Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010191203 | QA43 K42 2008 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution, and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
Reviews 1
Choice Review
Andreescu's 51 "introductory problems'' and 51 "advanced problems,'' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought. Kedlaya, Poonen, and Vakil recognize that, just as mastering music means more than merely playing correct notes, mastering mathematics means more than just acquiring a knowledge of theorems and techniques. While most mathematics texts for students contain copious exercises, some easy, some harder, authors generally target their exercises toward the narrow goal of reinforcing of the material just exposited. As such, mathematics students seldom meet open-ended challenges, problems that force them to draw, potentially, on all the tools they have ever acquired, or else, perhaps, just on sheer cleverness. The William Lowell Putnam Mathematical Competition stands as the best-known competitive mathematics examination administered to American students, and every year a team of world-class research mathematicians compiles the questions. Surely every student who plans to sit for the exam should work these problems and study all the offered solutions. But all students will benefit from confronting problem-solving challenges of this difficulty.The USA and International Mathematical Olympiad aims to spotlight the most talented high school mathematics students in the world. Now considered from the vantage of a typical college mathematics student, the test questions which make up these competitions come out of only the most basic mathematics, primarily elementary algebra and plane geometry, but even so, they require a sort of decisive cleverness that few will find they can muster. And here lies their value: away from difficult concepts and new abstractions, the student has the opportunity to contemplate naked ingenuity. Though this slender volume follows on the heels of Istvan Reiman's treatment of all the Olympiads from 1959-99, the new book seems free of the occasional editorial lapses that mar the earlier book. Summing Up: Recommended. All three books--general readers; lower- and upper-division undergraduates; 102 Combinatorial Problems--two-year technical program students and professionals; USA and International Mathematical Olympiads--faculty also. D. V. Feldman University of New Hampshire
Table of Contents
Introduction | p. vii |
1 Structure of this book | p. vii |
2 The Putnam Competition over the years | p. viii |
3 Advice to the student reader | p. ix |
4 Scoring | p. x |
5 Some basic notation | p. xi |
6 Acknowledgements | p. xi |
Problems | p. 1 |
Hints | p. 35 |
Solutions | p. 51 |
The Forty-Sixth Competition (1985) | p. 53 |
The Forty-Seventh Competition (1986) | p. 65 |
The Forty-Eighth Competition (1987) | p. 76 |
The Forty-Ninth Competition (1988) | p. 88 |
The Fiftieth Competition (1989) | p. 101 |
The Fifty-First Competition (1990) | p. 116 |
The Fifty-Second Competition (1991) | p. 135 |
The Fifty-Third Competition (1992) | p. 154 |
The Fifty-Fourth Competition (1993) | p. 171 |
The Fifty-Fifth Competition (1994) | p. 191 |
The Fifty-Sixth Competition (1995) | p. 204 |
The Fifty-Seventh Competition (1996) | p. 217 |
The Fifty-Eighth Competition (1997) | p. 232 |
The Fifty-Ninth Competition (1998) | p. 250 |
The Sixtieth Competition (1999) | p. 262 |
The Sixty-First Competition (2000) | p. 278 |
Results | p. 295 |
Individual Results | p. 295 |
Team Results | p. 301 |
Putnam Trivia for the Nineties | p. 307 |
Answers | p. 321 |
Some Thoughts on Writing for the Putnam | p. 311 |
Bibliography | p. 323 |
Index | p. 333 |
About the Authors | p. 337 |