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.
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About the Author
Robin Wilson is an Emeritus Professor of Pure Mathematics at the Open University, Emeritus Professor of Geometry at Gresham College, London, and a former fellow of Keble College, Oxford University. He is currently a Visiting Professor at the London School of Economics. A former President of the British Society for the History of Mathematics, he has written and edited many books on the history of mathematics, including Lewis Carroll in Numberland, and also on graph theory, including Introduction to Graph Theory and Four Colours Suffice. Involved with the popularization of mathematics and its history, he has been awarded the Mathematical Association of America's Lester Ford award and P lya prize for his 'outstanding expository writing', and the Ralph Stanton Award for outreach activities in combinatorics. He has Erd s Number 1.
Table of Contents
1. What is combinatorics?
2. Four types of problem
3. Permutations and combinations
4. A combinatorial zoo
5. Tilings and polyhedra
7. Square arrays
8. Designs and geometry