# The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

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*Kiran S. Kedlaya; Bjorn Poonen; Ravi Vakil*

MAA Press: An Imprint of the American Mathematical Society

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 & Endorsements

Each chapter solves several realistic problems while introducing the modelling optimization techniques and simulation as required. This allows readers to see how the methods are used, making it easier to grasp the basics.

-- CERN Courier

The book will be invaluable for anybody with an interest in mathematical competitions or just trying his or her hand at challenging Mathematics at university level. All theories begin with simple, easy to state and beautiful problems and this book has an abundant supply of those.

-- The London Mathematical Society

# Table of Contents

## The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary

- Introduction 88
- Contents 1414
- Problems 1616
- The Forty-Sixth William Lowell Putnam Mathematical CompetitionDecember 7, 1985 1616
- The Forty-Seventh William Lowell Putnam Mathematical CompetitionDecember 6, 1986 1919
- The Forty-Eighth William Lowell Putnam Mathematical CompetitionDecember 5, 1987 2121
- The Forty-Ninth William Lowell Putnam Mathematical CompetitionDecember 3, 1988 2424
- The Fiftieth William Lowell Putnam Mathematical CompetitionDecember 2, 1989 2626
- The Fifty-First William Lowell Putnam Mathematical CompetitionDecember 1, 1990 2828
- The Fifty-Second William Lowell Putnam Mathematical CompetitionDecember 7, 1991 3030
- The Fifty-Third William Lowell Putnam Mathematical CompetitionDecember 5, 1992 3232
- The F ifty-Fourth William Lowell Putnam Mathematical CompetitionDecember 4, 1993 3434
- The Fifty-Fifth William Lowell Putnam Mathematical CompetitionDecember 3, 1994 3636
- The Fifty-Sixth William Lowell Putnam Mathematical CompetitionDecember 2, 1995 3838
- The Fifty-Seventh William Lowell Putnam Mathematical CompetitionDecember 7, 1996 4040
- The Fifty-Eighth William Lowell Putnam Mathematical CompetitionDecember 6, 1997 4242
- The Fifty-Ninth William Lowell Putnam Mathematical CompetitionDecember 5, 1998 4444
- The Sixtieth William Lowell Putnam Mathematical CompetitionDecember 4, 1999 4646
- The Sixty-First William Lowell Putnam Mathematical CompetitionDecember 2, 2000 4848

- Hints 5050
- Solutions 6666
- The Forty-Sixth William Lowell Putnam Mathematical CompetitionDecember 7, 1985 6868
- The Forty-Seventh William Lowell Putnam Mathematical Competition (1986) 8080
- The Forty-Eighth William Lowell Putnam Mathematical Competition (1987) 9191
- The Forty-Ninth William Lowell Putnam Mathematical Competition (1988) 103103
- The Fiftieth William Lowell Putnam Mathematical Competition (1989) 116116
- The Fifty-First William Lowell Putnam Mathematical Competition (1990) 131131
- The Fifty-Second William Lowell Putnam Mathematical Competition (1991) 150150
- The Fifty-Third William Lowell Putnam Mathematical Competition (1992) 169169
- The Fifty-Fourth William Lowell Putnam Mathematical Competition (1993) 186186
- The Fifty-Fifth William Lowell Putnam Mathematical Competition (1994) 206206
- The Fifty-Sixth William Lowell Putnam Mathematical Competition (1995) 219219
- The Fifty-Seventh William Lowell Putnam Mathematical Competition (1996) 232232
- The Fifty-Eighth William Lowell Putnam Mathematical CompetitionDecember 6, 1997 247247
- The Fifty-Ninth William Lowell Putnam Mathematical Competition (1998) 265265
- The Sixtieth William Lowell Putnam Mathematical CompetitionDecember 4, 1999 277277
- The Sixty-First William Lowell Putnam Mathematical Competition (2000) 293293

- Results 310310
- Putnam Trivia for the Nineties 322322
- Some Thoughts on Writing for the Putnam 326326
- Bibliography 338338
- Index 348348
- About the Authors 352352