Proofs and Concepts: the fundamentals of abstract mathematics
by Dave Witte Morris, Joy Morris
Publisher: University of Lethbridge 2009
Number of pages: 220
This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.
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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 Patrick Keef, David Guichard, Russ Gordon - Whitman College
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
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.