Problem-Solving Through Problems
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Beschreibung
The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources. Each section features a single idea, the power and versatility of which is demonstrated in the examples and reinforced in the problems. The book serves as an introduction and guide to the problems literature (e.g., as found in the problems sections of undergraduate mathematics journals) and as an easily accessed reference of essential knowledge for students and teachers of mathematics. The book is both an anthology of problems and a manual of instruction. It contains over 700 problems, over one-third of which are worked in detail. Each problem is chosen for its natural appeal and beauty, but primarily to provide the context for illustrating a given problem-solving method. The aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of problems. Whenever possible, problems within sections are chosen to cut across expected course boundaries and to thereby strengthen the evidence that a single intuition is capable of broad application. Each section concludes with "Additional Examples" that point to other contexts where the technique is appropriate.
Problem-Solving Through Problems is a practical anthology of some of the best elementary problems in different branches of mathematics. This classroom tested material will teach its readers important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
Autor*in
Loren C. Larson
Themen in »Problem-Solving Through Problems«
Arithmetic Cauchy-Schwarz Inequality Derivative Division Problem solving Schwarz inequality calculus fundamental theorem mean value theorem pigeonhole principle
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From the reviews:
"This is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette)
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