By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.
"Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." ― Aimo Hinkkanen, University of Illinois at Urbana
"The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." ― John Konvalina, University of Nebraska at Omaha