Description

Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples. Proof techniques and strategies are thoroughly discussed and the underlying logic behind them is made transparent. Each chapter section begins with a set of guided reading questions intended to help students to identify the most significant points made within the section. Practice problems are embedded within chapters so that students can actively work with a key idea that has just been introduced. Each chapter also includes a collection of problems, ranging in level of difficulty, which are perfect for in-class discussion or homework assignments. (c) 2013 354 pages