2006: productionSecond Edition:• August – September 2009: preparing• October 2009 – April 2010: writing• May – August 2010: productionThe result
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Tensor algebra and tensor analysis were developed by Riemann, Christoffel, Ricci, Levi-Civita and others in the nineteenth century. The special theory of relativity, as propounded by Einstein in 1905, was elegantly expressed by Minkowski in terms of tensor fields in a flat space-time.
In 1915, Einstein formulated the general theory of relativity, in which the space-time manifold is curved. The theory is aesthetically and intellectually satisfying. The general theory of relativity involves tensor analysis in a pseudo-Riemannian manifold from the outset. Later, it was realized that even the pre-relativistic particle mechanics and continuum mechanics can be elegantly formulated in terms of tensor analysis in the three-dimensional Euclidean space. In recent decades, relativistic quantum field theories, gauge field theories, and various unified field theories have all used tensor algebra analysis exhaustively.
This book develops from abstract tensor algebra to tensor analysis in various differentiable manifolds in a mathematically rigorous and logically coherent manner. The material is intended mainly for students at the fourth-year and fifth-year university levels and is appropriate for students majoring in either mathematical physics or applied mathematics.
The first chapter deals with tensor algebra, or algebra of multilinear mappings in a general field F. (The background vector space need not possess an inner product or dot product.). The second chapter restricts the algebraic field to the set of real numbers R. Moreover, it is assumed that the underlying real vector space is endowed with an inner product (or dot product). Chapter 3 defines and investigates a differentiable manifold without imposing any other structure. Chapter 4 discusses tensor analysis in a general differentiable manifold. Differential forms are introduced and investigated. Next, a connection form indicating parallel transport is brought forward. As a logical consequence, the fourth-order curvature tensor is generated. Chapter 5 deals with Riemannian and pseudo-Riemannian manifolds. Tensor analysis, in terms of coordinate components as well as orthonormal components, is exhaustively investigated. In Chapter 6, special Riemannian and pseudo-Riemannian manifolds are studied. Flat manifolds, spaces of constant curvature, Einstein spaces, and conformally flat spaces are explored. Hypersurfaces and submanifolds embedded in higherdimensional manifolds are discussed in chapter 7. Extrinsic curvature tensors are defined in all cases. Moreover, Gauss and Codazzi-Mainardi equations are derived.
We would like to elaborate on the notation used in this book. The letters i, j, k, l, m, n, etc., are used for the subscripts and superscripts of a tensor field in the coordinate basis. However, we use the letters a, b, c, d, e, f, etc., for subscripts and superscripts of the same tensor field relative to an orthonormal basis. The numerical enumeration of coordinate components vi of a vector field is given by v1, v2, ... ,vN. However, numerical elaboration of orthonormal components of the same vector field is furnished by v(1), v(2), ..., v(n) (to avoid confusion). Similar distinctions are made for tensor field components. The flat metric components are denoted either by dij or dab. (The usual symbol η is reserved only for the totally antisymmetric pseudotensor of Levi-Civita.) The generalized Laplacian in the AT-dimension is denoted by Δ.
I would like to acknowledge my gratitude to several people for various reasons. During my stay at the Dublin Institute for Advanced Studies from 1958 to 1961, I learned a lot of classical tensor analysis from the late Professor J. L. Synge, F. R. S.. Professor W. Noll, a colleague of mine at Carnegie-Mellon University from 1963 to 1966, introduced me to the abstract tensor algebra, or the algebra of multilinear mappings. My research projects and teachings on general relativity for many years have consolidated the understanding of tensors. Dr. Andrew DeBenedict is has kindly read the proof, edited and helped with computer work. Mrs. Judy Borwein typed from chapter 1 to chapter 5 and edited the text diligently and flawlessly. Mrs. Sabine Lebhart typed the difficult chapter 7 and appendices. She also helped in the final editing. Mr. Robert Birtch drew thirty-four figures of the book. Last but not least, my wife, Mrs. Purabi Das, was a constant source of encouragement.
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Covina Statistics
...Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life?s experiences. Algebra II is designed to build on algebraic and geometric concepts.
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Department of Mathematics and Statistics
Mathematics is an ancient subject with roots in many cultures. The subject has developed and continues developing through steady exchange of ideas with other subjects. Mathematics is a fascinating and interesting subject on its own, but it also is a crucial tool for other subjects like physics, chemistry, biology, genomics, informatics and engineering science. In particular, the development of mathematical models connected to the use of computers is an important driving force which puts mathematics in the centre when it comes to interdisciplinary activity. Every science student has to acquire basic knowledge in mathematics at an early stage of the studies.
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COURSE DESCRIPTION:
This is a one-semester course whose main ideas are emphasized in the presentation of the polynomial, rational, trigonometric, exponential, and logarithmic functions. The core of the course is derived from materials best described as a compendium of college algebra, trigonometry, and analytic geometry, which would reinforce those skills essential to Analytical Methods or Calculus. Prerequisite: MA100 or equivalent high school background.
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a fairly short chapter. We will be taking a brief look at vectors and
some of their properties. We will need
some of this material in the next chapter and those of you heading on towards
Calculus III will use a fair amount of this there as well.
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The program
is open to public, private and home school students as well as middle school
students. All participants must have a basic knowledge of algebra.
Students
will take a practice test to determine their place in three levels of
instruction. Concept development, test-taking strategies and time management
will be discussed. Participants
may attend one or all sessions. Each session covers different material. No
early registration is required.
Students
should bring their own calculators. Other materials will be supplied. Students
also may bring snacks or purchase them on site.
Co-sponsors of the free sessions include Midwestern State University, Texas A&M University-Commerce, The University of Texas at
Austin, and The University of Texas at Dallas
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...I currently have a 3.9 GPA, which was really hard to achieve, but I believe the more you work hard the better your achievements will be. Algebra 2 is designed to build on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials, im...
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Basic Mathematical Skills with Geometry, 8/e by Baratto/Bergman is part of the latest offerings in the successful Hutchison Series in Mathematics. The eigth edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent one-semester basic math course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone.
1 Operations on Whole Numbers
1.1 The Decimal Place-Value System
1.2 Addition
1.3 Subtraction
1.4 Rounding, Estimation, and Order
1.5 Multiplication
1.6 Division
1.7 Exponential Notation and the Order of Operations
2 Multiplying and Dividing Fractions
2.1 Prime Numbers and Divisibility
2.2 Factoring Whole Numbers
2.3 Fraction Basics
2.4 Simplifying Fractions
2.5 Multiplying Fractions
2.6 Dividing Fractions
3 Adding and Subtracting Fractions
3.1 Adding and Subtracting Fractions with Like Denominators
3.2 Common Multiples
3.3 Adding and Subtracting Fractions with Unlike Denominators
3.4 Adding and Subtracting Mixed Numbers
3.5 Order of Operations with Fractions
3.6 Estimation Applications
4 Decimals
4.1 Place Value and Rounding
4.2 Converting Between Fractions and Decimals
4.3 Adding and Subtracting Decimals
4.4 Multiplying Decimals
4.5 Dividing Decimals
5 Ratios and Proportions
5.1 Ratios
5.2 Rates and Unit Pricing
5.3 Proportions
5.4 Solving Proportions
6 Percents
6.1 Writing Percents as Fractions and Decimals
6.2 Writing Decimals and Fractions as Percents
6.3 Identifying the Parts of a Percent Problem
6.4 Solving Percent Problems
7 Measurement
7.1 The Units of the English System
7.2 Metric Units of Length
7.3 Metric Units of Weight and Volume
7.4 Converting Between the English and Metric Systems
8 Geometry
8.1 Area and Circumference
8.2 Lines and Angles
8.3 Triangles
8.4 Square Roots and the Pythagorean Theorem
9 Data Analysis and Statistics
9.1 Means, Medians, and Modes
9.2 Tables, Pictographs, and Bar Graphs
9.3 Line Graphs and Predictions
9.4 Creating Bar Graphs and Pie Charts
9.5 Describing and Summarizing Data Sets
10 The Real Number System
10.1 Real Numbers and Order
10.2 Adding Real Numbers
10.3 Subtracting Real Numbers
10.4 Multiplying Real Numbers
10.5 Dividing Real Numbers and the Order of Operations
11 An Introduction to Algebra
11.1 From Arithmetic to Algebra
11.2 Evaluating Algebraic Expressions
11.3 Adding and Subtracting Algebraic Expressions
11.4 Using the Addition Property to Solve an Equation
11.5 Using the Multiplication Property to Solve an Equation
11.6 Combining the Properties to Solve Equations
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Prealgebra
edition: 6th
Author(s): Martin-Gay, Elayn
ISBN: 9780321628862No marked pages, or writing. DOES NOT come witht the "code", as the it can only be used once. However many websites sell the code for significantly less than buying the book NEW with the code.
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Information for incoming freshmen
1. For those with little or no
Calculus background
The Math Department offers two one-variable Calculus sequences:
Math 19 | 20 | 21 and
Math 41 | 42
Math 41 and 42 forms the basic single-variable
Calculus course. It consists of two 5-unit courses that meet three
times per week in lecture and twice per week in small sections.
This sequence is recommended for future Engineering, Science, and
Economics students. If you have had some Calculus in high school,
but not enough to place out of these courses via the AP exams, we
would advise you to begin with Math 41. If you are comfortable with
your Calculus background but did not pass the AP exam, you may elect
to begin in Math 42 or Math 51 with the permission of the Math Department.
Students who begin with Math 41 should
plan on taking Math 41 in the Fall, 42 in the Winter, and 51 (multivariable
calculus) in the Spring.
An alternative to Math 41 and 42 is
the Math 19, 20, 21 sequence. These three courses cover the same
material as 41 and 42 but proceed at a slower pace. These courses
are 3 units each for Math 19 and 20, and 4 units for Math 21. After
completing Math 21, you will be prepared to take the multivariable
course, Math 51.
In deciding whether to take Math 19
or 41, you should consider how comfortable you are with your high
school algebra and geometry. Feel free to consult with a faculty
member in the Math Department for advice.
2. Students with Calculus background
a. Students who scored a 4 on the AB advanced placement exam
or a 3 on the BC exam:
These scores earn you 5 units of credit and place you out of Math
41. You should begin with Math 42 in the Fall and Math 51(multivariable
calculus) in the Winter. In the Spring you have two basic options:
Take Math 52 (vector analysis, integration
of several variables)
Take Math 53 (differential equations
with linear algebra)
(Math 52 and 53 are independent of each other)
If you are in this category but feel
confident of your background in one-variable calculus, you may begin
with Math 51 (and take Math 51, 52 and 53 throughout the year).
We advise you to consult with a Math Department advisor if you wish
to do this.
b. Students who scored a
5 on the AB advanced placement exam or a 4 or 5 on the BCexam: These scores earn you 10 units of credit and place you out of
Math 41 and 42. You should take Math 51, 52, and 53, or the honors
version, Math 51H, 52H, and 53H during your Freshman year. These
are integrated courses in Multivariable Mathematics and were designed
specifically for students in your situation. After completing these
sequences you will have the Mathematics background for most Engineering
and Science majors.
SOPHOMORES AND UPPER CLASSMEN
The basic prerequisite for any of the
multivariable mathematics courses (Math 51, 104)
is one-variable calculus (completion of Math 42, 21, or the equivalent).
Students who have completed Math
42:
Take Math 51, 52, and 53 during this year. This is an integrated
sequence of multivariable calculus, linear algebra, and differential
equations, and will give you the necessary mathematics background
for most majors in Science, Engineering, and Economics.
Students who have completed Math
51:
A good program would be to take Math 52 (vector analysis) in the
Fall, Math 104 or 113 (linear algebra) in the Winter, and Math 53
during the Spring. These courses could also be taken in different
order. Consult the catalog and/or an adviser in the Math Department.
For students who have completed a basic
background in multivariable calculus, linear algebra, and differential
equations, there is a wide variety of 100-level courses you may
take. Which courses to take and the order in which to take them
depends on your major and your general mathematical interests. Consult
the catalog, your major advisor, and/or an adviser in the Math Department.
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Math Homework Answers
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Math Homework Answers GetMath answers Step by Step From Framing of Formulas to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations you get all Math Homework Answers online using our well structured and wel thought out Math tutoring program. Students get not just the answer but answers step by step. Below is provided a demo example of getting math answers step by step from us: Example: Find out the area of a triangle, height 8 cm, base 6 cm. Answer: 242 cm Steps to follow: 1. Since, Area of a triangle formula = 1/2 x b x h (b = base, h = height) 2. Here, base = 6 cm and height = 8 cm 3. Therefore, the area of the given triangle = 1/2 x 6 cm x 8 cm 4. Math answer to the given problem = 242 cm This is a geometry example. Likewise get free answers to al your math problems. Now make your math easy with Tutorvista.
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doing an extra credit assignment for algebra 2. We are supposed to write a paper on the algebra needed for the career path you want. It would be helpful if I could get some examples of formulas or anything else that could help me write this paper for being a physical therapist.
Cereal044
Feb 23, 2009, 10:04 PM
I am going to school for physical therapy, I am not sure what you are learning in you class but the most common we use that deals with math is angles of pull and torque. All the muscles in your body work at different angles to get the job done. Some muscles use bones (like the knee cap) to increase the angles, therefore increasing the efficiency of the muscle. Some muscles are made to help with more movement. Like you biceps while others are made to be more powerful like you deltoids. Let me know if this helps you. Remember to be a good PT you need to understand the way the muscles and everything else in the body works, so you can help it get better! Good luck!
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Discrete Mathematics Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
9780471476023
ISBN:
0471476021
Pub Date: 2005 Publisher: John Wiley & Sons Inc
Summary: Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can ...be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way. Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.[
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Introduction and Implementation Strategies for the Interactive Mathematics Program: A
Guide for Teacher-Leaders and Administrators
Appendix B:
Concepts and Skills for the IMP® Curriculum
The
Interactive Mathematics Program has developed an integrated four-year high
school mathematics sequence, designed to replace the traditional Algebra I -
Geometry-Algebra II/Trigonometry-Precalculus sequence.
The
following year-by-year lists describe the major topics covered in the IMP
curriculum. The lists are formulated in terms of traditional mathematics topic
organization, although the topics listed are covered in an integrated fashion,
in the context of meaningful larger mathematical problems. Generally, topics
taught in a given year are reviewed and extended through the curriculum of
subsequent years. The year-by-year content descriptions are followed by a list
of performance skills that are an integral part of this curriculum in all four
years.
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TAISM Logins
Grade 8 - Course Descriptions
Yearlong Courses
Introduction to Algebra:
Students take this course to build a strong foundation before entering high school, both by mastering skills and connecting their math concepts in meaningful ways. There will be an emphasis on written explanations and students will begin to justify and explain their work more thoroughly. The concepts covered include linear and exponential relationships, rational number operations, making sense of algebraic symbols, statistics, and geometry. This course will prepare students to think abstractedly, problem solve, and make connections between mathematical concepts. This course also allows students to improve their math skills by applying them to real-world examples.
Algebra I:
The Algebra I course is designed to provide students with important mathematical skills that have many real-life applications and lay the foundation for study in higher mathematics. In particular, the Algebra I course is structured around the following areas of study: Linear Equations, Polynomials, Factoring Polynomials, Fractions, Introduction to Functions, Systems of Equations and Radicals. Throughout all areas of study, there will be an emphasis on students developing a working mathematical vocabulary and a variety of approaches to problem solving.
Students study a variety of topics in the course. The distributive property and linear equations in one variable will be a focus of the first trimester. Equation solving and problem solving will be primary goals using equations with positive and negative numbers, parentheses, proportions and variables on both sides of the equal sign. Polynomials will be studied with emphasis on factoring for the solutions of quadratic equations. The course will continue with the manipulation of simple fractions and rational expressions with ratios and proportions. The course will include a major unit on graphing linear functions and systems of linear equations including inequalities. Finally, students will work with the complexities of square roots and their manipulation followed by quadratic equations without rational roots. The quadratic formula will be introduced as well as completing the square.
Social Studies:
The Social Studies program in eighth grade is a thematic study of three main topics: citizenship, economics, and global issues. Students will think critically about probing questions such as: What does it mean to be a global citizen? What basic human rights should be guaranteed for all? How is globalization impacting our planet? What is America's role in the world economy? What are the biggest issues facing our planet today? What should be America's role in facing the issues of the 21st century? Students should expect lively discussion, differing opinions, and a broader perspective on all issues. Students will also build and reinforce academic skills of critical reading, note taking, essay writing, and research.
Language Arts:
The eighth grade language arts course continues working with the writing process to develop voice for varied audiences and purposes. Both writing and reading skills are taught through short stories, novels, and articles with an emphasis on non-fiction. The value of reading as a lifetime skill is reinforced as well as the analysis of literary elements such as symbolism, irony, foreshadowing and imagery. Additionally, grammar and vocabulary development are essential aspects of the grade eight language arts program.
Science:
The eighth grade science course is designed to continue enhancing student interest in science through examining relevant material and creating a safe environment for students to investigate science. The course will refine the student's scientific processing skills through a curriculum of Life Science, Physical Science and Earth/ Space Science. Laboratory, projects, investigations, inquiry-based activities, group work, class discussions, and simulations will be the main methods used.
Throughout the year, there will be further opportunities to promote student creativity and problem-solving skills.
Major Concepts Studied:
Scientific Inquiry/Scientific Method
Astronomy
The Nature of Matter
Forces and Motion
Heredity
Natural Selection
Trimester Offering
The following three courses are one trimester (twelve weeks) in length. Students rotate through the three offerings in the course of the school year.
Health:
The eighth grade health program is designed to help students make informed and healthy choices as they are transitioning from Middle School to High School. Through the course students will gain an understanding of their personal health and wellness. Students will examine their physical, social and emotional health and apply the daily lessons to their lives. These lifelong skills will be taught, reinforced and assessed throughout the trimester. Areas of study include: Internet safety, substance abuse, refusal skills, nutrition, healthy relationships, reproduction and sex education.
Media Literacy:
The Media Literacy course teaches students to be aware of the pervasiveness of media in their lives and to evolve into critical media viewers. Students learn that advertisements and other media messages have been carefully crafted with the intent to send specific messages to the audience.
We explore the following questions: Who is the target audience of an advertisement? What are the biases of the authors/ editors of newspapers, magazines and web sites? How has personal identity been influenced by the media? How are gender roles portrayed and possibly defined by the market place, music videos, video games and other forms of media? Does violence in the entertainment industry (movies, computer games) have an impact on society?
The goal of this course is to help students become responsible and informed of the hidden biases in all forms of media, whether they are entertainment, information, or advertisement.
Art:
Students continue to work with the basic elements of design (line, shape, form, color, value, texture, and space), as well as the principles that balance and unite these elements to create a good composition. Through classroom exercises and projects, students will learn to evaluate and apply a variety of media, techniques and processes to a range of subject matter. Students will also explore the significance of art as it relates to personal experience, culture, and human history. They will also have many opportunities to apply both skills and concepts learned in art to other disciplines.
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Welcome to Maths
We've freshened up our Maths page, to make your web experience even better.
Here, you'll find everything in one place – from our latest maths publishing such as ActiveLearn, the popular Revise series for Edexcel and AQA and our new Edexcel Awards workbooks, to popular favourites likeEdexcel GCSE Mathematics, Level Up Maths and Edexcel AS And
A Level Mathematics.
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Hello, I am a senior in high school and require some guidance in expansion solver. My mathematics marks are terrible and I have decided to do something about this frustration. I am trying to find some product that will let me insert a math equation and provides a thorough stepwise method; basically the software program is required to take someone through the entire method. I really hope to improve my grades so please help me out.
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Unit specification
Aims
The programme unit aims to introduce quotient structures and their connection with homomorphisms in the context of rings and then again in the context of groups; present further important examples of groups and rings and develop some introduced in the context of rings, then used to construct roots of polynomials in extension fields. Factorisation in polynomial rings and rings of integers of number fields will also be studied in the first part.
The second part will begin by developing further properties of key examples, such as permutation groups, and will emphasise actions of groups. Then the construction of quotient objects and the connection with hom1. Definitions and examples (partly review): domains, fields and division rings; nilpotent and idempotent elements, products of rings; (many) examples; with students gaining familiarity with the ideas and examples through attempting exercises. [3]
2. Isomorphisms and homomorphisms (of rings): what is preserved and reflected; kernel of a homomorphism, ideals; principal ideals, operations on ideals. [3]
4. Polynomial rings and unique factorisation: unique factorisation domains, principal ideal domains and euclidean domains, with emphasis on rings of polynomials and rings of integers in number fields; construction of ring of fractions of a domain; tests for irreducibility, Gauss' Lemma. [3]
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Find a Nonantum Algebra 1Your skill set, learning preferences, and end goals are considered before making any recommendations for what to learn so you learn at your level. Don't let your problems with web or other digital tasks are slow you down. Don't feel overwhelmed.
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3DMath Explorer is a computer program that pilots 2D and 3D graphs of mathematical functions and curves in unlimited graphing space. It has many useful feature such as; 1-3D curve ploting in real time, 2-perspective drawing, 3-graph scaling (zooming), 4-active graph rotation, 5-fogging effect, 6-cubic draw, 7-unlimited space ploting, 8-four view plot screen, 9-auto rotate animation, 10-single coordinate system defination, 11-additional parameter function and loop variable definations, 12-3D surfaces with 3D volumes 13-curve line length and surface area calculation, 14-full control on all graphical elements, 15-drawing many curves in the same screen, 16-working with many graph screen in the same time, 3DMathExplorer is a very useful program for students to make experiment and observation, for teachers to teach the subjects more interesting and comfortable, for writers to select graphs for their books within more suitable, beautiful and comprehensible graphs, and for all people that interests in this subject to ... Microsoft WordAlgebra Vision is a unique educational software tool to help students develop algebraic problem solving strategies. It provides an environment to play and see algebra in a more tangible light. You can literally move expressions around! Draw lines connecting distributive elements!
Powerful and extensible computer system for scientific and technical calculations. No matter if you are a school student or recognized scientist, Algebrus serves your needs. It is easy to use and interactive means of solving problem in various areas of expertise. Console based scientific calculator, 2D and 3D graphs plotter, differential, algebraic and polynomial equation solver, unit converter, physical constants reference, statistical analysis, data fitting, programming environment, and many more. Or just simple ?evaluate-while-typing? calculator for your everyday arithmetics. If it doesn?t have something needed, you can use built-in integrated syntax-highlighted XPascal programming environment to create your own routines and libraries, define your own types and operators.
- Calculations and programming with vectors, matrices, complex numbers, fractions, quaternions, and polynomials
- 2D and 3D graphic plots and charts of functions and data
- Lines, scattered data, vector fields, contour plots, heights ... well as for everyone who is interested min geometry. With Archim, you will draw the graph of any function and form, just use your imagination.This application is a laboratory for the creation of automata. An automaton is a system of circles (actually planar coordinate systems) moving relative to one another in a hierarchical fashion. That is, every circle in the system except one will be rolling along the circumference of one other circle at every moment in time. Automata are a superset of the mathematical curves called epicycloids and hypocycloids.
any meaning of density; 4) Adds of volumes and masses of unequal parts of object; 5) Adds of volumes and masses of unequal apertures of object; 6) Uses metrical and american units; 7) Undo operation; 8) Support of localization tools for different languages
Enjoy.
Two programs in one. One that can Add, Subtract, Divide and Multiply fractions and another that can convert a
decimal to a fraction or a fraction to a decimal. It's a breeze with "Fractions". Quick and easy interface. No
confusing menus. Many fraction programs only convert fractions to a decimal. This unique program converts
decimals to fractions. Great for school or work. Handy for STOCK quote conversions.
Lite version converts several units of lenght. Plus version converts length, weight and capacity measures. By typing
a number into box provided will instantly display the results without the user having to search through a confusing
menu of choices. Great for mathematical problems, science or travel. Many different uses for this program. Small in
price and size - you can't go wrong! A nice little download!
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You scored above the minimum score for admission to the college but below 31 on the Algebra portion of the COMPASS Placement Test. This indicates that your math skills are not sufficient to be successful in college mathematics. This class is designed to improve your skills in basic algebra.
What will this course do for me?
It will help you improve your math skills in areas such as linear equations, polynomials, and exponents. It will prepare you for the next academic support course, Math 0099. These two courses together will give you the skills necessary to pass credit-level math courses.
How many of these non-credit math courses must I take?
Students who place into MATH 0097 must complete this course and one more before advancing to credit-level math. If you are in MATH 0097, you will be required to pass it and then to pass MATH 0099 and the COMPASS Exit test at the end of that course before you enroll in credit-level mathematics.
What if I don't pass MATH 0097?
You will be required to repeat the course. State regulations require that you complete any academic support work within three semesters (see information below). Therefore, it is very important that you pass MATH 0097 on your first attempt.
How long do I have to complete my MATH 0097 AND MATH 0099?
You have three (3) semesters to complete ALL required academic support math courses. This means that both MATH 0097 and MATH 0099 must be successfully completed within three (3) semesters. Otherwise state regulations require that you be dismissed from college. If you have qualifying disability paperwork from the disability office at your campus, you may qualify for additional attempts. See the disability specialist at your site for more information.
When do I take the COMPASS Exit test?
Students in MATH 0097 DO NOT TAKE the COMPASS Exit test. You will must pass Math 0097 and then take Math 0099 before you take the COMPASS Exit test.
What courses are open for me while I am in MATH 0097?
You are prohibited from taking any higher level math courses until you have successfully passed Math 0097, Math 0099 and the COMPASS Exit test. Other academic courses may be available to you depending upon your academic support requirements in other areas. You need to talk with your academic advisor for information about what is available for you.
Does this count in my grade point average (GPA)?
NO. Academic Support courses do not count in your GPA. However, they DO show on your transcript and they MAY AFFECT your eligibility for financial aid from either HOPE or Pell Grants.
Where can I get more information about this class?
Follow this link to Rule and Regulations, or contact the Office of Academic Support on the Floyd Campus at (706) 295-6357. For further discussion, see your instructor or one of the directors at your site of Georgia Highlands College. You can also contact any of these persons by e-mail.
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Algebra 2 for Distance Learning
The first semester of Algebra 2 reviews and expands concepts learned for graphing and solving linear and quadratic equations. Second semester the focus shifts to a more advanced look at radical, exponential, rational, and logarithmic equations and functions. The course introduces trigonometry, matrix algebra, probability, statistics, and analytic geometry to expose the students to higher mathematical studies. The TI-83 Plus graphing calculator is used throughout the year to build concepts and expand understanding of the material.
Mrs. Carrie Finney teaches this course.
Recommended Viewing Schedule: five 45-minute lessons a week; 176 lessons per year
>> Click the Resources tab to learn more about the instructor for this course.
About the Instructor
Mrs. Carrie Finney, BS, MEd
Mrs. Carrie Finney has wanted to teach math since ninth grade. The Lord gave her a desire to use teaching as a means of ministering to young people. With that goal in mind, she attended BJU, completing a BS and a MEd in Math Education. As a graduate assistant, she served with BJU Press Distance Learning as an assistant with Geometry, Precalculus, and Algebra 2. She looks forward to having a part in developing prepared servants of Christ. Carrie's favorite verse is Psalm 18:30.
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Promoting and exploring the accessibility of math
April 29, 2013
Rick Clinton, Accessibility Advocate and Leader at Pearson Higher Education, recently blogged in Accessible Mathematics: HTML eBooks about Pearson's work to create "screen-readable" eBook versions of their mathematics and statistics textbooks which are formatted in HTML and MathML. They have been gradually adding to this collection for a while, which now numbers 70 titles. That's a nice-sized library of accessible math textbooks in its own right. But what is really notable in his post is the statement that, "...beginning in 2014, every Pearson college math and stats text will have an HTML eBook version." That's an impressive commitment from a publisher like Pearson Higher Education, and means that every math textbook they publish from now on will include accessible mathematics. Pearson is setting an example for the whole publishing industry, and deserves commendation for their resolve to support math accessibility.
Of course, there are many other publishers of math textbooks, and they all need to hear from people like you who purchase and use textbooks. If you want to see more accessible math textbooks offered by more publishers, then you'll need to make your demands and expectations known to them.
Here are a few ways you can help:
If you are connected to a college, tell your math department about Pearson's accessible math titles. Teachers should strongly consider adopting one of their HTML eBook versions.
If you teach a college math or stats course and your favorite textbook isn't one of these Pearson titles, then contact the publisher and ask them how soon they will be creating an eBook version with accessible math like Pearson. If they don't have any realistic plans to create one, then tell them you are strongly considering switching to a Pearson title.
If you are connected to a K-12 school, then be sure to contact the publishers of your math textbooks with the same message. Even at Pearson, the higher education and K-12 divisions are not connected, so the K-12 publishing sector needs to hear the same message. Hold up the example of Pearson Higher Education as testimony that making *every* math title accessible is a vital goal that can--and should--be doneApril 26, 2013
Math accessibility is one of the biggest challenges faced by teachers
of students with visual difficulties or impairments. In February, Steve
Noble's blog post (MeTRC Research Underscores Need for Accessible Math)
talked about a study involving students with reading-related learning
disabilities. The study found that these students have 2-3 times as much
difficulty reading math than they do reading plain text. When given
accessible math materials, their outcomes on tests were much better than
those students who didn't have access to accessible materials.
This was a multiyear project to examine the
feasibility of implementing a digital math curriculum using MathML for middle
school students with learning disabilities who had reading accommodations
specified in their Individualized Education Program (IEP). An initial full year
pilot was conducted with seventeen students in both resource room and
collaborative setting, and followed by another full year case study with six
students in a single resource room. Although the relatively small sample of
students may limit the significance of the findings, this study nonetheless
provides important research findings which underscore the need for accessible
math in the classroom.
One relevant finding of this research is a confirmation
that students with learning disabilities have a problem with reading math
notation without math-enabled assistive technology. The common belief held by
many educators is that students with reading disabilities only need
text-to-speech (TTS) technologies for subject areas where lots of text has to
be read, and the only time TTS might be used in the math classroom is for
reading word problems. However, our study found that students who have reading
disabilities have two to three times as much difficulty reading math symbols
and notation than they do reading plain text. This finding helps to support the
conclusion that many students may need accessible content in the math classroom
even more than they do for subjects like English and social studies.
Our study findings also suggest that students with learning
disabilities who used accessible math with their assistive technology had
better learning outcomes than students who used standard print materials with
human provided read-aloud accommodations. During the case study period, the
students who used accessible math materials outpaced similar students who used
standard print materials by twice as much. Since this was a case study without
formal controls and a small sample, the results have limitations. Nonetheless,
this finding lends support to similar past research which has suggested
positive student learning outcomes when accessible math is provided.
If you are interested in reading more details
about this study, you may want to look over the presentation we gave last month
at ATIA, Accessible Digital Math Curriculum = Reading Words + Symbols. Our research team has also written an extensive article
on our findings, which should be published later this spring.
After reading about these results, many of you
will be energized about getting accessible math into your schools. In that
case, please be sure to look over the resource page, "What can you do to help promote math accessibility?" You'll
find a number of suggestions to get you and your school on the road to
accessible mathOctober 04, 2012
Following the Department of
Education's guidance for NIMAS publisher,
the NIMAS Center at CAST has recently issued recommended language
to be used by states and local districts in state contracts or purchase orders
for math and science textbooks. Wisconsin
and Rhode Island
have already moved to adopt this new language, and more states are on the way.
These proactive states are wasting no time to ensure that mathematical and
scientific instructional content will be fully accessible to their students
with disabilities.
If you live in these states that means much better math accessibility is coming
your way. If you live in another state, contact your NIMAS Primary Contact
person
and ask what you can do to persuade your state to also adopt this language. By
taking the time to point out the benefits of using this new language as
Wisconsin and Rhode Island have done, you can help ensure that you, your
children, your students, or your friends will have greatly improved access to
math and science materials.
Although the award recognizes the
school's use of Microsoft's Lync distance learning software for blind students
in the math classroom, that's only one aspect of the their cutting-edge use of
technology for learning.
Beginning this school year,
students at the school are using an accessible digital version of their Algebra
1 textbook created using MathML. As part of a federally-funded research grant
led by Purdue University, students are reading their math textbook with the
ReadHear™ DAISY player by gh in a distance education setting.
By providing math students with
accessible textbooks and an accessible testing environment--two very critical
components of instruction--the Washington State School for the Blind is showing
the world that math can be made accessible. We certainly want to congratulate
the Washington State School for the Blind on their recent award, and commend
them for their progress in math accessibility!
If you are interested in making
the math in textbooks or classroom materials accessible to students with print
disabilities, we have plenty of information available on our math
accessibility pages.
Steve
Noble is a research consultant with a core focus in mathematics
accessibility and assistive technology. Currently he serves on grant-funded
research projects with both the University of Kentucky and Bridge Multimedia,
and previously served as Director of Accessibility Policy for Design Science.
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College Mathematics
Credits: 3Catalog #10804107
This course is designed to review and develop fundamental concepts of mathematics pertinent to the areas of: 1) arithmetic and algebra; 2) geometry and trigonometry; and 3) probability and statistics. Special emphasis is placed on problem solving, critical thinking and logical reasoning, making connections, and using calculators. Topics include performing arithmetic operations and simplifying algebraic expressions, solving linear equations and inequalities in one variable, solving proportions and incorporating percent applications, manipulating formulas, solving and graphing systems of linear equations and inequalities in two variables, finding areas and volumes of geometric figures, applying similar and congruent triangles, converting measurements within and between U.S. and metric systems, applying Pythagorean Theorem, solving right and oblique triangles, calculating probabilities, organizing data and interpreting charts, calculating central and spread measures, and summarizing and analyzing data. Prerequisite: Basic Algebra, 74-854-793 with a "C" or better or appropriate placement score.
Course Offerings
last updated: 09:01:51
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We will
cover chapters 7, 8, 9, 10, 11, and 12 of the above text. Calculus
II consists of a study of the trigonometric functions, techniques
of integration, vector calculus, the differentiation and integration
of functions of several variables, infinite series, and differential
equations. Applications are presented from biology and the social
sciences. The computer will be used to study various concepts of Calculus.
OBJECTIVES:
Students
are expected to know the basic concepts and the fundamental theorems
of the course, to develop proficiency in applying the problem solving
techniques in the course, and to make connections between Calculus
and other areas of mathematics. Quizzes and exams will be used to
assess the level to which these objectives are being attained.
EARLY PERFORMANCE GRADES:
You will be assigned an early performance (near mid-term) grade around the end of February which will be based on your performance on the first exam.
EXAMS:
There will be 3 exams and a final and you will be given a week's notice for each exam. In addition there will be a quiz at the beginning of each class consisting of one problem from the assignment due that day. At the end of the semester your 4 lowest quizzes will be dropped. The quizzes will then be averaged and that average will count as 1 test grade. No quizzes can be made up for any reason. If you miss an exam, you must have a legitimate excuse to make up that exam.
GRADING
POLICY:
The
final will count as 1/5 of your grade as will each of your exams.
The grading system will be according to the current SVC bulletin.
CLASS
ATTENDANCE:
Please
make every effort to keep up with assignments and to attend all classes.
Since you are not permitted to make up quizzes, it is vital that you
be present for each and every class. Students who are planning to
participate in official sports activities must, at the beginning of
the semester, provide the instructor with a schedule of events which
may conflict with class attendance. Do remember, however, that no
more than 4 of your daily quizzes can be dropped.If for some reason class is cancelled, an announcement will be posted on the Blackboard site for this course.
CALCULATORS:
We will
be using the TI-86 or TI-84 Plus graphing calculator throughout the course.
You will be permitted to use this calculator both for homework and
for the quizzes and exams. This calculator will produce the graph
of a function within an arbitrary viewing window, differentiate and
integrate numerically, and solve equations.
MATHEMATICA:
In
addition to using graphing calculators, we will also use the powerful
computer algebra system known as Mathematica to study Calculus
and to solve difficult problems. There will be fourMathematica
assignments this semester. Each Mathematica assignment is equivalent
to two daily quizzes.
ACADEMIC
HONESTY:
"Saint Vincent College assumes that all students come for a serious
purpose and expects them to be responsible individuals who demand
of themselves high standards of honesty and personal conduct. Therefore,
it is college policy to have as few rules and regulations as are consistent
with efficient administration and general welfare.
Fundamental to the principle of independent learning and professional
growth is the requirement of honesty and integrity in the performance
of academic assignments, both in the classroom and outside, and in
the conduct of personal life. Accordingly, Saint Vincent College holds
its students to the highest standards of intellectual integrity and
thus the attempt of any student to present as his or her own any work
which he distractingand
FOR THE COURSE:
I will
be in my office (W-204, Science Center) at the following times during
the week. Do feel free to stop in when you are having any difficulty
with the material.
Office
Hours:
Monday: 9:30 to 10:30 and
3 to 4
Tuesday: 10:30 to 11:30
Wednesday: 9:30 to 10:30
and 3 to 4
Friday: 9:30 to 10:30
In addition
to my office hours, student tutors will be assigned by the Mathematics
Department and their hours will be given to you during the first week
of class. You are also free to come to them for help in the course.
If you would like to preview our mathematica assignments,
simply click here .
If
you would like to see an informal discussion of various areas of mathematics,
simply click on the following link. If you are interested in some
famous curves, click on the second link.
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AIEEE 2012 Syllabus (all subjects including Architecture)
July 02, 2011
As we count the number of days for AIEEE-2012 (expected to be held on 22nd April 2012 as per this blog post of mine) and prepare for the same, each AIEEE aspirants would like to know what is the syllabus for AIEEE-2012. Well let me tell you that syllabus of each AIEEE exam is published along with the notification which comes out in 2nd week of November. So your exact syllabus for AIEEE-2012 can be known only than. But than, since it would be too late, you can begin your preparation based on the syllabus of AIEEE-2011.
The same is also reproduced below to take care of server unavailability. To have an in-depth understanding about AIEEE, I also recommend you to go through following blog post of mine:
Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
UNIT 2 :COMPLEX NUMBERS AND QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
UNIT 3 :MATRICES AND DETERMINANTS:
Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
UNIT 4 :PERMUTATIONS AND COMBINATIONS:
Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.
UNIT 5 :MATHEMATICAL INDUCTION:
Principle of Mathematical Induction and its simple applications.
UNIT 6 :BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.
Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
UNIT 10 : DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:
UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.
UNIT 12: THREE DIMENSIONAL GEOMETRY:
Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.
UNIT 14: STATISTICS AND PROBABILITY:
Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Frame of reference. Motion in a straight line: Position time graph, speed and velocity. Uniform and nonuniform motion, average speed and instantaneous velocity Uniformly accelerated motion, velocity-time,
Force and Inertia, Newton's First Law of motion; Momentum, Newton's Second Law of motion; Impulse; Newton's Third Law of motion. Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force and its applications.
UNIT 4: WORK, ENERGY AND POWER
Work done by a constant force and a variable force; kinetic and potential energies, workenergy theorem, power. Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions.
UNIT 5: ROTATIONAL MOTION
Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion.
UNIT 6: GRAVITATION
The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Kepler's laws of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.
Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.
UNIT 9: KINETIC THEORY OF GASES
Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases -assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro's number.
Electric charges: Conservation of charge, Coulomb's law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field. Electric flux, Gauss's law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field. Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.
UNIT 12 : CURRRENT ELECTRICITY
Electric current, Drift velocity, Ohm's law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance. Electric Cell and its Internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff's laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer - principle and its applications.
UNIT 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
Biot - Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel currentcarrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances. Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.
Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers.Wave optics: wavefront and Huygens' principle, Laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster's law, uses of plane polarized light and Polaroids.
Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions. Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch's law and its applications. Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a Galvanic cell and its measurement; Nernst equation and its applications; Relationship between cell potential and Gibbs' energy change; Dry cell and lead accumulator; Fuel cells; Corrosion and its prevention.
UNIT 9 : CHEMICAL KINETICS
Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions, their characteristics and half -lives, effect of temperature on rate of reactions Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).
UNIT-10 : SURFACE CHEMISTRY
Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of
Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals -concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.
UNIT 13 : HYDROGEN
Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions and uses of hydrogen peroxide; Classification of hydrides - ionic, covalent and interstitial; Hydrogen as a fuel.
UNIT 14 : S - BLOCK ELEMENTS (ALKALI AND ALKALINE EARTH METALS)
Group - 1 and 2 Elements
General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships..
UNIT 15 : P - BLOCK ELEMENTS
Group - 13 to Group 18 Elements
General Introduction: Electronic configuration and general trends in physical and chemical properties of
elements across the periods and down the groups; unique behaviour of the first element in each group.
Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.
Diazonium Salts: Importance in synthetic organic chemistry.
UNIT 25 : POLYMERS
General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization; Natural and synthetic rubber and vulcanization; some important polymers with emphasis on their monomers and uses - polythene, nylon, polyester and bakelite.
Objects, Texture related to Architecture and build~environment. Visualising three dimensional objects from two dimensional drawings. Visualising. different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal).
Part - II Three dimensional - perception
Understanding and appreciation of scale and proportion of objects,
building forms and elements, colour texture, harmony and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2 D and 3 D union, substraction, rotation, development of surfaces and volumes, Generation of Plan, elevations and 3 D views of objects. Creating two dimensional and three dimensional compositions using given shapes and
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Supplementary Course Modules (Calculus)
The Supplementary Course Modules for introductory calculus courses have been created to provide students with the opportunity to review, and to demonstrate mastery of, prerequisite material. Each module covers a key skill area from secondary school mathematics, up to and including topics covered in the Ontario Grade 12 Advanced Functions course (i.e., there are no questions requiring calculus itself).
Reviewing this material through the Module Program will not only earn you bonus marks towards your final calculus course grade, but will also help you when completing course work such as problem/lab assignments and tests! See resulting grade comparisons from the 2010-11 academic year.
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Please indicate in detail the advanced subjects that you
have studied. Where possible, please indicate the books (titles, authors) that were used during your
advanced studies. You can paste a TeX document if you want.
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Undergraduate degree structure
The Modular System
The university operates a modular system. In mathematics most courses count as a half-module, and you must take the equivalent of twelve half-modules per year. These are usually split equally between the two semesters of the academic year. Examinations for most modules are taken at the end of each semester.
A half-module typically consists of two lectures of 50 minutes each plus one examples class plus private study. However, there are exceptions - for example, courses which contain a significant amount of project work. Such courses are generally restricted to years (or Levels) 3 and 4. Examples classes typically meet in smaller groups than lectures, and they provide opportunities to try out the theories presented during the lectures, to ask questions about the course and to discuss work with fellow students.
Assessment
Certain of the modules have some continuous assessment and others, especially in Statistics and in Applied Mathematics, have projects which count as part of the assessment; otherwise most of the assessment is by examinations which take place in January and June, at the end of each semester. There is also a large project component in the fourth year of the MMath degree, which counts for a third of the credits for that year.
In the first and second years, there are resit examinations to provide a second chance for those who do not pass their examinations at the usual time.
The first year examinations are qualifying examinations and do not contribute to the final degree classification; all subsequent examinations count towards the final degree classification.
Pastoral Care: Personal Tutors
All students are allocated to a tutor within the School throughout their undergraduate studies. This provides a personal contact with a member of staff who can keep an eye on your progress and provide a listening ear in case any problems arise.
In the first semester of your first year, you will meet in small groups with your personal tutor every second week to discuss mathematical problems from one of the core modules. In subsequent semesters your personal tutor will be more restricted to a pastoral role, with mathematical support provided in larger tutorial groups by lecturers and other academic staff.
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Understanding Mechanics has proved to be a popular text with students of A-level
Mathematics. Syllabuses are varied at this level. But the aim has been to cover
all topics that could appear on single Mathematics Papers, at the same time as
providing an extension into several Further Mathematics topics.
Recent changes to syllabuses have brought about the need for this new edition,
and there are two particular emphases in modern syllabuses that have been dealt
with. One of these is on the use of vectors, and for this reason we have
introduced vectors right at the beginning of the book. The other emphasis in of
the use of modeling. Students are required to understand the relationship
between real-life situations and mathematical models. They need to understand
the limitations of many common assumptions so that they can evaluate their own
assumptions when setting up mathematical models to solve problems. We have
provided some commentary to help with this.
In each chapter the theory sections are followed by a number of worked examples
which are typical of, and lead to the questions in the exercises. By reading the
theory sections and following the worked examples, the reader should be able to
make considerable progress with the exercise that follows. After the
introductory vector work, each chapter closes with a comprehensive selection of
recent examination questions, allowing the student to evaluate and apply the
skills learnt in the preparatory sections. These exercises are carefully graded,
progressing to some quite demanding questions at the end.
We are grateful to the following examination boards for permission to use their
questions specimen questions are denoted by spec. the answers provided for these
questions are the sole responsibility of the authors.
University of examinations and Assessment Council ULEAC.
University of Cambridge Local examinations syndicate UCLES.
University of Oxford delegacy of local examinations UODLE.
Oxford and Cambridge Schools examination Board OCSEB.
Midland examining Group MEG.
Associated examining board AEB.
Welsh Joint education committee WJEC.
Northern Ireland Council for his curriculum examinations and assessment NICCEA.
Southern Universities Joint Board SUJB.
Finally, we wish to acknowledge the help of four experienced teachers who helped
with the writing of the new text: Julian Berry Bloxham School , Dr Dominic
Jordan University of Keele. Robert Smedley Liverpool Hope University College.
And Garry Wiseman Radley College. Special thanks are due to Garry Wiseman, who
also played a central editorial role in melding the new and existing material
together.
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This is the second installment of a 3-course sequence in mathematical analysis for beginners. The course is intended for math majors and students with a serious mathematical interest. The topics covered will be approximately those of a standard Calculus II course (MA116). The style and format, though, will be rather different from the standard Calculus sequence. A higher level of mathematical rigor, and a deeper understanding of the few fundamental concepts involved, will be preferred to a more extensive syllabus.
Learning Outcomes
Uniform continuity: understand the concept of uniform continuity and what role it plays for integrability of continuous functions.
Taylor polynomials and error estimates: Know how to approximate functions by Taylor polynomials, how to evaluate the error of approximation, be familiar with Landauís symbols o and O and be able to apply Taylor polynomials to calculating limits of indeterminate form.
Hyperbolic functions and inverse trigonometric functions: Demonstrate a working knowledge of hyperbolic and inverse trigonometric functions and be able to derive derivatives for trigonometric functions using the implicit differentiation technique.
Improper integrals and tests for convergence: Understand the concept of improper integrals and know how to test improper integrals for convergence.
Series, convergence: Distinguish between the necessary and sufficient conditions for series convergence, recognize special types of series (geometric and alternating) and understand the concepts of absolute and conditional convergence.
Test for series convergence: Apply convergence tests such as the comparison test, integral test, ratio test, root test and Leibnitzís rule for corresponding types of series.
Sequences of functions: Distinguish between pointwise and uniform convergence and apply Weierstrass Test to test uniform convergence of series.
Power series: calculate the radius of convergence for power series and determine the radius of convergence of integrated and differentiated power series.
Taylor series: Know sufficient conditions for a function to be represented in the form of Taylor series, determine radius of convergence of Taylor series, be able to give an example of a function, which cannot be represented by a Taylor series and know Taylor series of elementary functions (sine, cosine, logarithm, exponential).
Basic operations of vector algebra: Demonstrate a working knowledge of basic operations with vectors (addition, subtraction and dot and cross products) and a working knowledge of basic concept of vectors (vector norm, orthogonal vectors and angle between two vectors).
Scalar and vector fields: Understand limits of functions of many variables and demonstrate a working knowledge of directional and partial derivatives, total differential and gradient of a scalar field.
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Algebra Demystified: A Self Teaching Guide (Paperback)
One of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to computing, engineering to mathematics. It can help you do better on plac......more
One of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to computing, engineering to mathematics. It can help you do better on placement exams, even before college, and it's useful in solving the computations of daily life. Now anyone with an interest in college algebra can master it. In College Algebra Demystified, entertaining author and experienced teacher Rhonda Huettenmueller breaks college algebra down into manageable bites with practical examples, real data, and a new approach that banishes algebra's mystery.
With College Algebra Demystified, you master the subject one simple step at a time—at your own speed. Unlike most books on college algebra, general concepts are presented first—and the details follow. In order to make the process as clear and simple as possible, long computations are presented in a logical, layered progression with just one execution per step.
This fast and easy self-teaching course will help you:
Perform better on placement exams
Avoid confusion with detailed examples and solutions that help you every step of the way
Get comfortable with functions, graphs of functions, logarithms, exponents, and more
Master aspects of algebra that will help you with calculus, geometry, trigonometry, physics, chemistry, computing, and engineering
Reinforce learning and pinpoint weaknesses with questions at the end of every chapter, and a final at the end of the book
Rhonda Huettenmueller (Sanger, TX) has taught mathematics at the college level for over 14 years. Popular with students for her ability to make higher math understandable and even enjoyable, she incorporates many of her teaching techniques in this book. She received her Ph.D. in mathematics from the University of North Texas.
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Nine PlanetsA Multimedia Tour of the Solar System: one star, eight planets, and more
Search for Benicia Geometry Tutors
Subject:
Zip:
...One good way to proofread is to read the paper aloud, especially if this is your final version. Reading aloud from a typed copy should allow you to spot typing errors, such as words left out or misspelled words (or words whose spelling you want to look up in the dictionary). If you are reworking...The concepts of Linear Algebra are at the heart of (1) numerical methods (used to develop and evaluate solution techniques that are used by computers to solve large numerical systems such as finite element analyses), (2) numerical solutions of overdetermined systems (i.e., "least squares" which a
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The Middle School Writing Workshop offers students the opportunity to focus on a variety of writing skills. The goal is to equip students with the necessary skills to accomplish more sophisticated writing tasks. Areas of concentration include descriptive, persuasive, analytical and creative writing, in addition to shorter reflections and poems. There is also an emphasis on preplanning and revision. During this one-week intensive workshop, students learn techniques and strategies that prepare them for further success in the classroom.
Instructors: David Fuder and Michael Mahany, Parker Faculty
Hours: 9 a.m.–12 noon
Session I: August 12–16 (for students entering grades 6 and 7)
Session II: August 19–23 (for students entering grades 8 and 9)
Tuition: $330
Advanced Explorations in Mathematical Thinking
for students entering grades 7 and 8
This course is available for students entering grades 7 and 8 who enjoy mathematics and want to delve into interesting math topics. Students enrolling should be comfortable and proficient with the mathematics that they have learned in school. They will investigate a sampling of mathematical topics through a balance of problem solving and hands-on activities. Students will gain greater mathematical knowledge and insight, and they will broaden their appreciation for the range of applications of mathematical thinking.
for students entering grades 10 and 11 who successfully completed high school Algebra I
This course, which is equivalent to a full-year course of Algebra II & Trigonometry, is available to students who wish to move ahead in their study of mathematics. Students learn trigonometric functions, their graphs and the unit circle. Students also look at linear equations, quadratic functions and their graphs. Additional topics include working with powers, roots, complex numbers and exponential and logarithmic functions.
For students entering grade 12 who have successfully completed Algebra 1+, Geometry+ and Algebra II/Trigonometry or students entering grade 11 who have successfully completed advanced Algebra I/II and Geometry/Trigonometry.
This course is available for students wishing to move ahead in their studies of mathematics and deepen their understanding of topics central to advanced mathematical coursework. The course will investigate functions from both an analytic and graphical approach, including polynomial, rational, exponential, logarithmic and trigonometric functions. Conic sections, complex numbers and polar coordinates will also be explored.
for students entering grades 10–12 (must be 15 years old to participate)
There are two segments to our driver's education program:
Classroom
The classroom portion of the program consists of 15 units of instruction, using visual aids, and learning the rules of the road in preparation for the learner's permit. We cover basic car maneuvers and defensive driving theory in anticipation of in-car driving lessons.
Behind the Wheel Training
Students may drive and schedule this training only after obtaining a learner's permit. The behind-the-wheel portion of the program includes eight hours of in-car sessions. Our instructors follow a full behind-the-wheel curriculum to cover different aspects of driving. We cover safe driving techniques, reinforce defensive driving skills and focus on proper seeing habits. Students qualify for a driver's license after complying with all State of Illinois laws and regulations.
Instructors: Central Driving Academy
Hours: 1–3 p.m.
Session: June 17–July 11 (no class July 4 and 5)
Tuition: $570
ACT Prep Class
for students entering grades 11 and 12
At the Academic Approach, we see ACT preparation as an opportunity to engage students in real learning. We, as teachers, are warm, supportive professionals who know how to make a classroom experience effective in raising scores, academically enriching and, just as important, enjoyable for the students.
Academic Approach classroom courses are uniquely effective and efficient because we provide a high level of customized teaching. As expert tutors, we know one size does not fit all, so we differentiate each class, customizing each study plan to the class's specific strengths and weaknesses. We begin with a diagnostic test, and our proprietary, diagnostic analysis provides us with a powerful, in-depth understanding of the class's most common and immediate learning needs.
Our extensive in-print and online coursework supports students with a comprehensive review of every rule and strategy necessary for test-taking success. Students retain access to Academic Approach's exceptional online courses after the summer session ends so they can prepare flexibly for the ACT throughout the year.
Instructors: The Academic Approach
Hours:
Monday, 9 a.m.–12 noon Tuesday–Friday, 9–11 a.m.
Session: August 5–23
Tuition: $990
PSAT/SAT Prep Class
for students entering grades 10–12
This week-long class begins with the administration and grading of a full-length PSAT. Instructors guide students through Academic Approach vocabulary, grammar, critical reasoning and math coursework, in both our in-print and extensive online materials, which students are able to access for continued preparation throughout the year. Students learn specific methods of critical reasoning, process of elimination and time management appropriate to the SAT standards.
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Tappan Trigonometry bio part involves biology, the study of living things. The statistics part involves the accumulation, tracking, analysis, and application of data. Biostatistics is the use of statistics procedures and analysis in the study and practice of biology have utilized all levels of Algebra within classwork but more importantly in my engineering background and can show how it all applies. Algebra 2 has several different topics within it but still has some basics that you must master before performing well in it. Many skills acquired in Algebra I are often the holdup from someone mastering Algebra 2
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Contents
This course gives an introduction to the field of linear algebra. Concepts and techniques from linear algebra are of fundamental importance in many scientific disciplines and provide the "language" for understanding the behavior of
linear mappings and linear spaces. Topics covered are linear systems and Gauss method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. In contrast to standard courses in linear algebra, we will combine the abstract concepts with application oriented examples in order to intensify the understanding in an algorithmically oriented way. Numerical methods for basic Linear Algebra problems will also be discussed.
Objectives
Learn linear algebra
Improve abstraction competences
Learn how to study on a math book
Learn about applications of Linear Algebra
Teaching mode
Lectures will be given following the standard systematisation of Linear Algebra. The lectures will mainly follow the book "Introduction to Linear Algebra" by Gilbert Strang. Moreover, the course will allow you to find and to use your favorite Linear Algebra book with profit - something we strongly advise you to do.
Tutorials will be given to discuss the weekly assignments.
References Introduction to Linear Algebra, by Gilbert Strang Introduction to Linear Algebra, by Serge Lang Video lectures by G. Strang at MIT A First Course in Linear Algebra a free book by Rob Beezer Linear Algebra a free book by Jim Hefferon
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College Calculus Study Guide
This study guide can help you learn material quickly and succeed in your college Calculus classes.
Northstar Workforce Readiness covers the full College Calculus course series curriculum (usually three, sometimes four semesters). Our study guide is comprehensive and includes 57 units with in-depth lessons, and practice questions with an explanation for each correct answer. Our online study guide contains randomly-generated numbers, so you don't see the same questions over and over. Northstar Workforce Readiness covers several critical topics including Limits, Differentiation, Integration, Transcendental Functions and Differential Equations, Parametric and Polar Funcations, Vectors and the Geometry of Space, and much more.
Northstar Workforce Readiness is online, available 24/7, and is very affordable. There is no software to download or install. You can work through the study guide at your own pace and master the types of questions that give you the most trouble. With individualized instruction, feedback, and grading, you can master the material you need to be successful in your College Calculus courses. In addition to practice questions, Northstar Workforce Readiness includes diagrams, graphs, illustrations, and other images to help you understand the material. Northstar Workforce Readiness Study Guides provide the best way to quickly learn challenging material and get higher grades in your classes.
Lesson Example and Practice Exam Question
Topics
Click on an image above to see examples of what our program looks like and how it works.
What our users are saying:
LOVES GETTING AN INSTANT REPLY…
"I appreciate getting an instant reply if the answer is correct or incorrect, and the fact that I can also find out why."
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UCD School of Mathematical Sciences
Scoil na nEolaíochtaí
Matamaitice UCD
The following are guidelines on how to use the Mathematics Support Centre (MSC).
Drop in!You do not have to make an appointment with us as the MSC works on a drop-in basis
Come early, use often! If you are having difficulties with maths,come along as earlyin the year as you can and visit us as frequently as you like!
Bear in mind that we are an additional service to lectures and tutorials. Do not try to use the MSC as a substitute for these! MSC is a free service for UCD students
Important: Tutors in the MSC should not do problems for students.You will be expected to engage with the material either in the centre or elsewhere. We can provide loads of help as you need it but you will ultimately do the work!
If you have a particular maths problem:
Try to prepare for your visit as much as possible by reading your lecture notes
Bring along your attempts at the problem
Bring along your lecture notes or at least know where they are if they are published on the web
If you have a more general problem with some area of maths
Bear in mind that you may need to vist the Centre on a regular basis
If you have difficulty with lecture notes, read them up as far as you understand them before you visit the centre.
Again bring along your lecture notes or at least know where they are if they are published on the web
If you have no particular problem with maths and you just want a place to work on your maths, then the MSC is for you as well! Many students find the MSC to be a great place to study your maths notes,sample problem sheets etc. and having a tutor on hand if you want to check your work is a bonus!
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Outcome
Type
Tuition Fees
Sponsors
College: College of Physical and Engineering Science
Department: Department of Mathematics and Statistics
Instructors
Prof. Joe Cunsolo
Description
Getting Ready for Calculus is a non-credit course designed as a preparation for university-level mathematics.
This course is for you if you lack a solid mathematics background and/or skills and find that you need to take more mathematics to reach your educational and/or career goals. In designing this course, the Department of Mathematics recognizes the diverse mathematical backgrounds and concerns of students. The material in this course spans Grade 9 through to and including part of the OAC Calculus course. The course starts with a basic review of algebra from Grades 9 and 10, and then it focuses on the mathematical material from Grades 10, 11 and 12 that allows the introduction of material from the OAC Calculus course. This design allows you to develop a more solid grounding in the mathematics that is needed for university-level mathematics courses.
Call us (519-767-5010) if you have any questions regarding this unique preparatory course.
Note: This is a non-credit course
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The Basic Mathematics portion of the M.S. in Ed is designed to increase a teacher's knowledge of mathematics as a preparation for taking the Praxis Exam 20069 for Middle School Mathematics. All classes are designed with the practicing middle school teacher in mind and feature hands-on and active classroom experiences with the appropriate use of technology and mathematical models.
NOTE: Students pursuing a M.S. in Ed with a Mathematics endorsement will take written comprehensive exams to finish the degree. There is no option for thesis or presentation. Sample questions from prior exams will be appearing soon.
Math 589: Algebraic Structures for Middle School Teachers The study of integers and algebraic skills; solving linear and quadratic equations, inequalities, functions, graphing and complex numbers. Connection of visual methods (using Math in the Mind's Eye curriculum and materials) to the NCTM standards with extensive use of group activities and hands-on models.
Math 591: Historical Topics in Mathematics for Middle School Teachers A survey of the historical development of topics in mathematics from ancient to modern times, with special emphasis on topics in arithmetic, algebra and informal geometry. Applications to middle school mathematics.
Math 592: Abstract Algebra for Middle School Teachers An introduction to abstract mathematics as a structured mathematical systems. This course will explore number sets and properties, and beginning group theory with concrete applications for the elementary and middle school classroom.
Math 593: Experimental Probability & Statistics for Middle School Teachers Advanced study of using basic elements of probability and statistics to solve problems involving the organization, description and interpretation of data. Concrete application will be explored through laboratory experiments, simulations and computer programs suitable for use in the middle school classroom.
Math 594: Geometry for Middle School Teachers Selected topics in informal geometry through the use of discovery and technology. Studies in how students learn geometry will be used in the development of geometric ideas.
Math 595: Calculus Concepts for Middle School Teachers An introduction to the limit concept and its role in defining the derivative, the integral and infinite series. Applications to middle school mathematics.
Math 597: Discrete Mathematics for Middle School Teachers In this course we will explore the topics of logical operators and sets, experimental vs. theoretical probability, the multiplication rule, permutations and combinations, and an introduction to graph theory.
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Specification
Aims
To demonstrate the power and the beauty of modern asymptotic methods via discussing the main ideas and approaches used in the theory of asymptotic expansions to simplify and to solve different mathematical problems which involve large or small parameters.
Brief Description of the unit
The development of the theory of asymptotic expansions, which serves as a foundation for perturbation methods, is one of the most important achievements in applied mathematics in the twentieth century. Perturbation methods represent a very powerful tool in modern mathematical physics and in particular, in fluid dynamics. This course unit will introduce students to a range of modern asymptotic techniques and illustrate their use in model problems involving ordinary and partial differential equations.
Learning Outcomes
On successful completion of the course unit the students will acquire thorough understanding of fundamental ideas used in the theory of asymptotic expansions and will develop appropriate practical skill in applying asymptotic methods for analysing mathematical and physical problems with small or large parameters.
Future topics requiring this course unit
None.
Syllabus
Asymptotic expansions. Taylor expansion as a conventional converging power series and as an example of an asymptotic expansion . Asymptotic expansions for definite integrals with the upper or lower limits of integration depending on small or large parameters. Functions defined by real integrals. Laplace's method for definite integrals the integrand being of the form f(t)exp(λt), where the parameter λ is large; Watson's Lemma. Generalisation for functions defined by contour integrals. Steepest descent. Applications.
Regular asymptotic expansions for functions depending on the coordinate x, scalar or vector, and on a small parameter ε. Solution of ordinary and partial differential equations with small parameters.
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Mathematics and Its History
(Undergraduate Texts in MathematicsAcceptable 3rd ed. 2010New:
New BRAND NEW BOOK! Shipped within 24-48 hours. Normal delivery time is 5-12 days.
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About the Book
From a review of the second edition:
"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."
(David Parrott, Australian Mathematical Society)
This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it 's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.
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More About
This Textbook
Overview
ELEMENTS OF MODERN ALGEBRA 7e, with its user-friendly format, provides you with the tools you need to get succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses.. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem solving skills.
Related Subjects
Meet the Author
Linda Gilbert is Professor of Mathematics at the University of South Carolina, Upstate. She received her Ph.D from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband and co-author Jimmie Gilbert, including Elements of Modern Algebra and Linear Algebra and Matrix Theory (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra. She and Jimmie have 6 children and 8 grandchildren. In her spare time, Linda enjoys salt-water fishing
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Intermediate Algebra
Remedial math course designed to prepare students for Math Problem Solving or College Algebra. Mathematical thought and reasoning developed through the study of polynomials, factoring, rational expressions, exponents, roots and radicals, quadratic equations, functions and graphing.
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Math
Mathematical Ideas
Mathematical ideas have always influenced societies, and artists are often among the first to explore and express their meanings and implications. This course presents a variety of mathematical ideas from across cultures and times, particularly those that are still useful to artists, craftspeople, architects, and designers, from the mathematics of nature to modern computers.
Each class involves visual presentations and hands–on activities from the course reader/workbook for exploring mathematical ideas. Weekly homework involves creating something original to demonstrate an understanding of the mathematical ideas. The textbook supplements the ideas and helps prepare for upcoming class sessions.
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Hi Frank,
I presume your looking to learn about matrices, determinants, row vectors,
inverses and all that good stuff
Any good book on Linear Algebra will have you covered and most of the
information and examples are freely available online.
I've had the book,
Introduction to Linear Algebra, Third Edition by Gilbert Strang
Recommended to me more then once for this.
Matrices are by no means difficult, but you need to grasp the notation.
And Maple, Mathlab, R, etc should be able to help you cheat just a little.
Hope that Helps,
- Karl
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