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.
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