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Very Short Introductions #474
Combinatorics: A Very Short Introduction
How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal)
Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
176 pages, Paperback
First published January 1, 2016
39 people are currently reading
320 people want to read
About the author
Robin J. Wilson
51 books12 followersRobin James Wilson (born December 1943) is a professor in the Department of Mathematics at the Open University, a Stipendiary Lecturer at Pembroke College, Oxford[1] and, as of 2006, professor of geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he guest teaches at Colorado College.
From January 1999 to September 2003 Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[2]
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He has two daughters: Catherine and Jennifer.
From January 1999 to September 2003 Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[2]
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He has two daughters: Catherine and Jennifer.
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Displaying 1 - 12 of 12 reviews
April 11, 2020
A nice introduction to the branch of discrete mathematics concerned with counting and enumerating various mathematical objects. However, the book is not completely self-contained, as it introduces some topics and terms that demand additional reading and problem-working. Fortunately, Wikipedia has articles for virtually everything in the book that I tried to look up, but some of those articles are even more technical and involved.
The book has a further reading section, which seems almost obligatory for anyone new to the topic who wants to learn much of it. One of the textbooks cited is How to Count: An Introduction to Combinatorics, and it says in its opening pages:
"A mathematics book cannot be read like a novel, sitting in a comfortable chair, with a glass at your side. Reading mathematics requires you to be active. You need to be sitting at a table or a desk, with pencil and paper, both to work through the theory and to tackle the problems. A good guide is the amount of time it takes you to read the book. A novel can be read at a rate of about 60 pages an hour, whereas with most mathematics books you are doing well if you can read 5 pages an hour."
To really do justice to a subject like combinatorics probably requires a lot of scribbling in addition to just reading. (It would be nice if by the year 2020 as I write this, someone had come up with a way to actually do mathematics on a computer as one can with pencil and paper or a chalkboard; but alas, I know of no such substitute. So we can read our math ebooks on a computer but we still seem to need the centuries-old methods to actually do math.) As this Very Short Introduction includes no practice problems, one would have to make do by redrawing many of the figures and re-deriving the equation derivations from the book. Or just get some of the textbooks the book cites and have a go at them.
The book has a further reading section, which seems almost obligatory for anyone new to the topic who wants to learn much of it. One of the textbooks cited is How to Count: An Introduction to Combinatorics, and it says in its opening pages:
"A mathematics book cannot be read like a novel, sitting in a comfortable chair, with a glass at your side. Reading mathematics requires you to be active. You need to be sitting at a table or a desk, with pencil and paper, both to work through the theory and to tackle the problems. A good guide is the amount of time it takes you to read the book. A novel can be read at a rate of about 60 pages an hour, whereas with most mathematics books you are doing well if you can read 5 pages an hour."
To really do justice to a subject like combinatorics probably requires a lot of scribbling in addition to just reading. (It would be nice if by the year 2020 as I write this, someone had come up with a way to actually do mathematics on a computer as one can with pencil and paper or a chalkboard; but alas, I know of no such substitute. So we can read our math ebooks on a computer but we still seem to need the centuries-old methods to actually do math.) As this Very Short Introduction includes no practice problems, one would have to make do by redrawing many of the figures and re-deriving the equation derivations from the book. Or just get some of the textbooks the book cites and have a go at them.
February 17, 2020
A stunningly average introduction to combinatorics. This book was really mixed for me. It did give a wonderful overview of all the different branches of combinatorics that are out there. But it hardly seemed like an introduction. Many parts were beyond following, and I'm not even someone who zones out at the sight of equations - I like math. But Wilson seemed to use numbers as sentences, and (in the interest of space?) squeezed the process of working out equations onto single lines so it was very difficult to see what was happening. This would be fine for the working professional, but not, of course, someone who needs a very short introduction.
I do feel smarter and like I understand the subject better but the book itself had highs and plenty of lows.
I do feel smarter and like I understand the subject better but the book itself had highs and plenty of lows.
October 5, 2016
Even though, this is a small introduction book –– I still did not completely understand everything. It seems that some of the concepts need deeper thinking, and reflecting on ideas. If you are into combinatorics, this is a small start. It relates to a lot of Computer science.
--Deus Vult
Gottfried
--Deus Vult
Gottfried
May 4, 2021
I need to revisit this book later this year. The latter half went way over my head.
Whatever I did understand, however, was FASCINATING.
Whatever I did understand, however, was FASCINATING.
March 14, 2020
A very short introduction series are an amazing set of books that brief you on any new topic that you are interested in. This book on combinatorics helped me understand the logic behind famous mathematical puzzles. A light and enjoyable read.
July 7, 2017
Partitions, got to do partitions!
November 18, 2024
This wonderful short introductory book on combinatorics sets out to do what it achieves in terms of giving a brief tour of the most famed subjects within combinatorics along with some of the most beloved results. Some these highlights include topics along the lines of enumeration problems, sequences (where the obligatory Fibonacci sequence pops in), binomial coefficients, multinomials, graph theory, magic squares and in the end we finally reach integer partitions for a terse discussion.
Surprisingly I assume for some, I am glad that it challenges the reader (who may either be familiar or not with mathematics) with a fair number of proofs as well as setting forth a writing style which leans heavily (although not pedantically) on mathematical notation. I understand that for some who don't carry an interest in mathematics that it may be at times hard to follow, but in my opinion it is worth the struggle as it will both give you a glimpse into the writing style of ordinary mathematical textbooks as well as give you a stronger mathematical exposure which should be very helpful to transfer to other popular math books that are not meant as university text books.
I should mention here that I used the same authors textbook on graph theory in university for a course on the subject which turns out to be also highly readable and in commonality with this book covers a lot of territory in few pages. My only complaint with this book is that it ends rather abruptly not fully having explained why it is that integer partitions are the highlight of the book except for mentioning that they do not behave in in a predictable manner. One would have done well to expand upon the concept of a generating function here and to observe the usefulness of partitions in this setting or to mention their applicability in computer science in relation to algorithms for example.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
Surprisingly I assume for some, I am glad that it challenges the reader (who may either be familiar or not with mathematics) with a fair number of proofs as well as setting forth a writing style which leans heavily (although not pedantically) on mathematical notation. I understand that for some who don't carry an interest in mathematics that it may be at times hard to follow, but in my opinion it is worth the struggle as it will both give you a glimpse into the writing style of ordinary mathematical textbooks as well as give you a stronger mathematical exposure which should be very helpful to transfer to other popular math books that are not meant as university text books.
I should mention here that I used the same authors textbook on graph theory in university for a course on the subject which turns out to be also highly readable and in commonality with this book covers a lot of territory in few pages. My only complaint with this book is that it ends rather abruptly not fully having explained why it is that integer partitions are the highlight of the book except for mentioning that they do not behave in in a predictable manner. One would have done well to expand upon the concept of a generating function here and to observe the usefulness of partitions in this setting or to mention their applicability in computer science in relation to algorithms for example.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
April 16, 2022
I didn't know this collection (A very short introduction) and I quite liked this book, because it lives to its promise.
This book is a very short introduction (150pages) on combinatorics. As such it explain concepts as permutations and combinations and the like, but also things like the 4 colour maps, NP problems and the salesman problem.
The book is more like a teaser, increasing the interest to study, but it lacks a formal explanation for many of the topics, nor an overarching theory.
In any case, well worth your time.
This book is a very short introduction (150pages) on combinatorics. As such it explain concepts as permutations and combinations and the like, but also things like the 4 colour maps, NP problems and the salesman problem.
The book is more like a teaser, increasing the interest to study, but it lacks a formal explanation for many of the topics, nor an overarching theory.
In any case, well worth your time.
September 6, 2020
What a treat! This short book manages to introduce graph theory, projectile planes, and partitions (and many other related stuff) by building upon simple concepts. It starts very gently but as it progresses one may need to spend time to fully appreciate the logic involved. I suspect the book has been edited such that later chapters seem to have been truncated and need more effort to follow. It is surely one of best mathematics books I have encountered. Five stars.
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July 13, 2022Definitely helped solidify the basic combinatorial formulas, but everything past the first two chapters was way over my head. Nice to get a vague appreciation of graph and partition theory. All seems a bit like insider baseball though, doesntit?
January 7, 2019
combination of various things,example
September 30, 2016
Excellent little book; not just talking about combinatorics but actually doing it. Also provides some feel for its historic development and its application in practice. Good diversity of topics. Richly illustrated.
Displaying 1 - 12 of 12 reviews