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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010138502 | QA167 H47 2003 | Open Access Book | Book | Searching... |
Searching... | 30000010156569 | QA167 H47 2003 | Open Access Book | Book | Searching... |
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Summary
Summary
This book can be seen as a continuation of Equations and Inequalities: El ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book.
Reviews 1
Choice Review
In the parlance of college catalogs, "finite mathematics'' and "discrete mathematics'' both signal applications-oriented courses treating various topics all largely or entirely independent from calculus. These courses share many common topics, but finite mathematics (the phrase originated in the 1950s with J. Kemeny's Dartmouth course and book) usually targets general education and business students, while discrete mathematics provides for computer science students especially. Although the gracious tone and elementary character of Lovasz, Pelikan, and Vesztergombi's book make it a natural for general education, the authors actually work just the topics that computer science students usually see. So, e.g., they treat cryptography but omit linear programming. Overall, their emphasis on proof seems wise and appropriate, unlike what one finds today in so many books whose authors cheat students by eviscerating the essential nature of mathematics in the name of reaching a wide audience. In Lovasz, particularly, one has a celebrated researcher and expositor, and so, as one might hope, readers will hear an informed and distinctive viewpoint, a contrast to the many cookie-cutter texts in this area that just ape one another in quest of mere market share. The title notwithstanding, the book may turn out to serve students best in the sort of "transition to abstraction course'' taken as prerequisite to more technical discrete mathematics courses. One may view mathematics as a particular body of knowledge and ideas, or alternatively, as a general way of looking at the world. The former viewpoint leads mathematics teachers to concentrate on merely imparting content, but the latter demands actually trying to make students smarter.Hirman and colleagues have created a discrete mathematics course woven out of solid problems, neither the mere exercises most texts use just to reinforce content, nor the disjointed, idiosyncratic puzzles that find their way into supplementary material and that only the smartest students can solve. Here students discover the principles of combinatorics for themselves. Though the actual coverage corresponds to just half the chapters in Lovasz, students who work this book will get a more detailed, more textured view of this slice of discrete mathematics; more importantly, they will acquire the habits of mind necessary for doing original research. Combinatorial optimization means, very simply, arranging things for the best. A vast subject, it has many facets depending on the sort of thing one wishes to arrange and what is counted as best. Only subtitles tell that books by G. Cornuejols, by B.H. Korte and J.Vygen, by M. Akgul and H. Hamacher, by C. Papadimitriou and K. Steiglitz, and by E. Lawler have their quite distinct concerns. Now any good course in discrete mathematics devotes a few weeks to matching theory and network flow algorithms, but that only scratches the surface. A generation of students has turned to L. Lovasz and M. Plummer's delightful Matching Theory (1986) for further reading.Now comes Schrijver's book, a current and extremely comprehensive account, running 1,451 pages; by itself the bibliography would make a long book. But even as the book provides reference material to satisfy the experts, strong undergraduates will profit by dipping straight into nearly any chapter. Mathematics and computer science students should consult it, both to supplement their theoretical coursework or to find algorithms for practical projects. ^BSumming Up: All three books: Recommended. Upper-division undergraduates through faculty. D. V. Feldman University of New Hampshire
Table of Contents
| Preface |
| Symbols |
| Combinatorics |
| Combinatorial Arithmetic |
| Combinatorial Geometry |
| Hints and Answers |
| Bibliography |
| Index |
