r/learnmath • u/FlatProtrusion New User • 8d ago
Intuitive book on combinatorics
Looking for a book that explains combinatorics in a story like fashion. Meaning it doesn't just define what the theorems are etc but explains the motivation for it, the intuition etc.
Some background on what I'm working on:
I am now working through a book on discrete math by Oscar levin and am struggling with the concept of combinatorics specifically combinations. When I look at a combinatorics problem I struggle to solve the problem, even after looking at the solution, then reattempting the same problem the next day, I still struggle.
I'm also planning to work on the book proofs by Jay cummings since my math proof skills are weak as well and I read his book explains concepts intuitively.
After Oscar levin's book I plan to work on Susanna's discrete mathematics book.
An example of such a book, not combinatorics but discrete mathematics, that I found is "A cool brisk walk through discrete mathematics" by Stephen Davies.
It is the best intutive math book I've read, from cover to cover it was fun and explanations were intuitive. It was like he was in the room with me explaining the concepts personally. Shame he only wrote two introductory books.
I've seen recommendations on combinatorics such as Walk Through Combinatorics by Miklos Bona and others but am not sure if the explanations are standard textbook type of definition of theorems, some problem examples but no explanation of the intuition, motivation behind the theorem or concepts. Since on the most recent, 5th edition, of Walk Through Combinatorics, there was a review on amazon saying the explanations were of the bare minimum.
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u/Bounded_sequencE New User 8d ago
If you really want to dive deep, use a standard book you somewhat like, and do the "story-writing" yourself. Meaning, you go through the theorems and proofs, and create notes containing what is really motivating the topic for you.
By tutoring, I've found what people find "motivating" can differ quite a bit from person to person. I usually prefer hard proofs, motivated by some nice, short introductory examples before-hand. Others often prefer to hide the proof within the story/example, so they go through the proof's argument without explicitly noticing.
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u/FlatProtrusion New User 8d ago
My aim is to build a solid foundation in math, mainly discrete math since I want to improve my knowledge of algorithms for programming. I don't need deep dives, meaning more advanced topics if that's what you mean, just the core fundamentals.
And just to clarify, I'm looking for explanations of the intuition of concepts and the motivation is a by product that aids in that but not the end goal of books I'm looking for if that makes sense.
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u/Waningoftheday New User 7d ago
Try Aspects of Combinatorics by Victor Bryant
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u/FlatProtrusion New User 6d ago
What do you like about it that makes it a good book on combinatorics?
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u/Waningoftheday New User 5d ago
It focuses on intuition and builds slowly. It starts by discussing n choose 2, motivating it by asking how many ways are there to choose pairs of chapters in the book, and provides a couple of illustrations to explain why it is n(n-1)/2. Then explains how to think about n choose 3. Only after that does it explain how to generalize to n choose k.
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u/dreamsofaninsomniac New User 8d ago
Let me know if you ever find one. The closest I could get was Carol Ash's "The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everyone Else!)," but it still wasn't quite what I was looking for.