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An Elementary Transition to Abstract Mathematics: Textbooks in Mathematics

Autor Gove Effinger, Gary L. Mullen
en Limba Engleză Paperback – 21 ian 2023
An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role.




The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials.




Features:







  • The material is presented in many short chapters, so that one concept at a time can be absorbed by the student.







  • Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student’s transition by working with familiar concepts.







  • Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns.







  • A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.


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Specificații

ISBN-13: 9781032475172
ISBN-10: 103247517X
Pagini: 292
Ilustrații: 12
Dimensiuni: 156 x 234 mm
Greutate: 0.41 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press
Seria Textbooks in Mathematics


Public țintă

Undergraduate

Cuprins

A Look Back: Precalculus Math


A Look Back: Calculus


About Proofs and Proof Strategies


Mathematical Induction


The Well-Ordering Principle


Sets


Equivalence Relations


Functions


Cardinality of Sets


Permutations


Complex Numbers


Matrices and Sets with Algebraic Structure


Divisibility in Z and Number Theory


Primes and Unique Factorization


Congruences and the Finite Sets Zn


Solving Congruences


Fermat’s Theorem


Diffie-Hellman Key Exchange


Euler’s Formula and Euler’s Theorem


RSA Cryptographic System


Groups-Definition and Examples


Groups-Basic Properties


Groups-Subgroups


Groups-Cosets


Groups-Lagrange’s Theorem


Rings


Subrings and Ideals


Integral Domains


Fields


Vector Spaces


Vector Space Properties


Subspaces of Vector Spaces


Polynomials


Polynomials-Unique Factorization


Polynomials over the Rational, Real and Complex Numbers


Suggested Solutions to Selected Examples and Exercises

Notă biografică

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.


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.

Descriere

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.