Reading, Writing, And Proving

This book, which is based on Pólya'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 mathematicsnbsp;and ends with suggestednbsp;projects for independent study. nbsp; Students will follow Pólya's four step approach:nbsp;analyzing the problem, devising anbsp;plan to solve the problem, carrying out that plan, and thennbsp;determining the implication of the result. In addition tonbsp;the Pólyanbsp;approach to proofs, this book placesnbsp;special emphasis on reading proofsnbsp;carefully and writingnbsp;them well. The authors have included a wide variety of problems,nbsp;examples, illustrations andnbsp;exercises,nbsp;some withnbsp;hints and solutions, designed specificallynbsp;to improve the student's ability tonbsp;read and write proofs. nbsp; 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.… (more)