Distilling Ideas: An Introduction to Mathematical Thinking (Mathematical Association of America Textbooks)

Designed for undergraduate students and lecturers, this text guides its users to develop the skills, attitudes, and habits of mind of a mathematician. It presents a carefully designed sequence of exercises and theorems so that its readers will be directed to discover mathematical ideas, strategies of proof, and strategies of thinking. Through the exploration of interesting mathematical content including graphs, groups, and calculus, this book helps to foster habits of inquiry. This book can be used by instructors as a text for an inquiry-based introduction to proof course, or as an independent study guide for mathematics students. The three core mathematical topics are presented separately, and each helps students develop theorem-proving skills and strategies of thinking whilst also providing an organised set of challenges that lead students to understand the process of mathematical creativity and development.

Brian Katz is an Assistant Professor of Mathematics at Augustana College in Rock Island, Illinois. He received his BA from Williams College in 2003 with majors in mathematics, music and chemistry, and his PhD from the University of Texas, Austin in 2011, concentrating on algebraic geometry. While at the University of Texas, Austin, Brian received the Frank Gerth III Graduate Excellence Award and the Frank Gerth III Graduate Teaching Excellence Award from the Department of Mathematics. Brian is a Project NExT Fellow, supported by Harry Lucas, Jr and the Educational Advancement Foundation.

Michael Starbird is Professor of Mathematics and a University Distinguished Teaching Professor at the University of Texas, Austin. He received his BA degree from Ponoma College and his PhD in mathematics from the University of Wisconsin, Madison. He has held visiting positions at the Institute for Advanced Study in Princeton, New Jersey, and at the Jet Propulsion Laboratory in Pasadena, California. He served as Associate Dean in the College of Natural Sciences at the University of Texas from 1989 to 1997. Starbird's mathematical research is in the field of topology. He has served as a member-at-large of the Council of the American Mathematical Society and on the national education committees of both the American Mathematical Society and the Mathematical Association of America.