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 Richard Hammack - Virginia Commonwealth University
This textbook is an introduction to the standard methods of proving mathematical theorems. It is written for an audience of mathematics majors at Virginia Commonwealth University, and is intended to prepare the students for more advanced courses.
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 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.