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Books For Combinatorics

Well I am starting to crave for combinatorics.The proofs seem so elegant and meaningful.But I haven't gone through any book that deals with only combinatorics. I am not a complete beginner in combinatorics but still I'd like to have your views on the books you've read on combinatorics so that I can get one and start counting on it. :)

Note by Soham Chanda
4 years, 8 months ago

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I would strongly recommend Arthur Engel's Problem Solving Strategies, if you have not already read it. It presents several combinatorics techniques, which are well developed. It's chapters on algebra and number theory are good too. The focus of the book is to present different techniques, as opposed to giving a full coverage of all the different combinatorial ideas.

The Art and Craft of Problem Solving by Paul Zeitz does a good preliminary exposition on Combinatorics. It covers the basics like counting, bijections, PIE, recurrence, extremal principle, pigeonhole principle, invariants, and provides more advanced areas that you can explore after that.

The above are introductory texts. Since you are not a complete beginner, it would be useful if you state various topics that you are interested in (say Ramsey Theory, Hall Marriage Principle, Recurrance Relations, Generating Functions, Graph Theory, etc), so that we can recommend books that specialize in that area, as opposed to a broad discussion of Combinatorics. Calvin Lin Staff · 4 years, 8 months ago

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Just a few days ago, I ran across a link to a free online resource called Combinatorics Through Guided Discovery by Ken Bogart. You can find it here. I've only skimmed the first chapter, but the problem-based approach seems kindred in spirit to Brilliant. Perhaps you'll enjoy it. There are of course many other good combinatorics resources out there--AOPS is always a good place to look. I hope this thread produces some other good combinatorics resources. Good luck! Justin Lanier · 4 years, 8 months ago

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Well I'm not intermediate though. Actually I can solve the combinatorics problems when they are in words,those which i can visualize like real life situations.An example -"Calvin goes to amusement part,there are 10 rides..." or a problem like that...But whenever technical terms like those with sets etc etc I get TOTALLY confused.How to tackle this? Soham Chanda · 4 years, 8 months ago

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i m weak at solving problems of function ,number theory please suggest a good book which starts from fundamental to apex with alot of illustrative examples exercise Nishant Manish · 2 years, 11 months ago

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http://www.worldscientific.com/worldscibooks/10.1142/1781 Matthew Fan · 3 years, 9 months ago

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Maybe you could give an example or two of problems that you would like to be able to solve, but don't really know where to start or what tools to use. That might help others to give you helpful suggestions of how to go forward. Justin Lanier · 4 years, 7 months ago

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If basic terminology is tripping you up, I would encourage you to constantly review it and gain familiarity with these concepts. Just like how arithmetic word problems require you to translate the written statement into mathematical equations, think about how to translate combinatorics problems in words to their theoretical construct (and vice versa).

While being able to visualize a problem is extremely useful, note that this might not always be done. The most common problem that you'd see is trying to visualize 4 dimensions. This could potentially be done with the hypercube of tesseract, but they do not convey the actual meaning of 4-dimensions. Moreover, it gets extremely complicated when you look at \(n\) dimensions - pictures rarely help unless it's a 2-dimension cutout. Calvin Lin Staff · 4 years, 7 months ago

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