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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.
Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.
The contributions in this book analyse the policy challenges of taxation in developing countries, including corruption, tax evasion, and ineffective political structures. After a comprehensive overview, each chapter uses modern empirical methods to study a single critical issue essential to understanding the effects of taxes on development. Topics addressed include the effect of taxation on foreign direct investment; forms of corruption, tax evasion, and tax avoidance that are specific to developing countries; and issues related to political structure, including the negative effects of fiscal decentralization on the effectiveness of developmental aid and the relationship between democracy and taxation in Asian, Latin American, and European Union countries that have recently experienced both political and economic transitions.
‘Whiteness’ is a politically constructed category which needs to be understood and dismantled because the system of racism so embedded within our society harms us all. It has profound implications for human psychology, an understanding of which is essential for supporting the movement for change. This book explores these implications from a psychoanalytic and Jungian analytic perspective. The ‘fragility’ of whiteness, the colour-blind approach and the silencing process of disavowal as they develop in the childhood of white liberal families are considered as means of maintaining white privilege and racism. A critique of the colonial roots of psychoanalytic theories of Freud and Jung leads to questioning the de-linking of the individual from society in modern day analytic thinking. The concept of the cultural complex is suggested as a useful means of connecting the individual and the social. Examples from the author’s clinical practice as well as from public life are used to illustrate the argument. Relatively few black people join the psychoanalytic profession and those who do describe training and membership as a difficult and painful process. How racism operates in clinical work, supervision and our institutions is explored, and whilst it can seem an intractable problem, proposals are given for ways forward. This book will be of great importance to psychoanalysts, psychotherapists, social workers and all those with an interest in the role of white privilege on mental health.
This concise, lucid study charts the complex sequence of events we know today as the War of the Roses. In the thematic chapters of the third section the author assesses the motives and relationships of the principal actors; the real character and impact of the Wars of the Roses; and the nature of Yorkist government.
The bestselling sales classic! Revised and expanded to help you supercharge personal and team performance in today's ultra-competitive sales environment "People make buying decisions emotionally and justify them logically." That shrewd, timeless insight from the first edition of this bestselling book has become a “no-brainer” among sales professionals. Now You Can't Teach a Kid to Ride a Bike at a Seminar comes with new insights, information, and tools every sales leader can use. It combines Sandler's classic, battle-tested advice on driving personal and organizational success by breaking the rules of conventional selling with up-to-date best practices from experienced trainers of Sandler, now run by David Mattson.
Revolutionary and innovative, Lacan's work lies at the epicenter of modern thought about otherness, subjectivity, sexual difference, and enjoyment.
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.