What math should I learn?

by Metus1 min read2nd Feb 201213 comments

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I am studying physics and like math. I just finished courses in mathematical logic and probality theory and attended courses in calculus and linear algebra. I intend to learn theoretical informatics next semester. Any more suggestions for interesting mathematics? I started algebra this semester but dropped it because of my other commitments.

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What are your goals? What are your constraints? This is off-topic, but without those, we can't give much advice anyways.

EDIT: Here is some generic advice.

Buy a copy of the Princeton Companion to Mathematics. It will serve you well. In particular, it will give you a good global understanding of math and how topics inter-relate. If you don't know what you are interested in, this book is a good place to learn.

If you want a technical understanding, buy a couple Dover books on vital topics like algebra or analysis. Work through them a page or two at a time, checking you remember definitions and theorems after you read. Do the problems. Not every single one, but enough that the material is actually sinking in. Fraliegh's First course in abstract algebra happens to have exemplary exercises.

When taking classes, the professor matters more for how interesting it is than the subject. Unless you need that particular subject, find out who is engaging and motivates their material well.

Strongly agree that anyone who's seriously interested in mathematics should read the Princeton Companion. Until you do something like this, your impression of what parts of mathematics look cool and interesting is largely determined by what parts of mathematics you've heard about.

Hey, I asked the same question a while ago. The predominant answer was that the question was underspecified however you seem to have provided a bit more information.

http://lesswrong.com/lw/8js/what_mathematics_to_learn/

I just finished reading about game theory which I found interesting.

I liked combinatorics when I took it a few years back, but I don't know how useful it would be for you personally.

Sadly my university does not offer combinatorics. It does not seem to be as interesting as logic, at least if it is anything like the bit of combinatorics one learns with probability theory. Generally, the more fundamental or philosophically relevant a part of math is the more interesting it seems to me.

Sadly my university does not offer combinatorics.

If your university offering a topic as a course is a prerequisite for you, you might be able to narrow down LW's suggestions by listing which mathematical courses are open to you.

I agree with the combinatorics recommendation, you may find it listed as "Discrete Mathematics" as a computer science course. (There are other things besides combinatorics included in discrete math, but elementary combinatorics is the major part of the course.)

ADDED: You might consider reading about math some. The book, The Mathematical Experience, by Philip Davis and Reuben Hersh is a wide-ranging discussion of philosophy and applications of math. It is sort of like listening to a group of math majors with a couple of grad students sitting around talking about what they've found interesting.

Wait. You dropped algebra? Do you just not need educational instruction in mathematics? If you are self-taught and just looking for an interesting course, go meet the professor before you choose one. If they seem like a fun person, sign up for it. Otherwise, go retake algebra at your earliest convenience--unless you were just taking it again for fun...

I second badger's recommendation of the Princeton Companion. In fact, I expect that reading it might give you some ideas of your own as to what math to study.

You say below that you are interested in "fundamental" mathematics. Based purely on that, I would recommend abstract algebra, number theory, or some sort of course in proofs.

Also, this might seem obvious, but go talk to a math professor if at all possible. Much of the answer to this question depends on what the specific courses open to you are.

There is an ambiguity in your question. Do you want to learn mathematical techniques or do you wish to learn mathematics? If it is the former, Badger's comment has some good recommendations. If it is the latter, then you just need to examine the patterns that interest you. There is an unfortunate gap between courses in mathematical techniques and the process of mathematics.

While there are many ways of approaching mathematics. I am a big fan of asking "why" of every assumption. Why must the pattern be like this? What happens if it is NOT like this? This method is great practice for identifying conclusions.