Reading, Writing, and Proving

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This book, which assumes only a precalculus background, aids students in their transition to higher-level mathematics. The authors begin by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and end with suggested projects for independent study. The reader will follow Pólya's four step approach to problem solving: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. Special emphasis is placed on reading proofs carefully and writing them well. The authors have included a wide variety of exercises with solutions, examples, illustrations, and problems, making the book ideal for independent study. The third edition provides the reader with significant changes, all of which have been artfully designed to enhance the learning and teaching experience. The topic of mathematical induction has been modified and moved to an earlier part of the text. Two