An Elementary Transition to Abstract Mathematics: 1st Edition (Hardback) book cover

An Elementary Transition to Abstract Mathematics

1st Edition

By Gove Effinger, Gary Lee Mullen

CRC Press

280 pages | 12 B/W Illus.

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Hardback: 9780367336936
pub: 2019-12-01
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Description

This text is intended to help students move from introductory courses to those where rigor and proof play a much greater role. The emphasis is on precise definitions of mathematical objects and rigorous proofs of properties. The text contains four parts. The first reviews earlier concepts more rigorously and covers methods to make a correct argument. In the second part, concepts and objects are introduced including induction, sets, functions, cardinality, complex numbers, permutations, and matrices. The third part covers number theory including applications to cryptography. In the final part, important objects from abstract algebra are introduced at a relatively elementary level.

Table of Contents

1 A Look Back: Precalculus Math 2 A Look Back: Calculus 3 About Proofs and Proof Strategies 4 Mathematical Induction 5 The Well-ordering Principle 6 Sets 7 Equivalence Relations 8 Functions 9 Cardinality of Sets 10 Permutations 11 Complex Numbers 12 Matrices and Sets with Algebraic Structure 13 Divisibility in Z and Number Theory 14 Primes and Unique Factorization 15 Congruences and the Finite Sets Zn 16 Solving Congruences 17 Fermat’s Theorem 18 Diffie-Hellman Key Exchange 19 Euler’s Function and Euler’s Theorem

About the Authors

Gove Effinger received his Ph.D. in Mathematics from the University of Massachusetts (Amherst) in 1981 and subsequently taught at Bates College for 5 years and then Skidmore College for 29 years. He is the author of two books: Additive Number Theory of Polynomials over a Finite Field (with David R. Hayes), and Common-Sense BASIC: Structured Programming with Microsoft QuickBASIC (with Alice M. Dean), as well as numerous research papers. His research focus has primarily been concerned with the similarities of the ring of polynomials over a finite field to the ring of ordinary integers.

He has also done work in classical number theory and combinatorics. Gary L. Mullen is Professor of Mathematics at the Pennsylvania State University, University Park, PA. He has taught both undergraduate and graduate courses there for over 40 years. In addition, he has written more than 150 research papers and five books, including both graduate as well as undergraduate textbooks. He also served as department head for seven years and has served as an editor on numerous editorial boards, including having served as Editor-in-Chief of the journal Finite Fields and Their Applications since its founding in 1995.

About the Series

Textbooks in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT018000
MATHEMATICS / Logic
MAT028000
MATHEMATICS / Set Theory
MAT034000
MATHEMATICS / Mathematical Analysis