Hammack R. Book of Proof

Ed. 3.4, corrected - Independently published, 2025. - 380 p. - ISBN 0989472132.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.Preface.
Introduction.
Fundamentals
Sets.
Logic.
Counting.
How to Prove Conditional Statements
Direct Proof.
Contrapositive Proof.
Proof by Contradiction.
More on Proof
Proving Non-Conditional Statements.
Proofs Involving Sets.
Disproof.
Mathematical Induction.
Relations, Functions and Cardinality
Relations.
Functions.
Proofs in Calculus.
Cardinality of Sets.
Conclusion
SolutionsTrue PDF