Basic Concepts of Mathematics
by Elias Zakon
Publisher: The Trillia Group 2007
Number of pages: 208
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, and basic properties of n-dimensional Euclidean spaces.
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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 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 Joseph Fields - Southern Connecticut State University
The point of this book is to help you with the transition from doing math at an elementary level (concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements).
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).