# A COURSE IN ENUMERATION AIGNER PDF

A Course in Enumeration by Martin Aigner. David Einstein is currently reading it May 15, An inviting text for self-study, with a generous collection of examples and a wealth of exercises. Chapter nine my personal favourite looks at graphs: Want to Read saving…. Algebraic Geometry Robin Hartshorne. There are no discussion topics on this book yet. Home Contact Us Help Free delivery worldwide.

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Take counting, for example. We all learn how to count things in grade school, and for much of our elementary education we think that this is the end of the story. We start to learn that there are often subtleties involved in counting.

Students who go further and pick up books such as Proofs That Really Count , by Benjamin and Quinn, or A Path To Combinatorics for Undergraduates , by Andreescu and Feng, will see more of these issues and really start to understand the beauty as well as the difficulty that counting can sometimes pose. But even that is not the end of the story. The book is divided into three parts: the first part is about "Basics" and actually starts at a very elementary level, discussing the inclusion-exclusion principle and binomial coefficients.

But the basics soon get much less basic as Aigner delves into Stirling numbers, lattice paths, generating functions, and infinite matrices. The second part of the book is about "Methods" and goes into greater depth on generating functions, hypergeometric summations, and sieve methods. This part is a bit dry to read, but is important in order to move on to what comes next.

The first chapter in this part of the book defines Catalan numbers in six different ways! Another chapter defines symmetric functions and examines their relationship with homogeneous functions and standard tableaux.

The final chapter looks at models which arise in statistical physics, such as the Dimer problem, which is a generalization of the famous question asking how many ways one can cover a chessboard with dominoes. This chapter is not as self-contained as most of the book, requiring a little more sophistication and background in graph theory than many readers might have.

One nice feature of the book is that each chapter concludes with a mostly self-contained "Highlight" which looks at one example in depth. One of these investigates how the Catalan number Cn counts the number of ways that 2n points on a circle can be connected into n chords none of which intersect with each other.

Another looks in depth at the Aztec Diamonds developed by Elkies, Kupperberg, Larsen, and Propp, which have a very nice way of counting tilings and a surprising connection to the alternating matrix theorem.

Furthermore, there are quite a few typos in the book, and some of these held up my reading quite a bit. I think it would be a good, if not a great, textbook for any graduate student wishing to learn about enumerative combinatorics.

However, if you are just looking for a casual book to learn a new area, there are better choices on the market. Darren Glass is an assistant professor of mathematics at Gettysburg College. His main mathematical interests include number theory, algebraic geometry, and cryptography.

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## A COURSE IN ENUMERATION AIGNER PDF

Darg Octipi marked it as to-read Mar 27, Just a moment while we sign you in to your Goodreads account. Basics, Methods, and Topics. A Course in Enumeration — Martin Aigner — Google Books Description Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. Chapter one covers elementary counting principles, binomial coefficients, Stirling numbers, permutations, number partitions and lattice paths, with fundamental coefficients as a kind of unifying idea. Saikat rated it it was amazing Mar 12, Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. My library Help Advanced Book Search. Lists with This Book.

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## A Course in Enumeration

Take counting, for example. We all learn how to count things in grade school, and for much of our elementary education we think that this is the end of the story. We start to learn that there are often subtleties involved in counting. Students who go further and pick up books such as Proofs That Really Count , by Benjamin and Quinn, or A Path To Combinatorics for Undergraduates , by Andreescu and Feng, will see more of these issues and really start to understand the beauty as well as the difficulty that counting can sometimes pose. But even that is not the end of the story. The book is divided into three parts: the first part is about "Basics" and actually starts at a very elementary level, discussing the inclusion-exclusion principle and binomial coefficients. But the basics soon get much less basic as Aigner delves into Stirling numbers, lattice paths, generating functions, and infinite matrices.

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Zucage The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. And though individual chapters do draw on earlier ones, that is usually only for core methods and a few results. There are exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result. Nitin CR added it Sep 06, Each chapter ends with a dnumeration, which is a specific, high-level application of the material learned in that chapter. The explanations, while often brief, are quite good. Just a moment while we sign you in to your Goodreads account. Yuri Popov rated it it was amazing Apr 04, Other books in this series.

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The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. There are exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result.