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Combinatorics of Finite Sets (Dover Books on Mathematics) epub download

by Ian Anderson


Series: Dover Books on Mathematics. Paperback: 272 pages.

Series: Dover Books on Mathematics. Publisher: Dover Publications (November 2, 2011). But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, and expertise of the subject-matter.

Download books for free. Combinatorics of Finite Sets (Dover Books on Mathematics). Download (pdf, . 8 Mb) Donate Read. Epub FB2 mobi txt RTF.

Combinatorics of Finite Sets. Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. An excellent text for a topics.

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Combinatorics of Finite Sets book. 0486422577 (ISBN13: 9780486422572).

Finding books BookSee BookSee - Download books for free. Category: Математика. 8 Mb. A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series). Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them

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Dover Books on Mathematics. Author Hans J. Zassenhaus. Tales Of Hope and Time. Combinatorics of Finite Sets - Ian Anderson. 1 Introduction and Sperner’s theorem. A simple intersection result

Dover Books on Mathematics. A simple intersection result. of subsets of a finite set S is described in terms of intersection, union, or inclusion conditions. An amazing richness and variety of results will be discovered, developed, and extended in various directions. Although our main initial theme will be a study of a theorem of Spemer which could be said to be the inspiration of all that follows, we get into training by first of all asking what must surely be one of the simplest questions possible.

series Dover Books on Mathematics. Books related to Combinatorics of Finite Sets. Discrete Mathematics DeMYSTiFied. Dover Books on Mathematics.

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Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics." — Bulletin of the American Mathematical Society.

Combinatorics of Finite Sets (Dover Books on Mathematics) epub download

ISBN13: 978-0486422572

ISBN: 0486422577

Author: Ian Anderson

Category: Math and Science

Subcategory: Mathematics

Language: English

Publisher: Dover Publications (November 2, 2011)

Pages: 272 pages

ePUB size: 1609 kb

FB2 size: 1387 kb

Rating: 4.7

Votes: 192

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Related to Combinatorics of Finite Sets (Dover Books on Mathematics) ePub books

Maveri
Have just started, but I can already imagine that this will open doors that many readers will never have known existed. Book does assume a significant mathematical maturity however. The reader has to be willing to pause and say to themselves initially, "ok, that is what he must mean". I am guessing the frequency of which will diminish exponentially as the reader progresses. For example |X| means the element count of set X. I can't imagine anyone not knowing that would ever be interested in this book in the first place. The author jumps right in with anti-chains, and despite the lack of belabored introduction to notation I found the first proof surprisingly clear. Interestingly enough he does have a short list of symbols and I can't imagine anyone except an expert not saying "wow I want to know what that means" / or better yet "my gut straight away tells me that this is going to fit nicely with my research".
Maveri
Have just started, but I can already imagine that this will open doors that many readers will never have known existed. Book does assume a significant mathematical maturity however. The reader has to be willing to pause and say to themselves initially, "ok, that is what he must mean". I am guessing the frequency of which will diminish exponentially as the reader progresses. For example |X| means the element count of set X. I can't imagine anyone not knowing that would ever be interested in this book in the first place. The author jumps right in with anti-chains, and despite the lack of belabored introduction to notation I found the first proof surprisingly clear. Interestingly enough he does have a short list of symbols and I can't imagine anyone except an expert not saying "wow I want to know what that means" / or better yet "my gut straight away tells me that this is going to fit nicely with my research".
Velan
When one thinks of combinatorics of finite sets, he or she might first think of codes and designs. But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, and expertise of the subject-matter. Moreover, the author provided solutions to *every* one of the 150+ problems!!! How many math books can boast such a claim? Aside from may be a rough presentation of Lemma 4.3.2 the rest of the book is a masterpiece which I hope will gain more recognition within the next twenty years.
I highly recommend this book to both mathematicians and computer scientists. Although the book has very few "algorithms" in it, the thinking and reasoning about discrete structures (e.g. families of finite sets and multisets) will do wonders in developing the mind of a computer scientist, whether advanced or undergraduate. Yet it is quite sad that many cs departments (and math for that matter) invest little if any curriculum in discrete mathematics. Hopefully this will change at least to the point where the cs major will take two or three semesters of discrete math instead of two or three of calculus. For, as this book demonstrates, calculus is not a prerequisite for engaging one's mind in some quite fascinating mathematical problems related to finite sets.
Finally, it should be noted that Bela Bollobas also has an interesting book titled "Combinatorics: Set Systems, etc...." which significantly intersects with this book, but not to the degree where the reader should think they are interchangeable. I recommend both, and to read Anderson's book first; as I believe this book lays a better foundation than the latter.
Velan
When one thinks of combinatorics of finite sets, he or she might first think of codes and designs. But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, and expertise of the subject-matter. Moreover, the author provided solutions to *every* one of the 150+ problems!!! How many math books can boast such a claim? Aside from may be a rough presentation of Lemma 4.3.2 the rest of the book is a masterpiece which I hope will gain more recognition within the next twenty years.
I highly recommend this book to both mathematicians and computer scientists. Although the book has very few "algorithms" in it, the thinking and reasoning about discrete structures (e.g. families of finite sets and multisets) will do wonders in developing the mind of a computer scientist, whether advanced or undergraduate. Yet it is quite sad that many cs departments (and math for that matter) invest little if any curriculum in discrete mathematics. Hopefully this will change at least to the point where the cs major will take two or three semesters of discrete math instead of two or three of calculus. For, as this book demonstrates, calculus is not a prerequisite for engaging one's mind in some quite fascinating mathematical problems related to finite sets.
Finally, it should be noted that Bela Bollobas also has an interesting book titled "Combinatorics: Set Systems, etc...." which significantly intersects with this book, but not to the degree where the reader should think they are interchangeable. I recommend both, and to read Anderson's book first; as I believe this book lays a better foundation than the latter.
Seevinev
This book provides excellent coverage of sperners theorem including multiple proofs ,like the original one by sperner and more concise proofs using closely related concepts. The various proofs of sperners theorem provides a firm understanding of its connections with many other fundamental topics in finite combinatorial mathematics.Great book for those that have a good grasp on algebraic concepts.
Seevinev
This book provides excellent coverage of sperners theorem including multiple proofs ,like the original one by sperner and more concise proofs using closely related concepts. The various proofs of sperners theorem provides a firm understanding of its connections with many other fundamental topics in finite combinatorial mathematics.Great book for those that have a good grasp on algebraic concepts.