Description: Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
Brief description: John Meier is Professor of Mathematics at Lafayette College, Pennsylvania, where he also served as Dean of the Curriculum. His research focuses on geometric group theory and involves algorithmic, combinatorial, geometric and topological issues that arise in the study of infinite groups. In addition to teaching awards from Cornell University, New York, and Lafayette College, Professor Meier is the proud recipient of the James Crawford Teaching Prize from the Eastern Pennsylvania and Delaware section of the Mathematical Association of America.
Review Quotes: Advance praise: 'Meier and Smith have written a wonderful introduction to higher mathematics, showing both the thrill of abstraction and the beauty in discovering proofs.' Tom Garrity, Williams College, Massachusetts