Fundamental Concepts of Mathematics
by Farshid Hajir
Publisher: University of Massachusetts 2005
Number of pages: 69
Contents: Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; (Equivalence) Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.
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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 James Franklin, Albert Daoud - Kew Books
This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. The book takes a straightforward, no nonsense approach to explaining the core technique of mathematics.
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.
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.