Jonathan Michael Kane is an emeritus professor of Mathematical and Computer Sciences at the University of Wisconsin – Whitewater and an honorary fellow of the Department of Mathematics at the University of Wisconsin – Madison. He has published papers in several complex variables, probability, algorithms, and the relationship between gender and culture in mathematics performance. He has taught dozens of courses in mathematics, statistics, actuarial mathematics, and computer science. Dr. Kane plays a major role in contest mathematics by chairing the American Invitational Mathematics Exam Committee, cofounding and coordinating the annual online Purple Comet! Math Meet, and teaching at the AwesomeMath summer program.

"Its objective is to make the reader understand the thought processes behind the proofs. In this it succeeds admirable, and then book should be in every mathematical library, public and private. ... The book is excellently produced with many coloured diagrams." (P. S. Bullen, Mathematical Reviews, January, 2017)

• What Are Proofs, And Why Do We Write Them?.- The Basics of Proofs.- Limits.- Continuity.- Derivatives.- Riemann Integrals.- Infinite Series.- Sequences of Functions.- Topology of the Real Line.- Metric Spaces​.

Jonathan Michael Kane is an emeritus professor of Mathematical and Computer Sciences at the University of Wisconsin – Whitewater and an honorary fellow of the Department of Mathematics at the University of Wisconsin – Madison. He has published papers in several complex variables, probability, algorithms, and the relationship between gender and culture in mathematics performance. He has taught dozens of courses in mathematics, statistics, actuarial mathematics, and computer science. Dr. Kane plays a major role in contest mathematics by chairing the American Invitational Mathematics Exam Committee, cofounding and coordinating the annual online Purple Comet! Math Meet, and teaching at the AwesomeMath summer program.

"Its objective is to make the reader understand the thought processes behind the proofs. In this it succeeds admirable, and then book should be in every mathematical library, public and private. ... The book is excellently produced with many coloured diagrams." (P. S. Bullen, Mathematical Reviews, January, 2017)

• What Are Proofs, And Why Do We Write Them?.- The Basics of Proofs.- Limits.- Continuity.- Derivatives.- Riemann Integrals.- Infinite Series.- Sequences of Functions.- Topology of the Real Line.- Metric Spaces​.

Jonathan Michael Kane is an emeritus professor of Mathematical and Computer Sciences at the University of Wisconsin – Whitewater and an honorary fellow of the Department of Mathematics at the University of Wisconsin – Madison. He has published papers in several complex variables, probability, algorithms, and the relationship between gender and culture in mathematics performance. He has taught dozens of courses in mathematics, statistics, actuarial mathematics, and computer science. Dr. Kane plays a major role in contest mathematics by chairing the American Invitational Mathematics Exam Committee, cofounding and coordinating the annual online Purple Comet! Math Meet, and teaching at the AwesomeMath summer program.

"Its objective is to make the reader understand the thought processes behind the proofs. In this it succeeds admirable, and then book should be in every mathematical library, public and private. ... The book is excellently produced with many coloured diagrams." (P. S. Bullen, Mathematical Reviews, January, 2017)

• What Are Proofs, And Why Do We Write Them?.- The Basics of Proofs.- Limits.- Continuity.- Derivatives.- Riemann Integrals.- Infinite Series.- Sequences of Functions.- Topology of the Real Line.- Metric Spaces​.