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I'm looking for a textbook recommendation for a first course in combinatorics that is purely focused on theoretical mathematics. Most of the books I've come across tend to have a significant emphasis on computer science or various applications, but I'm specifically interested in a text that delves into the foundational theory without any practical applications.

I familiar with Linear algebra, Real analysis, ODE, Calculus and Complex analysis. I also done many rigorous proofs so I am familiar with rigorous math books. Are there any prerequisites that I need?

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  • $\begingroup$ Whether this is appropriate for a "first course" depends on what you mean by that term, but Stanley's Enumerative Combinatorics is extremely comprehensive: math.mit.edu/~rstan/ec $\endgroup$
    – Qiaochu Yuan
    Commented Aug 11 at 17:57
  • $\begingroup$ What level are you looking for? What is the reader's mathematical sophistication? I liked Richard Stanley's "Enumerative Combinatorics," but it assumes some mathematical sophistication, up to and including some abstract algebra. $\endgroup$
    – Thomas Andrews
    Commented Aug 11 at 17:58
  • $\begingroup$ The other possibility is to look for older books - from the 1980s or earlier. Much less focused on applications, but maybe lacking in more modern approaches to things. $\endgroup$
    – Thomas Andrews
    Commented Aug 11 at 17:59
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    $\begingroup$ Put it in the question. Linear algebra is some use, but abstract algebra would really help for the Stanley book. But the real question is whether you are accustomed to "theorem-proof" type books. All of those topics you listed can be taught either more intuitively or more rigorously. It is really an unmeasurable question of what we sometimes call "mathematical sophistication." $\endgroup$
    – Thomas Andrews
    Commented Aug 11 at 19:48
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    $\begingroup$ Have you read the Wikipedia article on Combinatorics yet? $\endgroup$
    – Somos
    Commented Aug 13 at 19:17

3 Answers 3

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When I was in university, we used the textbook:

Mathematics of choice
subtitled How to count without counting

by Ivan Niven.

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Comtet, Advanced Combinatorics. https://books.google.com.au/books/about/Advanced_Combinatorics.html?id=C0HPgWhEssYC&redir_esc=y
Riordan, An Introduction to Combinatorial Analysis. https://press.princeton.edu/books/paperback/9780691615882/an-introduction-to-combinatorial-analysis?srsltid=AfmBOoqC_N99tx863V7DILYf5jLqm4G7pHCgrNNt5ErSWKMpQKKIrW_2
Herbert John Ryser, Combinatorial Mathematics. https://www.ams.org/books/car/014/

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Another selection that could be helpful:

Two more with special topics:

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    $\begingroup$ @Mathematicsenjoyer: Many thanks for granting the bounty. :-) $\endgroup$
    – Markus Scheuer
    Commented Aug 16 at 5:23

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