Extending the Frontiers of Mathematics: Inquiries into proof and argumentation

Edward B. Burger, Williams College

Mathematicians do not know in advance if their assertions are true. They need to verify assertions with rigorous proofs or produce counterexamples, then attempt to salvage the assertions by transforming them into theorems. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation invites students to experience this progression of mathematical discovery.

With Extending the Frontiers of Mathematics, award-winning professor and author Edward B. Burger has created a uniquely innovative text for either mathematics or secondary mathematics education majors. The book offers a discovery-based approach that is ideally suited for use in a proofs course, a discrete math course, or any bridge course to more abstract mathematics.

Brief, compelling, and inexpensive enough to be used as a supplement, Extending the Frontiers of Mathematics is also complete enough to serve as your primary text. Burger’s informal and humorous writing style, as always, engages students throughout the learning process.

Distinctive Features
Extending the Frontiers of Mathematics’ unique pedagogy will engage and challenge your students as never before:

• The text offers puzzles and patterns as precursors to proofs. 
• The “prove and extend or disprove and salvage” instruction is repeated, providing a consistent framework for approaching the problems.
• The book’s brevity gives it flexibility; it can be used as either a core or supplementary text.
• Investigative in nature, this discovery-based text leads but doesn’t tell.

About the Author

Edward B. Burger is Professor and Chair of Mathematics at Williams College. He is the recipient of the Mathematics Association of America’s (MAA) Haimo Award for Distinguished Teaching of Mathematics, the Polya Lectureship, and the MAA’s Chauvenet Prize for excellence in expository writing in mathematics.

Instructor resources are available to qualifying instructors. The printed reference includes teaching suggestions, solutions to all problems, and suggestions for grouping students for effective investigations.