Good rigorous intro combinatorics textbook?

In summary, the conversation discusses self studying combinatorics during the summer and recommends Cameron's Combinatorics as a good resource for those with some familiarity with basic concepts in mathematics. It is noted that the book does not require many prerequisites but does require a general comfort with mathematics.
  • #1
dh363
33
0
Hey guys,
I'm thinking of self studying some math this summer, and combinatorics is one field I never really got into but want to learn a bit of. I rigorous proof experience from reading other books/taking rigorous classes, so I wanted to start off with something relatively rigorous.

Thanks
 
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  • #2
Cameron's Combinatorics is very good if you already have some familiarity with the basics (counting, recurrence relations, etc.) It doesn't really demand much in the way of prerequisites, but you do have to be comfortable with mathematics in general.
 
  • #3
Thanks! That's exactly what I was looking for. Something that assumed a level of mathematical maturity but not necessarily a lot of prerequisites within combinatorics.
 

1. What is combinatorics?

Combinatorics is a branch of mathematics that deals with the study of counting, arrangements, and combinations of objects. It is used in various fields such as computer science, statistics, and physics.

2. What makes a textbook a good introductory text for combinatorics?

A good introductory combinatorics textbook should have clear and concise explanations of concepts, plenty of examples and exercises for practice, and a logical progression of topics. It should also include real-world applications and connections to other areas of mathematics.

3. What level of mathematical background is required for an introductory combinatorics textbook?

An introductory combinatorics textbook typically assumes a solid foundation in algebra and basic concepts in set theory. Some knowledge of probability and discrete mathematics can also be helpful.

4. How can I determine if a combinatorics textbook is rigorous?

A rigorous combinatorics textbook will have a strong emphasis on mathematical proofs, with detailed explanations of the logic behind each step. It will also cover a wide range of topics and provide challenging exercises that require critical thinking and problem-solving skills.

5. Are there any recommended textbooks for learning combinatorics?

There are many excellent textbooks available for learning combinatorics, and the best one for you will depend on your background and learning style. Some popular choices include "A Walk Through Combinatorics" by Miklos Bona, "Combinatorics: Topics, Techniques, Algorithms" by Peter J. Cameron, and "Applied Combinatorics" by Alan Tucker.

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