How To Write Proofs
by Larry W. Cusick
Publisher: California State University, Fresno 2009
Proofs are the heart of mathematics. If you are a math major, then you must come to terms with proofs--you must be able to read, understand and write them. What is the secret? What magic do you need to know? The short answer is: there is no secret, no mystery, no magic. All that is needed is some common sense and a basic understanding of a few trusted and easy to understand techniques.
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by Farshid Hajir - University of Massachusetts
Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.
by Peter J. Eccles - Cambridge University Press
This book introduces basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory.
by Elias Zakon - The Trillia Group
The book will help students complete the transition from purely manipulative to rigorous mathematics. It covers basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers, fields, etc.
by Ted Sundstrom - Pearson Education, Inc.
'Mathematical Reasoning' is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.