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I need to know soon how important math skill is to architecture?
I want to be an architect. I've wanted to do this since I was a little girl. I don't like math, and I've been stumbling through it all my life. Can someone tell me how much math will be used manually, and if I can do most of it on a computer or calculator. That is what I was counting on because my dad told me he uses computers and calculators for his construction business, and never needed all that heavy math. If I can pass courses, will I really rely on calculators and equipment mostly?
Asked By: Serra - 12/7/2011
Best Answer - Chosen by Asker
There are different jobs in architecture, so it depends on what you wish to do. Most will require a basic background in math skills as you seem to already know. You'll need to understand geometry, algebra and trigonometry. If you're wanting to be involved with large projects and industry, you'll likely need calculus...
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Geometry Module developed by The Rice University School Mathematics Project (RUSMP) Funding for the Geometry Module was provided by the Texas Education Agency and the Texas ... |
Precalculus: Real Mathematics, Real People - 6th edition
Summary: Ideal for courses that require the use of a graphing calculator, PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, 6th Edition, features quality exercises, interesting applications, and innovative resources to help you succeed. Retaining the book's emphasis on student support, selected examples include notations directing students to previous sections where they can review concepts and skills needed to master the material at hand. The book also achieves accessibility through careful writin...show moreg and design--including examples with detailed solutions that begin and end on the same page, which maximizes readability. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles. Reflecting its new subtitle, this significant revision focuses more than ever on showing readers the relevance of mathematics in their lives and future careers This is an AIE and includes answers. Ships same or next business day. NO INTERNATIONAL ORDERS PLEASE.
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Algebra II
Curriculum 2002-2003
American School of Alexandria, Egypt
GRADE LEVEL: Generally grade 10 and grade 11 students
OVERVIEW: This is the third of the required courses for high school graduation.
PREREQUISITES: Passing grade in Algebra I and Geometry
TEXT: Focus on Advanced Algebra, 1998
OTHER RESOURCES: Resources that accompany the text book: Teacher Edition
SPECIAL INSTRUCTIONAL PRACTICES:
A passing grade in each semester is required for a student to move on to the next course.
Generally in the 11th grade students are preparing for SAT I. Offering one night of extra-help solely for SAT prep has
become tradition, but very few students tend to come. Giving some SAT review built into the curriculum is
expected. The SAT book in the library is a great resource. It had divided the SAT into about 20 specific
areas, reviews each area in depth, and gives sample problems from this area only. Additionally it gives four
sample exams that are comprehensive. See the counselor for dates and registration information.
Students in the 2003-2004 school year may or may not have a TI 82 graphing calculator. If you feel it is necessary
you may want to require that students purchase one at the beginning of the year. They can be hard to find in
Egypt, but not impossible. Ask early and give a deadline.
The TI-83 is difficult to find in Egypt although it is unreliably found at Radio Shack.
In the 2002-2003 school year, I spent a lot of time reviewing Algebra I concepts.
Homework is always collected on a daily basis; many of the students here have a tendency to procrastinate. Teachers
have attempted collecting homework at the end of the chapters and have found it feeds this behavior. Be
forewarned!
Midterm exams are cumulative for the first semester; final exams are cumulative for the entire year. Some of their
other classes are not, so if you decide to continue the tradition be clear about your expectations early in the
year.
The book has very little rote practice many worksheets were the teacher personal material, so please feel free to bring
any reference material that you feel will enrich the textbook.
This is a prerequisite for Physics so Trigonometry should be introduced, they should also have good problem solving
skills, be able to manipulate equations, and be able to solve systems of equations.
2002-2003 finished chapters 1-3,5,7-10 (Will add exact topics at the end of the year.)
EVALUATION OF COURSE, GRADING SCALE: Flexible, generated by teacher.
Quarter Grade Semester Grade Yearly Grade
15% Homework 40% 1st Quarter 50% 1st Semester
45% Tests/Quizzes 40% 2nd Quarter 50% 2nd Semester
30% Citizenship 20% Final Exam
10% Presentations/Projects
LOCALLY AVAILABLE RESOURCES: None that we have found.
1.1.1* identify problem situations that could be
STANDARD 1: Problem Solving represented by given mathematical models
The student will engage in the process of (e.g., number sentences, equations, graphs,
mathematical problem solving. tables, diagrams)
1.1.2* recognize a problem that requires the use of a
1.1 Use problem-solving approaches to investigate and linear, quadratic or exponential
understand mathematical content equation/inequality
1.2 Apply integrated, mathematical problem-solving
strategies to solve real-world problems
1.2.1* identify the purpose or goal of a given The student will investigate the connections and
problem interplay among various mathematical topics and
1.2.2* apply algebra, geometry and other their applications.
mathematical areas together in order to
solve/analyze real-world problems 4.1 Recognize equivalent representations of the same
1.2.3 use matrices in solving real-world situations concept
4.1.1* relate polynomial equations (linear, quadratic
STANDARD 2: Communication and conical) to graphs
The student will use language and symbolism in 4.1.2* understand the relationship between the
order to communicate mathematical ideas. solution of a system of equations and their
graphs
2.1 Reflect upon and clarify his/her thinking about 4.1.3* recognize the equivalence of a function and its
mathematical ideas and relationships and graph
communicate his/her thoughts through the use of 4.1.4* convert an equation in logarithmic form to
mathematical language and symbolism exponential form and vise versa
2.1.1* create equations, expressions and inequalities 4.1.5* graph a complex number in a coordinate plane
that reflect his/her understanding of a problem or vise versa
situation 4.2 Relate procedures in one representation to procedures
2.1.2* express himself/herself using the language of in an equivalent representation
mathematics using clear and unambiguous 4.2.1 restate a given problem in an alternate form
terms and examples 4.2.2 use logarithms and antilogarithms to convert an
2.2 Use mathematical language and symbolism in expression/equation to an equivalent
order to communicate mathematical ideas expression/equation
visually, orally and in writing 4.3 Use and value the connections among mathematical
2.2 Use mathematical language and symbolism in order topics
to communicate mathematical ideas visually, orally 4.3.1* determine the connection between a graph
and in writing (limited to linear or quadratic), its equation and
2.2.2* express his/her mathematical ideas in writing a set of ordered pairs
2.2.3* read written presentations, view visual 4.4 Use and value the connections between mathematics
presentations, listen to oral presentations of and other disciplines
mathematics and ask clarifying and extending 4.4.1* apply mathematical concepts to solving
questions related to the mathematics he/she problems in other content areas (e.g., physics,
reads, views or hears chemistry, biology)
2.2.4* use appropriate symbols to express 4.4.2* create tables, graphs and equations in the
himself/herself mathematically context of a math investigation
2.2.5* translate a written statement into its correct
symbolic equivalent in order to analyze it
mathematically STANDARD 5: Functions
The student will investigate functional
relationships.
STANDARD 3: Reasoning
The student will use logical reasoning to clarify 5.1 Model real-world phenomena with a variety of
ideas in mathematics and in situations outside of functions
mathematics. 5.1.1 model a real-world situation with an appropriate
linear, quadratic or exponential function
3.1 Make and test conjectures 5.2 Represent and analyze relationships using tables,
3.1.1 use estimation to check the reasonableness of a verbal rules, equations and graphs
solution 5.2.1 create tables, graphs and ordered pairs from a
3.1.2* apply inductive reasoning to develop a function (with and without a graphing utility)
conjecture formulated by observing patterns of 5.2.2 interpret the results from tables, graphs and
numbers/expressions ordered pairs corresponding to a function or
identify a relationship as a function
5.2.3* determine the domain and range of a function
STANDARD 4: Connections (including logarithmic, exponential, polynomial
and radical functions)
5.2.4* determine the relationship between a function
and its inverse
5.3 Analyze the effects of parameter changes on the 6.4 Use a variety of methods to solve equations and
graphs of functions inequalities
5.3.1 recognize the effect of changing the slope or y- 6.4.1* solve linear equations and inequalities
intercept of a linear equation 6.4.2* solve absolute value equations and inequalities
5.3.2 recognize changes in a function resulting in 6.4.3* solve quadratic equations by completing the
horizontal or vertical shifts or reflection about square
an axis (including even, odd functions) 6.4.4* solve quadratic equations and inequalities and
5.4 Understand operations on and the general properties determine their graphs (including discriminate,
and behavior of classes of functions describe nature of roots)
5.4.1* perform operations on functions (e.g., sum, 6.4.5* simplify and solve equations containing
product and composition of functions) complex numbers
5.4.2 classify functions as being linear, quadratic, 6.4.6* solve rational and radical equations
exponential, etc. 6.4.7* solve polynomial equations of degree greater
5.4.3 describe the characteristics and properties of than two
classes of functions 6.4.8* solve logarithmic and exponential equations
6.4.9* use roots to create a polynomial equation or
find the sum and product of the roots
STANDARD 6: Algebra 6.5 Solve systems of equations
The student will use algebra concepts, use algebra 6.5.1* convert a system of equations into a matrix
as a means of representation and use algebraic equivalent
methods as a problem-solving tool. 6.5.2* solve systems of equations using a variety of
methods (e.g., graphing, elimination,
6.1 Use algebraic relationships to represent situations substitution, Cramer's Rule and inverse
that involve variable quantities matrices)
6.1.1 plot points and interpret information on a 6.5.3* solve systems of inequalities using a variety of
coordinate graph methods (e.g., graphing, substitution)
6.1.2 use the Pythagorean theorem to determine/solve
a right triangle
6.2 Use tables and graphs as tools to interpret STANDARD 7: Geometry
expressions, equations and inequalities The student will use geometry ideas and tools to
6.2.1* create tables and graphs to interpret linear, understand and represent two- and three-
quadratic and exponential functions dimensional situations.
6.2.2* create tables and graphs to interpret an
inequality 7.1 Represent problem situations with geometric models
6.2.3* graph linear and absolute value equations and and apply properties of figures
inequalities and determine the equations of lines 7.1.1 solve equations or word problems involving
in a plane triangles and rectangles and their areas
6.2.4* identify the graph of a logarithmic or 7.1.2* identify geometric figures defined by a system
exponential function of equations
6.2.5* determine the equation or inequality of a graph
that is quadratic
6.2.6* determine characteristics of a parabola (e.g., STANDARD 8: Statistics
axis of symmetry and vertex) The student will understand methods of
6.2.7 identify and describe the graphs and equations exploratory data analysis and statistical tools and
of the conic sections (circle, parabola, ellipse, apply these techniques to solving problems and
hyperbola)
evaluating statistical claims.
6.3 Operate on expressions, equations and inequalities
6.3.1* simplify expressions involving imaginary or
8.1 Construct and draw inferences from charts, tables
complex numbers (including radical
and graphs that summarize data from real-world
expressions)
situations
6.3.2* perform the basic operations on numbers
8.1.1 demonstrate an understanding for a "line of best
written in scientific notation, polynomials and
fit" when applied to a statistical model
rational functions (including factoring)
represented by a scatter plot
6.3.3* simplify algebraic expressions containing
8.2 Use curve fitting to predict data
negative or fractional exponents
8.2.1 demonstrate an understanding for "curve
6.3.4* apply the Binomial Theorem
fitting" by defining the equation of a line that
6.3.5* manipulate algebraic equations and
inequalities into equivalent forms
best describes a group of points on the 11.3.1* find the solution for a set of linear equations
coordinate plane and determine if they are consistent,
inconsistent or dependent
STANDARD 9: Probability
The student will employ the ideas of probability to STANDARD 12: Number Theory
deal with uncertainty and to interpret predictions The student will extend the concept of numbers to
based on uncertainty. include such constructs as irrational numbers,
complex number and vectors, and continue to
9.1 Use experimental or theoretical probability, as develop confidence in the use of real and complex
appropriate, to represent and solve problems involving numbers and their application to real-world,
uncertainty computational and estimation situations.
9.1.1* identify a sample space using the Basic
Counting Principle and utilize permutations and 12.1 Compare and contrast the complex number system
combinations to solve problems and its various subsystems with regard to their structural
9.1.2 recognizes and explain the difference between characteristics
independent and dependent events 12.1.1 explain the similarities and differences in the
9.1.3 solve problems involving compound events and subsystems of the complex number system
conditional probability (e.g., dice, cards) 12.1.2 compare the interrelation between various
numbers by using equivalent forms to
determine the same answer for a problem (e.g.,
STANDARD 10: Measurement fractions, decimals, integers, scientific notation)
The student will understand the essential role of 12.1.3* analyze the complex number system and
measurement as a link between the abstractions of demonstrate facility with its operations
mathematics and the concreteness of the real- 12.1.4* define abstract mathematical concepts (e.g.,
world. imaginary numbers, absolute value, irrationals)
12.2 Develop an understanding of the nature and purpose
10.1 Work with fundamental, measurable quantities of of axiomatic
physical object (length, area, volume, time, angle and 12.2.1 apply the properties of complex numbers
weight) in connection with other mathematics strands
and other subjects
10.1.1* explain the meaning of combined units (e.g.,
feet per second, person-hours)
STANDARD 11: Discrete Mathematics
The student will apply the concepts and methods
of discrete mathematics to problems arising from
the nonmaterial world.
11.1 Represent problem situations using discrete
structures such as finite graphs, matrices, sequences
and recurrence relations
11.1.1* perform operations on a set of matrices (e.g.,
addition, subtraction, scalar multiplication,
inverse, determinant)
11.1.2 determine information about arithmetic and
geometric sequence and series
11.2 Represent and analyze finite graphs using matrices
11.2.1* describe transformations of geometric figures
using matrices
11.2.2* use scalar multiplication of matrices to
determine size and scale changes in graphs and
solve equations
11.3 Represent and solve problems using linear
programming and combination equations |
Quick Review Math Handbook hot words hot topics
9780078601262
ISBN:
0078601266
Pub Date: 2004 Publisher: McGraw-Hill Higher Education
Summary: "Quick Review Math Handbook: Hot Words, Hot Topics" (available in English and Spanish) provides students and parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. This handbook also includes short-instruction and practice of key standards for Middle School and High School success.
Glencoe McGraw-Hill Staff is the author of Quick Rev...iew Math Handbook hot words hot topics, published 2004 under ISBN 9780078601262 and 0078601266. Three hundred sixty Quick Review Math Handbook hot words hot topics textbooks are available for sale on ValoreBooks.com, two hundred fifty nine used from the cheapest price of $0.01, or buy new starting at $13 |
Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey |
What is Mathematica, and where is it available at IU?
Mathematica is an interactive computational software package for
performing numerical, graphic, and algebraic calculations. Developed
and maintained by Wolfram
Research, Mathematica incorporates a high-level programming
language that lets you define your own procedures |
Visitors
Navigating the Math Major
As with any course of study at Guilford, successfully majoring in mathematics involves a certain amount of planning. The courses a math major completes can be divided into three types:
The Calculus Sequence and Math 320/325
The only calculus course required for the major is Math 225 (Multivariable Calculus). However, this course is the third step in a typical calculus sequence, and so students will need to study two semesters' worth of single-variable calculus to prepare for Math 225.
The set of courses students take before Math 225 depends on their background. Math 121 (Calculus I) is a typical entry point, but students who have already learned some calculus could potentially skip to Math 122 (Calculus II), or all the way to Math 225. This option is intended for students who are currently comfortable with the earlier courses; students who have taken calculus a long time ago are encouraged to retake the courses if they no longer remember the content.
Students who need a refresher on algebra, trigonometry, and exponential functions can choose to take Math 115 (Elementary Functions) before beginning the calculus sequence. Students who have covered the material in Calculus I and Calculus II but want to re-explore the material in more depth should consider Math 123 (Accelerated Calculus), offered every fall.
The math major also requires either Math 320 (Mathematical Physics) or Math 325 (Linear Algebra), each of which requires Multivariable Calculus as a prerequisite. For planning purposes, either of these courses can be thought of as a fourth step in the calculus sequence. Math 320 is typically offered in the fall, while Math 325 is typically offered in the spring.
Foundations of Mathematics and Upper-Level Courses
Math 231 (Foundations of Mathematics) is an introduction to proofs and abstract mathematical thinking, and in a sense it is a gateway to the upper-level courses of the mathematics department. This course is offered every spring, and potential math majors should strongly consider taking the course during the spring of their first or second year at Guilford.
Students must also take one upper-level course classified as theoretical, and one classified as applied. The three theoretical options are Math 335 (Topology), Math 430 (Algebraic Structures), and Math 435 (Real Analysis). Each of these courses requires Math 231 as a prerequisite. The three applied courses are Math 310 (Probability and Statistics), which requires Math 225; Math 412 (Discrete Mathematics II), which should be taken after Math 212; and Math 415, which requires Math 325. Any of these courses may be replaced by a 400-level seminar course; these seminars are occasionally arranged by faculty based on student interest.
Additional Electives
The mathematics major requires a minimum of 32 credits in courses numbered above 120; this includes three elective courses beyond the five courses specifically required. Students who take calculus courses at Guilford to prepare for Math 225 may satisfy one or two of these electives through Math 121, 122, and/or 123.
Suggested Tracks
As is apparent from the descriptions above, the mathematics major offers a high level of flexibility. The decision of which courses to take can be made based on a student's interest, schedule, and intended career path. Here are some suggested tracks:
Students primarily interested in theoretical mathematics, especially those planning to continue on to graduate study, should take all three of the upper-level theoretical courses (Topology, Algebraic Structures, and Real Analysis).
Students primarily interested in applying mathematics to non-mathematical areas should take Probability & Statistics and Linear Algebra, and perhaps consider arranging a seminar on a topic related to their area of interest.
Students primarily interested in computer-oriented mathematics should take Discrete Mathematics I, Discrete Mathematics II, and Linear Algebra. Numerical Analysis may also be a good choice.
Students preparing for secondary education are encouraged to take Geometry, Probability & Statistics, and Algebraic Structures. |
Welcome to Chapter Seven of the Math Planet
Algebra Crash Couse. In this chapter, we will talk about the most important area of
algebra - the functions. Functions are used everywhere from graphing and problem
solving. A good knowledge of function also helps you to do well on the more
adavanced math. But before you continue, you should learn the terms below so that
you can have a better understanding of the lesson afterward. Different parts of the
lesson are also provided so that you can go to the section of your choice. |
ForThe Basics
Variables, Notation, and Symbols
Real Numbers
Addition and Subtraction of Real Numbers
Multiplication of Real Numbers
Division of Real Numbers
Properties of Real Numbers
Subsets of Real Numbers
Addition and Subtraction of Fractions with Variables
Linear Equations and Inequalities
Simplifying Expressions
Addition Property of Equality
Multiplication Property of Equality
Solving Linear Equation
Formulas
Applications
More Applications
Linear Inequalities
Compound Inequalities
Linear Equations and Inequalities in Two Variables
Paired Data and Graphing Ordered Pairs
Solutions to Linear Equations in Two Variables
Graphing Linear Equations in Two Variables
More on Graphing: Intercepts
The Slope of a Line
Finding the Equation of a Line
Linear Inequalities in Two Variables
Systems of Linear Equations
Solving Linear Systems by Graphing
The Elimination Method
The Substitution Method
Applications
Exponents and Polynomials
Multiplication with Exponents
Division with Exponents
Operations with Monomials
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Binomial Squares and Other Special Products
Divide a Polynomial by a Monomial
Divide a Polynomial by a Polynomial
Factoring
The Greatest Common Factor and Factoring by Grouping
Factoring Trinomials
More Trinomials to Factor
The Difference of Two Squares
The Sum and Difference of Two Cubed
Factoring: A General Review
Solving Quadratic Equations by Factoring
Applications of Quadratic Equations
Rational Expressions
Reducing Rational Expressions to Lowest Terms
Multiplication and Division of Rational Expressions
Addition and Subtraction of Rational Expressions
Equations Involving Rational Expressions
Applications of Rational Expressions
Complex Fractions
Proportions
Direct and Inverse Variation
Roots and Radicals
Definitions and Common Roots
Properties of Radicals
Simplified Form for Radicals
Addition and Subtraction of Radical Expressions
Multiplication and Division of Radicals
Equations Involving Radicals
Quadratic Equations
More Quadratic Equations
Completing the Square
The Quadratic Formula
Complex Numbers
Complex Solutions to Quadratic Equations
Graphing Parabola
Appendices
Introduction to Functions
Functional Notation
Fractional Exponents
Equations with Absolute Value
Inequalities with Absolute Value |
Precal ... MORE8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers
8.7 Polar Equations and Graphs
8.8 Parametic Equations, Graphs, and Applications
9. Systems and Matrices
9.1 Systems of Linear Equations
9.2 Matrix Solution of Linear Systems
9.3 Determinant Solution of Linear Systems
9.4 Partial Fractions
9.5 Nonlinear Systems of Equations
9.6 Systems of Inequalities and Linear Programming
9.7 Properties of Matrices
9.8 Matrix Inverses
10. Analytic Geometry
10.1 Parabolas
10.2 Ellipses
10.3 Hyperbolas
10.4 Summary of the Conic Sections
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 The Binomial Theorem
11.5 Mathematical Induction
11.6 Counting Theory
11.7 Basics of Probability
Appendices
Appendix A. Polar Form of Conic Sections
Appendix B. Rotation of Axes
Appendix C. Geometry Formulas
Glossary
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications
Index
Photo Credits
Marge Lial has always been nowDavid Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking.
Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a bachelor's degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two master's degrees: one in Applied Mathematics and Statistics from the University of Missouri-Rolla, the second in Adult Education from the University of Missouri- St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students' understanding of mathematics, and creating materials that support classroom teaching and student understanding. |
Class 7 Mathematics Made EasyDesigned for the students in Class 7, Class 7 Mathematics Made Easy comprehensively covers 15 chapters in 15 LIVE interactive classes. In addition, you get access to comprehensive courseware: Videos + 10 PPTs + 10 PDFs.
Animated presentations and worksheets are included for every topic to give you a better understanding. Each chapter consists of more than 50 slides of Presentation and 10 worksheets for every chapter in word doc or jpg. You can download the courseware at anytime and can learn it at own pace of time.
Innovatively created content consists the following:
Animated PPTs are made for each chapter
Many examples from web based solutions
Includes lesson plan and game based instructions also
Educational articles for Maths
New creative ideas
Worksheets for every topic for practice exercise
Online multiple choice questions
Note - You decide which chapters you want to start with!
Class 7 Mathematics Made Easy online course package:
15 LIVE interactive online classes + Access to class recordings
Course timings: Monday-Wednesday-Friday between 9 AM to 12 PM (IST)
Courseware: Videos + 10 PPTs +10 PDFs + Docs
15 online tests to assess your performance
Course outline:
Chapter No.
Topic
Chapter 1
Integers 1
Chapter 2
Fractions and Decimals 29
Chapter 3
Data Handling 57
Chapter 4
Simple Equations 77
Chapter 5
Lines and Angles 93
Chapter 6
The Triangle and its Properties 113
Chapter 7
Congruence of Triangles 133
Chapter 8
Comparing Quantities 153
Chapter 9
Rational Numbers 173
Chapter 10
Practical Geometry 193
Chapter 11
Perimeter and Area 205
Chapter 12
Algebraic Expressions 229
Chapter 13
Exponents and Powers 249
Chapter 14
Symmetry 265
Chapter 15
Visualising Solid Shapes 277
About the Instructor
Bhakti Bhanushali Mumbai, India
Bhakti Mange has been involved in both private tuitions and online learning for last 10 years. She is experienced in use of e- teaching and educational software. She is a dedicated and dynamic e-teaching instructor who believes in creating and nurturing a lifelong love for knowledge in children. |
Intermediate Algebra 2nd Edition+ MathZone Allocation 1st Edition
9780073312682
ISBN:
0073312681
Edition: 2 Pub Date: 2006 Publisher: McGraw-Hill Higher Education
Summary: Miller/O'Neill/Hyde, built by teachers just like you, continues continues to offer an enlightened approach grounded in the fundamentals of classroom experience in the 2nd edition of Intermediate Algebra. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the ...textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates to students, the very points their instructors are likely to make during lecture, helping to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition, Problem-Recognition exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the first edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture ordistance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class, as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZone.
Miller, Julie is the author of Intermediate Algebra 2nd Edition+ MathZone Allocation 1st Edition, published 2006 under ISBN 9780073312682 and 0073312681. One hundred twenty four Intermediate Algebra 2nd Edition+ MathZone Allocation 1st Edition textbooks are available for sale on ValoreBooks.com, one hundred fifteen used from the cheapest price of $3.05, or buy new starting at $76.01May include moderately worn cover, writing, markings or slight discoloration. SKU:9780073312682682 [more.[less] |
Geometric Progression
A progression is another way of saying sequence thus a Geometric Progression is also known as a Geometric Sequence.
A Geometric Progression is a special sequence defined by the special property that the ratio of two consecutive terms is the same for all the terms in the sequence. Whereas in Arithmetic Progression we talked of difference, here we talk of ratios...
read more
Sequences and Series
Sequences
A sequence in mathematics is defined as an ordered list of elements (usually numbers) whose order defines some underlying property of the list. The order of the elements is very important and changing even one element would change the meaning of the entire
sequence.
The elements in a sequence are separated by commas and the length of a sequence is...
read more
Arithmetic Progression
A progression is another term for
sequence. Therefore, Arithmetic Progressions (also known as Arithmetic Sequences) are special sequences defined by the property that the difference between any two consecutive terms of the sequence are constant. Whereas the rule for regular sequences is
that the difference between consecutive terms has to have some kind of...
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Sets
A set is one of the most fundamental concepts in mathematics. Sets can be taught at an elementary level all the way through higher level mathematics.
A set is defined as a group or collection of distinct objects. The elements of a set can be anything: numbers, people, letters, etc. The way we usual denote sets is by giving them capital letters for a name.
Given set A and B
A...
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Radical Functions
Radical Functions contain
functions involving roots. Most examples deal with
square roots. Graphing radical functions can be difficult because the domain almost always must be considered.
Let's graph the following function:
First we have to consider the domain of the function. We must note that we cannot have a negative value under the square root...
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i am new with max script and i found things such atan, atan2 , delta, cos, sin and alot of more things related to maths that i know very little about it.
i just want to know what kind of math this it (its name) ? and where i found resources to learn such things? what books should i get............
thanx in advance.........
fuzzylizard
06-25-2009, 05:30 AM
For 3D stuff you need to have a good grounding in trigonometry (both 2d and 3d) as well as geometry, linear algebra, matrices, etc. There are probably other branches as well. You can probably leave number theory out of it, but a little bit of calculus probably wouldn't hurt.
st3dcenter
06-25-2009, 07:09 AM
Precalculus or Math 110 or (Math 100 and 102 together) in College.I think you should go until Math 108 for transfering to university.Good luck
eathquaketry
06-25-2009, 12:30 PM
Precalculus or Math 110 or (Math 100 and 102 together) in College.I think you should go until Math 108 for transfering to university.Good luck
Sorry, what is math 110 or math 100 ........... what is this you dont have to explain for your time, you can just drop me a link..........
Meloncov
07-10-2009, 07:34 AM
Sorry, what is math 110 or math 100 ........... what is this you dont have to explain for your time, you can just drop me a link..........
U.S. system of classification for classes. The hundreds refer to year (so one hundred is freshman, 200 is sophmore, ect. though it is sometimes possible to place into higher level classes), while the ones digit refers to a specific class. Math 100 is algebra, I believe, while I think math 110 is intro-calculus.
How much math you'll need depends on how ambitious you are. You can go a long ways with just geometry, but to do anything groundbreaking, you'll need advanced calculus at the very least.
CGTalk Moderation
07-10-2009, 07:34 AM
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MATLAB is a programming environment for algorithm development, data analysis, visualization, and numerical computation. Using MATLAB, you can solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran. Version 8.0 2012b: Major new releases of MATLAB and Simulink, featuring the new MATLAB Desktop, Simulink Editor, and Documentation Center. Two new products, MATLAB Production Server and Financial Instruments Toolbox. Updates and bug fixes to 82 other productsMAT , and Fortran.
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board.
The 1st edition of Tervo's Practical Signals Theory with MATLAB Applications offers an organized presentation around applications that introduces the actual behavior of specific signals and uses them to motivate presentation of mathematical concepts. The text sequences the presentation of the major transforms by their complexity to help visualize phenomena from an equation to develop intuition and learn to analyze signals by inspection. Furthermore the text provides examples and problems designed to use MATLAB, making presentation more in line with modern engineering practice. |
Preface-- 1 Elements of Group Theory-- 2 Some Related Algebraic Structures-- 3 Linear Vector Space-- 4 Elements of Representation Theory-- 5 Representations of Finite Groups-- 6 Representations of Linear Associative Algebras-- 7 Representations of the Symmetric Group-- 8 The Rotation Group and its Representations-- 9 The Crystallographic Point Groups-- 10 The Lorentz Group and its Representations-- 11 Introduction to the Classification of Lie Groups - Dynkin Diagram-- Index.
(source: Nielsen Book Data)
Publisher's Summary:
Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An authority on diverse aspects of mathematical physics, Professor K N Srinivasa Rao taught at the University of Mysore until 1982 and was subsequently at the Indian Institute of Science, Bangalore. He has authored a number of texts, among them being "The Rotation and Lorentz Groups and their Representations for Physicists" (Wiley, 1988) and "Classical Mechanics" (Universities Press, 2003). The first edition of "Linear Algebra and Group Theory for Physicists" was co-published in 1996 by New Age International, and Wiley, New York. (source: Nielsen Book Data) |
It can make the math easier to do-my head hurts less because of it-but if you don't know how to use it, you my end up banging your head against the wall in frustration at trying to get it to work. That little book they send with it doesn't help much either when you can't understand it. |
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More Trouble with Maths: A Complete Guide to Identifying and Diagnosing Mathematical Difficulties
David Fulton / Nasen
Author:
Chinn, Steve
Publisher:
Routledge - Taylor & Francis Ltd
Price: £41.99
There are many factors that can contribute to the learning difficulties children and adults have with mathematics. These include poor working memory, difficulties in retrieving so-called 'basic' facts and the ability to remember and apply formulas and procedures correctly. This highly practical teacher resource is for anyone who would like to accurately and effectively identify dyscalculia amongst their pupils. Written in an engaging and user-friendly style, Steve Chinn draws on his extensive experience and expertise and shows how to consider all the factors relating to mathematical learning difficulties explains how these factors can be investigated explores their impact on learning discusses and provides a range of tests ranging from pre-requisite skills such as working memory to a critique of normative tests for mathematics knowledge and skills. The book will guide the reader in the interpretation of tests, emphasising the need for a clinical approach when assessing individuals, and shows how diagnosis and assessment can become part of everyday teaching. This resource also includes pragmatic tests which can be implemented in the classroom, and shows how identifying the barriers is the first step in setting up any programme of intervention. |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
text offers a crucial primer on proofs and the language of mathematics. Brief and to the point, it lays out the fundamental ideas of abstract mathematics and proof techniques that students will need to master for other math courses. Campbell presents these concepts in plain English, with a focus on basic terminology and a conversational tone that draws natural parallels between the language of mathematics and the language students communicate in every day. The discussion highlights how symbols and expressions are the building blocks of statements and arguments, the meanings they convey, and why they are meaningful to mathematicians. In-class activities provide opportunities to practice mathematical reasoning in a live setting, and an ample number of homework exercises are included for self-study. This text is appropriate for a course in Foundations of Advanced Mathematics taken by students who've had a semester of calculus, and is designed to be accessible to students with a wide range of mathematical proficiency. It can also be used as a self-study reference, or as a supplement in other math courses where additional proofs practice is needed44.95
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Intermediate Algebra - 2nd edition
Summary: This student-focused text addresses individual learning styles through the use of a complete study system that starts with a learning styles inventory and presents targeted learning strategies designed to guide students toward success in this and future college-level courses.
Students who approach math with trepidation will find that Intermediate Algebra, Second Edition, builds competence and confidence. The study system, introduced at the outset and used c...show moreonsistently throughout the text, transforms the student experience by applying time-tested strategies to the study of mathematics. Learning strategies dovetail nicely into the overall system and build on individual learning styles by addressing students' unique strengths. The authors talk to students in their own language and walk them through the concepts, showing students both how to do the math and the reasoning behind it. Tying it all together, the use of the Algebra Pyramid as an overarching theme relates specific chapter topics to the 'big picture' of algebra. ...show less
Nice condition with minor indications of previous handling85 +$3.99 s/h
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Wonder Book Frederick, MD
Very Good condition. 2nd ed. Issued without dust jacket.
$2.93 |
The Hewlett Packard30S is the perfect calculator for high school science and math students. This scientific calculator with its two-line display helps perform complex math functions; also it has 250 built-in functions for all your math problems. This Hewlett Packard calculator is extremely user-friendly, so you don't have to worry about confusing keys or formulae. |
As part of the market-leading Graphing Approach SeriesEnhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles.
The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference.
Technology Support notes provided at point-of-use throughout the text guide students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystroke support.
Houghton Mifflin's Eduspace online classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.Book Description:McDougal-Littell. Hardcover. Book Condition: New. 0618394788 Premium Books are Brand New books direct from the publisher sometimes at a discount. These books are NOT available for expedited shipping and may take up to 14 business days to receive. Bookseller Inventory # Z0618394788ZN |
Math labs are used to help students to develop their mathematical abilities. They are usually staffed with tutors who encourage active participation of students in solving mathematical problems. The labs also have textbooks and solution manuals, computer access loaded with software used in math classes. Here, is an example of a college math lab |
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This book offers an innovative approach by focusing on learning through modeling and visualization with an integrated use of the graphing calculator. When introducing mathematical ideas, this text moves from the concrete to the abstract. The importance of mathematics is thus demonstrated to students and the material is presented in an accessible manner. The text consistently integrates mathematical concepts with real applications in order to enhance student intuition and understanding. Symbolic (algebraic), graphical, numerical, and verbal skills are continually demonstrated and reinforced throughout. |
Welcome to AlgebraLAB, an online learning environment that focuses on topics and skills from high school mathematics that students must be able to draw upon in their introductory science courses. Since math is the language of science, science courses are
The site includes really well done lessons, activities, practice pages (online), study aids, glossary, and word problems. Algebra Lab is like a free, living textbook. It has enough substance to help students work their way through algebra, while understanding the connections to how that algebra is used in a practical sense. "I feel like this would be very good to use as a resource in my classroom. As a middle school math teacher, I will be using a lot of algebra in my class. This would be a very helpful site to use as practice or review. Rather than having students bring their books home to complete their homework, they could just log into the site and complete the problems.
Algebra Lab is the project designed and implemented by Cathy Colwell a math teacher at Mainland High School at Daytona Beach, FL. The website was developed as the result of her participation in the CCTT Challenge Grant (1997-2002). The website is a resource for students and teachers containing activities, lessons, practice problems, as well as information on math related careers among many other educational materials.An online learning environment that focuses on topics and skills from high school mathematics that students must be able to draw upon in their introductory science courses. Since math is the language of science, science courses are often where students fi
We have used successful research-based design models to drive the project's design and implementation. AlgebraLAB focuses on building the connections between science and the basic mathematics required for its understanding by means of:
* Lessons on each topic/skill combination * StudyAids or "Recipes for Success" * Practice pages for each topic/skill combination * Hands-on science activities to support the use of mathematics in science * Interactive glossary of math and science terms with pronunciation guides, definitions, and examples * Career profiles illustrating the connections between math and science in a myriad of occupations. * Technical reading passages, word-problem mini-lessons, and interpretations of science graphs that integrate reading and math skills
Follow this link to read our recommendations on how to use the website.
The project was developed in conjunction with a Florida Department of Education Enhancing Education Through Technology (EETT) Competitive Grant, a National Council of Te |
A+ National Pre-apprenticeship Maths and Literacy for Hospitality book by Andrew Spencer
Pre-apprenticeship Maths and Literacy for Hospitality is a write-in workbook that helps to prepare students seeking to gain a Hospitality Apprenticeship. It combines practical, real-world scenarios and terminology specifically relevant to the Hospitality industry, and provides students with the mathematical skills they need to confidently pursue a career in the Hospitality trade. Mirroring the format of current apprenticeship entry assessments, Pre-apprenticeship Maths and Literacy for Hospitality includes hundreds of questions to improve students' potential of gaining a successful assessment outcome of 75-80% and above. This workbook will therefore help to increase students' eligibility to obtain a Hospitality Apprenticeship. Pre-apprenticeship Maths and Literacy for Hospitality also supports and consolidates concepts that students studying VET (Vocational Educational Training) may use, as a number of VCE VET programs are also approved pre-apprenticeships. This workbook is also a valuable resource for older students aiming to revisit basic literacy and maths in their preparation to re-enter the workforce at the apprenticeship level.
Buy A+ National Pre-apprenticeship Maths and Literacy for Hospitality book by Andrew Spencer from Australia's Online Bookstore, Boomerang Books.
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MTHS 645
Groups and Their Actions
Fieldsteel,Adam
06/28/2004 - 08/11/2004
Monday & Wednesday 01:30 PM - 04:00 PM
Science Tower 137
The concept of a group and its actions is fundamental in mathematics, and examples are found throughout the subject. Consider these examples: rearrange the vertices of a cube so that the distances between them are unchanged. Move the points of a plane so that every circle is carried to a circle. Twist the faces of a Rubik's cube. Shuffle a deck of cards. Every one of these is an example of an action of a group.
We will begin by studying specific examples of groups such as those above, and others, and these examples will be used to motivate the abstract development of the subject. The abstract development, which focuses on the ideas that are common to all the examples, can in turn be used to inform us about geometry, and other applications. For example, these ideas lead to a proof that there are only five regular solids, and only seventeen ways to tile the plane with congruent figures. In an application far from geometry, we can see why in Sam Loyd's famous 15 puzzle (the sliding block puzzle of our youth) exactly half of the possible arrangements of the blocks can be attained.
Readings will be taken from various sources. The textbook GROUPS: A PATH TO GEOMETRY, by R. P. Burn, will be especially useful because of its wealth of instructive problems.
Students will be given regular problem sets to complete, and grades will be based on their work on these assignments.
Students will be expected to have a good command of high school algebra, geometry, and precalculus, and be ready to follow extended logical reasoning.
Adam Fieldsteel (A.B. Brown University; Ph.D. University of California, Berkeley) is professor of mathematics. His research focuses on ergodic theory and topological dynamics, and his recent publications include: (with A. Blokh), "Sets that force recurrence," Proceedings of the American Mathematical Society (2002); (with K. Dajani), "Equipartition of interval partitions and an application to number theory," Proceedings of the American Mathematical Society (2001); (with R. Hasfura), "Dyadic equivalence to completely positive entropy," Transactions of the American Mathematical Society (1998). Click here for more information about Adam Fieldsteel R.P. Burn, GROUPS: A PATH TO GEOMETRY (Cambridge University Press), Paperback |
with unique features to allow you to enter more than one calculation, compare results and explore patterns, all on the same screen.
Enter and view calculations in common Math Notation via the MATHPRINT Mode, including stacked fractions, exponents, exact square roots and more.
Quickly view fractions and decimals in alternate forms by using the Toggle Key.
Scroll through previous entries and investigate critical patterns as well as viewing and pasting into a new calculation.
Features: Helps students develop skills in addition, subtraction, powers, and answer format.
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Backspace and edit capabilities.
Operates in well-lighted areas using solar and in other light settings using battery.
Features: TI-Navigator Classroom Learning System- 32 Users TI-Navigator is compatible with TI-83 Plus and TI-84 Plus families.
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Ideal for general math, algebra 1 and 2, geometry, trigonometry, statistics and science.
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What you will study
Stage 1
We recommend that you begin your studies with Mathematical thinking in schools (ME620)Mathematical thinking in schools::This course is designed to help you develop your knowledge and understanding of the teaching of mathematics. It is suitable for any Key Stage, and will broaden your ideas about how people learn and use mathematics. There is no formal examination: assessment is based on two tutor-marked assignments and an end-of-module assessment. In order to complete the assessments, you will need access to learners of mathematics. Students on this course have worked with a variety of learners from Key Stage 2 pupils to adults. Places are allocated on a 'first come, first served' basis, so you should register as early as you can.undergraduate.qualification.pathways.V14-1,module,ME620,,1. This 30-credit module will develop your knowledge and understanding of the teaching of mathematics, with an emphasis on Key Stage 3, and broaden your ideas about how people learn and use mathematics.
For the other 90 credits you can choose from the following:
Developing algebraic thinking (ME625)Developing algebraic thinking::This course is for you if you are interested in developing your knowledge and understanding of the learning of algebra particularly at Key Stages 2–4. It integrates development of the core ideas of algebra with relevant pedagogical constructs and principles, and will extend your awareness of how people learn and use algebra. There is no formal examination: assessment is based on three tutor-marked assignments and an end-of-module assessment. In order to complete the course assessments, you will need access to learners of algebra at Key Stages 2–4, which could include adult learners.undergraduate.qualification.pathways.V14-1,module,ME625,,1 – this 30-credit module will develop your understanding of how people learn and use algebra at Key Stages 2–4, and of different teaching constructs and principles.
Developing geometric thinking (ME627)Developing geometric thinking::Develop your knowledge and understanding of the learning of geometry particularly at Key Stages 2–4. This course integrates development of the core ideas of geometry with relevant pedagogical constructs and principles, and will extend your awareness of how people learn and use geometry. There is no formal examination: assessment is based on three tutor-marked assignments and an end-of-module assessment. To complete these assessments, you'll need access to learners of geometry at Key Stages 2–4, which could include adult learners.undergraduate.qualification.pathways.V14-1,module,ME627,,1 –this 30-credit module will develop your understanding of the learning of geometry at Key Stages 2-4, and explore a range of different teaching approaches and develop your geometric thinking.
Developing statistical thinking (ME626)Developing statistical thinking::This course will help you develop your knowledge, appreciation and understanding of the learning of statistics particularly at Key Stages 2 to 4. As well as improving your statistical thinking, you'll learn about different teaching approaches, including use of ICT tools such as scientific calculators and computers. There is no formal examination: assessment is based on three tutor-marked assignments and an end-of-module assessment. To complete these assessments, you'll need access to learners of statistics at Key Stages 2–4, which could include adult learners.undergraduate.qualification.pathways.V14-1,module,ME626,,1 – this 30-credit module explores the learning of statistics and data handling at Key Stages 2–4, and investigates different teaching approaches, including the use of ICT tools.
Researching mathematics learning (ME825)Researching mathematics learning::This course is designed for the professional development of anyone working with learners of mathematics – whether as a teacher, classroom assistant, lecturer, adviser or parent. You'll develop ways of exploring mathematics teaching and learning; interpret current thinking on the subject; and investigate aspects of the social and political context. You will consider tasks to generate pupils' activity and explore the impact of different tasks on learners. You'll also reflect and work on you own mathematics, develop your mathematical autobiography and explore further the readings and ideas that influence you most.undergraduate.qualification.pathways.V14-1,module,ME825,,1 – this 60-credit postgraduate module offers a valuable insight into the teaching and learning of mathematics for anyone involved – from classroom assistants and teachers to lecturers and parents two years part-time study to complete this qualification, but you can take anything from one (full-time study equivalent) to seven years.
Register
If you have already completed some successful study at higher education level at another institution you may be able to transfer credit for this study and count it towards an Open University qualification. If you wish to apply to transfer credit you must do so as soon as possible, and before you register for your chosen qualification. If you are awarded credit for study completed elsewhere, you may find that you need to study fewer OU modules to complete your qualification with us.
Visit our Credit Transfer site for more information and details of how to apply for credit transfer |
text should help readers to learn several problem solving techniques and introductory level engineering computation.
In my tenth year at the Institute,
I dedicate this book to
the dedicated members of the BCIT community.
This textbook has no goals to become The New York Times best-seller however it should help readers to learn several problem solving techniques and introductory level engineering computation. This text can also serve as a companion course manual for various engineering courses such as Engineering Laboratory, Applied Mechanics and Heat Transfer within the Power and Process Engineering program.
The best way to learn about engineering computation with spreadsheets is to actually do it. We will therefore solve many engineering problems mainly using Microsoft Excel in this book. Since the focus of the book is engineering computation, we will concentrate on the mathematical solutions, built-in engineering and scientific functions and, to a limited extent, the presentation of computational results. Thus, I assume the reader has a working knowledge of Microsoft Excel under either OS X or Windows operating systems. Those readers who are not comfortable with the basic functionality of Microsoft Excel should keep a good reference book handy as they read this text. I also assume that the reader is competent at first year Mathematics and Physics. However, access to good reference books are highly recommended.
Note:
Spreadsheets have evolved since their first appearance. I have used spreadsheets since 1997 and witnessed their visual transformation (i.e. GUI). While the current version of mainstream spreadsheet applications can offer attractive GUIs, process much more data and perform faster calculations, the commands and their syntax have hardly changed. What you will learn in this book is mostly independent of the various versions of Microsoft Excel available today |
I am a Mathematics graduate and I can say "2nd order non-homogeneous differential equation." but bugger me if I can remember where to start on solving such a thing. Good on you if you can still remember a single thing you did in your degree!
I can tell you exactly why in my case. Math majors (at least all of the ones in my classes, including me) tend to be interested in theory and concepts. If you're interested more in application, you probably are a physics or engineering major.
My college was small (only about 5,000 students total in undergrad) so they couldn't have separate differential equations classes for the math majors and the physics majors. The physics majors needed to know all about applications for their other classes to make sense, so we were forced to focus more on application than theory.
Well, if I was that into applications of math I would have been a physics major myself. I just don't remember math unless it was a theory/proof-based course, and this was not (despite the wishes of the professor) because it had to meet the needs of the physics majors as well.
I don't know if this is unique to my college, though, or if it's common to any math course that has significant overlap with physics students.
Well in all honesty, although maths was my major I am not an exceptional mathematician and few people are. When it got to differential equations I think I reached above my level and instead of understanding how to solve the more complex diff eq's I had to memorise a step by step method for solving most of them which maybe doesn't stick as well as the understanding? Just a thought.
Yeah. I mean this really is the only way anyone learns it. There are about 27 techniques for solving them, about 20 of which they try to cover in the intro courses. A cursory understanding is all you're going to get. But still, I remember how to do some very advanced linear algebra techniques years later, but couldn't solve more than the most basic differential equations.
I can tell you why that is in many cases. There is a style of teaching differential equations where the focus is on solution techniques. This is the bag of tricks method.
Another way is to teach a few tricks but mainly focus on qualitative and numerical techniques.
I think people who were taught the back-o- tricks way forget a lot of the tricks (I have). I retained much more with the qualitative and numerical method. (I'm in the strange situation of having experienced both teaching techniques.)
Differential equations are in theory rather simple but there are alot of tricks that you have to use to solve them. Math majors dont need these tricks because they dont need to "solve" a differential equation, they just need to know how they work.
Yeah we should only quote humorous tv personalities and memes and casual conversation can't be intelligent. Screw discussing the more intelligent things you have learned. If you act smart regardless of wether you are or not you put on sunglasses and are a douche.
The quote in question is a flowery way of saying that the study of astronomy tends to invoke a sense of wonder. If that quote is somehow one of the more informative, challenging, intellectually interesting things you've been exposed to, I really don't know what to tell you.
Yeah, I should say that I don't completely despise Plato. He was the first philosopher I ever read and even he was critical of his theory of forms. I love pretty much every philosopher that can get me to rant.
True enough, though I believe that the idea has continued influence in Neo-Platonism, particularly in mathematics, to this very day. This is harder to dismiss, though, because contemporary Platonists have suggested much more nuanced interpretations which I am not familiar with.
I love Socrates, but he almost always stooped to semantics when trying to prove people wrong, which is to say that he never allowed his opposition to base their arguments on assumptions, as he would just keep degeration the discussion down until he reached a point that the other person didn't have a concrete stance on, thereby "winning" the debate. I forget who it was in the Republic who called him out on this and pretty much stumped him, but I have a lot of respect for that guy (even if he could possibly be fictional).
Plato's claim to greatness is to have discovered such a law: that "all social change is corruption or decay or degeneration," and that the only way to break this cycle of decay is to arrest development and return to the Golden Age, where no change occurs. His belief in perfect and unchanging things, the Platonic Ideas from which all things originate, finds its expression in all fields of inquiry: be it social justice, nature and convention, wisdom and truth, or goodness and beauty.
Behind these lofty ideals, Popper uncovers a discomforting truth: Plato envisioned the ideal Greek polity as a totalitarian nightmare, where the 'race of the guardians' had to be kept pure from any miscegenation and where the role of the rulers was to breed the human cattle according to some esoteric formula (the 'Platonic Number', a number determining the True Period of the human race). Along his apology of Sparta came his endorsement of infanticide and his recommendation that children of both sexes be "brought within the sight of actual war and made to taste blood."
uncovers a discomforting truth? Plato came out and said this exactly in Republic. He said that he envisioned an ideal government as an aristocratic one, run by a group of philosophers who were prevented from enjoying wealth.
Because it implies that function and assumption of function are inherently linked; that is to say, an "ideal form" is not only ideal due to perfect function, but also perfect recognition. This is silly because it's not at all necessary for an object to be recognized for it to still be functional, and recognization is skewed by other influences like culture and media. Would the most "spaceshippy spaceship" be the most capable and efficient spaceship? Hell no it wouldn't.
The idea of forms works better for completely intangible ideas for me. The Form of Justice, or Beauty, for example, works. At least for me it does.
Yours was a criticism raised in our philosophy class as well, thank you for restating it here. It is one of the better arguments against Plato's philosophy, and I don't think it can readily be discounted.
I thought he sucked until I actually invested some time in reading him, carefully this time. The guy was bloody ace, he swings freely between poetry and prose, at times dipping deep into sweet, sweet logic.
That he was, in retrospect, often misguided, shouldn't count against him.
Seems that people take it too literally, that he actually believed that different modes of music affected your thinking and actions, that some are inherently bad, extrapolate that in broad strokes over his thought experiment's more elegantly stated points because they are too confused about them, and would prefer to close the book on your whole enthusiasm of dialectic.. so you don't have to get into it with them and they can go back to playing cornhole or whatever it is they do.
Yeah, I'd be all "Platonism is stupid because it doesn't take into account perspectivism. O You don't know what that is? I thought you actually knew something about Philosophy. I guess you we just trying to look smart."
Right, well I should say that when I said "transcendental idealism" I don't mean Kant's philosophy by that name, which is a trickier beast to wrestle, but rather Platonic idealism. I refer to this as "transcendental" because it holds that universals exist in a realm that transcends the particulars of this physical world, though we might return to these Forms through dialectical investigation. The way this relates to the quote mentioned in the OP is that Plato held stars to be non-material and mathematically perfect in accordance to this transcendental geometry that governed everything. Thus, for Plato, to contemplate the stars really was to lead away from this world to an independent world of ideas. My primary gripe with this is that it most reflects Plato's own story of Thales falling into the well having been too absorbed in admiring the stars to have noticed. This is the point I would have complained about in reaction to hearing the quote.
However, though I do believe that reflection is important, I still remain an empiricist closer to Aristotle in believing that knowledge is found by abstracting universals from the particulars found in the world. We can then deal with abstracts as mental activity, as in mathematics, but I don't buy the idea that we are born with knowledge of geometry having been exposed to it in a proto-heaven of ideas prior to birth. That strikes me as too close to the cultish metaphysics of Pythagoreanism.
Glazed over yet? I can't say that this is a sufficient critique of platonic idealism as its mostly just calling it unintuitive nonsense nor that it is sufficiently well-cited but I don't mean this to be a formal paper. Just kind of a rant.
No. The historical Socrates was also referenced by his contemporaries Xenophon and Aristophanes. I also don't see why Plato would entirely invent, for Athenian readers, a character who was a controversial influence in Athens. Aristotle also refers specifically to Socrates in such a way that suggests that, in his time, Socrates was a famous individual.
As to whether Socrates' philosophy was invented is a harder problem. However, I do believe that Plato's earliest dialogues were a sincere attempt to record Socrates' philosophy in light of the fact that Socrates refused to record it for himself, mostly because these dialogues reflect what was also mentioned of Socrates by Xenophon and Aristophanes. Later dialogue Socrates, the one who was increasingly more Pythagorean, I'm confident was invented by Plato.
Do you include the "Apology" amongst possible fictitious rhetoric, or do you think it more or less describes his Trial and execution?
BTW, thanks for your input. IDo you include the "Apology" amongst possible fictitious rhetoric, or do you think it more or less describes his Trial and execution?
I do believe that it is historically accurate that Socrates was put on trial for corrupting the youth and impiety, was found guilty, and drank hemlock as his execution. Xenophon also wrote an account of Socrates' apology, though Xenophon wasn't there but cited Hermogenes as his source. Xenophon, being a historian, is a good source to read if you want to cross-reference Plato's account.
As for Plato's account, it depends on who you ask. However, I believe that whatever liberties Plato took were a means of defending Socrates' reputation after a trial that actually existed.
IYeah, I see the parallels. Fiction or not, as far as I see it, Socrates was the original figure that made philosophy possible through his inquisitive search for wisdom. Whether or not he existed, that's a valuable pursuit.
I also wish to illustrate to christians that my reverence for Socrates need not be diminished should he be fictitious, or that his life is padded by hyperbole. It is his ideas, and what he represents that has value, not the pedantry of dogma. |
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Overview
Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice—evident in the narrative, the figures, and the questions interspersed in the narrative—is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections.
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Meet the Author
William Briggs has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.
Lyle Cochran is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and, since 1995, at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the Instructor's Mathematica Manual for Linear Algebra and Its Applications by David C. Lay and the Mathematica Technology Resource Manual for Thomas' Calculus. He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.
Bernard Gillett is a Senior Instructor at the University of Colorado at Boulder; his primary focus is undergraduate education. He has taught a wide variety of mathematics courses over a twenty-year career, receiving five teaching awards in that time. Bernard authored a software package for algebra, trigonometry, and precalculus; the Student's Guide and Solutions Manual and the Instructor's Guide and Solutions Manual for Using and Understanding Mathematics by Briggs and Bennett; and the Instructor's Resource Guide and Test Bank for Calculus and Calculus: Early Transcendentals by Briggs, Cochran, and Gillett. Bernard is also an avid rock climber and has published four climbing guides for the mountains in and surrounding Rocky Mountain National |
Basic Technical Mathematics - 8th edition
ISBN13:978-0321284433 ISBN10: 0321284437 This edition has also been released as: ISBN13: 978-0321131935 ISBN10: 0321131932
Summary: This tried-and-true text from the pioneer of the basic technical mathematics course now has Addison-Wesley's amazing math technologies MyMathLab and MathXL helping students to develop and maintain the math skills they will need in their technical careers.
Technical mathematics is a course pioneered by Allyn Washington, and the eighth edition of this text preserves the author's highly regarded approach to technical math, while enhancing the integration of te...show morechnology in the text. The bookAllyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over forty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be easily rearranged to fit the needs of both instructor and students. Above all, the author's vision of this book is to continue to show today's students that an understanding of elementary math is critical in many aspects of life. ...show less
Introduction to Functions. More About Functions. Rectangular Coordinates. The Graph of a Function. Graphs on the Graphing Calculator. Graphs of Functions Defined by Tables of Data.
4. The Trigonometric Functions.
Angles. Defining the Trigonometric Functions. Values of the Trigonometric Functions. The Right Triangle. Applications of Right Triangles.
5. Systems of Linear Equations; Determinants.
Linear Equations. Graphs of Linear Functions. Solving Systems of Two Linear Equations in Two Unknowns Graphically. Solving Systems of Two Linear Equations in Two Unknowns Algebraically. Solving Systems of Two Linear Equations in Two Unknowns by Determinants. Solving Systems of Three Linear Equations in Three Unknowns Algebraically. Solving Systems of Three Linear Equations in Three Unknowns by Determinants.
6. Factoring and Fractions.
Special Products. Factoring: Common Factor and Difference of Squares. Factoring Trinomials. The Sum and Differences of Cubes. Equivalent Fractions. Multiplication and Division of Fractions. Addition and Subtraction of Fractions. Equations Involving Fractions.
7. Quadratic Equations.
Quadratic Equations; Solution by Factoring. Completing the Square. The Quadratic Formula. The Graph of the Quadratic Function.
8. Trigonometric Functions of Any Angle.
Signs of the Trigonometric Functions. Trigonometric Functions of Any Angle. Radians. Applications of Radian Measure.
9. Vectors and Oblique Triangles.
Introduction to Vectors. Components of Vectors. Vector Addition by Components. Applications of Vectors. Oblique Triangles, the Law of Sines. The Law of Cosines |
In fact, it's so sophisticated that you may not know how to take advantage of many of its features and functions.
That's a good problem to have, and TI-84 Plus Graphing Calculator For Dummies is the right solution! It takes the TI-84 Plus to the next power, showing you how to: Display numbers in normal, scientific, or engineering notations Perform basic calculations, deal with angles, and solve equations Create and investigate geometric figures Graph functions, inequalities, or transformations of functions Create stat plots and analyze statistical data Create probability experiments like tossing coins, rolling dice, and so on Save calculator files on your computer Add applications to your calculator so that it can do even more TI-84 Plus Graphing Calculator For Dummies was written by C.C.
Edwards, author of TI-83 Plus Graphing Calculator For Dummies, who has a Ph.D.
in mathematics and teaches on the undergraduate and graduate levels.
The book doesn't delve into high math, but it does use appropriate math examples to help you delve into: Using the Equation Solver Using GeoMaster and its menu bar to construct lines, segments, rays, vectors, circles, polygons, perpendicular and parallel lines, and more Creating a slide show of transformations of a graph Using the Inequality Graphing application to enter and graph inequalities and solve linear programming problems There's even a handy tear-out cheat sheet to remind you of important keystrokes and special menus, And since you'll quickly get comfortable with the built-in applications, there's a list of ten more you can download and install on your calculator so it can do even more! TI-84 Plus Graphing Calculator For Dummies is full of ways to increase the value of your TI–84 Plus exponentially..
For more information about the title TI-84 Plus Graphing Calculator for Dummies,olecular Algebra in Mammalian Cells(June 4, 2012) — Researchers have reprogrammed mammalian cells in such a way as to perform logical calculations like a pocket calculator. The cells owe this ability to one of the most complex gene networks that has ... > read more |
Elementary Algebra : Concepts and Application - 7th edition
Summary: The goal of Elementary Algebra: Concepts and Applications, 7e is to help today's students learn and retain mathematical concepts by preparing them for the transition from ''skills-oriented'' elementary algebra courses to more ''concept-oriented'' college-level mathematics courses, as well as to make the transition from ''skill'' to ''application.'' This edition continues to bring your students a best-selling text that incorporates the five-step problem-solving process...show more, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This edition has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter. ...show less
Exponents and Their Properties Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Special Products Polynomials in Several Variables Division of Polynomials Negative Exponents and Scientific Notation
Systems of Equations and Graphing Systems of Equations and Substitution Systems of Equations and Elimination More Applications Using Systems Linear Inequalities in Two Variables Systems of Linear Inequalities Direct and Inverse Variation |
The first semester of a two-semester sequence in elementary algebra. Topics include solving linear equations and inequalities, graphing linear equations and inequalities, solving systems of equations and an introduction to polynomials. College credit will be awarded, but this credit will not count toward a degree. Skills prerequisite: MAT 018C. Skills corequisite: ENG 020 and/or ENG 060. |
Math Bootcamp (Grades 7-12) Registration Open
Back to School Math Bootcamp is a series of 2-day rigorous small group math workshops for students in grades 7-12 grade. Students can expect to receive a review in key concepts and introduction of upcoming concepts to be taught in the classroom. We pick 5 topics in the subject to focus on and lead students to a deeper understanding of fundamental skills. The cost of each course is $125.00 Students who register before August 19 are given a 20% discount (totaling to $100) and 5 hours of free tutoring over the fall semester.
Schedule is as follows: 7th grade math (pre-Algebra and beginning Algebra): 8/31 and 9/1 8th grade Algebra and Geometry: 8/31 and 9/1 High School Geometry 9/7 and 9/8 High School Algebra I 9/7 and 9/8 High School Algebra II 9/14 and 9/15 Trigonometry 9/21 and 9/22 Calculus 9/22 and 9/22 |
Math Review for Physics
Get math review for physics and study guides here. Learn about geometry, trigonometry, and algebra for physics or brush up on your skills. Thorough explanations and practice examples will help you review math concepts require to understand physics.
Study Guides
Introduction
An equation is a mathematical expression containing two parts, one on the left-hand side of an equals sign (=) and the other on the right-hand side. A formula is an equation used for the purpose of deriving a ...
Introduction
In algebra, it is customary to classify equations according to the highest exponent, that is, the highest power to which the variables are raised. A one-variable first-order equation , also called a first-order ...
Introduction
As the exponents in single-variable equations become larger and larger, finding the solutions becomes an ever more complicated and difficult business. In the olden days, a lot of insight, guesswork, and tedium were involved in ...
Introduction
A vector has two independently variable properties: magnitude and direction. Vectors are used commonly in physics to represent phenomena such as force, velocity, and acceleration. In contrast, real numbers, also called ...
Introduction
You should know about scientific notation , the way in which physicists and engineers express the extreme range of values they encounter. How many atoms are in the earth? What is the ratio of the volume of a marble to the ...
Introduction
Subscripts are used to modify the meanings of units, constants, and variables. A subscript is placed to the right of the main character (without spacing), is set in smaller type than the main character, and is set below the ...
Introduction
In printed literature, power-of-10 notation generally is used only when the power of 10 is large or small. If the exponent is between −2 and 2 inclusive, numbers are written out in plain decimal form as a rule. If the ... |
Explores approximation theory, interpolation theory, and classical analysis. This covers topics such as Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity. more... |
It is a wonderful book: very accessible and rigorous [at] the same time, containing basic and not-so-basic facts, discussing many (sometimes unexpected) applications ... Given that and the wonderful way this book was written and organized, I think it can be used by many readers: engineering students, mathematics students, research mathematicians, and researchers in any other field where linear algebra is applied. I strongly recommend this book to anyone interested in "working" linear algebra.
--MAA Reviews
Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students.
Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader.
In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises. |
WIRIS collection is intended to speed up your work in class. It is a free repository of real classroom exercises done and shared by teachers. Its aim is to cover all the topics in mathematics at any level, and it already contains a good number of exercises.
What happens if the student introduces a correct answer that we were not expecting? In other words, what happens if he gives an expression that is mathematically equivalent to the expected one, but that looks completely different to it?
The random functionality in WIRIS quizzes allows creating random questions that minimise the possiblity of cheating in an exam. Every student will get a different set of questions, so his answers will be of little use to his neighbour. |
This summer, Oglethorpe will offer an opportunity for entering students to jumpstart their college mathematics sequencing!
Who: New students for fall 2013 who plan to major in science, mathematics or engineering.
What: Condensed summer offerings of Intro to Functions (MAT-120) and Advanced Functions (MAT-130). When: July 1-16 (MAT 120), and/or July 17-31 (MAT-120 and MAT-130). Where: On campus (commuting only; no residential option). Why: To get a head start on the pre-/co-requisites for fall courses in science/math majors. Supplies: Textbook (included), laptop or computer, graphing calculator, pencil and notebook. Cost: $800/course (includes lunch and required textbook).
Why would I do the IMO?
These courses are for students who want to "get the math juices flowing" in a supportive yet academically intensive environment. You might wish to get a head start on your first semester by completing a mathematics course that is a pre-/co-requisite for a major-area course that you aspire to take in the fall (e.g. BIO-101). You might wish to be a step ahead as you adjust to a college classroom, meet faculty members, and prepare for your intended course of study.
Is it open to everyone?
These courses are only for new students whose first semester at Oglethorpe will be fall 2013, and who intend to major in science, pre-engineering or mathematics. Students must be able to commute or secure their own off-campus accommodations, as the residence halls will not be an option.
Do I need prior experience with pre-calculus or trigonometry?
The IMO is ideal for students who have already been exposed to coursework in these areas, and who wish to brush up on or expand their knowledge before the fall semester. The IMO will not be a leisurely overview of functions; students will begin solving problems on Day 1. If you are confident in your abilities but surprised by your placement score, the IMO may be for you. This is a good chance to "get the math juices flowing" and build on what you have already learned.
What if I decide not to do it, or I can't come on these dates?
That's okay. You are well-prepared to begin at Oglethorpe with or without the IMO sessions. Oglethorpe offers support for any student to finish any degree in four years, and you can always contact the professional advisors in the Academic Success Center to discuss your academic plan and consider your options. Remember, the IMO is simply for jumpstarting the course sequencing. It is exactly equivalent in content to what the mathematics professors will cover in the fall and spring semesters.
What if my mom says I should, but I'm unsure?
Given the intensive nature of the accelerated format, the IMO is only worthwhile if the student is self-motivated to participate. Your parent, coach, teacher or peers cannot provide the momentum for you to succeed, since you will need to focus, manage your time, and study hard in order to pass and demonstrate your mathematical proficiency. During the IMO, you will not have much time and energy to spare, so it's important that YOU want to invest that time and energy! You should also consider whether you have the mathematical skill level to feel comfortable in such an all-day, every-day mathematics setting.
Can I take both MAT-120 and MAT-130 this summer, before the semester starts?
Yes, providing that you earn a "C-" or higher in the first offering of IMO MAT-120. Keep in mind that these sessions are back to back: you would take a final exam in MAT-120 on Tuesday, and then begin MAT-130 on Wednesday! If your schedule, stamina, and placement grade allow, you are welcome to do both IMO sessions.
So these are real college courses, worth 4 credits? Yes. Although the syllabus is compressed into a short time period, the IMO sessions are equivalent to full semester courses. One full day of an IMO class is comparable to a week and a half of a semester course. The courses will appear on your transcript like any other 4-credit course, with no qualifying designation of "IMO" or "summer".
What if I haven't taken the mathematics placement test yet? Although MAT-120 is open to any new student, it is generally a good idea to find out your placement before investing your time in the intensive course format. Your AP, IB or college-level transcripts may suggest placement at Oglethorpe. If you do not have scores or transcripts yielding mathematics placement then you may request to take the Accuplacer placement test. The admission office will offer proctoring. Call the front desk at 404.364.8307 for more information and upcoming testing dates, or you may sign up online for placement testing.
How do I sign up for the IMO? Click here to be directed to the online registration form!
What material is covered?
MAT-120 and MAT-130 explore questions such as, "What is a function? How can I tell? How do they behave, and how do I work with them? What special categories of functions often show up?" In MAT-120, students will encounter linear, polynomial, rational, exponential and logarithmic functions. In MAT-130, you will work with more advanced topics such as trigonometry, polar and parametric functions, and vector analysis.
Who are the instructors? Dr. John Merkel, Associate Professor of Mathematics, will teach one of the MAT-120 offerings and the only MAT-130 offering. Dr. Brian Patterson, Assistant Professor of Computer Science and Mathematics, will teach the other MAT-120 offering. (Click to view faculty website.) Both courses will also feature Supplemental Instruction (SI), with an upperclassman peer teacher who sits in on all class time and helps lead small-group work, answers questions, etc.
Is there tutoring available? Tutoring is available by request during the IMO. Your SI peer teacher will also be available during daytime group sessions to help you review challenging material.
Am I allowed to be absent?
No. Attendance is mandatory. You should not miss part or all of any IMO class day—not for work, a doctor's appointment, a carpooling delay, a prior commitment or any other reason. Because one day of IMO is equal to a week and half of a regular semester, it will be extremely detrimental to your learning process if you are absent for any portion of it.
Can I drop the course after I start?
Yes, you will have until 5 p.m. on the second day of class to drop the course. Absolutely no drops will be allowed from the third day on. Dropping a class means that you are completely removed from the roster, and no record of having started the course will appear on your transcript.
What if I start, but after a couple of days I know I am really (really) struggling. What do I do?
College courses also have an option called "withdrawal." Withdrawal means that the course will still be listed on your transcript, but instead of a letter grade (A-F), you will have a W. If you withdraw from a course, it does not become part of your college GPA. It is not a dishonor to cut one's losses and withdraw from a course, and it is not unusual to see a W on an undergraduate transcript. The IMO withdrawal deadlines are 5 p.m. on the sixth day of the course.
What will the format be like? The course will meet in the Academic Success Center area, which is a large, comfortable room that allows for both classroom instruction and space for small groups to work together or for individual students to concentrate. The course assumes that students will be using a laptop or a computer, and your professor will use lots of collaborative learning techniques through the WebAssign program (part of your textbook). WebAssign includes tools such as example problems, interactive practice, and video tutorials. Only about 15% of his time will be spent lecturing. The rest will be for small groups to work together and ask questions or for individuals to practice concepts on their own.
Is there homework, too? Yes. For example, in MAT-120 you will have daily homework in WebAssign. The WebAssign format is adaptive, meaning that you can work a problem as many times as you wish until you get it right (and understand why you did). You will have the opportunity to do much of your homework in class while you are at OU. The better use you make of your class time, the less you will have to do later at home.
How is it graded? You will receive a letter grade A-F. Each course will have a midterm and a final exam, along with daily individual work, homework and frequent quizzes.
What is the textbook? Where can I get it?
The required textbook for both courses is Precalculus w/ WebAssign Code, edition 6, by Stewart (ISBN0-8400-6807-7). The price of the textbook ($248.99) is included in your $800 IMO fee. You will be provided with your copy of the book on the first day of class. Your copy will include a unique WebAssign code for setting up an account. Because of this unique code, you should not purchase used copies of the book.
Can't I just get a used copy on the Internet?
No. You must have a new (not used) copy of the book in order to obtain your WebAssign code. You will be unable to participate in the IMO sessions without one. Remember, if you are starting in MAT-120, you will use the same textbook and code in MAT-130, so your investment in a new book will serve you well for at least two courses.
Do I need a graphing calculator? Yes, you must have a graphing calculator for both IMO courses (and, looking ahead, for numerous other OU courses). If you need to obtain a graphing calculator for college courswork, the instructors suggest a TI-83 or TI-84.
You say I need to bring a laptop (or request computer access at OU). Why? The IMO courses will rely on computer-based practice sets, examples, videos and interactive learning tools. It is ideal for each student to bring his or her own laptop, or to arrange to borrow one from a family member or friend for the duration of the IMO session. If this is strictly impossible, let us know and we will pursue arrangements for computer access at OU.
Can I use an iPad?
No. WebAssign relies on a Flash feature, which Apple products do not support. Your laptop must be able to use Flash.
What should I bring with me on the first day? Before arriving on the first day, you should obtain and bring a laptop, a graphing calculator, a pencil and a notebook. You should be in class a little before 9:30 a.m. with these items ready. You should also bring excitement to bond with your new classmates while doing a lot of math!
What if I live out of town? The IMO is a non-residential program. Oglethorpe is unable to offer residence hall accommodations to any new students. All participants must be able to drive in or take transit in order to attend. We recognize that participation may not be possible for students who live outside the metro area. However, the IMO is open to any new student planning to pursue a science/mathematics major, as long as the student can make their own arrangements for transportation and a place to stay.
Why can't I stay on campus?
The summer is
a busy period for the residence life staff and the campus facilities team, who rely on this time to clean and prepare the residence halls for the fall semester. Because the staff needs time to prepare for fall move-in; and because there are many shifts in space happening as OU finalizes the construction of the new campus center, it is not possible to offer housing to IMO students this summer.
What about meals?
Oglethorpe will provide lunch in the dining hall on campus for each day of the IMO. Participants should indicate any requests for dietary accommodations when registering for the program.
Will there be a break in the program? Can I leave campus?
Yes, there will be a midday break each day for lunch. There will be an approximately 1 hour break between noon and 1:00 p.m. when class resumes. Students may spend this time as they choose.
Where will the course meet?
The courses will meet in the Academic Success Center. The ASC is on the ground floor of Weltner Library, which is located in Lowry Hall at the base of the academic quad. When you enter, take the stairs or elevator down one level, and make two right turns to get to the ASC. Parking is available in the lots near the baseball field and tennis courts.
What if I don't have access to a laptop?
If this is the case, Oglethorpe will arrange for you to use a computer terminal in the ASC while you are in class. Please register for the IMO at least one business day before the start date, so that the OU staff has adequate time to assist you. Remember that you will also need access to a computer to complete daily quizzes and homework after class, so you should consult the OU library summer hours or make arrangements within your household or neighborhood for "after hours" work.
What happens next after the IMO? If you pass the IMO session of MAT-120, you will be eligible to register for MAT-130 either in the next IMO session or in the 2013-2014 academic year. You will also become eligible for MAT-121, BIO-101 and CHM-101 in the fall. If you pass the MAT-130 session, you will be eligible to register for MAT-131, PHY-101 and PHY-201 as well as the courses listed above. This may mean that you need to complete a drop/add form to modify your course registration from Passport. A professional advisor will be available to guide you through your options.
Does the fee become part of my fall tuition?
No. The IMO is billed as a summer session course, so you will receive a separate charge. The IMO will not affect your fall balance, payment plan or financial aid.
Is there financial aid available for the IMO?
No, Oglethorpe is not planning to offer financial assistance for the IMO.
How and when do I submit the $800 fee? You must submit the IMO fee before the session begins, or by 9 a.m. on the first day. You may call the business office at (404) 364-8302 to pay by credit card, or you may visit the business office in person (ground floor of Lupton Hall). All credit card transactions incur a 2.99% service fee.
What if I forget to pay the $800 beforehand?
You must submit your fee on or before the first day of class. If you have not submitted payment by 5 p.m. on the first day of the session, you will be dropped from the IMO course session. The payment deadline for MAT-120 is 5 p.m. on 7/1 (or 7/17 for the second MAT-120 offering), and for MAT-130 it is 5 p.m. on 7/17.
What is the total expense? What else do I need to budget for?
In addition to the $800 course fee, if you do not own a graphing calculator, you will need to borrow or purchase one (a new TI-83 is approximately $100). You may also wish to plan on fuel or transit costs to and from Oglethorpe.
What if I have more questions? You can email advising@oglethorpe.edu with additional questions about the IMO. You will receive a reply from a professional advisor in the Academic Success Center who will help you obtain information or consider your options. |
practice exercise, you will answer just a few questions and you won't receive a ...
There is an answer key at the end. ... numerical skills/prealgebra, algebra,
college algebra, geometry, and trigonometry.
McDougal Littell Pre-Algebra will give you a strong foundation in algebra while
also ... This book will also help you become better at taking notes and taking tests
. .... Practicing Test-Taking Skills, 162.
with skills and concepts taught in pre-algebra classes. ... through the first problem
with your students, showing where the answers are to go, etc. An ... Book A
Operations with whole numbers, basic facts, ... Practice activities for first-year
algebra. |
201308150 / ISBN-13: 9780201308150
Mathematics All Around
Pirnot's Mathematics All Around offers the supportive and clear writing style that you need to develop your math skills. By helping to reduce your ...Show synopsisPirnot's Mathematics All Around offers the supportive and clear writing style that you need to develop your math skills. By helping to reduce your math anxiety, Pirnot helps you to understand the use of math in the world around you. You appreciate that the author's approach is like the help you would receive during your own instructors' office hours. The Fifth Edition increases the text's emphasis on developing problem-solving skills with additional support in the text and new problem-solving questions in MyMathLab. Quantitative reasoning is brought to the forefront with new Between the Numbers features and related exercises. Since practice is the key to success in this course, exercise sets are updated and expanded. MyMathLab offers additional exercise coverage plus new question types for problem-solving, vocabulary, reading comprehension, and more. 032192326X / 9780321923264 Mathematics All Around Plus NEW MyMathLab with Pearson eText -- Access Card Package Package consists of 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321836995 / 9780321836991 Mathematics All Around 5/eHide synopsis
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Reviews of Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing |
APPLIED MATHEMATICS
AND MODELING
The College of William
& Mary in Virginia
Applied mathematics concerns the application of mathematical tools and
processes to the solution of problems of practical interest to society. Consequently,
the applied mathematician frequently has one foot in an area of mathematics and
the other in physics, chemistry, biology, engineering, or some other branch of
applied science. The solution of scientific problems typically involves a
four-fold process:
Research to develop a depth
of understanding of the physical problem.
Restatement of the physical
problem in terms of a mathematical model. Math models most often take the
form of ordinary or partial differential equations or of matrix systems.
Inevitably mathematical models contain various levels of approximation, in
which certain (hopefully) insignificant factors have been neglected.
Solution of the mathematical
model, usually by numerical methods.
Interpretation of the
mathematical solution in terms of the original physical problem and
assessment of the validity of the solution in light of any approximations
that have been.
Thus the applied-math toolbox contains, among many other
mathematical tools, modeling techniques, approximation theory, linear algebra,
numerical analysis, probability and statistics, and optimization. The
successful student whose major is applied mathematics should be well equipped
for a variety of interesting career possibilities including university
positions, industrial applied mathematics, and research in national
laboratories.
Also, William and Mary's Institute for Integrative
Bird Behavior Studies (iibbs) is a newly formed initiative bringing
together researchers from Biology, Mathematics, School of Marine Sciences, and
our Center for Conservation to study the behavioral ecology and conservation of
populations and communities. Formed by several Applied Science affiliates,
Professors Dan Cristol, John Swaddle and Sebastian
Schreiber, the goals of iibbs/BioMath are to:
Formalize and strengthen William and
Mary's expertise in behavior and ecology, particularly in relation to
mathematical applications and modeling of populations and behaviors;
Provide strong, personalized mentorship for undergraduate
and graduate students at the interface of biology and mathematics;
Provide inspiring educational and research opportunities for
students, including Applied Science PhD students;
Support active collaboration among faculty and students from
different disciplines and departments, particularly in BioMath areas which are
of interest to Applied Science graduate students.
Recognizing the important overlap between computer science
and operations research, the College offers an M.S. with a specialization in Computational Operations
Research (COR) administered by the Computer Science Department in
cooperation with the Department of Mathematics. Qualified students may elect to
continue graduate work in operations research leading to a Ph.D. in either the
Computer Science Department (with a computational emphasis) or the Applied
Science Department (with an applied mathematics and modeling emphasis). These
opportunities are facilitated by the participation of the departments of
Mathematics, Computer Science, and Applied Science in the Computational Science Cluster, a
federation of departments and schools at William & Mary committed to
fostering research and education in computational science.
Computational
Science Training for Undergraduates in the Mathematical Sciences (CSUMS) is
a new collaborative program between the Departments of Mathematics, Applied
Science, and Computer Science at the College
of William & Mary. We
are actively recruiting William & Mary undergraduate students interested in
participating in a CSUMS research project. The benefit of participation in
CSUMS include the possibility of support to work on a research project with a
group of CSUMS faculty members during the Spring semester of your junior year. If
you wish to continue your research, competitive stipends are available to
provide support during the summer between your junior and senior years, along
with the possibility of on-campus housing. In addition, travel support is
available to attend conferences or visit research groups at other institutions
either in the U.S.
or abroad.
Follow the links below for
information about our various research groups. |
Second Edition News
RightStart™ Mathematics is coming out with a second edition! This new edition will have the same award-winning and innovative approach to teaching mathematics as the current program. The revised lessons and worksheets incorporate an easier-to-teach format and use the Common Core State Standards as a base minimum. In addition to the topics that are addressed in the Standards, RightStart™ Mathematics Second Edition will continue to advance and develop the child's conceptual understanding of critical math concepts.
Listen to a recorded webinar on the differences between RightStart™ Mathematics First Edition and RightStart™ Mathematics Second Edition.
When will RightStart™ Mathematics Second Edition (RS2) will be available?
Will RightStart™ Mathematics current edition (RS1) continue to be available?
Yes! RightStart™ Mathematics current edition lessons and worksheets will continue to be available for purchase and will be supported. You may continue to use this edition with your entire family. You will not be required to change editions.
What is updated with the RightStart™ Mathematics Second Edition (RS2)?
The first edition was written in the 1990s and made available to homeschoolers in 2001. Minor changes have been made over time; however, the Second Edition will be a complete rewrite. This includes new research and ideas that Dr. Joan A. Cotter has developed over recent years. The RS2 manuals have a slightly different and easier-to-follow format and will align with the Common Core State Standards. RightStart™ Mathematics Second Edition will not be limited by the Standards, rather it will encompass and exceed the Standards.
Forty-five states, the District of Columbia, four territories, and the Department of Defense Education Activity have adopted the Common Core State Standards. These standards identify the topics that the tests will be based on. You may not be concerned with tests; however, some states require periodic testing and some parents and teachers are affected.
Will RightStart™ Mathematics Second Edition (RS2) be limited by the Common Core State Standards?
No! We are making sure that everything that the Standards require is addressed in each grade level; however, we teach for understanding, exceeding the requirements. We will continue the same RightStart™ philosophy and approach for which we are recognized.
Does RightStart™ Mathematics current edition (RS1) cover the Common Core State Standards?
Yes. RS1 was written before CCSS were developed; this alignment is simply a reflection of an all-encompassing curriculum.
What if I have a child finishing Level C or D and one starting in Level A or Level B?
We will not have RS2 Level C, D, or E ready at this time, so you will need to continue with the current program for your older child. For your younger one, you could choose to move into the second edition or continue with the first edition.
Are there any changes with the manipulatives?
The lessons will utilize the same manipulatives; however, the order and use may change, therefore the kits will change.
What does the new format look like?
Objectives and materials are identified in the heading area. The Activities for Teaching in the left column details how to proceed with the lesson. Explanations provide additional information and are clearly written in the right column. Some examples are below. You may also download the first 15 lessons of RS2 Level B below these examples. |
approxima... read more
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An Introduction to the Approximation of Functions by Theodore J. Rivlin This text provides an introduction to methods of approximating continuous functions by functions that depend only on a finite number of parameters — an important technique in the field of digital computation. 1969 edition.
Product Description:
approximation, more. Includes many problems. Bibliography. Advanced undergraduate-beginning graduate-level |
Topic Review: Thinking Quantitatively I: Descriptions and Models
Published by the Nuffield Foundation, the Nuffield Advanced Biology Topic Reviews for students were an integral part of the Advanced Biological Science materials, but each could be read on its own. Thus, students could use them for their current work, or to pursue personal interests.
This topic review illustrated the use of mathematics to describe precisely the characteristics of living things, the processes that occur in their bodies, their numbers, and their relations to each other and their environments. It explained the importance of the use of mathematics in the design of experiments and when analysing the results obtained from them. It also covered the use of mathematics to build up models of living processes to serve as hypotheses on which investigations could be based |
What Is 005 in Math?
Answer
005 in math is an introductory level in an algebra course. Upon successful completion of the course, the students have a mastery of basic algebra concepts and operations. Students are able to perform operations with exponents, radicals, and algebraic expressions; factor polynomials; solve linear equations and graph linear equations. |
What is understanding and how does it differ from knowledge? How can we determine the big ideas worth understanding? Why is understanding an important teaching goal, and how do we know when studentsRevised to reflect the newly structured math section on the SAT, the new edition of this workbook offers students intensive preparation for the test's all-important math questions. The author ... > read more
This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this ... > read more |
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Editorial Reviews
Review
This is a book that can be used in courses in the fundamentals of mathematics., or for self-study. --Charles Ashbacher, Amazon.com
While the text is written with a a view to bridging the abstract divide that appears between high school mathematics and undergraduate mathematics, the book contains many valuable insights into the role of mathematics in society, its historical context, its visionaries, and valuable and interesting bits that would appeal to high-school students and teachers alike. --Layna Green, Australian Mathematics Teacher
Book Description
Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level and take courses in which proofs play a major role. There are also narratives on the nature of mathematics and the mathematics profession.
As a youngster, I loved baseball and read everything I could about how to play the game. Each book that I read started with the line, "You must first learn the fundamentals." This also applies to mathematics, where there is a small set of axioms, definitions and theorems that form the basis of most of what else can be learned. Many teachers have started applying this approach to their teaching of mathematics and are beginning to offer a class in the fundamentals of mathematics early in the undergraduate curriculum. This book is an introduction to the fundamentals, as well as the theory and philosophy of mathematics. The coverage begins with a basic explanation of what mathematics is, what kind of people do mathematics and some of the ways in which it is split into categories. Chapter one is a survey of the fundamentals of logic and chapter two covers set theory. Each of the next four chapters contains a brief coverage of the sets of numbers in increasing order of containment. The natural numbers are described in chapter three, the rational numbers in chapter four, the real numbers in chapter five and the complex numbers in chapter six. The explanations are well-done and a large number of exercises that advance your understanding are included. Written in a style well within the knowledge base of the beginning undergraduate math major, this is a book that can be used in courses in the fundamentals of mathematics. The highly motivated individual could also use it in a plan of self-study.
Published in the recreational mathematics e-mail newsletter, reprinted with permission. |
books.google.co.jp - This....
Topology
This. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
この書籍内から
ユーザーの評価
Review: Topology
This book is pretty much a standard. It has a number of strong points. It is self-contained relative to students even at a fairly elementary level. There are a lot of exercises, and they are ...
Review: Topology
ユーザー レビュー - Ronald Lett - Goodreads
An excellent introduction to point-set and light algebraic topology. If this is your first exposure to topology, I would recommend Kinsey's "Topology of Surfaces" as a companion of solid applications in the specific case of compact 2-dimensional topology.レビュー全文を読む |
Middlebury: Math Review
enMath Practice and Review
<p><span class="opening"><img class="small" src="/media/view/185201/small/Picture_for_Web2.jpg" border="0" alt="purple swirl_1" title="purple swirl_1" width="150" height="148" style="float:right; border:4pt solid black" />Middlebury students in a wide range of courses and majors benefit from the resources available through CTLR.</span></p>
<p>• If you are enrolled in an introductory course with moderate or significant quantitative content, check the Study Groups chedule (under <em>Resources for Students</em>, at right) to see if there is a drop-in session for your class.</p>
<p>• Perhaps you would like to get more practice with fundamental concepts, to either prepare for taking a course or to supplement your work in a current course—see below for links to practice and review materials, as well as other online resources.</p>
<p>• Some students haven't had a math class in several years, and aren't sure where to begin or how to assess their own skills. We can provide assistance to you as you plan your class schedule.</p>
<div><strong>Resources at CTLR</strong></div>
<p>If you are thinking of enrolling in a course that has a significant quantitative component but you're not sure if you have sufficient math preparation, we can help. The Director of Quantitative Skills Support, Jeanne Albert, can provide diagnostic and placement assistance, as well as practice exercises. To schedule an appointment with Jeanne, <a href=" here.</a></p>
<p class="big"><strong>Online Resources</strong></p>
<p>If your math skills are rusty or you just want some extra practice, the links below contain information and exercises to review several important math concepts and methods.</p>
<p><strong>Numbers and Equations</strong></p>
<ul>
<li><img src="/sites/all/modules/media/icons/pdf_icon.gif" border="0" alt="Operations with Numbers" title="Operations with Numbers" /><a href="/media/view/169831/original/Operations_with_numbers.pdf">Operations with Numbers</a>, including laws of exponents and radicals</li>
<li>
<div><span><a href="/media/view/170131/original/Solving_Equations.pdf"></a><a href="/media/view/170131/original/Solving_Equations.pdf"><img src="/sites/all/modules/media/icons/pdf_icon.gif" border="0" alt="Solving Equations" title="Solving Equations" /></a><a href="/media/view/170131/original/Solving_Equations.pdf">Solving Equations</a></span></div>
</li>
<li>
<div><span><a href="/media/view/170231/original/Algebra_Exercises_Part_1.pdf"></a><a href="/media/view/170231/original/Algebra_Exercises_Part_1.pdf"><img src="/sites/all/modules/media/icons/pdf_icon.gif" border="0" alt="Exercises" title="Exercises" /></a><a href="/media/view/170231/original/Algebra_Exercises_Part_1.pdf">Exercises</a></span></div>
</li>
</ul>
<p> </p>
<p>For students enrolled in calculus there are several useful resources linked through the course textbook, including algebra review and an extensive set of exercises with full solutions. These resources may be found <a href=" target="_blank">here</a>.</p>
mathMon, 11 Feb 2013 14:43:54 +0000Jeanne Albert jalbert@middlebury.edu165401 at |
This text provides a set of methods and guidelines that can help produce more accurate and transparent mathematical models for groundwater flow and transport, as well as other natural and engineered systems. The book's exercises enable users to maximize the potential of models and troubleshoot any problems that may arise. Most of the methods are based on linear and nonlinear regression theory. Fourteen guidelines show the reader how to use the methods advantageously in practical situations. The text can be used by students, researchers, and engineers to simulate many kinds of systems. |
graphingSwan Studios' 3D Graph Generator is an innovative program for creating animated three-dimensional graphs. Used responsibly, this software makes memorable and informative graphs that will give your presentations a professional appeal. If you're not careful, though, you'll need to pass out motion sickness bags at your next sales meeting.
The program's interface is fairly intuitive, although the Options menu, where the graph configuration takes place, is a bit confusing at first glance. The built-in Help file is brief but adequate. The program's sample data gives an immediate look at what's in store, and we quicklyGraphing Calculator 3D from Runitor is a handy and free 3D graphing utility that plots graphs for two-and three-dimensional mathematical functions and coordinates tables. It supports parametric equations and Cartesian and polar coordinates in 2D and 3D, inequalities in 3D, and other capabilities. It boasts dazzling 3D graphs with seemingly limitless variations. You can change the color, shading, and appearance of graphs, add animation and other features, and rotate and zoom them in real time. You can define your own functions and variables or use one of over 20 provided functions.
Graphing Calculator boasts an attractive and functional if slightly … Read more
Aquarium Lab provides an incredible amount of control tracking the fish, tank, and other elements that complete an aquarium. Its comprehensive tools and simple navigation make this an impressive choice.
We liked the program's interface, especially how it listed every element that makes up an aquarium and allowed for quick glances at each one's status. We never touched the instructional Help file because the program was so intuitive. We were impressed that every element from the water's PH balance, to food, to the electricity used allowed for its data to be inputted and monitored for a comprehensive … Read more
Home schoolers, high school tutors, and students needing additional mathematics study will find this many-featured app a handy addition to their toolbox. It provides assistance for grasping two-dimensional function graphs with animation, analyzing functions, understanding analytic geometry, solid geometry, and more.
Math Studio launches a three-paned interface similar to the familiar e-mail client design: the upper-left vertical pane is a graph manager, the lower-left pane is a result editor, and the large pane on the right is a plotting area for displaying graphs. However, the cluster of icons in the three toolbars aligned along the interface's top may intimidate … Read more
GS-Calc offers users an alternative spreadsheet maker by mimicking what the more famous versions do and adding little flourishes that many will like.
The program's interface will immediately be recognizable to those familiar with Excel. The rows, columns, and even commands feel like they are in the same place. However, if users need help with its slight difference, a Help file is available. The program functions almost exactly like the more popular spreadsheet option. Users input data into cells across various rows and columns. The data can be manipulated in multiple ways, including color-coding cells, rows and columns, sorting … Read more |
The company has released its latest version of Mathematics as a free download. The upgrade includes ink handwriting support and a full-featured grqphic calculator. It is designed to help middle and high school students learn to solve equations step by step while it provides an overview of fundamental STEM concepts.
The company has released its latest version of Mathematics as a free download. The upgrade includes ink handwriting support and a full-featured graphic calculator. It is designed to help middle and high school students learn to solve equations step by step while it provides an overview of fundamental STEM concepts.
Microsoft Math 4.0 is a free download and features a large collection of tools, tutorials, and instructions designed to help you tackle math and science problems quickly and easily. "With Microsoft Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus.
Microsoft Mathematics 4.0, for students in middle school, high school, and early college, shows how to solve equations while bolstering understanding of fundamental math concepts. It features built-in Ink Handwriting Support, which lets you hand-write math problems and equations in a worksheet area on a tablet or ultra-mobile PCs for immediate solving or later work. The software also includes a graphing calculator capable of plotting in 2D and 3D, a movie editor, a library of formulas and equations, a triangle solver, and more.
Microsoft Mathematics 4.0, designed for students in middle school, high school, and early college, is intended to teach users how to solve equations while bolstering their understanding of fundamental math and science concepts. Although the company charged for its last version, this latest edition is free. |
Math in Everyday Life
9780825142581
ISBN:
082514258X
Edition: 3 Pub Date: 2002 Publisher: Walch Education
Summary: Newton, David E. is the author of Math in Everyday Life, published 2002 under ISBN 9780825142581 and 082514258X. Two hundred twenty six Math in Everyday Life textbooks are available for sale on ValoreBooks.com, one hundred nine used from the cheapest price of $0.52, or buy new starting at $11.74 Math in Everyday Life, 1.[less] |
Mathematics Applications and Connections Course 3
9780078228520
ISBN:
0078228522
Publisher: Glencoe/McGraw-Hill School Pub Co
Summary: Motivate your students with relevant, real-world applications, correlated Internet connections, and additional skill practice in a variety of formats. Reach all your students by balancing practice and skill development with hands-on activities, technology, and projects and investigations. Prepare students for success on standardized tests and in future math courses with a wide variety of assessment options and strong... developmental links from arithmetic to algebra.
Collins Publishers Staff is the author of Mathematics Applications and Connections Course 3, published under ISBN 9780078228520 and 0078228522. One hundred fifty seven Mathematics Applications and Connections Course 3 textbooks are available for sale on ValoreBooks.com, one hundred fifty six used from the cheapest price of $2.39, or buy new starting at $546.71 |
Find a Newtown Square MathGraph theory deals with the study of graphs and networks and involves terms such as edges and vertices. This is often considered a very specific branch of combinatorics. Lastly, probability in discrete math deals with events that occur in discrete sample spaces. |
YTH-432 - Math (Grade 2)
This class will focus on relationships and computation within, geometry, measurement, statistics, probability and algebra patterns and functions. All topics are a review of concepts learned during the previous school year. |
Algebra is the branch of mathematics
that deals with numbers and their relations. Algebra is used throughout of people's
daily lives from buying groceries in the store to scientific researches. Algebra is so
useful that NASA is using binary numbers to communicate to the possible extraterrestrial
lives. So learning algebra is so important because that people's lives are depended
on algebra. Before you dive into the world of algebra, you need to know a few basics, and
this chapter is dedicated to that purpose.
Algebra deals
mainly with numbers. There are two types of numbers.
The first
type of number is a real number. Real numbers are the
numbers we see in everyday lives and most scientific researches.
Real numbers
can also be divided into two kinds of numbers. The first kind is called rational numbers.
An integer is a whole number (not a fractional number) that can be positive,
negative, or zero. A natural number is a number that occurs commonly
and obviously in nature, a whole, non-negative number. Rational numbers
are numbers determined by the ratio of an integer to a nonzero natural
number. Examples of these numbers include 5, 1/5 and 1/3. The decimal
expansion of a rational number is either finite or eventually periodic
(such as .333333333etc.)
The other kind of real number is called an irrational
number. An irrational number is a real number that cannot be reduced
to any ratio between an integer and a natural number. Examples of these
numbers are the square root of 2, the cube root of 3, the circular ratio
pi, and the natural logarithm base e. The square root of 2 and the cube
root of 3 are examples of algebraic numbers. Pi and e are examples of
special irrationals known as transcendental numbers. The decimal expansion
of an irrational number is always nonterminating (it never ends) and nonrepeating (the digits display no repetitive pattern).
The second type of number
is an imaginary number.
Imaginary numbers do exist; they were named before they were fully understood.
They are part of a complex number system. An imaginary number is a number
whose square is
negative. Every imaginary number can be written as ix, where x is a real number
and i is the positive square root of -1.
** To correct a couple of mistakes, the above paragraphs have been edited
by the ThinkQuest editor.
After you get to know the numbers, you
need to know the ways to express the numbers or algebraic expressions. The algebraic
expressions are made up of four different kinds of symbols: Variables, Numbers, Grouping
Symbols, and Operation Signs. The variables are the unknown values that need to be found
out through numeral steps of calculations. The numbers are the known values that are used
to find out the variables. The grouping symbols are the signs that put a group of numbers
or variables together so that they can be calculated first. The operation signs are the
signs that actually do the calculations. There are several basic properties of algebraic
expressions. By knowing them, you can do many algebra problems quickly and accurately.
These properties are listed below:
Trichotomy Properties:
For all real numbers a and b, one and only one of these statements is true-a<
b, a= b, a> b.
Transitive Property of
Order: For all real numbers a, b, and c, if a< b and b< c, then a< c.
Commutative Property of
Addition: For all real numbers a and b, a+ b=b+a.
Commutative Property of
Multiplication: For all real numbers a and b, ab=ba.
Associative Property of
Addition: For all real numbers a, b, and c, (a+b)+c=a+(b+c).
Associative Property of
Multiplication: For all real numbers a, b, and c, (ab)c=a(bc).
You can also jump to the chapter of your
choice by using the drop-down list at below. |
978140200ic-Geometric Codes (Mathematics and its Applications)
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes |
Polynomials are one of the most important areas of math. You
will see polynomials on any tests. So it is very important that you learn
polynomials well and firmly. Please take a few minutes
break and click here to continue to the next chapter. (You can also click on the drop-down
list below to jump to any chapter you like.)
You can also jump to the
chapter of your choice by using the drop-down list at below. |
DO PROSPECTIVE ELEMENTARY AND MIDDLE SCHOOL
TEACHERS UNDERSTAND THE STRUCTURE OF ALGEBRAIC EXPRESSIONS?
L. Pomerantsev and O. Korosteleva
Department of Mathematics and Statistics
California State University, Long Beach
1250 Bellflower Blvd.
Long Beach, CA 90840-1001
lpomeran@csulb.edu okoroste@csulb.edu
Abstract
A large number of students' mistakes in algebra are due to their inability to see the
structure of a mathematical expression. This study analyzes and compares the typical
mistakes made by prospective elementary and middle school teachers as these students
progress through the courses at California State University at Long Beach. The study
shows that the students have difficulties recognizing structures of algebraic expressions
not only at the introductory level but also later as the students take calculus and senior
level courses.
The need for a thorough understanding of the structure of an algebraic expression when
performing mathematical operations has been recognized by a number of authors. Kirshner
(1989) suggests that "the ability to comprehend the syntactic structure of an algebraic expression
is fundamental to competent performance in algebra." In Yerushalmy (1992), one can find that
"the ability to transform involves mastering of algebraic rules as well as analyzing structures of
expressions."
Much research (Booth, 1989; Booth, 1999; Herscovics et al., 1995; Kieran, 1989; Kieran,
1999; Lodholz, 1999; Sfard, 1991; Sfard et al., 1994; Wagner et al., 1999b) shows that the
difficulties in recognizing the structure of mathematical expressions are due to the different
treatment of expressions in algebra and arithmetic. "In algebra, [students] are required to
recognize and use the structure that they have been able to avoid in arithmetic" (Kieran, 1989).
In arithmetic, mathematical expressions are treated from the operational point of view, as a
command to perform operations, whereas in algebra, mathematical expressions are treated from
the structural viewpoint, as an object of algebraic manipulation. "Abstract notions can be
approached in two fundamentally different ways: structurally as objects, & operationally – as
processes" (Sfard, 1991).
For instance, in arithmetic, the expression "3 + 4 " is a "sum" of two numbers perceived by
students as a command to perform addition of the two numbers (operational approach), while in
algebra, the "sum" is the "name" of the expression (the structural approach). Thus, students
should be aware of the importance of the treatment of mathematical expressions from both points
of view (operational and structural), "… certain mathematical notions should be regarded as fully
developed only if they can be conceived both operationally and structurally" (Sfard, 1991).
In mathematical textbooks, the operational meaning of the word "sum" is explained
precisely. However, the structural meaning of it is explained only for expressions involving a
L. Pomerantsev, O. Korosteleva : Do Prospective Elementary and Middle School Teachers…
single operation (for example, " x + y " is a sum). For expressions with more than one operation,
there is no explanation. Students are not being taught that, for instance, "2 • 3 + 5 " is a sum as
well.
According to Sfard (1991), the structural understanding of an abstract notion can be
automatically acquired through much operational practice. However, at this time, students do not
have enough operational practice with evaluating mathematical expressions because of the
intensive use of calculators. Possibly, this is one of the reasons that at the present time students
cannot "see" the structure of a mathematical expression, and have enormous difficulties with
understanding symbolic language.
If students are to be adequately prepared for algebra – to transition successfully from
arithmetic to algebra – they must have a foundation in elementary school that prepares them for
conceiving a given arithmetic expression as a mathematical object as well as an operational
process. It is anticipated that students who understand this concept in the elementary grades
would approach algebra more confidently and perform more successfully.
In order to teach successfully algebraic language and algebraic thinking processes to
beginners, teachers should have a full command of the subject themselves. If an elementary
school teacher does not understand the structure of an expression in depth, his or her ability to
communicate the concept to students is severely impaired.
The intent of the study is to test whether the structural representation of mathematical
expression is understood by pre-service elementary and middle school teachers.
Methodology
In the study conducted at California State University, Long Beach (CSULB) in the Spring
term, 2002, a diagnostic test was administered to 366 students. The test assessed the students'
understanding of the terminology related to the structure of mathematical expressions and the
syntax of algebraic language. The students were given one multiple-choice question and four
free-response questions. In addition, the students were asked to explain their answers. The
questions are as follows:
Question 1. What is the name of the expression 4 x 2 − 9 y 2 ?
Choices: (a) difference of squares, (b) difference of products, (c) square of difference.
2+ x
Question 2. If possible, cancel out the common factor in the expression .
2
2x + 2
Question 3. If possible, simplify the expression .
2x
Question 4. Use the statement "If x 2 = 25 , then x = ±5 " to solve the equation ( x + 1) 2 = 25 .
Question 5. Use the statement " If 2 x + 3 = 5 , then x = 1 " to solve the equation 2( y + 1) + 3 = 5.
The first question aimed at finding out whether the students understood the structure of the
expression. The choices (a) or (b), difference of squares or difference of products, were
considered the acceptable answers. In the second and third questions, students were supposed to
ac a
use the fundamental property of fractions = , b, c ≠ 0, to cancel the common factor in the
bc b
2
Issues in the Undergraduate Mathematics Preparation of School Teachers
numerator and the denominator. Acceptable answers for the second question were "impossible"
x x+1 1
and "1 + ." For the third question, " ," and "1+ " were regarded as correct. The last two
2 x x
questions dealt with students' ability to recognize a similarity in the structures of the equations
and their ability to use the given statement wisely. The "ideal" solutions in these cases were
" x + 1 = ±5 ⇒ x = 4 or − 6 ," and " y + 1 = 1 ⇒ y = 0, " respectively.
The experiment was held in eight different classrooms. The responses were then combined
into seven major groups according to the level of the courses the participants were taking. The
purpose of administering the test to the different groups was to investigate whether the students'
skills in performing simple algebraic manipulations improve as they take more mathematics
courses towards their degrees. The choice of these particular courses was motivated primarily by
the large sizes of the classes and the willingness of the instructors to conduct the testing. The
total sizes and the description of the groups are summarized as follows:
Table 1. Description and size of the participating groups of students
Group Name Description Size
1 Beginning MATH 001 Elementary 28
Algebra Algebra and Geometry
2 Intermediate MATH 010 Intermediate 70
Algebra Algebra
3 Introductory MTED 110 (Math Education) 47
Real Numbers The Real Number System for
Elementary and Middle
School Teachers
4 Finite Math MATH 114 Finite Math 57
5 (Pre)calculus MATH 117 Precalculus 57
MATH 122 Calculus I
6 Calculus MATH 123 Calculus II 35
7 Advanced Education MTED 402 Problem Solving 72
Course Applications in Mathematics
for Elementary and Middle
School Teachers
The Liberal Studies Program at CSU, Long Beach, offers an Integrated Teacher Education
Program (ITEP) that prepares K-8 multiple subject teachers. To fulfill the concentration in
mathematics requirement, students must take the following core courses: Probability and
Activities-Based Statistics (MTED 105), Real Numbers (MTED 110), Geometry and
Measurements (MTED 312), and Problem Solving Applications (MTED 402).
The Department of Mathematics and Statistics offers a B.S. in Mathematics degree with
Option in Mathematics Education. This option is for students preparing to teach mathematics at
the secondary school level. The math course sequence required for this degree includes Calculus
I,II and III (MATH 122, 124, and 224), Introduction to Linear Algebra (MATH 247), Number
Theory (MATH 341), College Geometry (MATH 355), Ordinary Differential Equations I
3
L. Pomerantsev, O. Korosteleva : Do Prospective Elementary and Middle School Teachers…
(MATH 364A), Probability Theory (MATH 380), Statistics (MATH 381), and Introduction to
Abstract Algebra (MATH 444).
An appropriate score on the Entry-Level Math (ELM) requirement is a prerequisite for MATH
001 and MATH 010. About 20% of the students in these courses are future K-8 elementary
teachers (Groups 1 and 2).
As mentioned in the above paragraph, MTED 110 and MTED 402 are the capstone courses for
the K-8 pre-service teachers, who entirely populate these courses (Groups 3 and 7). MTED 110
serves as a prerequisite for MTED 402. Three years of high school mathematics is required for
MTED 110.
MATH 114 is offered primarily to Business majors, so the percentage of math education students
taking this course is not more than 5% (Group 4).
Calculus courses are mandatory for students preparing to teach mathematics at the secondary
school level. However, the majority of students in MATH 117, 122, 123 are Engineering or
Computer Science majors. Only about 20% of the course body is comprised of math ed students
(Groups 5 and 6).
Results
Overall, the study reveals that students have a strong conceptual misunderstanding of the
structures underlying the mathematical symbols. The table below gives the percentages of
students who answered the questions correctly in each of the seven groups.
Table 2. Percentages of correct responses
Question
Group 1 2 3 4 5
1 78.5%* 25.0% 0% 0% 14.30%
2 92.9% 28.6% 10.0% 2.9% 5.7%
3 95.8% 44.7% 29.8% 10.7% 21.3%
4 91.2% 63.1% 42.1% 29.8% 33.3%
5 94.8% 75.4% 36.8% 26.3%* 26.3%
6 97.2% 82.9% 71.4%* 42.9%** 34.3%
7 87.5% 44.4% 22.2% 5.6% 18.1%
* ** Percentages differ significantly from the other percentages in the same column (according to Duncan's multiple range test
with type I error a=0.1).
As shown in Table 2, the students performed uniformly poorly regardless of the question and
the group they belonged to.
Next, we will consider each question separately, analyzing the answers the students gave and
the types of mistakes they made.
Question 1 was a multiple-choice question, so the possible mistakes were picking (c), square of
difference, or failing to answer. The summary of the percentages of mistakes made is given in
4
Issues in the Undergraduate Mathematics Preparation of School Teachers
the table below. For comparison, the table also contains the percentages of correct answers (in
boldface).
Table 3. Percentages of mistakes made in answering Question 1
Answers
Groups (a) (b) (c) left blank
1 57.1%* 21.4% 17.9%* 3.5%
2 80.0% 12.9% 2.9% 4.2%
3 76.6% 19.2% 2.1% 2.1%
4 77.2% 14.0% 5.3% 3.5%
5 79.0% 15.8% 5.3% 0%
6 82.9% 14.3% 0% 2.8%
7 50.0%* 37.5% 5.6% 6.9%
* See the footnote after Table 2
As seen from the table, the majority of students in each group chose the difference of squares
as the name of the expression "4 x 2 − 9 y 2 ." One might think that the reason for this choice is
that the students noticed that 4x 2 and 9 y 2 are equal to ( 2 x ) 2 and ( 3 y ) 2 , respectively.
Therefore, as one might think, the students have skipped one step in their heads and come up
with difference of squares. Indeed, some of them did. They wrote that they picked the difference
the
of squares because " square root of 4 is 2 and the square root of 9 is 3" (Group 4, Finite
Math), or "both squares can be ( ) as well as their numbers" (Group 4), or "it is a subtraction
of two perfect squares" (Group 5, Precalculus). On the other hand, there were explanations of the
following type "both variables, x and y , are squared" (Group 1, Beginning Algebra, and Group
4), or "they both have squares and a subtraction sign" (Group 2, Intermediate Algebra), or "it is
x 2 − y 2 , just has coefficients" (Group 5). The message is clear here: the students see only the
squares of x and y , and ignore the fact that they are multiplied by coefficients. There w ere
other types of responses that showed that students are unfamiliar with the notion of the structure
of an expression. For instance, they circled the difference of squares because "it is two different
variables" (Group 5), or "I have always heard that terminology" (Group 6, Calculus), or "it is the
only phrase I have heard of " (Group 6), or "don't know why just sounds right" (Group 6).
Moreover, not all the students chose the correct answer because they understood the structures of
expressions well, but because "they have the same square and the products are different" (Group
2), or "they are two different variables" (Group 5). The person who selected the difference of
products as the answer, explained "it can't be the difference of two squares because x and y are
not the same number and therefore cannot be subtracted from each other while written in this
form" (Group 7, Advanced Education Course).
Students' mistakes on Question 2 can be divided into four categories: (1) Cancelled the twos
/
2+ x 2+ x
to get x or 1 + x or x / 2 ; (2) Made an equation = 0 and solved it getting x = −2 ;
/
2 2
2
(3) Multiplied by but ended up multiplying by 2 only the numerator obtaining 4 + 2 x
2
5
L. Pomerantsev, O. Korosteleva : Do Prospective Elementary and Middle School Teachers…
(or, erroneously, x + 4 or 2 + x or 2( x + 1) ); (4) Didn't attempt to do the problem or got unusual
x+1
answers like or 1 or 3/2, etc. Notice that the mistakes indicate a poor knowledge of the
x
structure of an algebraic expression and a poor command of the algebraic rules. Table 4 presents
the percentages of responses in the four categories (along with the percentage of the correct
responses).
Table 4. Percentages of mistakes made in answering Question 2
Categories of Mistakes
Group (1) (2) (3) (4) correct
1 71.4%* 0% 0% 3.6% 25.0%
2 54.3% 1.4% 1.4% 14.3%* 28.6%
3 38.3% 6.4% 10.6% 0% 44.7%
4 26.3% 0% 5.3% 5.3% 63.1%
5 15.8% 0% 3.5% 5.3% 75.4%
6 8.6% 2.9% 2.8% 2.8% 82.9%
7 41.7% 4.2% 4.2% 5.5% 44.4%
* See the footnote after Table 2
From the table is it apparent that an overwhelming majority of students in all the groups have
made a mistake in category (1) that shows their conceptual misunderstanding of the structural
form of the expression. The students in Group 1, Beginning Algebra, had the most trouble with
the question. This group had the lowest percentage who got the question right, and the largest
percentage who made a mistake in category (1). However, a high percentage (82.9%) of the
students in the Calculus group, Group 6, answered the problem correctly and only 8.6% made a
mistake in category (1). This indicates that more practice in higher level mathematics brings
understanding of algebraic language.
Some of the students who wrote the correct answer "impossible" also wrote correct
explanations like "no common factors" (Group 5, Precalculus) or "2 is not a common factor of
the numerator" (Group 5) or "the 2 does not factor in ( 2 + x) " (Group 5), or "it is already
simplified to the lowest terms" (Group 2, Intermediate Algebra). Some explanations, however,
were wrong and made it plain that students have difficulties with symbolic language. For
instance, some chose the correct answer "impossible" because "you don't know what x is"
(Group 2, and Group 7, Advanced Education Course), or "the solution to the problem is not
2+ x
defined (ex., = ? )" (Group 7).
x
Question 3, even though, seemingly analogous to Question 2, turned out to be
insurmountably difficult for some of the participants. Typical mistakes can be classified as
6
Issues in the Undergraduate Mathematics Preparation of School Teachers
2 2x
(1) Cancelled 2 x 's or 2's to obtain 2 or 3 or
or ; (2) Said "impossible"; (3) Left blank; or
2x 2
(4) Wrote incomprehensible answers (totaling 28 varieties). The percentages of each type of
mistakes are summed up below.
Table 5. Percentages of mistakes made in answering Question 3
Categories of Mistakes
Group (1) (2) (3) (4) correct
1 60.7%* 25.0%* 0% 14.3% 0%
2 58.6%* 2.9% 7.1% 21.4%* 10.0%
3 31.9% 2.1% 4.3% 31.9% 29.8%
4 24.6% 8.8% 3.5% 21.0% 42.1%
5 21.1% 14.0% 8.8% 19.3% 36.8%
6 5.7%** 0% 2.9% 20.0% 71.4%*
7 38.9% 11.1% 5.6% 22.2% 22.2%
* ** See the footnote after Table 2
The poorest performance was observed in Group 1, Beginning Algebra (none of the students
answered the question correctly, and 60.7% used the cancellation rule improperly), while the
students in the Calculus course (Group 6) did the best on this question. A significantly higher
percentage (71.4%) of the Calculus students came up with the right answer and only 5.7% of
them cancelled improperly.
As for Question 4, there were three kinds of typical mistakes: (1) Plugged x = ±5 into the
equation ( x + 1) 2 = 25 to get contradictions 36=25 and 16=25; (2) Tried to solve the quadratic
equation ignoring the given statement (sad to say, only two students managed to get the correct
answer this way); (3) did not do the problem or wrote "impossible" or something else. The
results are given below.
Table 6. Percentages of mistakes made in answering Question 4
Categories of Mistakes
Group (1) (2) (3) correct
1 32.1% 35.7% 32.2% 0%
2 34.3% 22.8% 40.0% 2.9%
3 31.9% 46.8% 10.6% 10.7%
4 21.1% 35.1% 14.0% 29.8%
5 17.5% 42.1% 14.1% 26.3%
6 11.4% 37.1% 8.6% 42.9%
7 26.4% 43.0% 25.0% 5.6%
Notice that none of the learners in Group 1, Beginning Algebra, did the problem correctly,
while the Calculus students, Group 6, got the highest percentage of correct answers (42.9%). A
7
L. Pomerantsev, O. Korosteleva : Do Prospective Elementary and Middle School Teachers…
large proportion of students in all the groups have committed the mistake of the first type, which
shows their understanding of the need to use the symbolic pattern but a misunderstanding of the
structure of the equation. Instructive was the reasoning behind the answers. For example, as an
explanation for why it was impossible, in his opinion, to solve the problem at hand, one of the
students in Group 7, Advanced Education Course, wrote "This is impossible to solve. If
x 2 = 25 , then ( x + 1) 2 = 25 is not solvable because no matter what x equals, positive or
negative, then if you add one to it and square it, it would not equal 25." This stresses once again
the students' lack of understanding when they are dealing with symbolic language.
Question 5 was easier for the participants but some of them were taken aback by the fact that
two different variables, x and y , were used. They explained "Can't solve because no x in
equation." (Group 3, Finite Math) or "I'm confused because the variable was changed from x to
y." ( Group 2, Intermediate Algebra). When working on this question, the students either
(1) Ignored the given statement and solved the equation in y directly; or (2) Left the space blank
or wrote something incoherent. The results are below.
Table 7. Percentages of mistakes made in answering Question 5
Categories of Mistakes
Group (1) (2) correct
1 32.1%* 53.6%* 14.3%
2 57.1% 37.2%** 5.7%
3 61.7% 17.0% 21.3%
4 52.6% 14.1% 33.3%
5 54.4% 19.3% 26.3%
6 57.1% 8.6% 34.3%
7 59.7% 22.2% 18.1%
* ** See the footnote after Table 2
A really low percentage of correct answers was observed in Groups 1 and 2 (Beginning and
Intermediate Algebra) (14.3% and 5.7%). The most mathematically advanced Calculus Group
(Group 6) did better (34.3%), even though the differences are not statistically significant.
Notably, the students in Group 1 have made the smallest proportion of mistakes of the first type
(trying to solve the equation in y ), and the largest proportion of untypical errors.
Discussion
The conducted study has shown that college students perform unsatisfactorily in the
manipulation of algebraic expressions. The questions on the test dealt with recognizing the
structure of an algebraic expression (Questions 1, 4 and 5), and applying rules for cancellation of
a common factor (Questions 2 and 3). The problem of conceptual misunderstanding of both
topics is most severe at the novices' level and is still substantial in Calculus classes. From Table
2, the poorest performance is shown by Groups 1 and 2, which is not surprising since these
students have failed the ELM. The future K-8 multiple subject teachers (Groups 3 and 7) did
8
Issues in the Undergraduate Mathematics Preparation of School Teachers
show slightly better results but not significantly better. Group 4 (predominantly Business majors)
gave noticeably more correct responses than the previously-considered groups. Finally, for the
pre-calculus and calculus students (Groups 5 and 6), the percentage of correct answers was the
highest but still quite low. Consequently, if students are not taught algebraic structures and the
language of algebra properly in elementary courses, the non-understanding will persevere
throughout their studies and later in their careers.
Researchers recognize the need of a powerful method to teach the subject to elementary
school teachers (Carpenter et al. 2000; CBMS, 2001; Kaput, 1995; Wagner et al, 1999a; Kieran,
1999). Unfortunately, researchers agree, no such method exists yet. As Kieran (1999) points out,
"… it is not obvious how the use of symbol manipulators in the early stages of learning algebra
can help students develop a structural conception of algebraic expressions. This is the question
for future research." The current study once again underscores the need for this research.
References
Booth, L. (1989). A question of structure. In S. Wagner & C. Kieran (Eds.), Research Issues in
the Learning and Teaching of Algebra (pp. 57-59). Reston, VA: National Council of Teachers of
Mathematics; Hillsdale, NJ: Lawrence Erlbaum.
Booth, L. (1999). Children's difficulties in beginning algebra. In B. Moses (Ed.), Algebraic
Thinking, Grades K-12 (pp. 299-307). Reston, VA: National Council of Teachers of
Mathematics.
Carpenter, T., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary
grades. Research report 00-2, University of Wisconsin-Madison, Madison, WI: National Center
for Improving Student Learning and Achievement in Mathematics and Science.
Conference Board of the Mathematical Sciences. (2001). The mathematical education of
teachers. Issues in mathematics education, v. 11. AMS, Providence, RI: CBMS.
Herscovic, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra.
Educational Studies in Mathematics, 27, 59-78.
Kaput, J. (1995). Transforming algebra from and engine of inequity to an engine of mathematical
power by "algebrafying" the K-12 curriculum. 73rd annual meeting of the National Council of
Teachers of Mathematics, Boston, MA.
Kieran, C. (1989). The early learning of algebra: a structural perspective. In S. Wagner & C.
Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra} (pp. 33-56). Reston,
VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.
Kieran, C. (1999). The learning and teaching of school algebra. In B. Moses (Ed.), Algebraic
Thinking, Grades K-12 (pp. 341-361). Reston, VA: National Council of Teachers of
Mathematics.
9
L. Pomerantsev, O. Korosteleva : Do Prospective Elementary and Middle School Teachers…
Krishner, D. (1989). The visual syntax of algebra. Journal for Research in Mathematics
Education, 20, 274-287.
Lodholz, R. (1999). The transition from arithmetic to algebra. In B. Moses (Ed.), Algebraic
Thinking, Grades K-12 (pp. 52-58). Reston, VA: National Council of Teachers of Mathematics.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and
objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification -- the case of algebra.
Educational Studies in Mathematics}, 26, 191-228.
Wagner, S., & Kieran, C. (1999a). An agenda for research on the learning and teaching of
algebra. In B. Moses (Ed.), Algebraic Thinking, Grades K-12 (pp. 362-372). Reston, VA:
National Council of Teachers of Mathematics.
Wagner, S., & Parker, S. (1999b). Advancing algebra. In B. Moses (Ed.), Algebraic Thinking,
Grades K-12 (pp. 328-340). Reston, VA: National Council of Teachers of Mathematics.
Yerushalmy, M. (1992). Syntactic manipulations and semantic interpretations in algebra: the
effect of graphic representation. Learning and Instruction, 2, 303-319 |
Synopsis
This workbook provides exam-style practice questions to test understanding of all the essential topics and provide invaluable exam preparation. All question types are covered including application of number and problem-solving skills. Answers are provided along with useful examiner tips. * Written by Trevor Senior, a senior examiner with a major awarding body * GCSE-style questions for invaluable exam practice * Topic-by-topic practice to support revision * Weighted coverage of all the assessment objectives to reflect the actual exam * Increasingly challenging questions to encourage progression within each topic * Pull-out answers with helpful hints |
We've made it through the trenches of Algebra. We've learned the ins and outs of variables, functions, and all of those rules. (So many rules.)
Now it's time to solve some of the great mysteries of life. What is the natural number, and why is it so friendly with logs? What is The Matrix? Are we inside it right now? To answer these questions, we need to learn more rules. (Yes, more rules.)
Why Should I Care?
Algebra II is another stepping stone to holding all of the math power. Not only will we be able to solve for x, we'll be able to solve for x when it's in messy equations involving x2. Better yet, once you've mastered Algebra II, we will have what it takes to handle many questions that the real world might throw at us. We'll be able to better understand concepts such as exponential growth. Ever wonder how fast bacteria really grow? It's exponential.
It will also add more to our arsenal in order to work through any problem we'll encounter in Precalculus, Calculus, and beyond. |
Topics in Group Theory
9781852332358
ISBN:
1852332352
Pub Date: 2000 Publisher: Springer
Summary: The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed to support a reader engaged in a first serious group theory course, or a mathematically mature reader approaching the subject for the first time, this book reviews the essentials. It recaps the basic definitions and results, up to and including Lagrange's Theorem, and then continues to explore topics such as the is...omorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" takes the basic theory and plays with it to obtain an assortment of results that will show a little of what can be done with the theoretical machinery. Adopting the slightly irreverent tone of Geoff Smith's previous book, Introductory Mathematics: Algebra and Analysis, this book is a key reference that will both stimulate and entertain its readers.
Smith, Geoff is the author of Topics in Group Theory, published 2000 under ISBN 9781852332358 and 1852332352. Six hundred forty Topics in Group Theory textbooks are available for sale on ValoreBooks.com, one hundred four used from the cheapest price of $32.93, or buy new starting at $35.97.[read more]
This item is printed on demand. The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject fo [more]
This item is printed on demand. The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic defi.[less] |
The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas.
Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..
For more information about the title Schaum's Outline of Calculus (Fourth Edition), read the full description at Amazon.com, or see the following related books: |
TTA is a full-year algebra support curriculum, forthcoming from Heinemann in 2014, designed to:
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raise the competence and confidence of students who may benefit from supports for algebra success.
TTA is designed to build students' algebraic habits of mind, key mathematical ways of thinking aligned with the Common Core Standards for Mathematical Practice. Students explore algebraic logic puzzles that connect to and extend algebra course topics and learn broadly-applicable tools and strategies to help them make sense of what they are learning in algebra. Students discuss and refine their ideas as they work through mental mathematics activities, written puzzles, spoken dialogues, and hands-on explorations that engage them in cultivating mathematical knowledge, intuition, and skills.
Looking for our field test materials? We want to keep track of who's using our materials so we can solicit your feedback for research. Please fill our brief inquiry survey for access to the materials. |
Algebra and Trigonometry - 2nd edition
Summary: Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors commun...show moreicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics're happy with your experience, we'd love for you to leave positive feedback with a 5 star rating. If you aren't satisfied for any reason please contact us immediately so we can make it right.Leave us positive feedback by clicking "Your Account" in the top right corner of Amazon.com. After signing in, select "Your Orders" & click "Leave Seller Feedback" next to the item you purchased. 6w926 ...show less
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2009-02-24 Hardcover Very Good Very minor wear, a clean copy with a tight binding. Textbook only |
extension of the quadratic function lesson plan: (Thislessonwill" target="_blank" allow the students to learn about the a, b, and c values of a quadratic function in standard form. They will be quizzed on their...
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Thislessonwill allow the students to learn about the a, b, and c values of a quadratic function in standard form. They will be quizzed on their learning and need to pass the mini quizzes in order to proceed to the next lesson.
After mastering quadratics in standard form, they will be led into beginning the quadratic formula. This is a nice introduction of quadratic formula, teaching them a song to remember the formula and then showing an example of how to apply the quadratic formula. This will lead them into a question on quadratic formula to test their knowledge and application.
**Please note: In the Detail page of the screencast, you will need to download the powerpoint**
Discussion for Quadratic Function-Stand Alone Instructional Resource
Seema Goghar
(Teacher (K-12))
This resource is clear and easy to navigate through. Being able to use and understand the quadratic formula is also an essential aspect of the Algebra 1 curriculum. In terms of the UDL principles, the content was represented using the author's "voice" and the embedded video. To make this StAIR even more effective, graphing the quadratic function with an emphasis on how the a, b, and c is connected to the function, and/or what the solution of the quadratic formula means, can add a different way of representing, expressing, and engaging students. Similarly, adding a real life connection will also enhance the level of motivation, engagement, and involvement of students. Another suggestion is to add some form of "timing" restrictions to each of the navigational button in order to enfore students to complete all the "work" on a slide before moving on to the next. Overall, this resource can be used as a learning as well as a reinforcement tool.
Technical Remarks:
One broken link.
Time spent reviewing site:
One hour
1 year ago
Chris Groenhout
(Teacher (K-12))
Strengths
The presentation was designed will to provide information and check for understanding. The UDL was satisfied bu including voice desriptions along with pictoral descriptions
The instrictional stategy on demonstrating the content and scafolding were evident. The ShowMe presentation was well done. Good use of technology to demonstrate the concept.
Weaknesses
Incorportaing a "Real World" application would give the user a better contextual mind set while learning this concept.
Technical Remarks:
Audio comes out a little chopy and was distracting.
Several broken links.
Embedding the ShowMe into the power point would streamline this lesson. |
Our users:
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Thank you for the responses. You actually make learning Algebra sort of fun. James Mathew, CA
Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them? |
Computational Discrete Mathematics: Combinatorics and Graph Theory
with Mathematica
is the definitive guide to Combinatorica,
perhaps the most widely used software for teaching and
research in discrete mathematics.
The Combinatorica user community ranges from students to engineers to
researchers in mathematics, computer science, physics,
economics, and the humanities.
Combinatorica has received the
EDUCOM Higher Education Software Award
and been employed in teaching from grade school to graduate levels.
Combinatorica is included with every copy of the popular computer algebra
system Mathematica.
Experimenting with Combinatorica provides an exciting new way to
learn combinatorics and graph theory.
This book provides examples of all 450 Combinatiorica functions in action,
along with the associated mathematical and algorithmic theory.
The book contains
no formal proofs, but enough discussion to
understand and appreciate all the algorithms and theorems
contained within.
We cover classical and advanced topics on the most important combinatorial
objects: permutations, subsets, partitions, and Young tableaux.
We also cover all important areas of graph theory:
graph construction operations, invariants, and embeddings as
well as algorithmic graph theory.
This book can also serve as a unique textbook with
enough material to teach or supplement full-semester,
experimentally-enhanced courses in combinatorics and graph theory
using Mathematica.
Three interesting classes of exercises are provided -- theorem/proof,
programming exercises, and experimental explorations, providing great
flexibility in teaching and learning the material.
The newest version of Combinatorica offers substantially improved efficiency and
graphics.
Thanks to our new sparse-graph representation,
is now possible to do interesting operations on graphs with thousands or even hundreds of
thousands of vertices.
Additional functionality in terms of new graph invariants and computations
have also been provided.
The new Combinatorica is distributed with Mathematica starting
with MMa version 4.2, but runs on older versions of MMa as well.
The latest Combinatorica is available
for download
as the file NewCombinatorica.m.
Let us know of your
experiences.
A short list of known
bugs is
available.
Mathematica now includes second graph drawing package
DiscreteMath`GraphPlot`, which works with
Combinatorica graphs.
It also includes a few other graph algorithms, the functionality of which
largely appears within Combinatorica as well.
Jason Alexander has produced an interesting
LocalInteractions
package
for experimenting with local interaction models of
evolutionary games
on top of the graph drawing and editing routines of Combinatorica.
Gabriel Valiente has built an interesting package
for graph grammars
on top of Combinatorica.
John Lattanzio developed
a graph
coloring heuristic which gives
better colorings than the Brelaz function in Combinatorica.
Local
and
WRI
copies of this page are also available.
The MuPAD-Combinat project has developed
an open-source algebraic
combinatorics package for the computer algebra system MuPAD, which will be of interest to those
focusing on algebraic
combinatorics.
The original version of Combinatorica was included with Mathematica
versions 1.1 through 4.1 in the Packages/DiscreteMath directory.
The on-line documentation for the original
Combinatorica covers
only a subset of these functions, which was
best described in
Steven Skiena's book:
Implementing Discrete Mathematics: Combinatorics and Graph Theory
with Mathematica,
Advanced Book Division, Addison-Wesley, Redwood City CA, June 1990.
ISBN number 0-201-50943-1.
Japanese translation published by Toppan, Tokyo, July 1992.
This book is now out of print, but might still be
ordered
on-line.
The author still has a very small supply of
copies which he may be induced to part with.
A Java-based
graph editor
for the old Combinatorica has been produced by Miguel Revilla.
Look this page up in
Google to enable translation from Spanish.
The latest release of the package, data
bases of interesting graphs, and additional files which may be of interest are available
by anonymous FTP from ftp.cs.sunysb.edu.
Animations produced using Combinatorica by Joan Trias are
also available. |
Book DescriptionEditorial ReviewsMore About the Author
James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart's books include a series of high school textbooks as well as a best-selling series of calculus textbooks. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those in Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, and Indonesian.
A talented violinst, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. Having explored connections between music and mathematics, Stewart has given more than 20 talks worldwide on Mathematics and Music and is planning to write a book that attempts to explain why mathematicians tend to be musical.
Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.
I used this textbook in a Calculus 3 course, so my primary experience is with chapters 12-16, but I did find myself referencing chapters 3, 4, 7, and 10 extensively to refresh my memory (and to learn some things I hadn't learned in high school BC Calculus).
The exposition is, for lack of a better word, "meh". It relies mostly on giving a few definitions, working through a few simple examples, then throwing hordes of problems at the reader. Now, this is perfectly fine for a lower division mathematics textbook -- such a process builds mathematical maturity (at least for me it did), but I would've liked the text, if anything, to rely *less* on showing by example and more on providing mathematical motivation for the given topics (the "big picture" of what we're trying to do, so to speak, rather than a few examples of technical details). The text's quality in this regard also has a fairly steep downward slope as the book progresses -- the text was readable and informative for, perhaps, the first 11 chapters, but from chapters 12-16 it's just really hard to learn from it on your own (and believe me, when you miss class, you have to do that).
Now, to the good part of the book (and the reason why the book gets a good 4 star rating rather than a 2 star one): problems! This book is filled to the brim with tons of exercises that range from routine to fairly difficult (and a special "problems plus" section, outside of the main exercise sets, that range from difficult to nightmarishly difficult). DO YOUR HOMEWORK! Seriously, if you are taking a course with this book, then you owe it to yourself to do the problems that are assigned at the *very least*. They are, for the most part, interesting and will help you build your mathematical ability and, more importantly, understand the material. Do extra problems, think about them, understand what you're doing instead of simply looking for the right thing to plug into. Believe me, it's worth it.
So the final verdict? The text isn't very well written and the examples are pretty poorly chosen (this especially applies to the last 1/3 of the book), but the problem sets are wonderful.
I am a college Calculus instructor, and I find this book terrible for many reasons. For students looking for a solid but much more inviting introduction to Calculus, I highly recommend Larson's book over Stewart's.
Here is a point-by-point breakdown of the faults I find in Stewart's text:
Clarity of Explanation and Content Level
Stewart's explanations are often verbose, unclear, and written at a level too high for the average Calculus student. Several of my students have told me reading the book only confused them and did not clarify the concepts. An introductory text should offer simpler, clearer, and more concise explanations more appropriate to the typical Calculus student.
Presentation
In this day and age, students expect visually engaging presentations that will hold their attention. Stewart's presentations are drab and uninteresting. His book is everywhere packed with dense plain text and formulas, giving the impression that Calculus is hard, dull, and very complex, further intimidating students who are already scared of the subject. Students are much more likely to carefully read a text that is visually appealing and makes Calculus seem interesting and less intimidating. This will also help reduce their anxiety over what many already consider a very difficult course.
Readability
Another important aspect of presentation is layout and readability. Here Stewart's text is again dismal: His pages are overstuffed with text and graphics throughout the book, making it difficult to reference a theorem, particular type of example, etc. It is hard to see where one example or proof ends and another begins. The average student is not going to read the entire contents of a section in full detail, but will rather reference the topics s/he is having trouble with, in order to get the details on a theorem or to find an example problem to help with a homework exercise. This is very difficult to do in Stewart's text due to the crowded and confusing layout.
Homework Exercises
Stewart's text is again particularly poor in terms of his homework sets in that he tends to offer a few low-level problems and then suddenly jump into extraordinarily difficult problems with no warning or transition. Stewart also tends to couch exceedingly difficult problems between a series of relatively straightforward ones, again without warning, which is very frustrating for students who find themselves struggling over what they think is an easy problem.
All in all, I strongly advise against this text, and would urge other Calculus instructors and mathematics departments to choose another Calculus book for their classes.Read more ›
I bought this book believing it'd be pretty much the same as the normal book. However, it wasn't. The material is exactly the same, but it only contains the lesson and examples, but not the homework or practice exercises. It came with the webassign code, but unless you're actually in a hybrid class, you'll find it really difficult to access those practice exercises. I attempted to just look at the ebook, but you need to register and to do that you need a teacher class code or something. I didn't like that the cover was paperback, and it was easily damaged.
If you're looking and need a hybrid book, then it's perfect for you. But if you're looking for a cheaper alternative and thought hybrid would suffice, I'd recommend you spend those extra bucks and get the real thing.
I attend UNLV and when I took Calc I, II and III a few years ago, this is the book we used. Its coverage for 1st semester calc up to the beginning of integrals is decent. However, they needlessly complicate some of the more advanced integration techniques for 2nd semester calc. I found it difficult material to get through without falling asleep, and I love math.
Its biggest weakness is in vector calculus. The coverage is sparse and lacking at times, and overly detailed in others. For instance, surface and volume integration were very important to me as an engineering student, but there just weren't enough examples and no "weird" geometries at all. Then, their coverage of planes, which for me is not all that important, was tremendously detailed.
You probably don't have much of a choice if you're using this book for a course, but if you're planning on taking courses like electromagnetics, I'd recommend supplementing the vector calc portion with an E&M book. |
Teaching High School Mathematics; First Course; Solving Equations: Informal Approach
Description:
Mathematician Max Beberman discusses the process of helping pupils to find solution set sentences and solve equations with a class from the Mathematics Institute. He suggests they make a game of finding solutions to open sentences so that students may understand the process of solving equations. Teaching students to use the natural discovery process to solve equation sequences is the reason Max Beberman created this film course. Mathematician Eleanor McCoy demonstrates Beberman's method when she leads a class in solving equations. Black and white picture with sound. Eastman Kodak edge code reads "circle triangle," which correlates to 1963. |
More About
This Textbook
Overview
The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.
Related Subjects
Meet the Author
Dr. Susanne Schmitt works at the Max Planck Institute for Computer Sciences at Saarbrücken, Germany. Horst-Günter Zimmer is Professor at the Mathematics Department of the University of the Saarland at Saarbrücken, |
Course in Mathematical Modeling - 99 edition
Summary: The emphasis of this book lies on the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. No advanced knowledge i...show mores assumed of the reader, making this book suitable for elementary modeling courses. The book can also be used to supplement courses in linear algebra, differential equations, probability theory and statistics4212 +$3.99 s/h
VeryGood
Oak Creek Books WV Mineral Wells, WV
1999-03-01 Paperback Very Good Nice cleanpaperback. Text unmarked, binding tight. APO/FPO orders welcomed! Real World pricing and out of this world service! Orders processed every day! Thanks for s...show morehopping with us on Alibris! ...show less
Brand new. We distribute directly for the publisher. A Course in Mathematical Modeling is intended as a text for a modeling course accessible to students who have mastered a one year course in calcul...show moreus. Mooney and Swift's approach to modeling is presented balancing theoretical versus empirical models, analytic models versus simulation, deterministic versus stochastic models, and discrete versus continuous models. Most examples are drawn from real world data or from models that have been used in various applied fields. The use of computers in both simulation and analysis is an integral part of the presentation.The authors emphasize teaching modeling as opposed to presenting models, beginning their book with the simple discrete exponential growth model as a building block, and successively refining it. This refinement includes adding variable growth rates and multiple variables, fitting growth rates to data, including random elements, testing goodness of fit, using computer simulations, and moving to a continuous setting.Students taking a course based on this book should have some mathematical maturity, but will need little advanced knowledge. The book presents more advanced topics on an as needed basis and serves to show how the different topics of undergraduate mathematics can be used together to solve problems. This perspective is valuable as either a road map for the beginning student or as a capstone for the more advanced students. The course presents elements of discrete dynamical systems, basic probability theory, differential equations, matrix algebra, stochastic processes, curve fitting, statistical testing, and regression analysis. Computer analysis is extensively used in conjunction with these topics. ...show less
$55.00 +$3.99 s/h
LikeNew
Chamblin Bookmine Jacksonville, FL
N/A N/A 1999 Soft Cover First Edition Fine 4to-over 9?"-12" tall.
$55 |
What math course is it?
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I always thought calc was easier than trig, as long as you understand trig, calc has a lot of shortcuts you can take (as long as you can understand the long way around). I just think it looks a whole lot more intimidating than it is.
I remember when I took numbers theory and combinatorics, the concepts required you to really let go of a lot of preconceived thoughts you had about numbers (which was the hard part) but at their core, they really weren't all that hard...people just look at you funny when you study because you talk to yourself a lot :-D
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...Show more appreciation of mathematics through their college careers and beyond. Blitzer's goal is to show students how mathematics can be applied to their lives in interesting, enjoyable, and meaningful ways. His accessible writing style helps students relate to and grasp the material Thinking Mathematically
Blitzer starts off with Inductive and Deductive reasoning and builds from there. Other chapters include Logic, Number Representation, Number Theory, Measurement , Geometry, Counting Methods, Probability Theory, Statistics, and ending with Mathematical Systems. Well written, easy to understand, using |
Welcome to Maths
Here, you'll find everything in one place – from our latest new KS3 Maths course to our exciting learner focussed ActiveLearn, the popular Revise series for Edexcel and AQA or our Edexcel Awards workbooks, to popular favourites likeEdexcel GCSE Mathematics and Edexcel AS And A Level Mathematics. |
More About
This Textbook
Overview
The abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
The book goes on to provide a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length. Other features include:
end-of-chapter summaries and numerous exercises to reinforce what has been learnt;
extensive cross-referencing to help the reader follow arguments;
a Cumulative Reference Chart, showing the dependencies throughout the book on a section-by-section basis as an aid to course design.
The book is designed for third- and fourth-year undergraduates and beginning graduates. Readers should have some practical knowledge of differential and integral calculus and have completed a first course in real analysis. With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications.
Editorial Reviews
From the Publisher
From the reviews:
"This book is truly about metric spaces. … The book is packed full of material which does not often appear in comparable books. … His use of questions to increase understanding and to move on to the next topic are also to be appreciated. … this is a great book and suitable … for third-and fourth-year under-graduates and beginning graduate students." (Marion Cohen, MathDL, January, 2007)
"The book is very readable. It includes appendixes on the necessary mathematical logic and set theory, and has a substantial number of exercises… Every concept is demonstrated via a large number of examples, starting with commonplace ones and expanding the reader's horizon with the more abstruse ones, to give a sense of the scope of the concepts… A useful addition to any library supporting an undergraduate mathematics major." (D. Z. Spicer, CHOICE, March |
Having trouble doing your Math homework? This program can help you master basic skills like reducing, factorising, simplifying and solving equations. A step by step explanation of problems concerning fractions,binomials, trinomials etc.
Having trouble doing your Math homework? This program can help you master basic skills like reducing, factorising, simplifying and solving equations. Step by step explanations teach you how to solve problems concerning fractions,binomials, trinomials etc. Each type of problem has three levels to help you to start with easy problems and slowly building up your skills. Algebra has three different functionalities: you start learning each type of problem by seeing the program solve it step by step. If you start to feel confident you can test yourself by using the "My answer" setting. Algebra will compare your answer to its own. The latest release has extended testing facilities and user administration. AlgebraNet can be used to teach and test Algebra at school.AlgebraNet Match at Super Shareware |
Book DescriptionThe Yaglom geometric transformation books are aimed at a mathematical Olympiad audience. The books are not primarily about transformations, they are mainly about how to use transformations to solve problems. Yaglom wrote the book in Russian back in the fifties, presenting geometrical transformations techniques to geometric problem solving. He introduces transformation types and then shows how they can be used to solve problems that otherwise would sometimes be almost unsolvable using elementary (synthetic) methods. Then he presents a set of problems that vary from difficult to fiendish. Full solutions are provided, you will need them. The Russian book has chapters on congruence, similarity and projective transformations that are contained in the three English translations published by the MAA. It continues with sections on inversion transformations that are not (yet?) translated into English.
This is the third of three books, it presents projective transformations and how to use them to solve geometric problems in the euclidean domain. Although dealing with projective transformations it is definitely not a book on projective geometry. It does contain a section on non euclidean geometry but that deals mainly with hyperbolic geometry. |
Algebra and Trigonometry
Description
Beecher, Penna, and Bittinger's Algebra and Trigonometry is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively.
Mid-chapter Mixed Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Guide summaries provide built-in tools to help them prepare for tests. MyMathLab has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Mixed Review exercises from the text, as well as example-based videos created by the authors.
Features
Functions appear early and integrated, reflecting the authors' belief that functions are best taught as a theme of the course, not as an isolated topic.
Functions are introduced in Chapter 1, so that students to start the course with a new topic rather than a review of equation-solving that was covered in previous math courses.
Students will come to understand the concept of a function by being exposed repeatedly to thelanguage, notation, and use of functions throughout the text.
The authors take a visual approach to the course. The early introduction to functions allows for the use of graphs to provide a visual aspect to solving equations and inequalities. In addition, specific features enable students to "see the math" and make connections between concepts.
Algebraic/Graphical Side-by-Side Examples present the solutions in a two-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.
Visualizing the Graph exercises help develop students' ability to make the mental link between different types of equations and their corresponding graphs.
Connecting the Concepts, a hallmark feature of the text, invites the student to stop and check their understanding of how concepts work together in one section or several sections. Concepts are summarized visually-using graphs, outlines, or charts-so that students deepen their understanding and make connections.
Ongoing review features throughout the text reinforce the concepts and help students build understanding.
NEW! Mid-chapter Review exercises are one-page mixed review sets at logical breaks in the chapter, helping students to reinforce their understanding of the concepts. These exercises are assignable in MyMathLab.
NEW! Study Summaries have been added to the Chapter Review, giving students a built-in study aid when reviewing and preparing for tests. In MyMathLab, these Study Summaries are accompanied by new videos to reinforce the key concepts and ideas.
Enhanced! Vocabulary Review exercises appear in the last section of each chapter, and check students' understanding of the language of mathematics. These are now assignable in MyMathLab and can serve as reading quizzes.
Enhanced! Synthesis exercises, included at the end of each exercise set, encourage critical thinking by asking students to apply multiple skills or concepts within a single exercise. For the Fourth Edition, these are assignable in MyMathLab.
Classify the Function exercises, appearing in the Skill Maintenance section of the exercise sets, ask students to identify a number of functions by their type (linear, quadratic, rational, etc.). Throughout the text, the variety of functions increases and these exercises become more challenging.
Review Icons refer students to an earlier, related section where they can go to review prerequisite concepts that are needed for the current section.
Study Tips are occasional, brief reminders in the margin, to promote effective study habits such as good note taking and exam preparation.
Technology Connections are optional sections that guide students in the use of the graphing calculator as another way to check problems.
Zeros, Solutions, andx-Intercepts are a theme of the text. The authors aim to help students see the connection between the real zeros of the function, the solutions of the associated equation, and the first coordinates of the x-intercepts of the graph. When students develop their understanding of these connections, their probability of success increases for this course.
New to this Edition
Additional ongoing review features have been integrated throughout, to help students reinforce their understanding and improve their success in the course.
Mid-chapter Review exercises are one-page mixed review sets at logical breaks in the chapter, helping students reinforce their understanding of the concepts.
Study Summaries have been added to the Chapter Review, giving students a built-in study aid when reviewing and preparing for tests.
MyMathLab is more closely integrated with the text and now offers new question types, for a more robust online experience that mirrors the authors' approach.
Example-based videos, created by the authors themselves, walk students through the detailed solution process for key examples in the textbook. Videos have optional subtitles.
Vocabulary exercises have been added, which can serve as reading quizzes.
Mid-chapter Reviews are new to the text and are assignable online, helping students to reinforce their understanding of the concepts.
Study Summaries are new to the text, and in MyMathLab theseare accompanied bysectionsummary videos, which cover key definition and procedures from the text.
Sample homework assignments are pre-selected by the authors for each section. These are indicated in the Annotated Instructor Edition by a blue underline within each end-of-section exercise set. These homework sets are assignable in MyMathLab.
The first four chapters of the text have been reorganized, to make the material easier to teach and learn. By presenting this material in four chapters rather than three, the level of difficulty is more balanced in this new edition.
Table of Contents
R. Basic Concepts of Algebra
R.1 The Real-Number Systemeal Numbers
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring Terms with Common Factors
R.5 The Basics of Equation Solving
R.6 Rational Expressions
R.7 Radical Notation and Rational Exponents
Study Guide
Review Exercises
Chapter Test
¿
1. Graphs; Linear Functions and Models
1.1 Introduction to Graphing
Visualizing the Graph
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
Visualizing the Graph
Mid-Chapter Mixed Review
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
¿
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions
Mid-Chapter Mixed Review
2.4 Symmetry and Transformations
Visualizing the Graph
2.5 Variation and Applications
Study Guide
Review Exercises
Chapter Test
¿
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
Visualizing the Graph
Mid-Chapter Mixed Review
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
¿
4. Polynomial and Rational Functions
4.1 Polynomial Functions and Modeling
4.2 Graphing Polynomial Functions
Visualizing the Graph
4.3 Polynomial Division; The Remainder and Factor Theorems
Mid-Chapter Mixed Review
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
Visualizing the Graph
4.6 Polynomial and Rational Inequalities
Study Guide
Review Exercises
Chapter Test
¿
5. Exponential and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
Mid-Chapter Mixed Review
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
Study Guide
Review Exercises
Chapter Test
¿
6. The Trigonometric Functions
6.1 Trigonometric Functions of Acute Angles
6.2 Applications of Right Triangles
6.3 Trigonometric Functions of Any Angle
¿ Mid-Chapter Mixed Review
6.4 Radians, Arc Length, and Angular Speed
6.5 Circular Functions: Graphs and Properties
6.6 Graphs of Transformed Sine and Cosine Functions
Visualizing the Graph
Study Guide
Review Exercises
Chapter Test
¿
7. Trigonometric Identities, Inverse Functions, and Equations
7.1 Identities: Pythagorean and Sum and Difference
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
7.3 Proving Trigonometric Identities
Mid-Chapter Mixed Review
7.4 Inverses of the Trigonometric Functions
7.5 Solving Trigonometric Equations
Visualizing the Graph
Study Guide
Review Exercises
Chapter Test
¿
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Complex Numbers: Trigonometric Form
Mid-Chapter Mixed Review
8.4 Polar Coordinates and Graphs
Visualizing the Graph
8.5 Vectors and Applications
8.6 Vector Operations
Study Guide
Review Exercises
Chapter Test
¿
9. Systems of Equations and Matrices
9.1 Systems of Equations in Two Variables
Visualizing the Graph
9.2 Systems of Equations in Three Variables
9.3 Matrices and Systems of Equations
9.4 Matrix Operations
9.5 Inverses of Matrices
9.6 Determinants and Cramer's Rule
9.7 Systems of Inequalities and Linear Programming
9.8 Partial Fractions
Study Guide
Review Exercises
Chapter Test
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10. Analytic Geometry Topics
10.1 The Parabola
10.2 The Circle and the Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Inequalities
Visualizing the Graph
Mid-Chapter Mixed Review
10.5 Rotation of Axes
10.6 Polar Equations of Conics
10.7 Parametric Equations
Study Guide
Review Exercises
Chapter Test
¿
Photo Credits
Answers
Index
Index of Applications
Author
Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University-Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children's camp.
Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University-Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children.
Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University-Purdue University Indianapolis (IUPUI), Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters. |
I was thinking about math courses for next year, and I do not know what I'm going to take. What is the differences between Alg 3 and Advanced math? And also, and does Trig involve? And I'm too scared of calculus to take it.
Yeah, I will talk to my counselor about thsi once I go back to school on Monday. I was just thinking about this an hour ago. I ran a search, and found that Alg 3 and Advanced math in highschool is almost exactly the same. Why the heck do they have both then?
Sometimes schools try to sort students into different tracks. I won't explain that. I doubt if a counselor actually knows the difference, in my experience. Often, they try to sell you a class based on how many seats are available in the "class", not your needs. Talk to a math teacher about the differences.
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4th grade math - how can thinking about 90 tens help you with 1901-297? |
Unrivalled in the way it makes the teaching of statistics compelling and accessible to even the most anxious of students, the only statistics textbook lecturers and their students will ever need just got better! more...
A no-nonsense, practical guide to help you improve your algebra II skills with solid instruction and plenty of practice, practice, practice. Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability andFor more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the |
linear equations, transposition of formulae, quadratic equations and completingThis toolkit from Plus magazine and Arctic Survey Education looks at models of climate change and sea ice growth.
The toolkit can be downloaded as a whole or as the individual components, which are:
• Arctic supermodels - background article
• Modelling ice thickness - worksheet and worksheet with guidance notes
•…
This toolkit, from the Plus magazine's collaboration with Arctic Survey Education, explores the navigational aspects of the expedition, including questions surrounding cartography and Global Positioning (GPS) systems.
The toolkit can be download as a whole or as individual components.
The individual components are:
• good practice which areA Mathematics Matters case study which looks at how advances in statistics allow us to analyse risks and consequences and so make informed decisions. Risks are an unavoidable part of modern life, but mathematicians and statisticians have developed a variety of methods to help mitigate its effects. These techniques enable hospitals,, from the Institute of Mathematics and its Applications, looks at how biometric identification systems rely on mathematical methods to convert images into data that can be digitally stored. It is essential that the biometric systems we depend on for national security can reliably identify individuals…
This Mathematics Matters case study, produced by the Institute of Mathematics and its Applications, looks at how industry relies on cutting-edge mathematics to develop better quality communications. The amount of information we can transmit though the air is limited by the laws of physics, but the mathematics of signal processing…
This Mathematics Matters case study, produced by the Institute of Mathematics and its Applications, looks at how mathematical research contributes to the development of new medical imaging technology. Brain scans play a vital role in the treatment of many serious medical conditions, but decoding the signals inside our minds would… |
Mathematics
Mathematics Curriculum Overview
Mathematics at Fresco Arts Academy is a journey into the world of patterns, symbolism, and application. Students will observe concrete situations and actively search for ways to explain what they perceive. Just like a foreign language, students will develop vocabulary to communicate with colleagues and discuss their ideas with each other. Like music, students will work with symbolic notation, which can quickly convey to the reader all necessary information. In fact, an emphasis is placed on learning mathematics in connection to all other subjects like music, art, history, science, language, and many more.
In the classroom, students will participate in class discussions, work in small groups, complete projects, and keep track of their own progress and learning throughout the year. Assignments will focus on the process of solving problems rather than simply finding the answer. Students will reflect on their problem-solving steps through verbal and written presentations. To help students record their understanding and develop their mathematics portfolio students will often provide written explanations of concepts using their own words.
Pre-Algebra 1
This course prepares students for Algebra. Students develop concepts through investigations, application problems, patterns, group work, and practice exercises. Active participation is essential for success in this mathematics class as well as any class. Online support for the class is available.
Pre-Algebra 2
This course continues to prepare students for Algebra. Students develop concepts through investigations, application problems, patterns, group work, and practice exercises. Active participation is essential for success in this mathematics class as well as any class. Online support for the class is available.
Working with graphs, graphing equations, operations with integers using patterns
Rational number (fraction) operations
Probability with fractions, decimals, and percents
Algebraic properties- order of operations and grouping terms, distributive property, and combining like terms
Equations in the form of tables
Solving equations and the balance of equations
Graphing- rates of change and slope, and inequalities
Geometric topics- area, surface area, and volume of shapes, relationship between lengths and perimeter and area, similarity of triangles, percentage and proportions, the Pythagorean Theorem, and two- and three-dimensional drawing
Exponents, scientific notation, and exponential growth
Algebra 1 Students learn beginning Algebra concepts by investigating patterns, using geometric representations, working in small groups, completing projects, and discussing topics as a class. An emphasis is placed on conceptual understanding and supported through activities and practice. Online support for the class is available.
Topics:
The language of Algebra
Variables and expressions
Algebraic properties
Logic and reasoning
Functions and graphs
Statistics
Operations of real numbers
Solving linear equations and inequalities
Characteristics of linear equations
Solving systems of linear equations and inequalities
Polynomials and Factoring
Quadratic and exponential functions
Radical and rational functions
Data analysis and probability
Algebra 2
Students expand their knowledge of Algebra with a more in-depth look at algebraic concepts and learn how to use those concepts as a tool to solve more complex problems. Topics build heavily from previous courses and require students to use multiple representations and comparisons. This course contains material extremely important for more advanced mathematic courses and is the minimum required math for college entrance. Beginning Algebra topics are reviewed briefly.
Topics:
Solving equations and inequalities
Linear relations and functions
Systems of equations and inequalities
Matrices
Polynomials and radical equations and inequalities
Quadratic functions and inequalities
Polynomial functions
Conic sections
Rational expressions and equations
Exponential and logarithmic relations
Sequences and series
Probability and statistics
Trigonometric functions
Geometry
Students develop the mathematical system of geometry and discover the many amazing properties it contains. While learning about the physical concepts in geometry, students will also develop logical/deductive reasoning and proof. The focus will be on Euclidean Geometry, however Non-Euclidean Geometry topics will be discussed.
Tools for analyzing and measuring shapes (such as the Pythagorean Theorem, trigonometric ratios, properties from trigonometry, and coordinate geometry)
Investigation and proof
Geometric construction
Probability
Points, Lines, Planes, and Angles
Reasoning and Proof
Parallel and Perpendicular Lines
Congruent Triangles
Relationships in Triangles
Proportions and Similarity
Right Triangles & Trigonometry
Quadrilaterals
Transformations
Polygons & Circles
Surface Area & Volume
Trigonometry / Pre-Calculus
Students begin with right triangles to develop the trigonometric ratios and expand on that knowledge to include trigonometric functions, identities, equations, and properties. An emphasis is placed on the geometric representation on concepts and a development from founding definitions. Related trigonometric topics are included and then followed by Pre-Calculus topics and an introduction to Calculus. Students will need a strong understanding of algebraic properties and graphing as well as geometry. After completing this course, students will be well prepared for Calculus.
Topics:
The Trigonometric Functions
Graphs of Trigonometric Functions
Trigonometric Identities and Equations
Vectors and Parametric Equations
Polar Coordinates and Complex Numbers
Conics
Exponential and Logarithmic Functions
Sequences and Series
Combinatorics and Probability
Statistics and Data Analysis
Introduction to Calculus
AP Calculus The study of calculus begins with an intuitive introduction through the examination of graphical problems like the "tangent line problem" and "area under the curve problem." Other topics such as limits are developed through numerical data analysis. Topics are initially motivated by trying to solve specific conceptual problems and only afterwards do students begin representing concepts algebraically with functions and crunching problems. Once students understand the development of the calculus concepts and attain proficiency in procedural skills, students must use calculus to solve application problems represented verbally. Students must apply their knowledge and respond to these "real-world" examples verbal, illustrating their understanding of what the mathematics represents and symbolizes in the situation by providing justification to their solution (such as in applied max and min word problems, related rates, and exponential and logistic growth models). An emphasis is placed on the connection between all of these representations (graphical, numerical, analytical, and verbal), strengthening students' understanding of the concepts and ability to apply them.
Topics:
A review of functions
Limits and Continuity: The Building Blocks of Calculus
The Derivative
Properties and Derivatives of Inverse, Logarithmic, and Exponential Functions |
Quickmath.com - automatic math solutions, What can quickmath do? quickmath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students..Yahoo answers - home, Yahoo answers is a new way to find and share information. you can ask questions on any topic, get answers from real people, and share your insights and experience..
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Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). The aim of such sutra is to simplify the entire calculations and arithmetical operations.
Vedic Maths Course
There are 16 sutras in vedic mathematics as per Sri Bharati Krsna Tirthaji Maharaj. The below mentioned list of topics (course content) is how I look at it.
Cube Roots (by seeing only & not by working on it). Different methods for perfect cube and non-perfect cube
Dates and calendar
Magic Square
Special mathematical tricks and techniques
Application of vedic mathematics in trigonometry, geometry, algebra and calculus
Value (finding and remembering) of fractions
Checking the accuracy of different mathematical operations
Differential calculus
Solving an algebraic equation of one variable
"Transpose and adjust (the coefficient)"
Solving simultaneous equation and quadratic equation
"If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero"
By the Paravartya rule
"If one is in ratio, the other one is zero."
Solving cubic equation
Solving fractional equation
"The ultimate (binomial) and twice the penultimate (binomial) (equals zero),"
Through (QM) I'll try to cover all the above vedic maths related topics. Lot of other topics, techniques, shortcuts will be part of QM. Mathematical games, puzzles, riddles, etc. are also included to make every kid sharp.
Hello , thanks admin for writing so many methods , tricks , techniques for solving Additions ,Subtractions , Multiplications & Divisions in Quicker math"s ! Interested students are requested to Learn one by one to know Basic Math's & Vedic Maths !! I am also one of the Tutor to teach Basic Math's & Vedic Maths as Home Tuition Classes & through Mail id for Outstation Students .To know more details please do write on my mail id is basic.maths483@gmail.com thanks once again Quicker Math's * I have passed M.Sc. ( STAT ) in Ist class from Nagpur University in 1981 .
Sir,
I wanted to solve data interpretation questions (Bank Po Exam) fast.
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Mathematics for Elementary School Teachers: A Process Approach, 1st Edition
Freitag's MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS: A PROCESS APPROACH was developed using the five Content Standards from the NCTM Principles and Standards for School Mathematics, and the Common Core State Standards for Mathematics. Traditionally, textbooks for pre-service elementary teachers have focused on problem solving. However, problem solving is not the only process through which mathematics is learned. It is also learned through mathematical reasoning, communication, representation, and connections. Recent trends in mathematics education now advocate implementing all five processes as a vital part of learning and doing mathematics. Consequently, you need to have concrete experiences with these processes that you will be required to teach.
The goal of this textbook is to treat each of the processes equitably by using an approach in which the five processes serve as the central pedagogical theme. Most of the examples, exercises, and activities are designed to either model the processes or to directly engage you in working with them. As a result, you will not only come to understand the different processes, but also appreciate them as an integral to learning and doing mathematics. If this broader view can be instilled, you are more likely to give your students a more well-rounded and holistic view of mathematics once you enter the classroom.
The content of the book is directly related to the mathematics that is taught in grades K – 8. The purpose is not to reteach elementary mathematics. Rather, the intent is to look at the content from a theoretical or generalized point of view, so that you can better understand the concepts and processes behind the mathematics you will teach. In short, the book focuses on the "why" behind the mathematics in addition to the "how."Hardcover $131.49
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Discrete Mathematics
9780023596902
ISBN:
0023596902
Edition: 2 Publisher: Prentice Hall PTR
Summary: This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Re...lations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics.
Johnsonbaugh, Richard is the author of Discrete Mathematics, published under ISBN 9780023596902 and 0023596902. Twenty one Discrete Mathematics textbooks are available for sale on ValoreBooks.com, twenty used from the cheapest price of $0.18, or buy new starting at $135.36.[read more] |
Developmental Mathematics for College Students - With CD - 2nd edition
Summary: Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. In this text, students get a thorough review of arithmetic and geometry along with all the topics covered in a standard elementary algebra course. The authors build the strong mathematical foundation necessary to give students confidence to apply their newly acquired skills in further mathematics cour...show moreses, at home, or54Used - book in POOR condition - cover shows extensive wear - pages soiled from use - has many creased pages - this is the student on a budget money saver copy - we ship immediately - our goal is to se...show morerve you! ...show less
$98 |
Subject Description
This course enhances students? skills gained from manipulating algebraic functions and equations and introduces the basic concepts of differential calculus. It also introduces basic data management as it relates to the applications of counting techniques and probability and statistics. Students will broaden their understanding of the mathematics associated with rates of change; and develop facility with the concepts and skills of differential calculus as applied to polynomial, rational, exponential and logarithmic functions. Students will use techniques gained from these skills to solve various applications.
Learning Outcomes
Upon successful completion of this subject the student will be able to:
1. Demonstrate an understanding of limits and continuity and rates of change; 2. Demonstrate an understanding of average rates of change and instantaneous rate of change; 3. Demonstrate an understanding of the definition of derivative; 4. Demonstrate an understanding of the first-principle definition of derivative; 5. Apply power rule, product rule, quotient rule and chain rule to various functions; 6. Demonstrate an understanding of implicit derivative; 7. Apply the differential calculus to related rates, curve sketching and optimization problems; 8. Analyze data and compute mean, mode, median, standard deviation; 9. Apply the basic laws of probability and the binomial probability; 10. Apply counting principle to binomial probability; 11. Demonstrate an understanding of probability distribution, random variable and expected values; 12. Demonstrate an understanding of the normal distribution |
This is a free textbook offered by BookBoon.'This book is a guide through a playlist of Calculus instructional videos. The...
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This is a free textbook offered by BookBoon.'This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level first Calculus course, or equivalently an AP Calculus AB course. The book further provides simple summary of videos, written definitions and statements, worked out examples--even though fully step-by-step solutions are to be found in the videos-- and an index. The playlist and the book are divided into 15 thematic learning modules. At the end of each learning module, one or more quiz with full solutions is provided. Every 3 or 4 modules, a mock test on the previous material, with full solutions, is also provided. This will help you test your knowledge as you go along. The book can be used for self study, or as a textbook for a Calculus course following the "flipped classroom" model'Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data...
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'Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.''Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum...
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'Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the pro-cesses of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are as follows:To help students learn how to read and understand mathematical definitions and proofs;To help students learn how to construct mathematical proofs;To help students learn how to write mathematical proofs according to ac-cepted guidelines so that their work and reasoning can be understood by others; andTo provide students with material that will be needed for their further study of mathematics.'
The |
Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study. less |
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