Reading, Writing, and Proving: A Closer Look at Mathematics

This book, which is based on Polya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematicsand ends with sugge [...]
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This book, which is based on Polya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematicsand ends with suggestedprojects for independent study. Students will follow Polya's four step approach: analyzing the problem, devising aplan to solve the problem, carrying out that plan, and thendetermining the implication of the result. In addition tothe Polyaapproach to proofs, this book placesspecial emphasis on reading proofscarefully and writingthem well. The authors have included a wide variety of problems, examples, illustrations andexercises, some withhints and solutions, designed specificallyto improve the student's ability toread and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.