An Introduction to Higher Mathematics
by Patrick Keef, David Guichard, Russ Gordon
Publisher: Whitman College 2010
Number of pages: 144
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction, Indirect Proof); Number Theory (The Euclidean Algorithm, The Fundamental Theorem of Arithmetic); Functions (Injections and Surjections, Cardinality and Countability, Uncountability of the Reals).
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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 Jim Hefferon - Saint Michael's College
Introduction to Proofs is a Free undergraduate text. It is inquiry-based, sometimes called the Moore method or the discovery method. It consists of a sequence of exercises, statements for students to prove, along with a few definitions and remarks.
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 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.