What is the best intuitive combinatorics book for beginners?

[Heisenberg7]

Hello,

I'm looking for an intuitive combinatorics book. I would like to cover most of the important topics in a relatively short time, so that's mostly the reason why I'm looking for an intuitive book. I have no prior knowledge in combinatorics.

Thanks in advance

 

[Vanadium 50]

One develops intuition by working problems, not by finding the magic book.

 

[Heisenberg7]

One develops intuition by working problems, not by finding the magic book.

Well, obviously. But, I don't want a book that's going to hit me with tough mathematics immediately on the start. Right now, I'm doing number theory, algebra and geometry. I just need a friendly introduction to combinatorics, that's all. I don't have much time to dedicate to practice really, but I obviously will dedicate some.

 

[Vanadium 50]

But, I don't want a book that's going to hit me with tough mathematics immediately on the start.

And what is "tough?" For some people, it's multiplication. For others, its derivatives, and for others integrals. And so on.

You will get out of PF what you put into it. Yes, we might eventually guess what you are looking for, with enough back and forth. Or you could tell us.

Right now, I'm doing number theory, algebra and geometry. I just need a friendly introduction to combinatorics, that's all. I don't have much time to dedicate to practice reall

Then,
(A) You are looking for magic
(B) This is not a path to success - look at all the people who tried it, and how few (likely none) have succeeded
(C) The absolute last thing you should be doing is covering even more topics.

 

[Heisenberg7]

And what is "tough?" For some people, it's multiplication. For others, its derivatives, and for others integrals. And so on.

Anything that dives into deep roots of combinatorics immediately.

Then,
(A) You are looking for magic
(B) This is not a path to success - look at all the people who tried it, and how few (likely none) have succeeded
(C) The absolute last thing you should be doing is covering even more topics.

No, I'm certainly not looking for magic. In fact, I'm ready to put myself through the pain of studying something you've never touched. For (B), I guess, but I don't really care about that. For (C), I know, but that's what I have to do.

 

[Vanadium 50]

Anything that dives into deep roots of combinatorics immediately.

Then that's easy. There is no such book. The "deep roots" are addition and multiplication.

 

[Heisenberg7]

Then that's easy. There is no such book. The "deep roots" are addition and multiplication.

Then, I need an introductory combinatorics book (suggest a few).

 

[Vanadium 50]

Then, I need an introductory combinatorics book (suggest a few).

"Hop to it, Bud!" is not the best way to motivate others. Just sayin'.

 

[Baluncore]

Google: Introduction Combinatorics.

A Walk Through Combinatorics: An Introduction to Enumeration, Graph Theory, and Selected Other Topics.
Author(s): Miklos Bona
Publisher: World Scientific Publishing Company, Year: 2023
ISBN: 9811277842,9789811277849,9789811277856,9789811277863
Now in 5th edition.

 

[Frabjous]

"Hop to it, Bud!" is not the best way to motivate others. Just sayin'.

You need to chill.

 

[Heisenberg7]

"Hop to it, Bud!" is not the best way to motivate others. Just sayin'.

By saying "suggest a few", I wasn't giving you an order. I meant that, if you are going to suggest anything, then suggest a few books so that I can try out more and see which one suits me best.

 

[Heisenberg7]

Google: Introduction Combinatorics.

A Walk Through Combinatorics: An Introduction to Enumeration, Graph Theory, and Selected Other Topics.
Author(s): Miklos Bona
Publisher: World Scientific Publishing Company, Year: 2023
ISBN: 9811277842,9789811277849,9789811277856,9789811277863
Now in 5th edition.

Thank you very much.

 

[WWGD]

Drop by a technical library or college library and check out their Combinatorics section, see which one feels right to you.

 

[Heisenberg7]

Drop by a technical library or college library and check out their Combinatorics section, see which one feels right to you.

I come from a poor country, so sadly I have no access to those.

 

[WWGD]

I personally suggest you browse casually through topics and when you have enough knowledge, you buy the book. Otherwise if you want to go into a book directly, I liked Van Lint and Wilson's book.
Edit: You may get a " Combinatorics lite" book using a Discrete Math book.
Edit 2: Sorry, this book is way too expensive. It was around $25 when I bought it in the 00's. Will look up another one.

 

[Vanadium 50]

You need to chill.

Perhaps. On the other hand, a little "How to win friends and influence people" might ne more useful to the OP than a superficial understanding of combinatorics.

 

[Heisenberg7]

Perhaps. On the other hand, a little "How to win friends and influence people" might ne more useful to the OP than a superficial understanding of combinatorics.

Damn.

 

[Heisenberg7]

I personally suggest you browse casually through topics and when you have enough knowledge, you buy the book. Otherwise if you want to go into a book directly, I liked Van Lint and Wilson's book.
Edit: You may get a " Combinatorics lite" book using a Discrete Math book.

Alright, thank you!

 

[MidgetDwarf]

Depends on your mathematical level. Combinatorics is a very large field.

Do you want to learn graph theory? Probability Theory? Do you want to learn how to solve combinatorics problems using the tools of algebra? Etc.

For the very basics, one can read a discrete math book such as the one by Levin. I believe its titled Introduction to Discrete Mathematics. Its open source, so it is free.

If you want to learn graph theory,

Then the green dover book by Gary Chartrand and one other author, titled Introduction to Graph Theory.

What topics are you most interested in?

 

[Heisenberg7]

Depends on your mathematical level. Combinatorics is a very large field.

Do you want to learn graph theory? Probability Theory? Do you want to learn how to solve combinatorics problems using the tools of algebra? Etc.

For the very basics, one can read a discrete math book such as the one by Levin. I believe its titled Introduction to Discrete Mathematics. Its open source, so it is free.

If you want to learn graph theory,

Then the green dover book by Gary Chartrand and one other author, titled Introduction to Graph Theory.

What topics are you most interested in?

Here's a list:
-Permutations and Combinations
-The Pigeonhole Principle
-Generating Permutations and Combinations
-The Binomial Coefficients
-The Inclusion-Exclusion Principle and Applications
-Recurrence Relations and Generating Functions
-Special Counting Sequences
-Combinatorial Designs

 

[MidgetDwarf]

Again. What mathematical level?

Maybe we should add a new rule to these forumns. When requesting a book, please state a bit of background in terms of preparation and what level they are looking for.

 

[Muu9]

Here's a list:
-Permutations and Combinations
-The Pigeonhole Principle
-Generating Permutations and Combinations
-The Binomial Coefficients
-The Inclusion-Exclusion Principle and Applications
-Recurrence Relations and Generating Functions
-Special Counting Sequences
-Combinatorial Designs

Try intermediate counting and probability by David Patrick if you can pass this placement test: https://data.artofproblemsolving.com//products/diagnostics/intermediate-counting-pretest.pdf