Problems and Proofs in Numbers and Algebra by Richard S. MillmanProblems and Proofs in Numbers and Algebra by Richard S. Millman

Problems and Proofs in Numbers and Algebra

byRichard S. Millman, Peter J. Shiue, Eric Brendan Kahn

Hardcover | February 26, 2015

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Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school" course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Richard S. Millman,Ph.D., Director, Center for Education Integrating Science, Mathematics, and Computing (CEISMC) Georgia Institute of Technology Atlanta, GA 30332-­0282 Peter J. Shiue Department of Mathematical Sciences University of Nevada, Las Vegas 4505 Maryland Pkwy Las Vegas, NV 89154-4020 Eric Brendan Kahn Department of Mathemat...
Title:Problems and Proofs in Numbers and AlgebraFormat:HardcoverDimensions:223 pagesPublished:February 26, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:331914426X

ISBN - 13:9783319144269


Table of Contents

? ?I. The Integers 1. Number Concepts, Prime Numbers, and the Division Algorithm 2. Greatest Common Divisors, Diophantine Equations, and Combinatorics 3. Equivalence Classes with Applications to Clock Arithmetics and Fractions II. The Algebra of Polynomials and Linear Systems 4. Polynomials and the Division Algorithm 5. Factoring Polynomials, Their Roots, and Some Applications 6. Matrices and Systems of Linear Equations

Editorial Reviews

"Aimed at introducing postcalculus students tohigher mathematics by way of solving rigorous problems and learning how toprove. . the content is less focused on basic mathematical concepts seen inupper-division college mathematics coursework and more so on topics thatteachers might present in their classrooms, and on interesting applications . .Teachers of mathematics at the secondary level would be well served by taking acourse based on this text. Summing Up: Recommended. Upper-divisionundergraduates through faculty." (D. S. Larson, Choice, Vol. 53 (1), September,2015)