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 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.
by Martin Day - Virginia Tech
The book helps students make the transition from freshman-sophomore calculus to more proof-oriented upper-level mathematics courses. Another goal is to train students to read more involved proofs they may encounter in textbooks and journal articles.
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 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.