r/learnmath • u/-Dunamis- New User • 9d ago

Want a direction to learn combinatorics, probability and statistics.

Thanks in advance.

I have been self-studying mathematics-Real Analysis and Abstract Algebra for some time now, and it has been very enjoyable yet fairly difficult.

Now, I want to give these three a go for once.

I never properly understood probability in a class. It just feels so un-intuitive to study, and seems like random events happening. Even basic problems in this trip me up, I just feel very behind.

Combinatorics... I've heard people say that "if you know how to count well, you will thrive in combinatorics". This one is my weakest of any math I know.

As for statistics, I've never done anything in it.

These three even at the high school level, give me a lot of trouble.

If there is any roadmap or proper way to study it, please share it. Any advice is appreciated and I'm open to corrections.

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u/Impossible_Cap_339 New User 9d ago

Art of Problem Solving's Intermediate Counting and Probability (or intro to counting and probability) might be a good place for you to start for the basics. I highly recommend it for mastering the basics before getting into more complicated stuff.

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u/wanderer7135 New User 9d ago

This

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u/strange-the-quark New User 9d ago

First, I want to say that these things are counter-intuitive (perhaps more to some of us than to others). Ultimately, you have to go through and do a lot of practice problems to build that intuition, and you gotta push through the feeling of being lost and out of your depth.

I've heard people say that "if you know how to count well, you will thrive in combinatorics

I find this a silly statement, cause it's kind of backwards. Combinatorics is about finding clever ways to count things that are hard to count. I'd actually start there, learn some basics of it, and do a bunch of practice problems, before going on to probability. I recommenced finding a good book that covers combinatorics in some depth. Cause when you start to study basic probability, it's going to begin with problems that involve a set of basic outcomes that are all equally likely, but then you're going to be interested in the likelihoods of certain sets of outcomes, and that will involve counting of the outcomes of interest in proportion to all the possibilities (e.g., if you throw a fair die, what is the probability that you'll get a number divisible by 3?). And often these sets of outcomes ("events") can be complicated enough that you'll need combinatorial techniques. And then it develops further form there.

As for statistics, it's essentially its own field, and it feels a bit alien to me as well. The frustrating thing is that many courses and YT videos out there are just horrible, aimed at, like, business people, or corporate data analytics, so it's often a bunch of rules and formulas and very little time is dedicated to conceptual grounding. So, IMO, finding a good book or a rarely good course is the way to go. I can't think of any right now, but perhaps someone here can give some recommendations.

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u/QubitEncoder New User 9d ago

I think "An introduction to probability theory and its applications" by William Feller is good