A Problem Seminar (problem Books In Mathematics)
by D.J. Newman /
1982 / English / PDF
5.1 MB Download
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.
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.
