Sets
Logic
Counting
Direct proof
Contrapostivie proof
Proof by contradiction
Proving non-conditional statements
Proofs involving sets
Disproof
Mathematical induction
Relations
Functions
Cardinality of sets
Conclusion
Solutions

"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."