Introduction to Mathematical Structures and Proofs

by Larry J. Gerstein

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 for instructors adopting the text for a course.

Genres: Mathematics, Logic

414 pages, Hardcover

First published April 4, 1996

Reviews

[Breena Weller · Rating 4 out of 5]

this is a good math book

[Isaac C · Rating 4 out of 5]

Solid Textbook. Good for beginners.

[Zaid Barghouthi · Rating 4 out of 5]

I used this book in my first -real math- course .. it was mostly clear. Didn't do chapter 5 though.

it has nice set of exercises after each section. few of them were really difficult.

All in all .. I had good time with this book.