This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

Richard Hammack is an associate professor of mathematics at Virginia Commonwealth University in Richmond. A native of rural southern Virginia, he studied painting at Rhode Island School of Design before an interest in computer graphics and visualization led him to mathematics. He works mostly in the areas of combinatorics and graph theory.

Home page: www.people.vcu.edu/~rhammack/