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An essential tool for standardized tests, the Spectrum Math series offers grade-appropriate coverage of basic arithmetic and math skills. Each book features drill and skill practice in math fundamentals, as well as applications of mathematics in everyday settings. Chapter Pre-Tests, Chapter Tests, Mid-Book Tests and Final Tests all contribute to an extended familiarity with developmental, problem-solving and analytical exercises. An assignment record sheet, record of test scores sheet and answer key are included.
Both of my sons used an earlier edition of this book for "afterschooling" when they came home from the public school each day. I loved how concise this series was compared to all the other math textbooks at this grade level, so I could be sure I was tutoring them on all the typical Gr. 3 math topics, without the "twaddle."
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Review 2 for Spectrum Math, 2007 Edition, Grade 3
Overall Rating:
5out of5
Date:May 7, 2010
Lisa
My daughter used this workbook this year for 3rd grade. She did wonderfull with math! She does very well with her CAT tests too. When she needs extra practice on something we just make up quick worksheets on the computer to go along with what she is doing in this book. It's a great guide for what they need to learn in thier grades at a good price with great explainations so they can do it on thier own and with the key in the back so no need for a teacher manual. |
More About
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Overview
Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese)for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.
A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to bea significant contribution to this highly applicable and stimulating subject.
Editorial Reviews—Monatshefte F. Mathematik |
Summary: The authors help students ''see the math'' through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class2.00 +$3.99 s/h
Acceptable
Campus_Bookstore Fayetteville, AR
Used - Acceptable Hardcover. moderate water and other liquid damage 4th Edition Not perfect, but still usable for class. Ships same or next day. Expedited shipping takes 2-3 business days; standard sh...show moreipping takes 4-14 business days5.42 +$3.99 s/h
Good
1upbooks Columbia, MO
"Fast shipping! May contain notes, highlighting, and/or cover wear." |
an introduction to matrix theory and aims to provide a clear and concise exposition of the basic ideas, results and techniques in the subject. Complete proofs are given, and no knowledge beyond high school mathematics is necessary. The book includes many examples, applications and exercises for the reader, so that it can used both by students interested in theory and those who are mainly interested in learning the techniques. |
Modern Geometries
This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern ...Show synopsisThis comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.Hide synopsis
Description:Very Good. No Dust Jacket. Fifth edition. Very good copy with...Very Good. No Dust Jacket. Fifth edition. Very good copy with markings in pencil to a few pages and minor shelfwear to red boards. |
...
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This Book
prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra.
Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to:
*notice and describe consistencies across problems
*articulate generalizations about the behavior of the operations
*develop mathematical arguments based on representations to explain why such generalizations are or are not true.
Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies.
Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles.
PLCs and book-study groups! Save $47.25 when you purchase 15 copies with the Book Study Bundle.
Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course.
For information on the PD course offered through Mount Holyoke College, download the flyer.
Related Subjects
Meet the Author
Susan Jo Russell is a principal scientist at the Education Research Collaborative at TERC. Following ten years of classroom teaching and coaching in elementary schools, Dr. Russell directed projects focused on mathematics professional development, research on students' and teachers' understanding of mathematics, and mathematics curriculum. She co-directed the development of the NSF-funded elementary curriculum, Investigations in Number, Data, and Space and the professional development materials, Developing Mathematical Ideas. Her recent work is on supporting teachers to integrate a focus on generalizing about the operations into their core arithmetic instruction.
Deborah Schifter is Principal Research Scientist at the Education Development Center (EDC) where she leads a range of projects concerning professional development in mathematics and research into student learning. Working with a variety of colleagues, she is coauthor of Reconstructing Mathematics Education, Developing Mathematical Ideas, The Mathematical Education of Teachers, and the Second Edition of Investigations in Number, Data, and Space. She also edited What's Happening in Math Class? (an anthology of teacher writing) and is co-editor of A Research Companion to the NCTM Standards. Deborah loves learning from the teachers with whom she works.
Virginia Bastable has been the Director of the SummerMath for Teachers Program at Mount Holyoke College since 1993. She taught middle school and high school mathematics for more than twenty years. She is coauthor of the Developing Mathematical Ideas professional development curriculum and the Second Edition of Investigations in Number, Data, and Space. Dr. Bastable particularly enjoys helping others to discover their interest and abilities in mathematics, even if those interests and abilities have been blunted by past negative experiences with |
Instead of requiring my senior students to do an essay on a math topic, I tried
the following activity-based independent study. The students loved it! We used the
last few days of the course to present the demonstrations. It gave them an overview
of what computers can be used for in mathematics, ensured that they had some time
using one piece of software, allowed them to venture into the online math environment,
and was lots of fun.
Software
My students used The Geometer's Sketchpad, Maple,
and a spreadsheet called Aseasy 5.7. Other possibilities are Mathematica, MathView,
JavaSketchpad, Mathcad, and many spreadsheets, the most available of which are probably
MsWorks, ClarisWorks and Microsoft Excel.
Directions
Work in the lab 4 days:
either after school - I will be available every Tuesday and Thursday in May
or at lunch, by appointment
Investigate one of the following topics on the computer with a partner:
The GLAD proof using the Geometer's Sketchpad
Using the Geometer's Sketchpad to create tesselations
Using the Scripting tool in Sketchpad to create the Koch snowflake
and other fractals
Creating ellipses and hyperbolas through animation using Sketchpad
Polar graphs with Maple
Graphs of planes, cylinders, and/or spheres using Maple
Linear transformations using a spreadsheet
Polar graphs on a spreadsheet
Recursive relationships using a graphics calculator
Using the CBL to collect data from a light source and determine the equation
of the resulting curve.
Famous curves: for example, the cycloid and the witch of Agnesi
The Sierpinski triangle using Sketchpad or a graphics calculator
The relationship between Euler's line and the 9 point circle using Sketchpad
Construct sine and cosine wave tracers using Sketchpad
Three proofs of the Pythagorean theorem using Sketchpad
This list is not exhaustive. If there is a topic you would like to pursue, please
see me.
On the last two days of class be prepared to present a three-minute demonstration
of your findings using the computer. In the demonstration explain briefly what your
project is about and show how the computer program helped in investigating.
Hand in a disk, to include the animation/graph/sketch and a brief explanation
of the mathematics involved.
Evaluation
The project will be assessed as follows:
attendance at lab sessions - 25%
your presentation - 50%: The presentation will be evaluated as to creativity,
organization, accuracy, and ability to communicate clearly.
handin - 25%: This will be evaluated on its clarity and ability to explain
the mathematics underlying your project. |
Description of Horizons Math 4: Student Book 2 by Alpha Omega
Give children a firm foundation in mathematics with Horizons Math, the highly acclaimed course that utilizes hands-on teaching techniques and the use of household manipulatives to make difficult concepts "stick." Designed specifically for homeschoolers, this curriculum provides detailed instructions for teachers, as well as a variety of teaching suggestions and supplemental activities for additional practice.
This student workbook contains the second set of lessons for the Horizons Grade 4 Math curriculum.
Product:
Horizons Math 4: Student Book 2
Vendor:
Alpha Omega
Subject:
Math
Curriculum Name:
Horizons/Alpha Omega
Learning Style:
Auditory, Kinesthetic, Visual
Teaching Method:
Charlotte Mason, Classical, Traditional, Unit Study, Unschooling
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Comments
My daughter likes this curriculum, because she can write in the book. The lessons seem easier to her, even though they are in her grade level. She hates having to read a lesson and then write the problems all over again as they are in the book. She would rather solve the problem right there in the book. The book is very colorful and it reminds me of her little sister's math book - which we love (again, because we are able to write in the book). It actually does seem to make a difference.
We have looked at other Math curriculum programs and this is the one my daughter enjoys and requests. We have a primarily unschooling type of homeschool setting; however, with subjects such as math that require more textbook type work, my daughter prefers to work independently but have me available for assistance or new concepts.
Horizons Math is excellent in introducing new concepts. New ideas aren't just sprung upon the student randomly. Pieces and parts are gradually introduced while consistantly reinforcing older already leaned concepts. When a new concept is added, there have been building blocks of learning already done so the new concepts just seems to flow in a natural and logical manner. |
Brief Calculus: Applied Approach - rev edition
Summary: This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. Applications using real data enhances student motivation. Many of these applications include source lines, to show how mathematics is used in the real world.
NEW! Conceptual probl...show moreems ask students to put the concepts and results into their own words. These problems are marked with an icon to make them easier to assign.
More opportunities for the use of graphing calculator, including screen shots and instructions, and the use of icons that clearly identify each opportunity for the use of spreadsheets or graphing calculator.
Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned.
Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items, Fill in the Blanks and Review Exercises.
Chapter 1. Functions and Their Graphs. Chapter 2. Classes of Functions. Chapter 3. The Limit of a Function. Chapter 4. The Derivative of a Function. Chapter 5. Applications: Graphing Functions; Optimization. Chapter 6. The Integral of a Function and Applications. Chapter 7. Other Applications and Extensions of the Integral. Chapter 8. Calculus of Functions of Two or More Variables. Appendix: Graphing Utilities. Appendix 1. The Viewing Rectangle. Appendix 2. Using a Graphing Utility to Graph Equations. Appendix 3. Square Screens. Appendix 4. Using a Graphing Utility To Locate Intercepts and Check for Symmetry. Appendix 5. Using a Graphing Utility to Solve Equations. Answers to Odd-Numbers Problems. Photo Credits |
Find a Gainesville, GA StatisticsCan help you understand the basics of the Microsoft Word toolbar. Frequently used Microsoft PowerPoint during MBA coursework. Can help you use templates, create appealing transitions, and link or embed various items.
...In addition, I have tutored students in different concepts pertaining to discrete math. I have taught a Quantitative Reasoning course which contains some of the concepts covered in discrete math. Finite math is a compilation of various mathematical topics. |
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). |
This algebra unit from Illuminations includes three lessons which highlight Pick's Theorem. Students will be introduced to the theorem, determine the coefficients of the equation, and explore the concept of rates of...
This lesson from Illuminations uses the real world example of hanging chains to demonstrate how naturally occurring shapes relate to parabolic functions. Students will learn to substitute points on a graph into a...
This is a basic course, produced by Gilbert Strang of the Massachusetts Institute of Technology, on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including... |
More About
This Textbook
Overview
The new edition of Calculus continues to bring together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful for those going into mathematics and those going into the sciences and engineering. This new text exhibits the same strengths from earlier editions including an emphasis on modeling and a flexible approach to technology.
Editorial Reviews
Booknews
Revisions to the latest edition of this venerable calculus text include a new section on graphing functions on calculators and computers; an increased emphasis on mathematical modeling and on making connections between calculus and real world experiences; a new appendix on solving polynomial equations; a number of sections reorganized for clarity; and updated computer graphics 28, 2010
The free e-book is not Anton's work
I downloaded the free e-book only to find it is a Google book version of a text from the 1920s. Equations are essentially unreadable, the OCR used couldn't make sense of it, it seems. Don't bother. Anton's actual Calculus text books are worth their weight in gold. I absolutely recommend hunting them down if you are a student of Calculus.
5 out of 5 people found this review helpful.
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A Mathematical Introduction to Logic22384520New:
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$84 Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students |
Mathematics is about number operations and algebra,
motion and change (calculus and differential equations), logical analysis,
scientific visualization, structure and geometry, the prediction of random
events (probability), the extraction of useful information from large sets of
data (statistics), the discovery of the best ways to do things (optimization).
It is abstract and theoretical, and intensely down-to-earth and practical, all
at the same time.
The
mathematics major and minor prepare students for exciting and rewarding work in
industry, careers in teaching, and for advanced post-baccalaureate study.Our calculus, differential equations,
analysis, and probability and statistics courses enable science students to
analyze data and predict outcomes in static and dynamic situations.Our foundations, discrete math and algebra
courses give students the tools they need for rigorous logical and structural
analysis and a deep conceptual understanding of quantitative situations.Our mathematics education courses prepare
students to be outstanding teacher leaders with a deep knowledge of mathematics
and the best practices in teaching.Our
general education courses give the general student the mathematical background
she or he needs to function in life as an educated and informed citizen in an
increasingly quantitative and data-driven world.
The
Mathematics Department makes every effort to attempt to offer its courses at
times that are convenient for students.Courses in the mathematics option of the major are generally offered in
the morning.Courses in the mathematics
education option of the major and Master of Arts in Teaching Mathematics are
generally offered at night to accommodate the needs of working students.
Students are welcome to see a math advisor at any time
when faculty are available.All
full-time math faculty serve as advisors.To schedule an appointment with an advisor, please call the math
department office (310) 243-3378 or drop by NSM A-122 during regular business
hours.The math department requires
majors to meet with an advisor at least once each semester.
Preparation
High School students should complete Algebra II, a
year of geometry and trigonometry.A
mathematics course should be taken in the senior year.Transfer students should complete three
semesters of calculus and one additional course if possible.
Career Opportunities
A degree in mathematics is a key that opens the door
to a world of opportunity.Students who
major in mathematics are able to pursue a diverse range of careers.They are sought out by profit and no-profit
institutions for their ability to use reasoning and logic and for their ability
to solve problems.Many are interested
in passing their learning on to future generations through teaching.Others seek advanced degrees in mathematics
or other sciences and pursue cutting-edge research.Some will pursue degrees in business or
economics, where the ability to work with numbers can be a great
advantage.Those with mathematical
training have gone on to careers as business executives at major software
companies, as analysts for stock trading companies, as actuaries and risk
management experts for insurance companies and the healthcare industry, as
scientists and data analysts in engineering and biotech firms, as software
designers and programmers, and a whole host of other careers.
Graduation With
Honors
An undergraduate student may graduate with Honors in
Mathematics provided that the following criteria are met:
1.A
minimum of 36 units in residence at CSU Dominguez Hills;
2.A minimum grade point
average of at least 3.5 in all courses used to satisfy the upper division
requirements in the major;
3.Recommendation by the
faculty of the Mathematics
Department.
Bachelor of Science in Mathematics
Total Course
Requirements for the Bachelor's Degree
See the "Requirements for the Bachelor's
Degree" in the University Catalog for complete details on general
degree requirements.A minimum of 40
units, including those required for the major, must be upper division.
Elective Requirements
Completion of elective courses (beyond the
requirements listed below) to reach a total of a minimum of 120 or a maximum
of132 units.
General Education Requirements (55-62
units)
See the "General Education" requirements in
the University Catalog or the Class Schedule for the most current
information on General Education requirements and course offerings.
Graduation Writing Assessment Requirement
See
the "Graduation Writing Assessment Requirement" in the University
Catalog.
Minor Requirements
Single field major, no minor required.
Major Requirements (59-67 units)
Students must select one of the options listed
below.The following courses, or their
approved transfer equivalents, are required of all candidates for this degree.
All courses used to satisfy this major must be passed with a grade of
"C" or better.
Subject to approval by the California Commission on
Teacher Credentialing (CCTC), this option will satisfy the subject matter
preparation necessary for a secondary teaching credential in mathematics.Students do not get Subject Matter
Preparation on their diploma, the diploma says Mathematics Education
option.
Students not seeking a degree in mathematics, but
wishing to satisfy the requirements for the teaching credential in mathematics
must take at least nine (9) units of upper division mathematics at CSUDH,
including MAT 490.
Students must submit an application to the University
for admission (or readmission) with graduate standing, and official transcripts
of all previous college work in accordance with the procedures outlined in the Graduate
Admissions section of the University Catalog.If the student is currently enrolled as a
post-baccalaureate student, he/she must obtain a Request for
Postbaccalaureate/Graduate Change of Objective form from the department
office and submit it to the program's Graduate Coordinator.
Admission
Requirements
The student will qualify for admission to the program if he/she:
1.has a baccalaureate
degree from an accredited university.(See the University Catalog for requirements of graduates of
non-accredited institutions.);
2.has completed two years
of teaching and is currently teaching mathematics in a California school;
3.a)has
a California Single Subject Credential in Mathematics or
b)is eligible for a
California Single Subject Credential in Mathematics or
c)has completed a major
in mathematics or
d)has completed, with an average grade of
"B" or better, 20 semester units in college level mathematics and
passed a department administered entrance examination;
4.has submitted three
letters of recommendation, including one from the principal at the applicant's
school;
5.has completed a
successful interview with the program's Graduate Coordinator and
representatives from the department's mathematics education faculty;
6.has achieved a TOEFL
score of 550 (for those applicants who do not possess a bachelor's degree from
a postsecondary institution where English is the principal language of
instruction);
7.has a grade point
average of at least 2.5 (on a 4.0 scale) in his/her last 60 semester units of
upper division course work; lower division courses taken after obtaining the
bachelor's degree and extension courses, (except CSU Dominguez Hills upper
division resident extension courses or the equivalent on other campuses), will
be excluded from the calculation; and
8.is in good standing at
the last college attended.
Graduate
Standing:Conditionally Classified
To qualify for admission with a graduate degree
objective, students must meet the admission requirements for postbaccalaureate
unclassified standing as well as any additional requirements of the particular
program.Students who apply to a
graduate degree program but who do not satisfy all program requirements may be
admitted to conditionally classified status.Program coordinators will outline all conditions for attainment of
classified status.
Graduate
Standing:Classified
Students applying for master's degree programs will be
admitted in classified status if they meet all program admission requirements.
Classified standing as a graduate student is granted
by the academic unit to which the student is applying.Classified standing is normally granted when
all prerequisites have been satisfactorily completed for admission to a master's
degree program.Students must have
classified standing to qualify for Advancement to Candidacy.
Graduation Writing
Assessment Requirement
All graduate students entering the University in the
Fall of 1983 or thereafter are required to satisfy the Graduation Writing
Assessment requirement (GWAR) in accordance with the established policies of
the university.Students must satisfy
the requirements before being Advanced to Candidacy.(See "Graduation Writing Assessment
requirement" section of the University Catalog.
Advancement to
Candidacy
Advancement to candidacy recognizes that the student
has demonstrated the ability to sustain a level of scholarly competency
commensurate with successful completion of degree requirements.Upon advancement to candidacy, the student is
cleared for the final stages of the graduate program which, in addition to any
remaining course work, will include the thesis, project, or comprehensive
examination.
Following are the requirements for Advancement to
Candidacy:
1.A minimum of 15
resident units
2.Classified standing
3.An approved Program of
Study
4.Successful completion
of the GWAR
5.A cumulative GPA of
3.0 in all courses taken as a graduate student
6.No grade lower than a
"C" in the degree program
Advancement to Candidacy must be certified on the
appropriate form to the Graduate Dean by the department prior to the final
semester, prior to the semester of the comprehensive exams, and prior to
enrolling in thesis or project.
Acceptable Progress
and Graduation Requirements
The following are specific graduation requirements
which must be met to earn this graduate degree:
1.Completion of a minimum
of 32 semester units of approved graduate work within five years.An extension of time may be granted if warranted
by individual circumstances and if the outdated work is validated by such means
as examination, independent study, continuing education, relevant additional
course work, or by such other demonstration of competence and/or currency as
deemed acceptable by the Graduate Coordinator and mathematics education
faculty.
Distribution pattern of
the 32 units:
a.at least 16 semester
units will be completed in residence after admission to graduate standing in
the program;
b.not more than 4
semester units of Graduate Seminar in Mathematics Education (MAT 590) can be
used to meet graduation requirements;
c.not more than 9
semester units may have been earned from approved extension and/or transfer
course credit; and
d.upon approval by the
Graduate coordinator and representatives from the mathematics education
faculty, courses taken previously may be used to meet the course content
requirements if they have been completed within the five years immediately
preceding the completion of the requirements of the degree.However, no courses (with the exception of
GED 500 - Research Methods in Education) previously used to meet their
requirements of another degree may apply toward the required number of 32
semester units of approved graduate work.
2.achievement of a grade
point average of 3.0 or better in all courses taken to satisfy the requirements
for the degree, except that an approved course in which no letter grade is
assigned shall not be used in computing the grade point average;
3.satisfactory completion
of the research project.The subject of
the research project will depend upon that which is educationally most
appropriate to the student and mathematics education.The research project is equivalent in rigor
to the thesis, will be supervised by a committee of three faculty, and may
include an oral defense or presentation as part of the culminating experience;
4.satisfactory completion
of the graduation Writing Assessment Requirement (GWAR); and
5.filing of an
application for the award of the Master's degree.
Upon completion of the CSU Dominguez Hills' graduation
requirements, award of the graduate degree must be approved by
the program, the school dean, and the faculty of the University.
Degree Requirements
(30 -36 units)
The Master of Arts Degree in Mathematics requires
completion
of 30 units of course work and one of the following:
a.Passing score on a
comprehensive written examination.After
completion of all course work or during the last semester of course work, the
MAT degree candidate may apply to take the comprehensive examination.There is only one retake opportunity.
b.Completion of an
approved thesis or creative project (MAT 599 - 6 units).Students must have the approval of a faculty
thesis advisor prior to enrolling for thesis credit.
The credit value for each course in semester units is
indicated for each term by a number in parentheses following the title.For course availability, please see the list
of tentative course offerings in the current Class Schedule.
Students need to take the ELM test, or to have an
exception from the ELM test prior to enrolling in any mathematics course.The ELM test score will be used to place the
students into the proper mathematics course.
Sets and set
theoretic operations as related to counting numbers and rational numbers and
arithmetic operations. Real number system and its origins, development,
structure and use.Special emphasis on
problem solving and the development and application of algorithms.Does not satisfy General Education
Quantitative Reasoning Requirement.
A practical course in
probability and statistics including such topics as the binomial and normal
distributions, confidence intervals, t, F, and chi-square tests, linear
regression and correlation, and conditional probability.Satisfies the General Education Quantitative
Reasoning Requirement.
Introduction to
computers for teachers of mathematics.Topics include flowcharting, programming in LOGO on microcomputers.Applications of computers to problem solving,
statistics, and other areas of mathematics relevant to teachers of
mathematics.Applications packages, CAI
and social issues are studied.A-C/NC
grading.Does not satisfy General
Education Quantitative Reasoning Requirement.
Objective is to
increase students abilities to use knowledge and experience when encountering
new and unexpected situations.Develop
higher level thinking skills, learn to formulate, analyze, and model
problems.Choosing relevant information,
making conjectures, devising plans and testing solutions.A-C/NC grading.Does not satisfy General Education
Quantitative Reasoning Requirement.
Not available for
credit to students who have credit in MAT 191 or its equivalent or courses
which have MAT 191 as a prerequisite. Functions, linear equations, the
derivative and its applications, the integral and its applications, and partial
derivatives.Satisfies the General
Education Quantitative Reasoning Requirement.
Differentiation and
integration of transcendental function.Techniques and applications of integration.Polar coordinates.Infinite sequences and series, power series,
convergence.Satisfies the General
Education Quantitative Reasoning Requirement.
Primarily for
prospective elementary school teachers.Geometry from an intuitive problem solving standpoint.Constructions, symmetry, translations,
rotations, patterns, area, volume, and the metric system.Topics from graph theory and topology.Two hours of lecture and two hours of
activity per week. Does not satisfy General Education Quantitative Reasoning
Requirement.
MAT 241Programming and Technology for Teaching Secondary School
Mathematics(3).
Prerequisite:MAT 193 or equivalent with a grade of "C" or
better.
Introduction to
application software appropriate for the teaching of secondary school
mathematics.The programs include
spreadsheet, geometric modeling, and statistics modeling.Writing simple programs for graphing
calculators to demonstrate and solve mathematical problems.
Prerequisite: MAT 153 or equivalent with grade of "C" or
better.MAT 191 with grade of
"C" or better is recommended.
Topics include logic,
methods of mathematical proof, set theory, relations and functions. Introduction
to complex numbers and proof strategies using ideas of vector algebra.Meant to prepare students for mathematics
program as well as concepts of computer scienceTopics covered
include first and second order linear equations including existence and
uniqueness theorems, series solutions; nonlinear equations; systems of linear
equations. Other topics may include the Laplace transform, qualitative
theoryPrerequisites:MAT 311 with a grade of "C" or better is
required; MAT 213 is recommended.
Solutions to partial
differential equations by separation of variables and Fourier series.
Applications to heat flow and diffusion, wave motion, and potentials.Some discussion of existence and uniqueness
of solutions.
Prerequisite: 9 units of 300/400-level mathematics with a
grade of "C" or better.
Synthesis and
analysis of secondary mathematics and its teaching.Emphasis on algebraic thinking and its
teaching in high school.Observation and
discussion of teaching is an important activity in this course.
Prerequisite:9 units of 300/400 mathematics courses with a
grade of "C" or better.
The synthesis and
analysis of the secondary mathematics curriculum from an advanced
standpoint.Emphasis will be on the
integration of problem solving, investigations, reasoning, and communication as
recommended in state and national standards.
A course in a topic
of special interest to both faculty and students for which no current course
exists. Topic will be announced in schedule of classes.Repeatable for credit.One to four hours of lecture per week.
Prerequisites:Students must have graduate standing and must have completed one
year of full time secondary mathematics teaching.
Includes topics such
as normal distribution, confidence intervals, t, F, chi-squared tests, linear
regression, and correlation.These
topics are presented in the context of mathematics education research in
typical classrooms.
Prerequisites: MAT 543 or concurrent
enrollment.Students must have graduate
standing and must have completed one year offull time secondary mathematics teaching.
Topics include the
algebraic properties of sets and operations applied to classical number systems,
equivalence, modular arithmetic, Diophantine equations, decomposition of
natural numbers, special families of natural numbers, current research on
understanding and learning these topics.
Prerequisites:Possession of a baccalaureate degree and one
year of full-time secondary mathematics teaching.
Topics from areas of
Modern Mathematics which relate to the high school mathematics curriculum such
as:algorithms, graph theory, coding
theory, game theory, finite probability theory, difference equations, voting,
recursion.
Prerequisites: Students must have graduate
standing and must have completed one year of full time secondary mathematics
teaching.
Patters, functions,
and multiple representations; independent and dependent variables; discrete and
continuous functions; linear and nonlinear relationships in context;
connections to arithmetic operations; algebraic expressions and equations.Examines current research on the
understanding and learning of these topics.
Prerequisites:Graduate standing and one year of full time secondary teaching.
Traces the
development of the mathematics curriculum K-12 in the United States and
internationally, concentrating both on content taught at different stages and
the teaching methods employed.Reviews
the various mathematics reform efforts over the past 170 years.
Overview of the
current research literature pertaining to mathematics education in elementary
and secondary schools. Topics such as mathematical reasoning, communication,
problem solving, algebra, and geometry will be discussed and analyzed.
Overview of the
current research literature pertaining to mathematics education in elementary
and secondary schools. Topics such as mathematical reasoning, communication,
problem solving, algebra, and geometry will be discussed and analyzed.
Completion of
classroom based project under the guidance of faculty advisor.The culminating learning experience of the
program which emphasizes the application of the mathematics education
curriculum in the classroom.
Graduate students who
have completed their course work but not their thesis, project, or
comprehensive examination,
or who have other requirements remaining for the completion of their degree,
may maintain continuous attendance by enrolling in this course.Signature of graduate program coordinator
required.
Infrequently Offered
Courses
The following courses are scheduled on
a "demand" basis.Students
should consult the department office for information about the next schedule
offering.
Integrates previous
work and experience by emphasizing the application of theoretical models and
research designs to the field of mathematics education.Special emphasis will be given to analyzing,
organizing, and evaluating findings, and communicating the results. |
Introduction to Mathematica
Posted by: Nicholas O'Brien on November 18, 2010
Mathematica is a mathematical package that is quite intuitive and easy to use. On the plus side it is very good for calculus, graph theory, and 3D graphic rotations. It also allows easy in-line commenting. On the down side Mathematica requires one use strict syntax, and that you load external packages to perform many functions. Additionally, it undergoes big changes version to version so reverse compatibility is a problem.
At Bates, Mathematica is used some in math, and also in the physics department.
For more information about using Mathematica, thes resources are available online for you and yous students: |
studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis. In fact, throughout the book, the author introduces a variety of ideas and constructs theories around them, incorporating much of the classical theory of polynomials as he proceeds. These ideas are used to study a number of unsolved problems, bearing in mind that such problems indicate the current limitations of our knowledge and present challenges for the future. However, theories also lead to solutions of some problems and several such solutions are given including a comprehensive account of the geometric convolution theory. This is an ideal reference for graduate students and researchers working in this area. less |
Math "Head Start" Workshops
The Tunxis Community College Academic Support Center offers Tunxis students who are planning to enroll in Elementary or Intermediate Algebra the opportunity to get a free head start in math before the stress of the semester begins.
You will refresh your memory on the foundations of the course, and you will learn key math study skills. This is your chance to ask the questions that have always plagued you about math.
Elementary Algebra
The session is designed to prepare you for MAT*095 Elementary Algebra Foundations by refreshing your memory on key concepts like:
Integers/ Fractions
Combining Like Terms
Word problems
And more
When?
Tuesday, January 21st at 9:30 – 11:30am OR Wednesday, January 22nd at 2:00 – 4:00pm OR Thursday, January 23rd at 5:00 – 7:00pm
Sign Up for an Elementary Algebra Workshop
If you have registered for Elementary Algebra Foundations
Intermediate Algebra
The session is designed to prepare you for MAT*137 Intermediate Algebra by refreshing your memory on key concepts like:
Fun with polynomials
Laws of exponents
Linear Equations
Word problems
And more
When?
Tuesday January 21st at 5:00 – 7:00pm OR Wednesday, January 22nd at 9:30 – 11:30am OR Thursday, January 23rd at 2:00 – 4:00pm
Sign Up for an Intermediate Algebra Workshop
If you have registered for Intermediate Algebra |
Discovery: Must be completed for each lesson, and kept in your math binder-
Assignment Guide
**** The following assignments are an outline of the content that will be covered. If you are absent, you will need to complete the assignments listed here. However, in class we will not necessarily complete all of these problems, and other information may be presented. We may also complete group activities not listed here. Make sure to copy another student's agenda when you return from an absence for the most up-to-date information.
~Principles of Algebra- Chapter 1- review basics
- Calculators will not be used in Chapter 1
Discovery: Must be completed for each lesson, and kept in your math binder-
8/21: Chapter 3 Assessment, HW: TCAP Test Prep, p. 156-157, ALL including Short and Extended Responses, ***make sure to justify your answer on every problem- you will not receive credit if your work does not justify your answer.*** |
Algebra for College Students-Myworkbook - 7th edition
Summary: MyWorkBook provides extra practice exercises for every chapter of the text. MyWorkbook can be packaged with the textbook or with the MyMathLab access kit and includes the following resources for every section:
Key vocabulary terms, and vocabulary practice problems
Guided Examples with stepped-out solutions and similar Practice Exercises, keyed To The text by Learning Objective
References...show more to textbook Examples and Section Lecture Videos for additional help
Additional Exercises with ample space for students to show their work, keyed To The text by Learning Objective
Workbook. All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780321715524-5-0
$431 +$3.99 s/h
VeryGood
BookCellar-NH Nashua, NH
0321715527 |
If they are missing I go all the way back where it stared and fill in the gaps so math won't be magical and start making sense for the students. I got my algebra II teacher's recommendation. Algebra has always been piece of cake for me |
Featured Events
ACE Pre-Conference
Tip Of The Week
Did You Know... Students often have difficulty with algebra because of misconceptions in various areas. One common misconception is that students think that algebraic variables stand for things, such as 6d = 12 , where d stands for donuts, not the cost of a donut.
How can the problem be solved?
Make sure students understand the difference between abbreviations and variable, such as: "6 meters" instead of "6m."
Have students write out the literal translation of an equation, such as: 6P=S, where 6 times the number of professors is equivalent to the number of students. It's all in how we teach the basics!
About IPDAE
The Institute for the Professional Development of Adult Educators is an initiative supported by Florida Department of Education to offer information, resources and professional development for adult education career pathways programs. Learn more |
Learn About:
Do I Need a Calculator?
Technology plays an integral role in the mathematics curriculum at Washington and Lee. Beginning in Math 221, Multivariable Calculus, the computer algebra system MAPLE is introduced via the department's computer laboratory. It is used heavily in several subsequent courses, such as Math 332 (Ordinary Differential Equations) and Math 333 (Partial Differential Equations). It is in such courses that 3-D graphics, high-speed computation, and symbolic manipulation have much to offer. It is the strong feeling of the W&L mathematics faculty that the emphasis in its introductory level calculus courses must be focused on calculus, itself. This firm grounding enhances students appreciation of both theoretical and computational aspects of advanced courses. Thus, perhaps unlike the calculus course you may have had in high school, Math 101, Math 101B (for calculus beginners) and Math 102 do NOT require a graphing calculator. |
Numerical Analysis A Mathematical Introduction
9780198502791
ISBN:
0198502796
Publisher: Oxford University Press, Incorporated
Summary: 'Numerical Analysis' explains why numerical computations work or fail. These are mathematical questions, and the text provides students with a complete and sound presentation of the interface between mathematics and scienctific computation.
Schatzman, Michelle is the author of Numerical Analysis A Mathematical Introduction, published under ISBN 9780198502791 and 0198502796. Fifteen Numerical Analysis A Mathe...matical Introduction textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $32.93, or buy new starting at $99.20.[read more]
0198502796 LIKE NEW/UNREAD! ! ! Text is Clean and Unmarked! --Be Sure to Compare Seller Feedback and Ratings before Purchasing--Has a small black line on bottom/exterior edge [more]
0198502796 |
Man... I hate to break this to you but if you are really serious about mathematics you will need to pick up where you left off. Take it from me; I fought this losing battle for many years. I am currently a cs PhD student at a very large research university in the uk.
Unlike many other subjects, you cannot advance very far in math without very solid building blocks of previous material. Understanding concepts makes you feel good but its not what mathematics is about. It really is about all of those little details and rules that make everything work out properly. The history of math is build on combining very small and simple results to get larger and more interesting ones. As you have seen, going the opposite direction of tackling a more advanced branch of math, and then trying to learn the learn the fundamentals as you go isn't going to work. You need to practice math A LOT and for most people college classes are the best way to do this.
Start over. Find a community college and first semester take calc 1 and linear algebra. Second semester take discrete math and calc 2. It will take one year and then you will be in good shape. This will give you a decent background for pursuing more advanced subjects. Note that while the calculus might not contribute directly to the math that you are more interested in, the problem solving practice will make a huge difference. I promise.
I am about to start my phd in computer science after finishing my masters and I can tell you that I actually enjoyed programming much more before I learned all of the formal stuff. My background was originally in earth science doing GIS and I started writing lots of code that way. Like many people have mentioned, the cs degree is about abstractions and algorithms -- none of which needs any real code be interesting. I found that after formal training that I only wanted to work on the algorithmic aspects of problems and that the implementation was just a very annoying and specific detail. Ignorance is bliss... |
MATHEMATICS
MATH-050 Fundamental Mathematics 3 cr.
Instructs the student on basic arithmetic concepts, addition, subtraction, multiplication, and
division of whole numbers and fractions as well as signed numbers. This course is a
PASS/FAIL course; students are allowed only two attempts to pass the course. This course
is not available to students who place in Math 095 or higher. Prerequisite: Accuplacer
score of 25 or below. Semester offered: Fall, Spring.
MATH-095 Pre-Algebra (3 + 2P) 4 cr.
Instructs the student on the basic operations of arithmetic applied to whole numbers,
integers, fractions and decimals. Topics include measurement, conversions, scientific
notation, percents, ratio and proportions, basic geometry, formulas, and the introduction of
variable expressions and linear equations. (RR option course). Prerequisite: Accuplacer
score of 26-65 in Arithmetic and 0-40 in Algebra. Students with an Accuplacer score of
26-35 should also enroll in LRNS 095 as a corequisite. Semester offered: Fall, Spring and
Summer.
MATH-096 Introductory Algebra (3 + 2P) 4 cr.
Instructs students in the knowledge of algebra involving linear content, equations,
functions, and inequalities in one variable or two variables. This course demonstrates
simplifying, and solving methods. Topics such as expressions, radicals, exponents, two and
three-dimensional geometric shapes, linear systems and polynomials are also introduced.
(RR option course). Prerequisite: Grade of "C" or better in MATH 095 or Accuplacer score
of 66-120 in Arithmetic or 41-60 in Algebra. Semester offered: Fall, Spring and Summer.
MATH-105 SPIN: (Special Interest) 1-3 cr.
Course is designed to address a variety of subjects required to meet the needs of lifelong
learning students. Not available for transfer nor applicable as an elective.
MATH-113 Applied Mathematics for Vocational Studies 3 cr.
Instructs students in the knowledge of addition, subtraction, multiplication and division of
whole numbers, fractions and decimals. Topics also include ratios and proportions,
percents, standard and metric measurements and conversions. Basic fundamentals of
algebra, operations of rational numbers, algebraic expressions, solving equations,
formulas, geometry and trigonometric concepts of sine, cosine, tangent and the
Pythagorean Theorem. This course emphasizes application models required in vocational
programs. Prerequisite: Grade of "C" or better in MATH 095 or Accuplacer score of 66+
(arithmetic) or 41+ (algebra). Semester offered: Fall and Spring.
MATH-114 Math for Health Careers 3 cr.
This course introduces the computational skills needed to study in health careers programs.
Topics include operations on fractions, decimals, percents, as well as the use of formulas,
ratio and proportion, and measurement. Students will solve word problems specific to
medication orders. Prerequisite: Grade of "C" or better in MATH 095 or Accuplacer score
of 66+ (arithmetic) or 41+ (algebra). Semester offered: Fall, Spring and Summer On
Demand.
MATH-115 Intermediate Algebra-Applications 4 cr.
Instructs students in the knowledge of algebra involving nonlinear content, expressions,
equations, functions, and inequalities. This course demonstrates simplifying, factoring, and
solving methods emphasizing polynomial, quadratic, rational, radical, exponential and
logarithms. Prerequisite: Grade of "C" or better in MATH 096 or Accuplacer score of 61 –
103 (algebra). Semester offered: Fall, Spring and Summer.
MATH-116 Math for High Tech Careers 3 cr.
Instructs students in the knowledge of mathematics related to the electronics field. Topics
include: scientific calculations, conversions, methods of algebra leading to solving and
manipulation of formulas, relations, functions including logarithmic and exponential,
radicals, fundamentals of trigonometry involving angular and circular functions, vectors
and phasors. Prerequisite: Grade of "C" or better in MATH 096 or Accuplacer score of 41-
60 (algebra). Semester offered: Fall and Spring.
MATH-121 Mathematics for the Elementary Teacher I 3 cr.
A development of the properties, concepts, and logical reasoning of the arithmetic of
whole numbers. Topics include problem solving techniques, set theory, numeration
systems, algorithms of arithmetic in base ten and other bases, estimation and mental
computation techniques, and number theory. Prerequisite: Grade of "C" or better in MATH
115 or Accuplacer score of 104 - 120 (Algebra). Semester offered: Fall and Spring.
MATH-122 Mathematics for the Elementary Teacher II 3 cr.
A development of the properties, concepts, and logical reasoning of (1) the arithmetic of
real numbers, (2) statistics, and (3) probability. Topics include fractions, decimals, ratios,
proportions, percent, integers, rational numbers, real numbers, algebra, statistics, and
probability. Prerequisite: Grade of "C" or better in MATH 121. Semester offered: Fall and
Spring.
MATH-130 Conceptual Mathematics 3 cr.
This course covers a variety of practical mathematical concepts for non-science majors.
Topics include set theory, geometry, counting methods, probability, statistics and finance.
Critical thinking and problem solving skills are stressed. Prerequisite: Grade of "C" or
better in MATH 096 or Accuplacer score of 61 – 103 (algebra). Semester offered: Fall,
Spring and Summer.
MATH-180 Trigonometry 3 cr.
Instructs the student in the knowledge of triangles, radian and degree measure,
trigonometric functions, trigonometric identities, properties, inverse trigonometric
functions, polar coordinates, vectors. Prepares the student to utilize trigonometry in the
analysis of calculus. Prerequisite: Grade of "C" or better in MATH 115 or Accuplacer
score of 104-120. Semester offered: Fall, Spring and Summer.[NM Common Course
Number MATH 1213, Area II: Mathematics Core]
MATH-185 College Algebra 3 cr.
Instructs students in the knowledge of linear, piecewise, quadratic, polynomial, rational,
inverse, exponential and logarithmic functions; function topics include finding the average
rate of change, analyzing graphs, graphing using transformations, finding roots in the real
and complex number systems, and constructing functions to model real-world applications.
Other topics include systems of linear equations and inequalities, matrices, linear
programming, sequences and series. Prerequisite: Grade of "C" or better in MATH 115 or
Accuplacer score of 104-120. Semester offered: Fall, Spring and Summer.[NM Common
Course Number MATH 1113, Area II: Mathematics Core]
MATH-187 Applications of Calculus 4 cr.
An introduction to the methods of differential and integral calculus. Polynomial, rational,
exponential and logarithmic functions are used in topics such as rates of change, limits,
derivatives, continuity, extrema, graphing, antiderivatives, definite integrals and techniques
of integration. Applications involving optimization, related rates, growth and decay models
and marginality will be studied primarily in context of business related topics. Prerequisite:
Grade of "C" or better in MATH 185. Semester offered: Spring.
MATH-188 Calculus I (3 + 2P) 4 cr.
Instructs the student in the methods of differential calculus. Topics include elementary
algebraic and transcendental functions, limits, continuity, differentiation and optimization.
Other topics include L'hopital's rule, Newton's method, Riemann sums, indefinite and
definite integration, and the fundamental theorem of calculus. Mathematical software will
be utilized throughout the course to expose students to computer algebra systems.
Prerequisite: Grade of "C" or better in MATH 185 and MATH 180. Semester offered: Fall,
Spring, and Summer.[NM Common Course Number MATH 1614, Area II: Mathematics
Core]
MATH-189 Calculus II (3 + 2P) 4 cr.
A continuation of MATH 188; extending to topics in Techniques of Integration, Numerical
Integration, Infinite Series, Power Series, Maclaurin & Taylor Series and Taylor
Polynomials. Prerequisite: Grade of "C" or better in MATH 188. Semester offered: Fall,
Spring, and Summer. [NM Common Course Number MATH 1623, Area II: Mathematics
Core]
MATH-215 Mathematics for Elementary and Middle School Teachers 3 cr.
A development of the properties, concepts, and logical reasoning of geometry. Topics
include analysis of geometric shapes, measurement, triangle congruence and similarity,
basic Euclidean constructions, coordinate geometry, transformations, and tessellations.
Prerequisite: Grade of "C" or better in MATH 121. Semester offered: Fall and Spring
MATH-231 Discrete Mathematics 3 cr.
An introductory course encompassing set theory, logic, induction and recursion, number
theory, matrices, combinatorics, graph theory, trees, boolean algebra, and models of
computation. Prerequisite: Grade of "C" or better in MATH 188. Semester offered: Fall.
MATH-251 Statistics (3 + 2P) 4 cr.
Instructs the student in the knowledge of an introduction to descriptive and inferential
statistics, which includes the following topics: sampling theory, experimental design,
probability, probability distributions, confidence intervals, correlation and regression, tests
of hypotheses (using the normal, student-t, chi-square, and F-distributions) and ANOVA.
Lab time is provided for data analysis using statistical software. Prerequisites: Grade of
"C" or better in MATH 115, MATH 130, or higher or Accuplacer score: 104-120.
Semester offered: Fall, Spring and Summer. [NM Common Course Number MATH 2113,
Area II: Mathematics Core]
MATH-268 Calculus III (3 + 2P) 4 cr.
Instructs the student in the techniques of multivariable calculus. Topics include partial
differentiation, linear and quadratic approximations, optimization, multiple integration,
vector fields, line and flux integrals, curl, divergence, and the three fundamental theorems.
Prerequisite: Grade of "C" or better in MATH 189. Semester offered: Fall and Spring. [NM
Common Course Number MATH 2614, Area II: Mathematics Core]
MATH-275 Linear Algebra 3 cr.
An applications approach to introductory linear algebra. Covers systems of linear
equations, matrices, linear independence, vector spaces, inner product spaces, linear
transformations, eigenvalues, eigenvectors and applications. Prerequisite: Grade of "C" or
better in Math 189. Semester offered: On Demand.
MATH-282 Differential Equations 4 cr.
A course which gives an in-depth introduction to ordinary differential equations. Theoretical
questions such as existence and uniqueness will be addressed but emphasis
will be on concepts and applications. Topics include first order techniques and applications,
second order techniques and applications, Laplace Transform methods, Cauchy-Euler
equations, infinite series techniques, systems, numerical techniques and qualitative aspects.
Prerequisite: Grade of "C" or better in MATH 268. Semester offered: Spring or On Demand.
[NM Common Course Number MATH 2814, Area II: Mathematics Core]
MATH-295 SPTO: (Special Topics) 1-4 cr.
Special or specific topic course to meet the needs of students. Topics and credits are
announced in the Schedule of Classes. These courses may be used as electives for
Associate degree requirements. May be repeated one or more times for additional credit.
No more than 6 credits of special topic courses can be used toward a |
Mathematics - Algebra (529 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics which the engineer must emphasize, such as numerical computations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid.<br><br>The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject.<br><br>The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytic geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of effort.<br><br>The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
Francis William Newman was an emeritus professor of University College in London and an honorary fellow of Worcester College, Oxford. Considered quite the renaissance man, Newman's interests ranged wildly, from writings on philosophy, English reforms, Arabic, diet, grammar, political economy, Austrian Politics, Roman History, and math. He wrote at length on every subject he found of interest, and this book, Mathematical Tracts is a testament to his very successful career as a mathematician and his eloquence as an impassioned author. At its core, this book explores many of the basics theorems and principles behind geometry, aimed at the budding mathematician to encourage interest and educate. A wonderful beginners guide, but also an interesting read for anyone wanting to refresh their foundational knowledge in geometry, this book is an easy to understand and approachable guide to mathematics. After establishing the basics, this book goes in-depth on many geometrical concepts such as the treatment of ration between quantities incommensurable and primary ideas of the sphere and circle. Newman's vast knowledge of mathematics is put to excellent use in this text, expounding on mathematical concepts and explaining them with such clarity that regardless of prior mathematical knowledge, the reader is guaranteed to understand the concepts. Newman highlights a variety of shapes such as pyramids and cones in their geometric context and explains their mathematical significance. He also expands the reader's understanding of parallel straight lines and the infinite area of a plane angle, and ends the book with a plethora of tables and helpful mathematical examples intended to further clarify the core concepts of the text. Truly a one of a kind, Mathematical Tracts is the perfect book for anyone interested in mathematics. Whether you're an early learner or a seasoned professional, you will find new information that is communicated in such a passionate and compelling way that it is impossible not to be enthused and excited about the topic. An incredibly approachable book laden with mathematical concepts that are made both interesting and exciting by the overwhelming passion of the author, this book is highly recommended for all readers.
Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections.
Isaac Todhunter's Algebra for Beginners: With Numerous Examples is a mathematics textbook intended for the neophyte, an excellent addition to the library of math instructionals for beginners. Todhunter's textbook has been divided into 44 chapters. Early chapters highlight the most basic principles of mathematics, including sections on the principal signs, brackets, addition, subtraction, multiplication, division, and other topics that form the foundation of algebra. Simple equations make up the large majority of the material covered in this textbook. Later chapters do introduce quadratics, as well as other more advanced subjects such as arithmetical progression and scales of notation. It is important to note that Todhunter sticks very much to the basics of algebra. The content of this book lives up to its title, as this is very much mathematics for beginners. The content is provided in an easy to follow manner. This book could thus be used for independent learning as well as by a teacher. A great deal of focus has clearly been given to providing examples. Each concept is accompanied by numerous sample questions, with answers provided in the final chapter of the book. The example questions are every bit as important as the explanations, as one cannot begin to grasp mathematical concepts without having the opportunity to put them into practice. The basics of algebra are explained in an easy to follow manner, and the examples provided are clear and help to expand the knowledge of the learner. If given a chance, Isaac Todhunter's Algebra for Beginners: With Numerous Examples can be a valuable addition to your library of mathematics textbooks.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves.
The Principles of Mathematics: Vol. 1 is a terrific introduction to the fundamental concepts of mathematics. Although the book's title involves mathematics, it is not a textbook packed with equations and theorems. Instead philosopher Bertrand Russell uses mathematics to explore the structure of logic. Russell's ultimate point is that mathematics is logic and logic itself is truth. The book is substantial and covers all subjects of mathematics. It is divided into seven sections: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. Russell covers all the major developments of mathematics and the contributions of important figures to the field. His sharp mind is evident throughout The Principles of Mathematics, as he challenges established rules and teachers readers how to think through difficult problems using logic. Russell was one of the great minds of the 20th Century. In this book he discusses how his ideas were influenced by the logician Peano. He also debates other philosophers and mathematicians, and even anticipates the Theory of Relativity, which had not yet been published by Einstein. One does not need to love mathematics to gain insights from The Principles of Mathematics: Vol. 1. Those who are interested in logic, intellectualism, philosophy or history will find significant insights into logical principles. Readers who desire an intellectual challenge will truly enjoy The Principles of Mathematics: Vol. 1.
The present work is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, which in the former work were treated in an elementary manner; and we have here introduced theorems and examples which are unsuitable for a first course of reading.<br><br>From this point the work covers ground for the most part new to the student, and enters upon subjects of special importance: these we have endeavoured to treat minutely and thoroughly, discussing both bookwork and examples with that fulness which we have always found necessary in our experience as teachers.<br><br>It has been our aim to discuss all the essential parts as completely as possible within the limits of a single volume, but in a few of the later chapters it has been impossible to find room for more than an introductory sketch; in all such cases our object has been to map out a suitable first course of reading, referring the student to special treatises for fuller information.<br><br>In the chapter on Permutations and Combinations we are much indebted to the Rev. W. A. Whitworth for permission to make use of some of the proofs given in his Choice and Chance.
The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value.
Having prefixed my name to the present edition of Euler's Algebra, it may be proper to give some account of the Translation; which I shall do with the greater pleasure, because it furnishes a favorable opportunity of associating my own labors, with those of my distinguished pupil, and most excellent friend, the late Francis Horner, M.P.<br><br>When first placed under my tuition, at the critical and interesting age of seventeen, he soon discovered uncommon powers of intellect, and the most ardent thirst for knowledge, united with a docility of temper, and a sweetness of disposition, which rendered instruction, indeed, a "delightful task." His diligence and attention were such, as to require the frequent interposition of some rational amusement, in order to prevent the intenseness of his application from injuring a constitution, which, though not delicate, had never been robust.
The Directly-Useful Technical Series requires a few words by of introduction. Technical books of the past have arranged themselves largely under two sections: the Theoretical and the Practical and the exercises are to be of a directly-useful character, but must at the same time be wedded to that proper amount of scientific explanation which alone will satisfy the inquiring mind. We shall thus appeal to all technical people throughout the land, either students or those in actual practice or those in actual practice.
It is the purpose of this work to present a through investigation of the various systems of Symbolic Reasoning allied to ordinary Algebra. The chief examples of such systems are Hamilton's Quaternions, Grassmann's Calculus of Extension and Boole's Symbolic Logic. Such algebras have an intrinsic value for separate detailed study; also they are worthy of a comparative study, for the sake of the light thereby thrown on the general theory of symbolic reasoning, and on algebraic symbolism in particular.<br><br>The comparative study necessarily presupposes some previous separate study, comparison being impossible without knowledge. Accordingly after the general principles of the whole subject have been discussed in Book I. of this volume, the remaining books of the volume are devoted to the separate study of the Algebra of Symbolic Logic, and of Grassmann's Calculus of Extension, and of the ideas involved in them. The idea of a generalized conception of space has been made prominent, in the belief that the properties and operations involved in it can be made to form a uniform method of interpretation of the various algebras.<br><br>Thus it is hoped in this work to exhibit the algebras both as systems of symbolism, and also as engines for the investigation of the possibilities of thought and reasoning connected with the abstract general idea of space. A natural mode of comparison.between the algebras is thus at once provided by the unity of the subject-matters of their interpretation. The detailed comparison of their symbolic structures has been adjourned to the second volume, in which it is intended to deal with Quaternions, Matrices, and the general theory of Linear Algebras. This comparative anatomy of the subject was originated by B. Peirce's paper on Linear Associative Algebra, and has been carried forward by more recent investigations in Germany.
There are many men and women who, from lack of opportunity or some other reason, have grown up in ignorance of the elementary laws of science. They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge.<br><br>Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance.<br><br>To meet this double need - the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him - is the aim of the "Thresholds of Science" series.<br><br>This series consists of short, simply written monographs by competent authorities, dealing with every branch of science - mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
The old order in mathematics teaching is rapidly giving way to a newer one more interesting, more vital, and more effective. Formerly, all phases of arithmetic were taught in the seventh and eighth grades. In the ninth grade, the foundations of algebra were laid. The latter had practically no connection with the arithmetic that came before nor with the geometry that came after. It was mostly the juggling of symbols that symbolized nothing. This algebra took on some meaning later for the few who continued the study of mathematics in higher schools. But for the many, it never functioned.<br><br>With the organization of the junior high schools has come a reorganization of mathematics. It is now taught in cycles, each complete in itself and adapted to the needs and abilities of the pupil, regardless of whether he continues the study of mathematics in school or applies it in the office, store, or shop. The purpose of the junior cycle is to give the pupil a broad knowledge and usable power and skill in the field of elementary mathematics. This cannot be done by the old tandem courses of arithmetic, algebra, geometry, and trigonometry. Nor will alternate bits of formal algebra, geometry, and trigonometry solve the problem. The result is a mastery of none and a confusion of all.<br><br>In this series the elements of arithmetic, geometry, algebra, and trigonometry are taught as one subject. Book One is largely arithmetical, but it uses the graph and the formula.
The theory of linear associative algebras (or closed systems of hypercomplex numbers) is essentially the theory of pairs of reciprocal linear groups (52) or the theory of certain sets of matrices or bilinear forms (53). Beginning with Hamilton's discovery of quaternions seventy years ago, there has been a rapidly increasing number of papers on these various theories. The French Encyclopedia of Mathematics devotes more than a hundred pages to references and statements of results on this subject (with an additional part on ordinary complex numbers). However, the subject is rich not merely in extent, but also in depth, reaching to the very heart of modern algebra.<br><br>The purpose of this tract is to afford an elementary introduction to the general theory of linear algebras, including also non-associative algebras. It retains the character of a set of lectures delivered at the University of Chicago in the Spring Quarter of 1913. The subject is presented from the standpoint of linear algebras and makes no use either of the terminology or of theorems peculiar to the theory of bilinear forms, matrices, or groups (aside of course from 52-54, which treat in ample detail of the relations of linear algebras to those topics).<br><br>Part I relates to definitions, concrete illustrations, and important theorems capable of brief and elementary proof. A very elementary proof is given of Frobenius's theorem which shows the unique place of quaternions among algebras. The remarkable properties of Cayley's algebra of eight units are here obtained for the first time in a simple manner, without computations. Other new results and new points of view will be found in this introductory part.<br><br>In presenting in Parts II and IV the main theorems of the general theory, it was necessary to choose between the expositions by Molien, Cartan and Wedderburn (that by Frobenius being based upon bilinear forms and hence outside our plan of treatment).
This book is an outgrowth of the conviction of the authors that Higher Algebra, to be worthy of the name, must employ advanced methods, and that the method which chiefly marks advanced work in analysis is that of limits. In all but a few chapters the work is based upon limits, the proofs being made as rigorous as seems advisable for immature students, with occasional comment on points where the proof is not rigorous, or where theorems not yet proved are employed. It is our hope that there is nothing to be unlearned in later work. The ordinary Algebra course in college covers a semesters work about forty-five class appointments. It has been found by actual use that in this time Chapters III, IV, V, Vi, VII, XII can be covered, while Chapter Xhas been taught in connection with a course in Trigonometry. The chapters on Rational and Irrational Numbers are intended for reference rather than for detailed study, while the chapters on Permutations, Combinations and Probability, Partial Fractions, Complex Numbers, and Integration may be substituted for other chapters as subjects of study, or serve for reference in later work.
This little book was written at the instance of Messrs. Adam Y)Hilger, and, in accordance with their desire, it contains just what is required for the purpose of reading and handling my Simplified Method of Tracing Rays, etc. (Longmans, Green Co., London, 1918). With this practical aim in view, all critical subtleties have (js been purposely avoided. In fact, it is scarcely more than a synoptical presentation of the elements of Vector Algebra covering the needs of those engaged in geometrical optics. At the same time, however, it is hoped that this booklet will serve a more general purpose, viz. to provide everybody unacquainted with the subject with an easy introduction to the use of Vector Algebra. It is scarcely necessary to explain that the deductions given in this book are based on Euclids axioms, notably with the inclusion of his postulate of parallels upon which the equality of vectors is most essentially based. Those readers who are desirous of seeing how the formal rules here given can be generalized so as to be valid independently of the axioms of congruence and of parallels, may consult the authors Projective Vector Algebra (Bell Sons, 1919), and a sequel to it published in Phil. Mag. for July, 1919, pp. 115-143.It is, however, advisable for the student to become first thoroughly familiar with the euclidean vector algebra as here presented. I tajce the opportunity of expressing my sincere thanks to Messrs. Hilger for enabling me to make this further contribution towards the promotion of the more general use of this powerful and convenient language of vectors, and to the Publishers for the care they have bestowed upon this little book. L.S. London, August 1919.
This little book on Algebra has been prepared for the use of students in their First Year at the University other than those following the special course in Mathematics and Physics. Students of those of whom is required the Algebra of the General Course will find the work covered in the first four chapters, while students who are taking any of the special courses in Pure Science or any of the courses in the School of Practical Science will read in addition Chapters V and VI. Chapter VII has been added to meet the needs of those students who are to study the Calculus in their Second Year.
This new Dover edition first published in 1958 is an unabridged and unaltered republication of the first edition which was originally entitled Memorabilia Mathematica or The Philomath's Quotation-Book.
It is evident that the problem of preparing a work upon the teaching of elementary mathematics may be attacked from any one of various standpoints. A writer may confine himself to model lessons, for example; or to the explanation of the most difficult portions of the subject matter; or to the psychology of the subject; or to the comparison of historic methods; or to the exploiting of some hobby which he has ridden with success; or to those devices which occupy so much time in the ordinary training of teachers. He may say, and with truth, that elementary mathematics now includes trigonometry, analytic geometry, and the calculus; and that therefore a work with this title should cover the ground of Dauge's "Methodologie," or of Laisant's masterly work, "La Mathematique." He may proceed dogmatically, and may lay down hard and fast rules for teaching, excusing this destruction of the teacher's independence by the thought that the end justifies the means. But with a limited amount of space at his disposal, whatever point of attack he selects he must leave the others more or less untouched; he cannot condense an encyclopedia of the subject in three hundred pages thisThis tract is intended to give an account of the theory of equations according to the ideas of Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of Abel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations.<br><br>More than to any other treatise, I feel indebted to Professor H. Weber's invaluable Algebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit.<br><br>I am obliged to Mr Morris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with Art. 52. |
Practical Algebra: A Self-Teaching Guide
With a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or ...Show synopsisWith a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or high school text, the format is reader friendly, particularly in this Second Edition, and clear enough to be used for self-study in a non-classroom environment. "Pre-test" material enables readers to target problem areas quickly and skip areas that are already well understood. Some new material has been added to the Second Edition and redundant or confusing material omitted. The first chapter has undergone major revision. Chapters feature "post-tests" for self-evaluation. Thousands of practice problems, questions and answers make this algebra review a unique and practical text |
Find an Evans, CO AlgebraThese and other basic skills form the core to all future mathematical endeavours. Differential equations (both ordinary and partial) are a foundation for learning methods used to solve ODEs (for example Bernoulli and Euler style solution methods). Learning how to apply methods to apply to rate |
McGraw-Hill Education has introduced ALEKS 360, a mathematics solution that combines an artificial intelligence and personalized learning program with a fully integrated, interactive e-book package. ALEKS 360 delivers assessments of students' math knowledge, guiding them in the selection of appropriate new study material, and recording their progress toward mastery of course goals. Through adaptive questioning, ALEKS accurately assesses a student's knowledge state and delivers targeted instruction on the exact topics a student is most ready to learn.
The e-books featured within ALEKS 360 are interactive versions of their physical counterparts, which offer virtual features such as highlighting and note-taking capabilities, as well as access to multimedia assets such as images, video, and homework exercises. E-books are accessible from ALEKS Student Accounts and the ALEKS Instructor Module for convenient, direct access.
The initial e-books to be offered in ALEKS 360 include: Introductory Algebra, Second Edition, by Julie Miller and Molly O'Neill; Intermediate Algebra, Second Edition, by Miller and O'Neill; College Precalculus, Second Edition, by John W. Coburn; and College Algebra, Second Edition, by Coburn. |
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Starting at $25Friendly Introduction to Number Theory, A
Friendly Introduction to Number Theory, A
Summary
A Friendly Introduction to Number Theory, Fourth Editionis designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.
Author Biography
Joseph H. Silverman is a Professor of Mathematics at Brown University. He received his Sc.B. at Brown and his Ph.D. at Harvard, after which he held positions at MIT and Boston University before joining the Brown faculty in 1988. He has published more than 100 peer-reviewed research articles and seven books in the fields of number theory, elliptic curves, arithmetic geometry, arithmetic dynamical systems, and cryptography. He is a highly regarded teacher, having won teaching awards from Brown University and the Mathematical Association of America, as well as a Steele Prize for Mathematical Exposition from the American Mathematical Society. He has supervised the theses of more than 25 Ph.D. students, is a co-founder of NTRU Cryptosystems, Inc., and has served as an elected member of the American Mathematical Society Council and Executive Committee. |
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citation: Int. J. Engng Ed. Vol. 16, No. 5, pp. 401±407, 2000.
Conclusions
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references available if requested.Algebra is often the point in school when students begin to struggle in math. It is the point where more thorough understanding of the material is necessary in order see how to solve the problem. While many students learn in different ways, teachers do not always have time to explain the material in a way that is clear to every student |
Welcome to Beyond Calculus
Developed by Jake Chipps
Why Use This Site?
Beyond Calculus is an online video-based textbook that provides support to students taking AP Calculus AB. Are you sitting at home wracking your brains over your homework, and need help? Try watching the videos in whatever section you are stumped. Is your math class going too fast? The instructional videos on this site may just provide the understanding you need to excel. Cramming for the AP exam or a final? Why not review by going through this e-book? You will find instructional videos here rather than academic text.
How to Use This Site
Each section of Calculus A and B is organized in the table of contents. Click on any topic to view that particular lesson. Videos are organized to enhance understanding. The first video provides a big-picture view of the topic, and each subsequent video provides the user with more difficult examples. For the best experience, It is suggested that you press pause when you need to think about a concept. Rewatch videos if necessary, and you will be amazed at your level of understanding by the end.
Why Is This E-Book Free?
Information should be free and available to all. Not only should information be free, but it should be available anywhere at any time. This e-book can be viewed on all devices, including desktops, iPads and other mid-size devices, and phones with internet access. After creating online videos to supplement and enhance my classroom instruction, I decided to compile my work into an online textbook. Rather than charge for these services, I am providing my work to the world free of charge, as it should be. |
Undergraduate Algebraic Geometry - 89 edition
ISBN13:978-0521356626 ISBN10: 0521356628 This edition has also been released as: ISBN13: 978-0521355599 ISBN10: 0521355591
Summary: Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differen...show moretial geometry, and number theory. The book contains numerous examples and exercises illustrating the theory. ...show less
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Thank You! Once a strong foundation in Prealgebra is achieved, a student is ready to tackle the challenges of the algebraic language. The main concepts that a student must work hard on for success in Algebra I are expressions, solving and checking all forms of |
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Student Solutions Manual for Tussy/Gustafson/Koenig's Introductory Algebra, 4th:Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in INTRODUCTORY ALGEBRA, 4th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples. |
Importance of Finding Analytic Solutions to
Problems
Overview
The importance of finding analytic solutions
to assigned problems is (or should be) emphasized in physics
courses. Many students perform poorly on assigned problems simply
because they generate numerical solutions without first achieving
an analytic solution. So, it seems to be worthwhile to emphasize
the importance in a different way and by a different medium than
classroom discussion. Therefore this module.
In my own courses, analytic solutions are
encouraged by the grading scheme. Full credit is given for a
correctly derived analytic solution to any assigned problem,
whether or not a numerical solution is presented. Only if the
problem statement requires a numerical value of the solution is the
numerical value part of the credit awarded. A purely numerical
solution, even if correct, never receives full credit, and may
receive zero credit if there is no hint of analysis in the
student's work.
What is meant by an "analytic solution"?
There are several short answers to this question. One is:
"Always completely solve the problem before substituting any
numerical values." Another is: "Solve the problem
'by the symbols' instead of 'by the
numbers'." These short answers deserve some added
details.
Every assigned problem is to be addressed by
applying to the problem one or more of the fundamental
relationships of the physics we have studied. Each problem provides
one or more items of known quantities, the data of the problem. The
data may or may not be given numerical values. If data are
presented only as numerical values, it is the responsibility of the
student to assign symbols that algebraically represent each item of
data. Every problem asks that one or more initially unknown
quantities be determined. If the problem does not provide algebraic
symbols for unknown quantities, it is again the student's
responsibility to assign symbols to them.
An analytic solution for an unknown quantity
is an equation that explicitly states how the unknown quantity,
isolated by itself on one side of an equal sign, depends upon the
symbols assigned to data. The solution should be written in the
simplest form available. The solution will often also contain
mathematical constants (such as "π" or Cartesian
unit vectors) and physical constants (such as "g", the
local gravitational field strength). An analytic solution does not
contain other unknown quantities. Sometimes it is useful in
simplifying a solution to define a symbol for a collection of known
quantities. It is OK for such a symbol to appear in a solution, but
only if it is clearly defined.
Scenario
Forget for a moment that I am a professor in
a college course. Assume instead that I am a Project Manager for
Apex Engineering, Inc., and that you are a freshly-minted
engineering graduate assigned to work for me on a project. This
scenario may be of some interest, because if you are reading this
module you are probably an undergraduate student with a declared
major in the sciences, mathematics, or engineering. So you have
expressed a desire to be educated for technical work.
As your supervisor, I assign you project
tasks (instead of class problems), and I am responsible for
recommendations to company management regarding your salary, your
continuing employment, your raises, and your promotions (instead of
awarding grades). (By the way, the author actually did this kind of
work in private industry for 15 years.)
Each task I assign to you contains several
technical problems (usually more difficult than the ones you are
given as a student). Your solutions to those problems will greatly
influence my recommendations to management regarding your
employment with the company. Now, ask yourself, do I want to see
analytic solutions from you, or would I prefer only numerical
solutions to the problems?
The answer, as you might have already
guessed, is that I definitely want analytic solutions. (More than
once, I quickly fired "engineers" who either refused to, or were
incapable of, generating analytic solutions to problems. Fellow
Project Managers were often quicker about this than I was.) You may
wonder why the preference is so strong. There are a number of
reasons.
Reason 1: Is the Solution Correct?
It is usually very difficult to guarantee
that a numerical solution is correct. On the other hand, an
analytic solution is easily checked, and one can often be certain
that it is either correct or incorrect. About the only way to
validate a numerical solution is to have several people
independently perform the calculation. This is too expensive, in
both time and money, to normally be done, because the project must
be completed within a budget and to meet a deadline.
A Project Manager who lets incorrect
solutions "out the door", will also soon be "out the door"!
Reason 2: The Data will Change
Every Project Manager knows that the data on
which calculations are done is subject to change. Maybe the
original foundations designed for a building are found to violate a
city zoning ordinance. Maybe someone in the marketing department
discovers that consumers want a smaller widget, or the competition
has added a feature that our widget must also include. Or maybe the
EPA has issued a new regulation that means the smokestack emissions
have to be lowered.
The likelihood of getting all the way to the
end of a project without some significant changes in the original
data is virtually zero. (Projects usually take weeks or months,
some much longer.) So, how much time and money does it cost to
adjust the solutions to changes in the values of the data?
If the original calculations produced only a
numerical result, and the data have changed, then the only recourse
is to do the entire calculation over again from scratch. This is
generally prohibitively expensive. If the original calculations
produced analytic solutions, changes in the data may not affect the
solution at all, or the changes may be accommodated by the solution
much more quickly and easily than doing the calculations over again
from the beginning.
Reason 3: Numerical Solutions have Little Value
In the great preponderance of problems
encountered in real-world practice, a numerical solution is of
little value. What is always of importance is how the solution
depends upon the data, which is precisely what an analytic solution
tells you. This is especially true of design projects.
Take for example a calculation of the amount
of concrete needed to pour the foundations of a new building. The
shape and size of the foundations may have changed six times over
the course of the design project. The very first time that the
numerical solution is actually needed is after everyone involved
(the engineer, the Project Manager, other company management, the
client, and the building inspector) has signed off on the design to
actually be used, and it is time to order the concrete from the
concrete vendor. Any numerical values for the amount of concrete
prior to the final design are simply useless, of no value
whatsoever. The original analytical solution for the amount of
concrete needed may still be correct. Even if the design changes do
change the original solution, if the derivation of that first
solution is documented, it is probably a quick and easy task to
change the derivation for a correct final solution.
Reason 4: Numerical Solutions Waste Effort
This is the least important reason to prefer
analytic solutions, but it is significant nonetheless. A
characteristic of numerical solutions is that often quantities that
algebraically "cancel out" of the final analytic solution are
multiplied (perhaps several times) by individual terms, then the
final sum is divided by the same quantity. A simple example can be
seen in the calculation of the final velocity of a particle in free
fall, using the energy equation. The mass of the particle appears
in the energy equation, but vanishes from the solution for the
final velocity. Such quantities may be multiplied and divided
several times in a numerical solution, but simply vanish from an
analytic solution.
What if an Analytic Solution is Impossible?
Problems for which no analytic solution is
possible are rare in introductory courses. You may see one or two
like this in an introductory course in physics. On the other hand,
such problems are fairly frequent in upper-level and graduate
courses, and very common in actual professional practice.
Such problems are usually solved using
computerized numerical techniques.
What is most difficult about problems that
require numerical techniques is validating that the solution is
indeed correct. This always requires much more analysis than is the
case for problems that admit of analytic solutions. This is why you
are not exposed to such problems until your analytical skills have
reached a certain level.
The validation of the solution of a problem
that cannot be solved analytically usually means a validation of
the computer code that generates the numerical solution |
The quadratic formula expresses the solution of the degree two equation in terms of its coefficients .
Algebra (from Arabical-jebr meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form algebra is the study of symbols and the rules for manipulating symbols[2] and is a unifying thread of all of mathematics.[3]As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Near East, by such mathematicians as Omar Khayyam (1050-1123).
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[4] For example, in the letter is unknown, but the law of inverses can be used to discover its value: . In , the letters and are variables, and the letter is a constant. Algebra gives methods for solving equations and expressing formulas that are much easier (for those who know how to use them) than the older method of writing everything out in words.
The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology (see below).
How to distinguish between different meanings of "algebra"
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Such a situation, where a single word has many meanings in the same area of mathematics, may be confusing. However the distinction is easier if one recalls that the name of a scientific area is usually singular and without an article and the name of a specific structure requires an article or the plural. Thus we have:
As a single word without article, "algebra" names a broad part of mathematics (see below).
Algebra as a branch of mathematics
Algebra began with computations similar to those of arithmetic, with letters standing for numbers.[4] This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation
can be any numbers whatsoever (except that cannot be ), and the quadratic formula can be used to quickly and easily find the value of the unknown quantity .
Before the 16th century, mathematics was divided into only two subfields, arithmetic and geometry. Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from 16th or 17th century. From the second half of 19th century on, many new fields of mathematics appeared, most of which made use of both arithmetic and geometry, and almost all of which used algebra.
History
The start of algebra as an area of mathematics may be dated to the end of 16th century, with François Viète's work. Until the 19th century, algebra consisted essentially of the theory of equations. In the following, "Prehistory of algebra" is about the results of the theory of equations that precede the emergence of algebra as an area of mathematics.
The Hellenistic mathematicians Hero of Alexandria and Diophantus[11] as well as Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brahmasphutasiddhanta are on a higher level.[12] For example, the first complete arithmetic solution (including zero and negative solutions) to quadratic equations was described by Brahmagupta in his book Brahmasphutasiddhanta. Later, Arabic and Muslim mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi contribution was fundamental. He solved linear and quadratic equations without algebraic symbolism, negative numbers or zero, thus he has to distinguish several types of equations.[13]
In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is much debate over whether al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.[14] Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[15] Those who support Al-Khwarizmi point to the fact that he introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to,[16] and that he gave an exhaustive explanation of solving quadratic equations,[17] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[18] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems".[19]
The Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. Another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various cases of cubic equations.[20] He also developed the concept of a function.[21] The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji,[22] and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations using numerical methods. In the 13th century, the solution of a cubic equation by Fibonacci is representative of the beginning of a revival in European algebra. As the Islamic world was declining, the European world was ascending. And it is here that algebra was further developed.
Areas of mathematics with the word algebra in their name
Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example. Others do not: group theory, ring theory, and field theory are examples. In this section, we list some areas of mathematics with the word "algebra" in the name.
Elementary algebra, the part of algebra that is usually taught in elementary courses of mathematics.
Elementary algebra
Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z). This is useful because:
It allows the general formulation of arithmetical laws (such as a + b = b + a for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.
It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these. (For instance, "Find a number x such that 3x + 1 = 10" or going a bit further "Find a number x such that ax + b = c". This step leads to the conclusion that it is not the nature of the specific numbers that allows us to solve it, but that of the operations involved.)
It allows the formulation of functional relationships. (For instance, "If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied".)
Polynomials
A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the product of a constant and a finite number of variables raised to whole number powers. For example, x2 + 2x − 3 is a polynomial in the single variable x. A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication. For example, (x − 1)(x + 3) is a polynomial expression, that, properly speaking, is not a polynomial. A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression. The two preceding examples define the same polynomial function.
Two important and related problems in algebra are the factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials that can not be factored any further, and the computation of polynomial greatest common divisors. The example polynomial above can be factored as (x − 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
Teaching algebra
It has been suggested that elementary algebra should be taught as young as eleven years old,[26] though in recent years it is more common for public lessons to begin at the eighth grade level (≈ 13 y.o. ±) in the United States.[27]
Since 1997, Virginia Tech and some other universities have begun using a personalized model of teaching algebra that combines instant feedback from specialized computer software with one-on-one and small group tutoring, which has reduced costs and increased student achievement.[28]
Abstract algebra
Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Here are listed fundamental concepts in abstract algebra.
Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property specific for the set. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups, which are the groups of integers modulon. Set theory is a branch of logic and not technically a branch of algebra.
Binary operations: The notion of addition (+) is abstracted to give a binary operation, ∗ say. The notion of binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure. Addition (+), subtraction (-), multiplication (×), and division (÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices, vectors, and polynomials.
Identity elements: The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. Not all sets and operator combinations have an identity element; for example, the set of positive natural numbers (1, 2, 3, ...) has no identity element for addition.
Inverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is written −a, and for multiplication the inverse is written a−1. A general two-sided inverse element a−1 satisfies the property that a ∗ a−1 = 1 and a−1 ∗ a = 1 .
Associativity: Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum. For example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (a ∗ b) ∗ c = a ∗ (b ∗ c). This property is shared by most binary operations, but not subtraction or division or octonion multiplication.
Commutativity: Addition and multiplication of real numbers are both commutative. That is, the order of the numbers does not affect the result. For example: 2 + 3 = 3 + 2. In general, this becomes a ∗ b = b ∗ a. This property does not hold for all binary operations. For example, matrix multiplication and quaternion multiplication are both non-commutative.
Groups
Combining the above concepts gives one of the most important structures in mathematics: a group. A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties:
An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a.
Every element has an inverse: for every member a of S, there exists a member a−1 such that a ∗ a−1 and a−1 ∗ a are both identical to the identity element.
The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is identical to a ∗ (b ∗ c).
If a group is also commutative—that is, for any two members a and b of S, a ∗ b is identical to b ∗ a—then the group is said to be abelian.
For example, the set of integers under the operation of addition is a group. In this group, the identity element is 0 and the inverse of any element a is its negation, −a. The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c)
The nonzero rational numbers form a group under multiplication. Here, the identity element is 1, since 1 × a = a × 1 = a for any rational number a. The inverse of a is 1/a, since a × 1/a = 1.
The integers under the multiplication operation, however, do not form a group. This is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer.
Semigroups, quasigroups, and monoids are structures similar to groups, but more general. They comprise a set and a closed binary operation, but do not necessarily satisfy the other conditions. A semigroup has an associative binary operation, but might not have an identity element. A monoid is a semigroup which does have an identity but might not have an inverse for every element. A quasigroup satisfies a requirement that any element can be turned into any other by either a unique left-multiplication or right-multiplication; however the binary operation might not be associative.
Rings and fields
Groups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied. The most important of these are rings, and fields.
A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not required. The additive (+) identity element is written as 0 and the additive inverse of a is written as −a.
Distributivity generalises the distributive law for numbers, and specifies the order in which the operators should be applied, (called the precedence). For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +.
The integers are an example of a ring. The integers have additional properties which make it an integral domain.
A field is a ring with the additional property that all the elements excluding 0 form an abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1.
The rational numbers, the real numbers and the complex numbers are all examples of fields.
See also
Notes
^I. N. Herstein, Topics in Algebra, "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964
^I. N. Herstein, Topics in Algebra, "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964
^ abc(Boyer 1991, "Europe in the Middle Ages" p. 258) "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."
^(Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."
^(Boyer 1991, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions."
^Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".
^(Boyer 1991, "The Arabic Hegemony" p. 239) "Abu'l Wefa was a capable algebraist as well as a trigonometer. ... His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus – but without Diophantine analysis! ... In particular, to al-Karkhi is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered)," |
Intermediate Algebra - 4th edition
Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief.Intermediate Algebra, Fourth Editionwas written to provide students with a solid foundation in algebra and to help them transition to their next mathematics course. The new edition offers new resources like theStudent Organizerand now includesStudent Resourcesin the back of the book to help...show more students on their quest for CD MISSING. Minimal wear/tear. Please contact us if you have any Questions. Item is clean and free from answers, writing, and/or highlighting. No pages missing.
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Student Book Higher 1: Higher 1: Edexcel Linear (A)
Collins New GCSE Maths Student Books are the perfect way to help students working at Grades G to C tackle the 2010 EDEXCEL GCSE Maths specification. ...Show synopsisCollins New GCSE Maths Student Books are the perfect way to help students working at Grades G to C tackle the 2010 EDEXCEL GCSE Maths specification. Packed with functional skills, problem solving and graded maths practice, it will give your students the confidence to take on all aspects of the new curriculum in their exams and own lives. Collins New GCSE Maths EDEXCEL Linear Student Book Higher 1, written by experienced teachers and examiners, is organised exactly according to the 2010 EDEXCEL GCSE Maths specification. It is the ideal resource to help students get the best results: * Enable students to monitor their own progress through the GCSE Maths course with Collins' colour-coded grades on every page and a grade booster at the end of every chapter * Be confident that students are practising the key elements of the new curriculum in every lesson with functional skills, problem solving and new exam-style questions within every exercise * Use the colourful functional skills and problem-solving pages at the end of every chapter to engage students with rich tasks that will develop their process skills and allow them to apply maths in stimulating real-life contexts * Show students exactly why each chapter matters to them with new chapter openers that develop the cross-curricular nature of maths * Give students the opportunity for self-assessment and guidance for their exam technique by using the comprehensive exam practice and worked exam questions with examiner notes at the end of every chapter * Deliver the key facts to students with the comprehensive glossary and mathematics fact sheet, designed to ensure that students understand crucial maths vocabulary and processes |
Practice Makes Perfect Statistics
With more than 1,000,000 copies sold, Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Statistics, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: Statistics is not focused on any particular test or exam, but complementary to most statistics curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied statistics. Its all-encompassing approach will appeal to both U.S. and international students.Sandra Luna Mc Cune has contributed to Practice Makes Perfect Statistics as an author. Sandra Luna McCune, Ph.D., is a Regents professor and test preparation specialist in the Department of Elementary Education at Stephen F. Austin State University in Texas. She resides in Nacogdoches, Texas. Vi Cain Alexander, Ph.D., is a professor and Reading Coordinator in the Department of Elementary Education at Stephen F. Austin State University in Texas. She resides in Nacogdoches, Texas. less |
Human Calculator 2.70 description
Advanced yet easy-to-use math calculator that immediately and precisely computes the result as you type a math expression. It allows multiples math expressions at same time. It also allows fractions a Free Download |
Euclidean and Non-Euclidean Geometry - 4th edition
Summary: This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two a...show moreppendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometryback NEAR FINE Hardback, 500 |
9780321654274
ISBN:
0321654277
Edition: 3 Pub Date: 2010 Publisher: Addison Wesley
Summary: Beckmann, Sybilla is the author of Mathematics for Elementary Teachers with Activity Manual (3rd Edition), published 2010 under ISBN 9780321654274 and 0321654277. Four hundred fifty five Mathematics for Elementary Teachers with Activity Manual (3rd Edition) textbooks are available for sale on ValoreBooks.com, two hundred fifty two used from the cheapest price of $5.54, or buy new starting at $28 |
Summary: This valuable activities-based text offering integrated experimental exercises appropriate for preservice mathematics and science teachers, and also serves as a practical resource for in-service graduate students desiring knowledge on how to integrate mathematics and science with technology.
Integrating Mathematics, Science, and Technology explores a broad range of sciences: physics, earth science, chemistry and biology. Basic mathematics skills in algebra...show more, statistics, and geometry are expanded by the use of classroom-appropriate technology such as graphing calculators, handheld data collection devices, and simple analytical instrumentation.
The lessons presented in this experimental guidebook have all been field-tested. They work! Set-up time is minimal, chemicals used are mostly household available, and waste disposal is not a problem. Most chapters begin with a historical approach, laying the foundation in both mathematics and science. Students are guided through one or more experimental exercises per concept. Interpretations of the data and conclusions, along with additioinal practice problems for the student. Features
A separate Solutions Manual is available online at the Allyn & Bacon C&I Supersite. This online manual offers actual data sets collected from real classrooms, teaching suggestions for preparing the lessons, developing a grading scheme and general background knowledge, and solutions worked out for all problems.
An end-of-text Glossary defines all key terms.
Students are encouraged to expand their content base, construct new knowledge, and develop a new understanding of how mathematics is used to communicate in science.
Science teachers will find the mathematics readable and understandable and math teachers will find the traditional science labs enhanced with relevant mathematics. Students will finally be able to see how math and science work together |
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MODERN GEOMETRY was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. MODERN GEOMETRY provides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics |
Intermediate Algebra With Early Functions and Graphing
9780321064592
0321064593
Summary: The Lial/Hornsby developmental mathematics paperback series has helped thousands of students succeed in math. In keeping with its proven track record, this revision includes a sharp new design, many new exercises and applications, and several new features to enhance student learning. Among the features added or revised include a new Study Skills Workbook, a Diagnostic Pretest, Chapter Openers, Test Your Word Power, F...ocus on Real-Data Applications, and increased use of the authors' six-step problem solving process.
Lial, Margaret L. is the author of Intermediate Algebra With Early Functions and Graphing, published 2001 under ISBN 9780321064592 and 0321064593. Twenty nine Intermediate Algebra With Early Functions and Graphing textbooks are available for sale on ValoreBooks.com, twenty eight used from the cheapest price of $0.64, or buy new starting at $34.31 |
Tucson SAT Math the student must learn to see it from the perspective of functions: polynomial, rational, radical, exponential and trigonometric functions. Calculus, as Algebra, is an art; the artist needs a pallet. In this case the pallet is the coordinate plane and the student must learn to draw the faces (graphs) of all the functions and recognize them from their faces am very familiar with methods for teaching these concepts. I |
MATH 210 Introduction to Proofs
Introduces the central idea of proof in mathematics and some standard proof formats that are used throughout the math major. The course includes propositional logic, an introduction to predicate logic, direct proof, proof by contradiction, and mathematical induction. Liberal Arts. |
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About the book:
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, repectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
Hardcover, ISBN 0387965327 Publisher: Springer 1987 Used - Very Good, Usually ships in 1-2 business days, Very good near fine condition with clean interior and no previous owner's inscriptions or names. No underlining or highlighting. NOT an ex-library copy. Very clean and crisp !We ship fast !
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Book DescriptionEditorial Reviews
Review
"Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen, University of Illinois at Urbana
"The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina, University of Nebraska at Omaha
From the Publisher
A solid presentation of the analysis of functions of a real variable -- with special attention on reading and writing proofs.
--This text refers to an out of print or unavailable edition of this title.
I bought this book because I have been looking for a Introductory analysis text that isn't too advanced, but yet doesn't gloss over the essential stuff, and I found it in Lay's book. For the self-studier, this book is excellent! I have several books on analysis: Shilov, Kolomogorov, Rosenlicht, Ross,etc... For the beginner, this book is superior to all of them. A plethora of examples. Also, a good range of problems:from straight forward problems requiring only the use of a definition to more advanced problems requiring a little thought. If you already have had some Analysis, then this book is probably not for you. But, if you are a student who wants to learn Analysis on your own, then this book would be hard to beat. After this book, one should be able to tackle "Papa Rudin". For according to Rudin, all that is needed to study his "Real and Complex Analysis" tome, is the first seven chapters of his "Principles of Mathematical Analysis". This book covers all that Rudin covers with the exception of Riemann-Stieltjes integration. On the whole, this is a great start! If proof-based math is new to you, then you will appreciate the first chapter on proofs. Would have given five stars, but I would have liked to seen Riemann-Stieltjes integration. That's really only nit picking, though.
I didn't think this book was going to be very good, but the author has "proved" me wrong ;-) This book starts out so basic that in my class (which was the first analysis course in our math department) we actually skipped the first 1/3 or so of the book. The first 9 or 10 sections consist of stuff like basic set theory, logic, definition of a function, etc. I would think that even the most elementary Analysis books would completely leave this out and expect that the reader is already familiar with this. So if you need it, this book will be a good resource for you. Then the book goes into a very nice introduction to topology. Basic concepts like open/closed sets, accumulation points, compact sets, etc. Topology can be a little intimidating simply because it's _so_ abstract, but this book makes the basic concepts very easy to understand, and prepares one for a more advanced course in topology. Alot of (good) Elementary Analysis books leave topology out, but I'm glad this book contained it. It is a very interesting subject. All the material in the book is explained probably about as easily as the concepts CAN be explained. If you still have trouble with it, you might consider a different major. Not to say that this book transforms a very difficult subject into a pathetically easy piece of cake because that's impossible, but the material is presented probably as easily as it can be in order to maintain precision and detail (which is the whole point of Analysis). The book is definitely not running short in the examples or end-of-section problems department, so that is another plus. The problems at the end of each section range in difficulty from problems that almost exactly match an example worked in detail in the section, to fairly challenging problems. With enough time though the average student could probably do every problem at the end of every section. I'd recommend this book for self study as well as a supplement to any introductory analysis course. If you have already have exposure to rigorous proof of calculus theorems, then this book will probably be too basic for you. The reason this book got 4 stars instead of 5 is because of its utterly ridiculous price. Just as good is Elementary Analysis: The Theory of Calculus, ISBN: 038790459X, except that it doesn't include the section on Topology ...Read more ›
This is fairly basic introduction to Principles of Analysis, on intermediate undergrad level, strictly in R^1. The only other similar book I'm familiar is Kirkwood. The books of Rudin, Apostol, etc present the subject on much higher level.
My original intention was to take a course with Rudin, but after I've realized I had a hard time digesting his style, I've decided to take more elementary course. I knew the course would be using Lay, so I got this textbook and tried to learn it on my own, but wasn't sure how I was doing and ended up taking the course (still with Lay) anyway. So I'm quite familiar with this textbook. The only topics we didn't cover is "series" and "sequences and series of functions".
Now overall I would say it's a mixed bag. First, the good things. The first few introductory sections on sets and proof techniques are excellent, highly recommended, that's how I learned how to prove. I found exercises very useful.
Now things I don't like. First, lots of typos. I think I had 4th edition, and still I've managed to find over 20 misprints, incorrect references, etc, etc, all were reported directly to author. Second, and that's probably more important, in several instances the proofs are too convoluted and not self-motivating. To be more specific, the proof of Heine-Borell theorem is less than adequate. It is correct, but that's the kind of proof you read and then entirely forget how it went. I remember on the first reading I didn't feel comfortable with this proof at all. When I discussed this book with professor I was going to take that course with, he (surprisingle) agreed with me and told me he would present a different proof (and he did, much better one). Another example: proof that the modified Dirichlet function is Riemann-integrable. The proof can be substantially simplified. In fact, I've managed to simplify it. Finally, the same professor told me Lay's presentation of Riemann integrals had some holes in them, so he used Kirkwood instead. In fact he told me he was making choice between Kirkwood and lay (but ended up choosing Lay because he didn't like Kirkwood's book layout. Kind of funny reason, I think.)
In any case, I think Kirkwood is a bit better for self-study. Unfortunately it doesn't have intro to proofs, logic and sets. Ideally you should have both books, if you plan for self-study.
(note: I did took the Principles of analysis, after I've finished that one with Lay, and did quite well.)Read more ›
This is a very good book for someone to look at before going into an analysis class with Rudin. If you have never done proofs or seen metric spaces or uniform continuity, etc., this is a nice, but brief, intro. This book will NOT teach you analysis - you have to use Rudin for that. But it is great for acquainting/preparing you for Rudin. |
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 and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra! |
Lesson 8.1ExploringExponentialModels Mrs. Snow, Instructor Exponential functions are similar in looks to our other functions involving exponents, but there is a big difference. The variable is now the power, rather than the base.
Title: ExploringExponential Growth and Decay Functions Brief Overview: ... 1Answers will vary, but to insure accurate ... Which models of cars are more/less likely to become antiques? When is that likely to happen?
Understand and use basic exponential functions as models of real phenomena. f ... reviewed and students practice working with rational exponents. ... where a is a non-zero real number and b is a positive real number other than 1. An exponential growth function has a value of b that is greater ...
exploringexponentialmodels more accessible. It is important to emphasize the patterns in the tables, graphs, and algebraic rules for ... 1. Answers will vary. Number of M&M's Remaining Trial Number Number of M&M's remaining 0 140 1 76 2 39 3 22 4 12 5 8 6 3
when a > 0 and b > 1 when a > 0 and 0 < b < 1 This is called an exponential regression model. You will need to plot data points using the STAT menu. 1) Plot Data Points as described on previous worksheet. 2) Press [STAT], press [ ] ( Calc). Press ...
Describe the scenario from page 1 of the Exploring "Geometric sequences and series." ... What is the constant multiplier of the exponential function that models this situation? What is its domain? ... More practice, pages 6-8 Student Activity Sheet 3, question 6.
[SAS 3, question 1] Exploring "Geometric sequences and series" ... What is the constant multiplier of the exponential function that models this situation? ... Have them practice writing the sum in sigma notation. [SAS 3, question 4]
linear and exponentialmodels. ... Common Core State Standards for Mathematical Practice1. Make sense of problems and persevere in solving them. ... When making statistical models, technology is valuable for varying assumptions, exploring
... quadratic, and exponential through graph models and algebraic models. ... answers by using "benchmarks" to estimate measures and other strategies to approximate a ... Thinking With Mathematical Models (Inv. 1, 2) 8.SP.4
The Mathematical Practice Standards apply throughout each course and, ... (1) Exploring Data: observing patterns and departures from patterns (2) ... be able to explain their answers using arguments, graphs, and statistical skills that they will learn in the |
Math Courses of Study: Grade by Grade
See Below For Grade by Grade Goals
Although mathematics curricula will vary from state to state and country to country, you'll find that this list provides the basic concepts that are addressed and required for each grade. The concepts have been divided by topic and grade for easy navigation. Mastery of the concepts at the previous grade is assumed. Students preparing for each grade will find the listings to be extremely helpful. When you understand the topics and concepts that are required, you will find tutorials to help you prepare under the perspective subjects on the home page. Calculators and computer applications are also required as early as kindgarten. Most curriculum documents request that you are also able to use the corresponding technologies such as software applications, regular calculators, and graphing calculators.
For more specific details regarding the math requirements for each grade, you may want to do a search for the curriculum in your state, province or country. Most boards of education will provide you with the details to access the documents. |
With an emphasis on problem solving and critical thinking, Dugopolski's Trigonometry, Fourth Edition gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find carefully placed learning aids and review tools to help them do the math.
This program will provide a better teaching and learning experience–for you and your students. Here's how: |
Mathematics 2, Essential
When we paint a room, put up a fence, buy a rug, or wrap a present, we are using shapes. Essential Math 2 deals with the nature and property of shapes such as circles, triangles and squares. In doing so, this course provides an introduction to geometry and algebra. Essential Math 2 also acquaints students with the metric system of measurement.
What others are saying:
I find it amazing that a school that big would actually find the time to grade and comment on each test individually. The study guides teach me everything I need to know in order to finish the tests because they are so clear. The tests in the study guides are organized and easy to understand. — Luis, Florida |
Program that include this Course:
Having trouble fitting a class into your schedule? Want a relevant and engaging learning experience? Then consider online learning at Butler. With two different types of courses, Online and Blended, you can customize your education to fit your needs. Blended Courses enable you to combine the best of both worlds - the classroom and the computer.
This course will enable the student to interpret mathematical symbols and notation, simplify expressions, factor polynomials, solve equations (including systems, quadratic and systems of linear equations) perform operations on radical expressions, write equations of lines and evaluate functions after a review of some topics from basic algebra. The student will begin to conceptualize abstract ideas. |
While computational technologies are transforming the professional practice of mathematics, as yet they have had little impact on school mathematics. This pioneering text develops a theorized analysis of why this is and what can be done to address it. It examines the particular case of symbolic calculators (equipped with computer algebra systems) in... more...
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.... more...
Multiplicative invariant theory is as a research area in its own right within the wider spectrum of invariant theory. This work text offers an account of the basic results. It is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and invariant theory. more...
Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn?t the Divine that which is immeasurable ? The present... more...
The study of mathematics, with other 'gendered' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers. more...
Examining the pioneering ideas, works, and applications that have made math the language of science, Mathematics and the Laws of Nature looks at the many ways in which so-called ''pure'' math has been used in the applied sciences. For example, the volume explores how mathematical theories contributed to the development of Kepler's laws of planetary... more...
The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to... more...
Provides an introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. This book presents several symbolic, numeric, and symbolic-numeric techniques, including algorithmic methods in algebraic geometry and computational algebra, complexity issues, and a range of applications. more... |
College Algebra : Graphs and Models -Text Only - 4th edition
Summary: The approach of this text is more interactive than most precalculus texts and the goal of the author team is to enhance the learning process through the use of technology and to provide as much support and help for students as possible. In Connecting the Concepts, comprehension is streamlined and retention is maximized when the student views a concept in visual, rather than paragraph, form. Zeros, Solutions, and X-Intercepts Theme Carried Throughout helps students vi...show moresualize and connect the following three concepts when they are solving problems: the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function. Each chapter begins with a relevant application highlighting how concepts presented in the chapter can be put to use in the real world. These applications are accompanied by numerical tables, equations, and grapher windows to show students the many different ways in which problems can be examined. End-of-Chapter material includes a summary and review of properties and formulas along with a complete set of review exercises. Review exercises also include synthesis, critical thinking, and writing exercises. The answers to all of the review exercises appear in the back of the text and have text section references to further aid students. For anyone interested in learning algebra2.00 +$3.99 s/h
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Campus_Bookstore Fayetteville, AR
Used - Good Hardcover. Textbook only |
According to Leonard M. Keenedy and Steve Tipps (2000): "Mathematics is alanguage for describing common events in everyday life and complex events in business,science and technology"Below are some examples of application of Mathematics in traveling, astronomy,engineering and manufacturing.When a family plans a vacation, they use mathematics to estimate distances, timesfor departure and return, fuel needed, food and other supplies required and costs of maintaining the family vehicle. As astronomers and engineers plan space travel,mathematics is used to calculate distances, times for departure and return, fuel needed,food and other supplies and costs of maintaining the space vehicle. When manufacturers plan for distribution across the Brunei Darussalam, they employ mathematics to calculatedistances, time for departure and return, fuel needed, food and other supplies required,and costs of maintaining the vehicle.Three different problems, three levels of mathematics and three needs for precision, and all these three require the same thinking process. As a result of this,mathematics is a tool and a language for solving problems great and small.
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PS 4305 CT Mathematics I
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This report will focus on the use of mathematics in other subject includingdifferent aspect of mathematics in different area or field. New mathematics courses have been developed that focus on "nontraditional" topics and applications in real world. Astoday's student learn mathematical concepts and thinking, they must apply, adapt andextend old concepts to new tasks and existing ideas into real world. In the 21
st
century,children will need mathematics for complex and common applications.The report of the Cockcroft Committee Mathematics Count (HMSO, 1982)comments that although there are some books linking mathematics to other subjects suchas art and science, more are needed. Paragraph 292 of the Report states:
Almost all children find pleasure in working with shapes, and work of this canencourage the development of positive attitudes towards mathematics in those who are finding difficulty with number work.
In later chapter, we will discuss about mathematics in different fields, namelymathematics through art and design, mathematics in everyday life, mathematics inmedicine, mathematics in sports, mathematics in cooking, mathematics in psychology,mathematics in architecture and mathematics in nature. |
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This Textbook
Overview
The third edition of this ground-breaking text continues the authors' goal - a targeted introduction to precalculus that carefully balances concepts with procedures. Overall, this text is designed to provide a solid foundation to precalculus that focuses on a small number of key topics thereby emphasizing depth of understanding rather than breath of coverage. Developed by the Calculus Consortium, FMC 3e is flexible enough to be thought-provoking for well-prepared students while still remaining accessible to students with weaker backgrounds. As multiple representations encourage students to reflect on the material, each function is presented symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples and problems enable students to create mathematical models that will help them understand and interpret the world in which they |
April 24, 2008
High school geometry - a review
It's done! Finally! Took me some time to finish this review, perhaps because it involved three products:
The book Geometry: A Guided Inquiry. As the name suggests, this book is based on letting students learn about theorems and their proofs in the setting of "guided inquiries" or interesting problems. It is quite unique in its approach.
A Home Study Companion which includes solutions and about 300 interactive demonstrations
Geometer's Sketchpad - dynamic geometry software.
This review isn't just what you typically find on the web; someone called it an "exquisite in-depth review". It's fairly long... with sample pages and other pictures, examples, and more.
I encourage you to read it even if you don't need a high school geometry book right now... because you'll get valuable insight just HOW GOOD geometry instruction can be, how the book handles proof, or what to think about an axiomatic vs. discovery based geometry text.
Maria Miller is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com. |
Summary: As in previous editions, the focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar problems, he...show morelps them build their confidence and eventually master theMore Than Words MA Waltham, MA
Good24 |
This textbook provides an introduction to the techniques used in group theory. It spans the wide arc from the elementary nilpotent groups to finite simple groups, which constitute the building blocks for all finite groups and thus represent an important tool for all structural investigation of finite groups. more... |
Measure Theory
Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure ...Show synopsisUseful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWSHide |
supplementary text for introductory courses in Calculus-Based Physics.
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful–and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
Most Helpful Customer Reviews
Highly recommended supplemental book for my Calculus-based physics class. It provided an excellent quick review on some topics from a while back, and a great summary and introduction to topics I needed to know for the course but had never been taught. Its not a substitute for taking a calculus course, but it is a great review if calculus was a while back, or if you never covered certain topics. Either way, this book will come in handy throughout your physics courses. |
29,744 1, algebra 2 and calculus |
What is the answer to the punchline algebra book b worksheet "Did You Hear..."?
Answer:
Is it possible for you to give me the whole question because i do not have the book and and am unable to find an answer based on the information you provided. Thanks, AnswerParty!
More Info:
Data collection usually takes place early on in an improvement project, and is often formalised through a data collection plan which often contains the following activity.
Prior to any data collection, pre-collection activity is one of the most crucial steps in the process. It is often discovered too late that the value of their interview information is discounted as a consequence of poor sampling of both questions and informants and poor elicitation techniques. After pre-collection activity is fully completed, data collection in the field, whether by interviewing or other methods, can be carried out in a structured, systematic and scientific way.
Grammar
Human communication, or anthroposemiotics, is the field dedicated to understanding how people communicate:
QuestionPunchlineAlgebraLinguisticsIt's one of the simplest constructions of abstract algebra. What's really fascinating about it ... beyond what's required to make the group operator work properly. You can define a group whose values are a set of points, a set of numbers, a set ...
(See answers to Tracey's dilemma's below) Until one day, my curiosity piqued, I went to Waterstones to buy a book on how communication develops ... so she has to shush to hear you. Keep calm, stay strong and remember that everything is just a phase!'
Your workbook may include different methods of teaching and levels of information depending upon the age group to which you gear your workbook. Note on the cover who this book ... page math worksheet using this system (students should write their answers ...
I always get asked about Georgia Tech- I did not go there, but did get my math degree from A Univ. Of Georgia System School, which G. Tech is a member of- and Mustangs- which I actually drive, but not a GT model.
The AJC has a long, thoughtful piece about what can be learned from the controversy over the slave questions given to third graders in a Norcross elementary school math ... Why did they do this?' He had a lot of questions for me I couldn't answer ... |
Algebra By Example - Self Help Materials and More!
Do you find it difficult to follow your Algebra lessons? Do you get the feeling that you understand it in principle, but not enough to use it to solve a problem? You're not alone. I felt that way a few times before.
This problem might occur if you have done any of the following:
Missed a few lessons of related concepts
Read about the concept, but was never given an example
Never applied your understanding to a problem
Skipped on practice exercises
Kept all your knowledge to yourself
It's never too late to catch up - unless you needed the information yesterday! Of course, you'll need reasonable time and effort to find out what you don't know and fill in the gaps. Then you have to make sure the gaps stay closed. How?
Here you'll find worked (and explained!) examples that will help you identify the concepts you need to solve a problem you may be facing. Keep your knowledge in your head by re-trying the worked examples, or take a shot at our worksheets (they're on the way). In the future, there will also be games and books to help you get on top of your game to ace that test! You'll also be able to find algebra homework help here.
Self-help is always possible given enough time and correct information. However, if you feel you're too far behind or lack the time to catch up, a good tutor can really make a difference. You can find an algebra tutor closest to you. A good one should be able to quickly point out where you need to improve in order to understand more advanced topics.
Before you dive into the pages, let me leave you with a word of advice. If you don't understand a concept right away, take time to review the more basic materials to see what you've missed. Always get help as soon as you can. After that, practice practice and practice to keep it in your head! When you revisit the concept, you'll likely find it a lot easier to understand.
Finally, please pay it forward by helping a friend. You'll learn better that way, besides. Good luck and see you on the sunny side of success! |
Math and Computer Science Courses
Mathematics can be described as a language, a tool, a science, and an art. Computer Science is an area of study that continues to gain importance for its rich theory and wide applications to physical and social sciences. In CTY's math and computer science courses, students move beyond basic skills to gain greater understanding of both the underlying principles and the intriguing ways these concepts can be applied and extended to a range of contexts.
Students have the opportunity to explore challenging material and strengthen their problem-solving skills. They investigate advanced concepts through a process of discovery and engagement that promotes a lifelong interest in the discipline. Through hands-on, thought-provoking exercises, students learn to make connections between abstract ideas and their uses in a range of fields, including science, engineering, economics, and advanced mathematics.
Math Course Descriptions and Syllabi
Paradoxes and Infinities
The second sentence is true. The first sentence is false. Are these sentences true or false? How is it that observing an orange pumpkin is seemingly evidence for the claim that all ravens are black? Students in this course explore conundrums like these as they analyze a range of mathematical and philosophical paradoxes.
Students begin by considering Zeno's paradoxes of space and time, such as The Racecourse in which Achilles continually travels half of the remaining distance and so seemingly can never reach the finish line. To address this class of paradoxes, students are introduced to the concepts of infinite series and limits. Students also explore paradoxes of set theory, self-reference, and truth, such as Russell's Paradox, which asks who shaves a barber who shaves all and only those who do not shave themselves. Students analyze the Paradox of the Ravens as they study paradoxes of probability and inductive reasoning. Finally, they examine the concept of infinity and its paradoxes and demonstrate that some infinities are bigger than others.
Through their investigations, students acquire skills and concepts that are foundational for higher-level mathematics. Students learn and apply the basics of set theory, logic, and mathematical proof. They leave the course with more nuanced problem-solving skills, an enriched mathematical vocabulary, and an appreciation for and insight into some of the most perplexing questions ever posed.
Geometry through Art
"Geometry is the right foundation of all painting." In this way, the German artist Albrecht Dürer described a connection between mathematics and art that can be found in every culture. In this introductory geometry course, students learn about geometric figures, properties, and constructions, and use this knowledge to analyze works of art ranging from ancient Greek statues to the modern art of Salvador Dalí.
Beginning with the foundations of Euclidean geometry, including lines, angles, triangles, and other polygons, students examine tessellations and two-dimensional symmetry. Using what they learn about points, lines, and planes, students investigate the development of perspective in Renaissance art. Next they venture into three dimensions, analyzing the geometry of polyhedra and considering their place in ancient art. Finally, students explore non-Euclidean geometry and its links to twentieth-century art, including the drawings of M. C. Escher.
Through lectures, discussions, hands-on modeling, and small group work, students gain a strong foundation for the further study of geometry, as well as an appreciation of the mathematical aspects of art.
Note: Students who have taken CTY's Geometry and Its Applications class, or a high school geometry class, should not take this course.
Note: This course exposes students to geometric properties and concepts but should not be used to replace a year-long high school geometry course.
Sample text:Squaring the Circle: Geometry in Art and Architecture, Calter.
Mathematical Modeling
Mathematics is more than just numbers and symbols on a page. Applications of mathematics are indispensable in the modern world. Math can be used to determine whether a meteor will impact Earth, predict the spread of an infectious disease, or analyze a remarkably close presidential election. In this course, students learn how to create mathematical models to represent and solve problems across a broad range of disciplines, including political science, economics, biology, and physics.
Students in this class investigate voting systems by constructing mathematical models of how groups make decisions and how elections are conducted. They consider how goods, property, and even political power can be fairly divided and apportioned. Students learn how to use Euler and Hamilton circuits to find the optimal solutions in a variety of real-world situations, such as determining the most efficient way to schedule airline travel. While investigating growth and symmetry, students develop linear and exponential growth models and explore fractals and the Fibonacci numbers. Students leave this course with the ability to use the seemingly abstract language of mathematics to gain a greater understanding of the world around them.
The Mathematics of Money
From managing one's personal investments to examining the profitability of a multibillion-dollar global corporation, the mathematics of money is at the heart of successful financial endeavors. Why are round-trip fares from Orlando to Kansas City higher than those from Kansas City to Orlando? How do interest rate adjustments made by the Federal Reserve affect the real estate market? How does one calculate the price-earnings ratio of a stock and use that result to help predict that stock's future performance? Mathematics plays an indispensable part in answering each of these questions.
This course provides students with a mathematical grounding in central concepts of business and finance. Students investigate the mathematics of buying and selling, and apply these principles to real- world situations. They gain fluency with the concepts of simple and compound interest and learn how these affect the present and future value of loans, mortgages, and interest-bearing accounts. Students investigate various forms of taxes, considering their impact on personal and governmental budgets. In their examination of these topics, students manipulate and solve algebraic expressions, and also learn to apply a range of mathematical concepts including direct and indirect variation and arithmetic and exponential growth. Through simulations, entrepreneurial projects, and classroom investigations, this course provides students with the foundation required to be more secure in their financial management and enhances their understanding of the broader economic conditions that shape investments in the public and private sector.
Game Theory and Economics
Thomas J. Watson, the founder of IBM, once said, "Business is a game—the greatest game in the world if you know how to play it." In today's global marketplace, understanding game theory, the branch of mathematics which focuses on the application of strategic reasoning to competitive behavior, is crucial to understanding business and economics.
In this course, students use game theory as a framework from which to analyze a variety of real-world economic situations. Students begin the course by analyzing simple games, such as two-person, zero-sum games, and learn how these games can be used to model actual situations encountered by entrepreneurs and economists. For instance, students may apply the concept of Nash equilibria to find the optimum strategy for the pricing of pizza in the competition between Domino's and Pizza Hut.
As they acquire an understanding of more complex games, students apply these methods to analyze a variety of economic situations, which may include auctions and bidding behavior, fair division and profit sharing, monopolies and oligopolies, and bankruptcy. Through class discussions, activities, research, and mathematical analysis, students learn to predict and understand human behavior in a variety of real-world contexts in business and economics.
Discrete Math
Can any given map be colored with just four different colors such that no two regions sharing a common edge are the same color? Mathematicians took more than 100 years to answer this question in the affirmative, establishing the result known as the Four-Color Theorem. Discrete math introduces students to questions such as this as they learn math from a range of disciplines including set theory, combinatorics and graph theory, and number theory. This leads them to important real-world applications such as determining the number of ways to create a password of a given length or finding the shortest path for a taxi between multiple locations.
Students in this course begin by building a foundation in set theory and proof. They then explore combinatorics, examining the number of possible configurations of different sets of objects. Students move on to investigate graph theory, an area that introduces them to both historic problems such as the Bridges of Königsberg and the Traveling Salesman, as well as more modern applications such as the analysis of social networks and traffic patterns.
Students leave the course not only with a familiarity with a flourishing branch of mathematics, but also with an enriched mathematical vocabulary and an improved ability to understand and create mathematical arguments.
Computer Science Course Descriptions and Syllabi
Foundations of Programming
Students in this course gain insight into methods of computer programming and explore the algorithmic aspects of computer science. They learn the theoretical constructs common to all high-level programming languages by studying the syntax and basic commands of a particular programming language such as Java, C, C++, or Python*. Building on this knowledge, students move on to study additional concepts of programming, such as object-oriented programming or graphical user interfaces. By solving a variety of challenging problems, students learn to start with a concept and work through the steps of writing a program: defining the problem and its desired solution, outlining an approach, encoding the algorithm, and debugging the code.
Through a combination of individual and group work, students complete supplemental problems, lab exercises, and various programming projects in order to reinforce concepts learned in class. By the end of the course, students can develop more complex programs and are familiar with some of the standards of software development practiced in the professional world. Students leave with an understanding of how to apply the techniques learned to other high-level programming languages.
*Note: The programming language learned may change based on the instructor's preference. |
Black's Academy
Online electronic mathematics textbooks where all problems also have solutions worked out. Covers mathematics for AQA, OCR, and Edexcel. Suitable for K12+.
Symmetry
Visual journey through the worlds of symmetry, with many photos and drawings.
Precalculus Concepts
A different approach to algebra and trig that is designed to prepare students for calculus. Graphics calculators play an important role.
Computational Beauty of Nature, The
Companion site for the book by Gary William Flake. Contains applets and source code for simulations of fractals, chaos, complex systems, and adaptation. mitpress.mit.edu/books/FLAOH/cbnhtml
Advanced Math SAT Workbook
Workbook with strategies for students striving for a perfect score on common standardized admissions tests.
Handbook of Analysis and Its Foundations
Mathematics mini-encyclopedia for advanced undergraduates and beginning graduate students. Excerpts about the Axiom of Choice, orderings, norms, etc. math.vanderbilt.edu/~schectex/ccc
Ecological Numeracy
By Robert A. Herendeen, published by John Wiley & Sons. Relatively simple mathematics to understand quantitative aspects of environmental issues. |
books.google.com - This text covers mathematics of finance, linear algebra, linear programming, probability and descriptive statistics, with an emphasis on cross-discipline principles and practices. Designed to be student friendly and accessible, it develops a thorough, functional understanding of mathematical concepts... mathematics for business, economics, life sciences, and social sciences
Finite mathematics for business, economics, life sciences, and social sciences
This text covers mathematics of finance, linear algebra, linear programming, probability and descriptive statistics, with an emphasis on cross-discipline principles and practices. Designed to be student friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem-solving. |
Product Description
Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each lesson concept in Saxon's textbook is taught step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; and because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. Taught from a Christian worldview, Dr. David Shormann also provides a weekly syllabus to help students stay on track with the lessons. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guide.
Algebra 1/2 covers traditional algebra 1/2 topics, as taught in the 2nd Edition Saxon textbook, as well as topics from geometry and discrete mathematics. For use with 2nd Edition texts.
Please Note! The current edition of Saxon Math Algebra 1/2 is the 3rd Edition. This 2nd edition is offered for families using older versions of Saxon. |
An interactive simulation designed to help students understand fourier series. Includes a discrete-only module and a module...
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An interactive simulation designed to help students understand fourier series. Includes a discrete-only module and a module that illustrates the transition from discrete to continuous transforms. A wave game module in which students try to match a given waveform is also included.
The Graphical representation of complex eigenvectors simulation aims to help students make connections between graphical and...
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The Graphical representation of complex eigenvectors simulation aims to help students make connections between graphical and mathematical representations of complex eigenvectors and eigenvalues. The simulation depicts two components of a complex vector in the complex plane, and the same vector under several transformations that can be chosen by the user. A slider allows students to change the second component of the initial vector. The simulation shows whether or not the vector is an eigenvector, and if so displays the associated eigenvalue. The simulation includes a small challenge in asking the student to find the elements of one of the transformation matrices Graphical representation of eigenvectors simulation aims to help students make connections between graphical and...
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The Graphical representation of eigenvectors simulation aims to help students make connections between graphical and mathematical representations of eigenvectors and eigenvalues. The simulation depicts the two components of a unit vector in the xy-plane, and the same vector under several different transformations that can be chosen by the user. A slider allows students to change the orientation of the initial vector. The simulation shows whether or not the vector is an eigenvector, and if so displays the associated eigenvalue. The simulation includes a small challenge in asking students to find the elements of one of the transformation matrices 4This applet demonstrates the resulting wave from the combination of the fundamental frequency and a combination of all or...
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This applet demonstrates the resulting wave from the combination of the fundamental frequency and a combination of all or none of the first three overtones of a vibrating system. The user is able to adjust the amplitude of these waves and let it run continuously or step by step. The wave may be free at both ends, fixed at one end, or fixed at both ends. All or none of the waves may be shown in different colors or just the sum of all the waves in black.
A simulation of masses hung from a scale including gravity. Virtual lab tools, including a ruler and a stopwatch can be used...
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A simulation of masses hung from a scale including gravity. Virtual lab tools, including a ruler and a stopwatch can be used to make quantitative measurements. Friction and spring constants can be adjusted, and energy graphed.Key topics: Hooke's Law, Springs, Conservation of Energy, Measuring Mass and GravityFor Teaching Tips, see: " target=״_blank״ |
More About
This Textbook
Overview
The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts.
Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical |
Graham, WA GeThe use of numbers and symbols, which may be frightening to students, has already begun in the use of numerals, for example, 1, 2, 3, etc., in arithmetic. Algebra uses additional symbols, which can easily learned by using the basic rules of arithmetic, such as addition, subtraction, multiplication, and division. Algebra has these same rules and also others to be learned. |
Linear Algebra with and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems. Each chapter contains integrated worked examples and chapter tests. The book stresses the important role geometry and visualization play in understanding linear algebra.For anyone interested in the application of linear algebra theories to solve real world problems. |
geogebra
Download
Download geogebra here. It works for all operating systems (Windows, Mac, Linux).
Why Geogebra?
Geogebra is a great program for dynamically visualizing graphs. Since the heart of calculus is change and graphs -- a program which allows you to quickly and easily see nearly any type of graph and then allows you to change that graph in a smooth fashion is hugely valuable. Geogebra does this excellently.
Sample Geogebra Files
After you have downloaded geogebra, download and explore these examples.These all rely on "sliders" (upper right hand corner) which let you dynamically change values.
You should create "Sliders" before you create a function which depends on a slider. Example: 1) create a slider for "m" 2) create a slider for "b" 3) create: y = mx + b
1) Geometry of Derivatives
You have a polynomial f(x) = e(x-a)(x-b)(x-c)+d. a,b,c,d, and e are freely-adjustable by sliders which changes the graph smoothly and "in real time" as you adjust them. You can then see how the first derivative are used to find local min/max of the graph and the second derivative is used to find the point of inflection.
Click the screenshot to enlarge
2) Exploring the function f(x) = a*sin(bx+c)+d
The constants a,b,c, and d are controlled by sliders which change the graph as you manipulate them.
Click the screenshot to enlarge.
3) Visualize parametric equations r = f(theta) as they are traced out in real time!
Say you have a curve like: r = 5sin(2t)
To find the x and y components of any equation of the form r = function of t , just multiply by cos(t) and sin(t) respectively:
The x component of this curve is cos(t) * (5sin(2t)) The y component of this curve is sin(t) * (5sin(2t))
Now go into geogebra and perform the following steps:
1) Create a slider, name it "t". Make it run from -2*pi to 2*pi in steps of pi/60 (so you get a nice smooth curve)
What you should have is a vector from the origin to the point (r,t). (The vector command is saying create a vector from point (a,b) to (c,d) ==> Vector[(a,b),(c,d)] ) It will automatically trace itself out as t varies. You can click pause, ctrl+click to drag and zoom, make the vector visible/invisible, etc.
You can create points (a,b) or (a, f(t)), etc. where a is a constant (or a slider value) and f(t) (or f(x), whatever you like). Try graphing (t, length[v]) where "v" is the vector you created in step 2. |
Calculus I
The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This ...Show synopsisThe goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies. The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelled almost exactly on the exam ples; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best students. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. The exercises come in groups of two and often four similar ones Calculus I (Undergraduate Texts in Mathematics) This book...Good. Calculus I (Undergraduate Texts in Mathematics |
This easy-to-follow teaching aid for algebra teachers explores the fundamental concepts of functions and relations with the use of a graphic calculator. Algebra Nspirations: Functions and Relations movie The program leads viewers through a series of lessons, demonstrating the keystrokes involved in each example, and uses animations to illustrate ideas. |
Inverrary, FL ACTAdd and subtract fractions with like denominators and add and subtract decimals. Cover properties of, and the relationships between plane geometric figures. Collect, represent, and analyze data to answer questions
...We translate a known signal into a mathematical model and then apply noise interference. We do quite a bit of analysis using probabilistic methods and analysis techniques. Probability concepts are central to this analysis |
Walk through Combinatorics An Introduction to Enumeration and Graph Theory
9789812568861
9812568867
Summary: This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.
Bó...na, Miklós is the author of Walk through Combinatorics An Introduction to Enumeration and Graph Theory, published 0016 under ISBN 9789812568861 and 9812568867. Eleven Walk through Combinatorics An Introduction to Enumeration and Graph Theory textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $15.94, or buy new starting at $49 |
Calculus brings a new concept for students, approaching infinity. It needs a strong foundation but the concepts carry through the course that is basically differentiation and integration. After learning the basic skills, application becomes very important. |
GENERAL NOTES
This course is targeted for grade 12 students, whose test scores on the Postsecondary Educational Readiness Test (P.E.R.T.) are at or below the established cut scores for mathematics, indicating that they are not yet "college ready" in mathematics or simply need some additional instruction in content to prepare them for success in college level mathematics. This course incorporates the Florida Standards for Mathematical Practices as well as the following Florida Standards for Mathematical Content: Expressions and Equations, The Number System, Functions, Algebra, Geometry, Number and Quantity, Statistics and Probability, and the Florida Standards for High School Modeling. The standards align with the Mathematics Postsecondary Readiness Competencies deemed necessary for entry-level college courses. |
sequences of geometric patterns and encourages students to generate rules and functions describing relationships between the pattern number and characteristics of the pattern. S... More: lessons, discussions, ratings, reviews,...
This packet contains a copy of the original problem used to create the activity, rationale and explanation behind the "I Notice, I Wonder" focal activity, and some thoughts on why this activity works ... More: lessons, discussions, ratings, reviews,...
This packet contains a copy of the original problem used to create the activity, rationale and explanation behind the "Doing it Wrong" focal activity, and some thoughts on why this activity works well... More: lessons, discussions, ratings, reviews,...
These guided, interactive activities present sequences of geometric patterns and encourage students to generate rules and functions describing relationships between the pattern number and characterist... More: lessons, discussions, ratings, reviews,...
This mini-lesson explains the concept of the distributive property. It also explains how to solve an equation by simplifying both sides of the equation by clearing out any parentheses, and then combin... More: lessons, discussions, ratings, reviews,...
This mini-lesson explains how an equation can be a true sentence, a false sentence or an open sentence, as well as how to find the solution set of an open sentence, and what it means to be an identity... More: lessons, discussions, ratings, reviews,...
Students play a generalized version of connect four, gaining the chance to place a piece on the board by solving an algebraic equation. Parameters: Level of difficulty of equations to solve and type o... More: lessons, discussions, ratings, reviews,...
An algebra practice program for anyone working on simplifying expressions and solving equations. Create your own sets of problems to work through in the equation editor, and have them appear on all of... More: lessons, discussions, ratings, reviews,...
This Flash program is a way to give your students endless practice on solving simple linear equations. It randomly generates ten problems which you can print and distribute. An answer sheet is also |
Algebra can be defined as the study of quantity, relation, and structure and is such a complex subject. It is the gateway to more rigorous courses. Most don't realize how complex mathematics is until they are faced with courses that prepare them for scientific and engineering type careers. Personally, I had never heard of these rigorous types of math courses until I entered my first calculus course in college.
There are many concepts that must be learned in order to advance to a higher level of mathematics in general. Thus being a tutor if you are strong in mathematics or a tutee if you are weak in mathematics is necessary.
Throughout your algebra courses, which for most are numerous depending on your proficiency level in mathematics, you will be faced with many terms and definitions. On this page you will find a list of briefly described terms and definitions but will be able to access examples through the links on this page.
associative property – is a basic property in which three or more numbers are involved that deals with the use of parenthesis to group numbers "associated" in order to solve an equation involving order of operations.
commutative property – is a basic operation in which two numbers when changed around does not change the end result.
completing the square – a term that is used primarily for solving quadratic equations.
complex number – a number that can be written in a form in which one part of it is real and the other part is imaginary.
exponential equation – an equation that contains a variable for an exponent.
integers – all natural numbers and negative numbers that are not written in the form of fractions or decimals.
inverse operation – an operation that reverses another operation like addition to subtraction and multiplication to division.
logarithm – the power to which a given base number must be raised in order to obtain for a variable.
math variables – is (known as variables) a symbol that represents an unknown or changing number.
order of operations – used in solving problems correctly based on precedence.
polynomial – a variable like expression that uses addition, subtraction, and multiplication and whole number exponents.
quadratic equation – is a second degree (two as the highest power) polynomial equation. real number – any number that can be placed on a number line excluding only imaginary numbers.
system of linear equations – a collection of linear equations involving the same set of variables. |
AP Calculus AB provides an understanding of the fundamental concepts and methods of differential and integral calculus with an emphasis on their application, and the use of multiple representations incorporating graphic, numeric, analytic, algebraic, and verbal and written responses. Topics of study include: functions, limits, derivatives, and the interpretation and application of integrals. An in-depth study of functions occurs in the course. Technology is an integral part of the course and includes the use of graphing calculators, computers, and data analysis software. On a regular basis, graphing calculators are used to explore, discover, and reinforce concepts of calculus.
Though our system has an open enrollment policy, students should understand that this course is designed to be a fourth-year mathematics course and the equivalent of a year-long, college-level course in single variable calculus. The course requires a solid foundation of advanced topics in algebra, geometry, trigonometry, analytic geometry, and elementary functions. The breadth, pace, and depth of material covered exceeds the standard high school mathematics course, as does the college-level textbook, and time and effort required of students. AP Calculus AB provides the equivalent of the first course in a college calculus sequence, while AP Calculus BC is an extension of AP Calculus AB, and provides the equivalent of a second course in a college calculus sequence. Students are expected to take the AP Calculus AB Exam at the end of this course |
figures released by ACT Inc., many more U.S. high school students are taking courses in mathematics than was the case a decade ago. In fact, the portion of college-bound students taking calculus increased from 16 percent in 1987 to 27 percent in 2000. Let's face it, most students and adults who take calculus do so not for the fun of it, but rather to advance within a job or fulfill a degree requirement. The Complete Idiot's Guide(R) to Calculus will take the sting out of this complex math by putting it's uses, functions and limitations in perspective of what is already familiar to readers-algebra. Once readers have brushed up on their algebra and trigonometry skills, they'll be eased into the fundamentals of calculus. |
worked with both: middle schoolers and college students. Algebra 1 is a transition from working with numbers to applying abstract mathematical concepts. Many students begin to have problems in pre-algebra |
Summary: Demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. Focuses on repeating and growing patterns, introducing the concepts of variable and equality, and examining relations and functions. Features activities with questions that stimulate students to think more deeply about the mathematical ideas. Discusses expectations for students' accomplishment and provides helpful margin notes and blackline masters.
Edition/Copyright:01 Cover: Paperback Publisher:National Council of Teachers of Mathematics Published: 01/28/2001 International: NoAeden Stclair Marietta, OH
Used book. Normal wear.Disc included.
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Algebra & Trigonometry Enhanced with Graphing Utilities
Michael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with ...Show synopsisMichael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Serieshas evolved to meet today's course needs by integrating the usage of graphing calculator, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.Hide synopsis
Description:Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 97803217848100% BRAND NEW ORIGINAL US STUDENT Edition / Mint condition /...100% BRAND NEW ORIGINAL US STUDENT Edition / Mint condition / Never been read / ISBN-13: 9780321784834 / Shipped out in one business day with free tracking5060Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780321785060New in Hardback jacket. Brand new instructor's edition....New in Hardback jacket. Brand new instructor's edition. Includes answers/notes in margins. Ships same day or next business day. Free USPS Tracking Number. Excellent Customer Service. Ships from TN.
Description:Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321785060 |
Yes, and there exist web applications that already do this for the easier mathematics. It would be much more difficult to implement for Undergraduate-level maths, since the questions are generally no longer about symbolic manipulation, but rather rely on deeper thought to solve. This means that generating questions/answers with a computer would not be possible with current technology.
It certainly would be possible to pre-define question sets for certain, and have the parameters generated randomly to discourage cheating (e.g. with calculus problems). But this approach would simply not work with any difficult maths: how are you going to make a computer generate interesting problems in Group Theory, or Predicate Logic?
For these problems, there are already libraries full of books, some of which are entirely devoted to providing examples, available to students. What would be so much better about a web application?
TL;DR; If you can program a computer to create and solve higher-level problems, why don't you use it for mathematical research? |
A Survey of Mathematics with Applications
In a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applications continues ...Show synopsisIn a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applications continues to be a best-seller because it shows students how we use mathematics in our daily lives and why this is important. The Ninth Edition further emphasizes this with the addition of new "Why This Is Important" sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and a wide range of exercises help students to develop their problem-solving and critical thinking skills. Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math course. Note: This is a standalone book, if you want the book/access card please order the ISBN listed below: 0321837533 / 9780321837530 A Survey of Mathematics with Applications plus MyMathLab Student Access Kit Package consists of: 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321759664 / 9780321759665 Survey of Mathematics with Applications, AHide3928839288 Missing components. May include moderately...Good. Hardcover. Missing components. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321759665. (9th edition). Text Only! ! !
Description:Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780321639288Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321639288 Corners/spine worn/dented, covers lightly scuffed...Good. Corners/spine worn/dented, covers lightly scuffed/scratched, pages tight/bright with light/moderate highlighting on some, 2nd custom ed |
chapter we will be introducing two topics that are
very important in an algebra class. We
will start off the chapter with a brief discussion of graphing. This is not really the main topic of this
chapter, but we need the basics down before moving into the second topic of
this chapter. The next chapter will
contain the remainder of the graphing discussion.
The second topic that we'll be looking at is that of
functions. This is probably one of the
more important ideas that will come out of an Algebra class. When first studying the concept of functions
many students don't really understand the importance or usefulness of functions
and function notation. The importance
and/or usefulness of functions and function notation will only become apparent
in later chapters and later classes. In
fact, there are some topics that can only be done easily with function and
function notation.
Here is a brief listing of the topics in this chapter.
Graphing In this section we will introduce the
Cartesian coordinate system and most of the basics of graphing equations.
Lines Here we will review the main ideas from the
study of lines including slope and the special forms of the equation of a line.
Circles We will look at the equation of a circle and
graphing circles in this section.
The Definition of a Function We will discuss the definition of a function
in this section. We will also introduce
the idea of function evaluation.
Graphing Functions In this section we will look at the basics of
graphing functions. We will also graph
some piecewise functions in this section.
Combining functions Here we will look at basic arithmetic
involving functions as well as function composition. |
calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world...
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'Taking calculus? Then you need the Wolfram Calculus Course Assistant. This definitive app for calculus--from the world leader in math software--This app covers the following topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II:- Evaluate any numeric expression or substitute a value for a variable.- Plot basic, parametric, or polar plots of the function(s) of your choice.- Determine the limit of a function as it approaches a specific value.- Differentiate any function or implicit function.- Find the critical points and inflection points of a function.- Identify the local and absolute extrema of a function.- Integrate a function, with or without limits.- Sum a function given a lower and upper bound.- Find the closed form of a sequence or generate terms for a specific sequence.'This app costs $3.99
״Solve is a calculator like no other! Whether you need a simple calculator for everyday use or a graphing calculator for high...
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״Solve is a calculator like no other! Whether you need a simple calculator for everyday use or a graphing calculator for high school math, Solve is everything you'll ever need in a calculator app.Featuring an innovative memory system to store and recall answers, Solve has four tabs that select four different calculators each with its own color. Multiply numbers, plot a graph and solve an equation all without clearing your results! Solve also includes several interactive tutorials to help you get started.HELPFUL TIPSSwipe the button pad left and right to reveal more buttons, options and tutorials.GRAPHING INSTRUCTIONSSolve plots 2D and 3D functions using the x, y and θ variables. When you use the x, y and θ variables in an equation the answer will say Touch to Plot. Touch this label to graph the equation.Plot 2D functions using the x variable. For example, "y=sin(x)" is just entered as "sin(x)״.• cos(x)• abs(x)• x^2+2x+6Plot polar equations using the θ variable. For example, "r=2θ" is just entered as "2θ״.• 2θ• sin(2θ)Plot 3D functions by using the x and y variables. For example, "z=x+y" is just entered as "x+y״.• cos(x)+sin(y)• x^2+y^2Graph multiple functions by separating each equation with a comma. • sin(x),cos(x)• x,x^2,x^3The T variable is used to create animated or time plots. • cos(x+T)• sin(x+T)*x• cos(x+T)+sin(y+T)״This app costs $2.99
״TouchCalc is a comfortable calculator program and offers several different modes.- The scientific mode offers all the usual...
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״TouchCalc is a comfortable calculator program and offers several different modes.- The scientific mode offers all the usual functions and operations like the basic arithmetical operations, power, logarithm, roots, trigonometry etc.- The bit/integer mode offers logical operations (AND, OR, XOR, >>, etc.) on bit level. All values can be displayed as binary, octal, decimal or hexadecimal numbers. Calculations can be done in 8, 16 32 or 64 bits.- In the statistics mode you can create a sample by adding several values and then calculate mean, median, quantil values, variance, standard deviation, range etc.Colorized keys will help to distinguish between the different categories of the functions and operations.״This is a free app
״Calc XT is a full feature scientific calculator for iPad. It turns your iPad into a life-size realistic calculator. In...
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״Calc XT is a full feature scientific calculator for iPad. It turns your iPad into a life-size realistic calculator. In landscape mode, a memo pad is also available that you can jot note easily.״Features include:״ * scientific: 200+50%=200.5, 200*50%=100 * financial: 200+50%=300, 200*50%=100- memo can set left or right hand side- multiple memos- Label tape, that you can type text on the memo or store numbers from calculator* there is an option to erase memo completely in action button beside the pen selections.״This app costs $.99
This is a free resource hub dedicated to the learning student. I have dished out free question sets (with full detailed...
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This is a free resource hub dedicated to the learning student. I have dished out free question sets (with full detailed solutions) here, together with personally written summary notes for various topics including differentiation, integration, AP/GP, vectors, complex numbers etc. Hope it helps. Peace
We provide FREE Solved Math problems with step-by-step solutions on Elementary, Middle, High School math content. We also...
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We provide FREE Solved Math problems with step-by-step solutions on Elementary, Middle, High School math content. We also offer cost-effective math programs which include Math Lesson Plans aligned to state-national standards and Homework Help
A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution...
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A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution portals -״The Question Locker" and "Beyond H2 maths״which are relevant to the general high school and early college maths student. |
Finite Mathematics - 7th edition
ISBN13:978-0495118428 ISBN10: 0495118427 This edition has also been released as: ISBN13: 978-0495118480 ISBN10: 0495118486
Summary: Get the background you need for future courses and discover the usefulness of mathematical concepts in analyzing and solving problems with FINITE MATHEMATICS, 7th Edition. The author clearly explains concepts, and the computations demonstrate enough detail to allow you to follow-and learn-steps in the problem-solving process. Hundreds of examples, many based on real-world data, illustrate the practical applications of mathematics. The textbook also includes technology g...show moreuidelines to help you successfully use graphing calculators and Microsoft Excel to solve selected49511842878 +$3.99 s/h
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Hardcover Fair 0495118427 Wear on cover, no writing or highlighting, does not come with an access code or CD, expedited shipping available.
$6.62$7.58 +$3.99 s/h
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SellBackYourBook Aurora, IL
04951184 |
0716736527
9780716736523
Discrete Mathematics Through Applications:Written specifically for the high school discrete math course, Discrete Mathematics Through Applications lets the recently revised NCTM Standards be its guide. The book focuses on the connections among mathematical topics and real-life events and situations, emphasizing problem solving, mathematical reasoning and communication. |
More About
This Textbook
Overview
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, Third Edition focuses on the fundamentals: preparation for class, practice with homework, and reviewing of key concepts. With the Concepts Through Functions series, the Sullivans expose students to functions in the first chapter and maintain a continuous theme of functions throughout the text. This approach ensures students master basic skills and develop the conceptual understanding they need for the course, ultimately preparing students for future math courses as wellProduct Details
ISBN-13: 9780321926036
Publisher: Pearson
Publication date: 1/24/2014
Edition description: New Edition
Edition number: 3
Pages: 1100
Product dimensions: 8.90 (w) x 11.20 (h) x 1.70 (d)
Meet the Author
Mike Sullivan is Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago's South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.
Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf |
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