Introduction to Mathematical Structures and Proofs

Larry J. Gerstein (Autor)

Buch | Softcover

401 Seiten

2016 | Softcover reprint of the original 2nd ed. 2012
Springer-Verlag New York Inc.
978-1-4939-5146-8 (ISBN)

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As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader.

The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com forinstructors adopting the text for a course.

Larry Gerstein's primary areas of research have been in quadratic forms and number theory and he has published extensively in these areas. The author's first edition of "Introduction to Mathematical Structures and Proofs" has sold to date (8/2/2010) over 6000 copies and has gone through 5 printings. Gerstein himself has a transition course at UC, Santa Barbara (Math 8-A transition to higher mathematics) from his book since its first publication date. The first edition also received 2 glowing reviews by Steve Krantz for the American Mathematical Monthly, and S. Gottwald for Zentralblatt.

Preface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.

Erscheinungsdatum	19.08.2017
Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	XIII, 401 p.
Verlagsort	New York
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
Schlagworte	Cantor's theorems • counting principles • fundamental theorem of arithmetic • Mathematical Induction • number-theoretic functions • Proof Techniques • relations and partitions • set constructions • transition course
ISBN-10	1-4939-5146-7 / 1493951467
ISBN-13	978-1-4939-5146-8 / 9781493951468
Zustand	Neuware