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Integer Partitions, by George E. Andrews, Kimmo Eriksson
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The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.
- Sales Rank: #1314003 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2004-10-11
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .35" w x 5.98" l, .48 pounds
- Binding: Paperback
- 152 pages
- Used Book in Good Condition
Review
"...until now there has not been a good introduction to the subject at an elementary level. Integer Partitions...is written at a level that most undergraduates, and even many high school students, could follow quite easily."
-MAA Reviews, Darren Glass, Columbia University
"This book is written in a very easy and friendly style. The authors start from scratch and lead the readers from the easy to the unsolved problems. It is really a pleasure to read."
-Mathematical Reviews
About the Author
George E. Andrews is Evan Pugh Professor of Mathematics at the Pennsylvania State University. He has been a Guggenheim Fellow, the Principal Lecturer at a Conference Board for the Mathematical Sciences meeting, and a Hedrick Lecturer for the MAA. Having published extensively on the theory of partitions and related areas, he has been formally recognized for his contribution to pure mathematics by several prestigious universities and is a member of the National Academy of Sciences (USA).
Kimmo Eriksson is Professor of Mathematics at Mälardalen University College, where he has served as the dean of the Faculty of Science and Technology. He has published in combinatorics, computational biology and game theory. He is also the author of several textbooks in discrete mathematics and recreational mathematics, and has received numerous prizes for excellence in teaching.
Most helpful customer reviews
7 of 7 people found the following review helpful.
A Beautiful Presentation of Mathematical Reasoning
By Charles Neuhauser
This is a wonderful little book about a very simple mathematical object known as the "integer partition". The concept is simple: a partition of a positive integer is the set of positive integers that when summed give that number. (i.e. one integer partition of 6 is [5, 1] another is [3, 2, 1]). Order is unimportant so [5,1] and [1,5] are the same partition.
Amazingly this simple idea gives rise to many rich investigations that are the basis for this book. Many of these relate to "counting" the number of partitions with a given property and relating the number of partitions with various properties to one another. In fact, the mere counting of the number of partitions of a large integer, like 200, requires a foray into generating functions, an extremely important area of combinatorics. The formal properties of integer partitions have been investigated for over 200 years by some of the brightest lights in the mathematical constellation, such as Euler and Ramanujan. One of the authors (Andrews) is probably the current leading expert in this field.
Using integer partitions as a starting point the authors take the reader into many areas of mathematics (for example, generating functions, bijective proofs, Ferrers graphs and partially ordered sets). Each chapter also provides a selection of graded exercises ranging from the simple to problems that in some cases would be considered research areas. An outline of the answers to problems is provided in the back of the book. Working the problems will certainly give your powers of reasoning a real workout.
I am not particularly skilled at mathematics, however, I found the discussion relatively easy to follow although most topics require serious study if a full understanding is to be had. I would think that this book would certainly appeal to the math hobbyist, but could easily be the basis for a semester seminar for the advanced undergraduate.
Five stars for this gem!
0 of 0 people found the following review helpful.
Truly great introduction to one aspect of additive number theory
By Customer
One of my favorite books. There is variety in the discussion, but the account is entirely coherent and self-contained, touching on a series of beautiful results. This is one of the most perfect books for an undergraduate thesis, I would imagine. The ideas are sophisticated, but they don't bog the reader down with technicalities or notation. It gives the reader what they need as smoothly as possible, then they're prepared to tackle some of the open problems discussed or go their own way. Best introduction I've seen to q-series. A decent introduction to generating functions (not the best, but for most students probably self-contained). Researchers unfamiliar with this area would love it too I bet because there's so little fuss. Lastly, though this is more tangential, the font is well chosen for a pleasing, visually appealing reading experience. If this book isn't on my desk, then it's under my pillow. Highly recommended.
1 of 2 people found the following review helpful.
Really like it, but cost is a bit high
By Stephen Desalvo
If you like to dabble in combinatorics, this is a very nice self-contained book on integer partitions, written at the undergraduate level. There is a lot of expository material and examples, with exercises as well, and the proofs are easy to read and follow.
The book is pretty thin, which in my opinion isn't a bad thing since they do a very good concise treatment of all the major topics. My only problem with this book is the cost on Amazon right now. I can access a university library so that's how I found it but I would like to have a copy for myself but wouldn't pay more than $10 or $15 for it, and if you ever see it I think you will agree. It should be a Dover book.
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