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.
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'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
'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
'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
Book Description
This collection of problems from the William Lowell Putnam Competition is unlike the two previous volumes: it places the problems in the context of important mathematical themes. The authors highlight connections to other problems and to more advanced topics. It will appeal to students, teachers and anyone interested in problem solving.
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Most Helpful Customer Reviews
16 of 17 people found the following review helpful:
5.0 out of 5 stars
A Great Book...,
By wp (Ithaca, N.Y. United States) - See all my reviews
This review is from: The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary (MAA Problem Book Series) (Paperback)
Not much can be said about this book: you get exactly what you have in mind. First part of the book lists every problem from 1985-2000 Putnam exams, the second part provides hints to each of the problems in case you are stuck. The last part contains detailed solution(s) to every problem. It is an excellent book... Good luck on the test if you will be taking it.
2 of 2 people found the following review helpful:
5.0 out of 5 stars
excellent book,
This review is from: The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary (MAA Problem Book Series) (Paperback)
problems and answers are clearly explicated. great for studying or just satisfying your curiosity
7 of 10 people found the following review helpful:
5.0 out of 5 stars
Good reference for the budding problem solver.,
By bal gombak (Cambridge, MA USA) - See all my reviews
This review is from: The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary (MAA Problem Book Series) (Paperback)
I did Putnam in 2002 and solved 6 full problems. The future Putnam competitor should make it a point to consult past Putnam problems to successfully make the switch from olympiad problems to the Putnam. Not that it is a big change, but to do well in Putnam you have to know at least some basic trick in calculus, analysis and such. This is a good starting point in making that transition.On a whole another level, even research mathematicians (problem solver type) can benefit from the 'tricks' and nuances of the 'toy' problems (e.g Putnam problems) in honing their problem solving instinct.
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Inside This Book
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First Sentence:
"A1. Determine, with proof, the number of ordered triples (A1, A2, A3) of sets which have the property that (i) A1 A2 A3 = {1,2,3,4,5,6,7,8,9,10}, and (ii) A1 A2 A3 = 0, where 0 denotes the empty set." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
balanced strings, distinct real zeros, doubled letter, minimum perimeter, positive eigenvector, triangular number, distinct real numbers, polynomial with integer coefficients, nonnegative entries, integer entries Key Phrases - Capitalized Phrases (CAPs): (learn more)
Harvard University, Princeton University, University of Waterloo, Massachusetts Institute of Technology, Pigeonhole Principle, Putnam Fellows, Questions Committee, Duke University, International Mathematical Olympiad, University of Toronto, Rolle's Theorem, Noam Elkies, California Institute of Technology, Elizabeth Lowell Putnam Prize, Pick's Theorem, Cornell University, Problems Subcommittee, University of California, Washington University, Yale University, Ciprian Manolescu, Gauss's Lemma, New York University, Perron-Frobenius Theorem, Taylor's Formula New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
"A1. Determine, with proof, the number of ordered triples (A1, A2, A3) of sets which have the property that (i) A1 A2 A3 = {1,2,3,4,5,6,7,8,9,10}, and (ii) A1 A2 A3 = 0, where 0 denotes the empty set." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
balanced strings, distinct real zeros, doubled letter, minimum perimeter, positive eigenvector, triangular number, distinct real numbers, polynomial with integer coefficients, nonnegative entries, integer entries Key Phrases - Capitalized Phrases (CAPs): (learn more)
Harvard University, Princeton University, University of Waterloo, Massachusetts Institute of Technology, Pigeonhole Principle, Putnam Fellows, Questions Committee, Duke University, International Mathematical Olympiad, University of Toronto, Rolle's Theorem, Noam Elkies, California Institute of Technology, Elizabeth Lowell Putnam Prize, Pick's Theorem, Cornell University, Problems Subcommittee, University of California, Washington University, Yale University, Ciprian Manolescu, Gauss's Lemma, New York University, Perron-Frobenius Theorem, Taylor's Formula New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
7
books
cite this book:
See all 7 books citing this book
- Around the World (Fantastic Journeys) by Steve Skidmore in Front Matter
- The Inquisitive Problem Solver (MAA Problem Book Series) by Paul Vaderlind in Front Matter
- Princeton University by Alison Fraser on page 299
- A Problem Seminar (Sources in the History of Mathematics and Physical Sciences) by D.J. Newman in Back Matter
- Mathematical Olympiads, 2000-2001: Problems and Solutions from Around the World (MAA Problem Book Series) by Titu Andreescu in Front Matter
- The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (Maa Problem Books Series.) by J. Michael Steele in Front Matter
- William Lowell Putnam Mathematical Competition: Problems & Solutions: 1938-1964 by Andrew M. Gleason in Front Matter
- The William Lowell Putnam Mathematical Competition: Problems and Solutions 1965–1984 (MAA Problem Book Series) by Gerald L. Alexanderson in Front Matter
- International Mathematical Olympiads, 1986-1999 (MAA Problem Book Series) by Marcin E. Kuczma in Front Matter
See all 7 books citing this book
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