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 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 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 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 Larry W. Cusick - California State University, Fresno
Proofs are the heart of mathematics. What is the secret? 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.