Proofs and Fundamentals: A First Course in Abstract Mathematics

Rating:
Summary: an excellent introduction to formal mathematics
Review: This book is an excellent and thorough intorduction to the world of formal mathematics. Typically, a new mathematics student finds himself or herself picking up random mathematical concepts and techniques of proof along the way, without ever having the chance to sit down and go through the fundamentals of formal mathematics and proof. This book covers a little of everything, and has a thorough introduction to sets, functions, inverses, equivalence and order relations. There are also sections on introductory number theory, algebra, combinatorics, logic, and much more. It provides an excellent overview for the student who will be using these tools on a daily basis, for the layman who is interested in finding out what mathematics is really about, or for the seasoned mathematician who needs a good general reference book. There are also extensive and thorough sections on the construction and writing of mathematical proofs -- somthing on which many new and not-so-new mathematicians could use some improvement.