Reddit mentions of Combinatorics: Topics, Techniques, Algorithms

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-Solving

• The Art of Problem Solving - Lehoczky/Ruczyk - in two volumes, both have full solutions available separately
  
  Calculus
  
  
• Calculus - Stewart - ignore the bad reviews, it's very clear and covers all of basic calculus well - it's just the book that most intro students use and as a consequence gets a bad rap
  
  
• Calculus - Spivak - this will take your understanding of calculus to the next level
  
  
• Calculus - Apostol - there are two volumes and they are very comprehensive, albeit difficult
  
  Linear Algebra
  
  
• Linear Algebra - Lay
  
  
• Linear Algebra Done Right - Axler
  
  Differential Equations
  
  
• Elementary Differential Equations - Boyce/DePrima
  
  
• Ordinary Differential Equations - Tenenbaum
  
  Number Theory
  
  
• Number Theory - Pommersheim for a change of pace and proof skills
  
  Proof-Writing
  
  
• Transition to Higher Mathematics - Dumas/McCarthy - helps to bridge the gap between "lower" and higher math
  
  Analysis
  
  
• The Way of Analysis - Strichartz
  
• Principles of Mathematical Analysis - Rudin
  
• Real and Complex Analysis - Rudin
  
  Complex Analysis
  
  
• Complex Analysis - Ahlfors
  
  Functional Analysis
  
  
• Functional Analysis - Rudin
  
  
• Introductory Functional Analysis with Applications - Kreyszig
  
  Partial Differential Equations
  
  
• Partial Differential Equations for Scientists and Engineers - Farlow
  
  Higher-dimensional Calculus and Differential Geometry
  
  
• Calculus on Manifolds - Spivak - for a modern take on multivariable calculus
  
  
• Differential Geometry - Kreyszig
  
  Abstract Algebra
  
  
• A First Course in Abstract Algebra - Fraleigh
  
• Abtract Algebra - Dummit and Foote
  
  Geometry
  
  
• The Elements - Euclid - for culture and for understanding where math has come from, plus it's still an awesome book after all these years; don't need to go through all of it
  
• Euclidean and Non-Euclidean Geometries - Greenberg
  
  Topology
  
  
• Introduction to Topology - Mendelson
  
  
• Topology - Munkres
  
  Set Theory and Logic
  
  
• Introduction to Set Theory - Hrbacek/Jech
  
  
• Elements of Set Theory - Enderton
  
  
• Mathematical Logic - Kleene
  
  
• Set Theory and the Continuum Hypothesis - Cohen
  
  Combinatorics / Discrete Math
  
  
• Combinatorics - Cameron
  
  
• Concrete Math - Graham/Knuth/Patashnik
  
  
• Discrete Math - Biggs
  
  Graph Theory
  
  
• A First Course in Graph Theory - Chartrand/Zhang
  
  P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
  

http://www-math.mit.edu/~rstan/ec/
I'll give you a brief about the book: It's really dense and probably will take you a while to get through just a couple of pages, however, the book introduces a lot of interesting and difficult concepts that you'd definitely see if you pursue the field.

https://math.dartmouth.edu/news-resources/electronic/kpbogart/ComboNoteswHints11-06-04.pdf
Is a Free book available online and is for a real beginner, basically, if you have little to no mathematical background. I will however say something, in Chapter 6, when he talks about group theory, he doesn't really explain it at all (at that point, it would be wise to branch into some good pure math text on group and ring theory).

https://www.amazon.ca/Combinatorics-Techniques-Algorithms-Peter-Cameron/dp/0521457610
This is a fantastic book when it comes to self studying, afaik, the first 12 chapters are a good base for combinatorics and counting in general.

https://www.amazon.ca/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025
I've heard fantastic reviews about the book and how the topics relate to Math 2 3/4 9. Although I've never actually used the book myself, from the Table of Contents, it appears like it's a basic introduction to counting (a lot lighter than the other books).

Regarding whether or not you can find them online, you certainly can for all of them, the question is whether legally or not. These are all fairly famous books and you shouldn't have trouble getting any one of them. I'm certain you can study Combinatorics without statistics (at least, at a basic level), however, I'm not sure if you can study it without at least a little probability knowledge. I'd recommend going through at least the first couple of chapters of Feller's introduction to Probability Theory and it's Applications. He writes really well and it's fun to read his books.

When I took 322 with Jing, we mostly used Peter and Gary's course notes, with some content from Cameron's Combinatorics. In many ways, I found 322 to be much different from 222; 222 focuses a lot on counting, generating functions, pigeonhole, etc. while 322 focused a lot more on proving the existence of and enumerating different combinatorial objects.

Here's an open source book on the topic. And also a more computationally focused texted as well.

I've also heard good things about [this one](Combinatorics: Topics, Techniques, Algorithms https://www.amazon.com/dp/0521457610/ref=cm_sw_r_cp_api_iCKzxbCVJHRQ4), [this one ](Combinatorics: A Guided Tour (MAA Textbooks) https://www.amazon.com/dp/0883857626/ref=cm_sw_r_cp_api_ZCKzxb7XY8RJS), and [this one](A Walk through Combinatorics: An Introduction to Enumeration and Graph Theory (Third Edition) https://www.amazon.com/dp/9814460001/ref=cm_sw_r_cp_api_pDKzxbR3CYQGF)

I always liked C. L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, 1968. It's old but i think still one of the best introductions on that subject.

Peter J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994 is imho also decent. More information on the book is available here.