A Problem Seminar (Problem Books in Mathematics) by Donald J. Newman (PDF)

Description

There was once a bumper sticker that read, “Remember the good old days when air was clean and sex was dirty?” Indeed, some of us are old enough to remember not only those good old days, but even the days when Math was/un(!), not the ponderous THEOREM, PROOF, THEOREM, PROOF, . . . , but the whimsical, “I’ve got a good prob­ lem. ” Why did the mood change? What misguided educational philoso­ phy transformed graduate mathematics from a passionate activity to a form of passive scholarship? In less sentimental terms, why have the graduate schools dropped the Problem Seminar? We therefore offer “A Problem Seminar” to those students who haven’t enjoyed the fun and games of problem solving. CONTENTS Preface v Format I Problems 3 Estimation Theory 11 Generating Functions 17 Limits of Integrals 19 Expectations 21 Prime Factors 23 Category Arguments 25 Convexity 27 Hints 29 Solutions 41 FORMAT This book has three parts: first, the list of problems, briefly punctuated by some descriptive pages; second, a list of hints, which are merely meant as words to the (very) wise; and third, the (almost) complete solutions. Thus, the problems can be viewed on any of three levels: as somewhat difficult challenges (without the hints), as more routine problems (with the hints), or as a textbook on “how to solve it” (when the solutions are read). Of course it is our hope that the book can be enjoyed on any of these three levels.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I did not buy this book on Amazon, rather I got it at my college library.This book is aimed at graduate students who do not have ‘a problem seminar’ course. The questions need some knowledge from number theory, probability, linear algebra and calculus.

⭐It is sad that this text is out of print. There are so many amazingly useful concepts developed here. For example, the estimation of difficult integrals and the use of polynomial generating functions as a way to handle many combinatoric problems are carefully developed here. These are the “nuts and bolts” of analysis that are usually taken for granted in other textbooks. The author sincerely tries to develop the ideas behind each of the concepts. My only complaint is that there are not enough exercises that illuminate the important concepts that are discussed. Also, sometimes the author seems rushed in his exposition, which really makes it hard for the reader to keep up. This book is part of the series that in general I highly recommend. In fact, this is probably one of the top five books in the problem series.

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