strangequark humbly asks for your advice before he leaves

So I just finished high school and im going to college next semester. I want to have a math and philosophy double major. I like number theory, complex analysis, epistemology, and philosophy of religion the most. I have had no philosophy college courses. The math college courses that I have taken are: Calculus 1,2,3, and a proving course (sometimes called "set theory and logic"). What should my track be like?

 

What fun math should I do over the summer? I have been interested in Godel numbering for a long time, but I might take the lame option and just get a head start on linear algebra which will be my first course in the fall. 

Any advice is much appreciated!

Well hun what you said means nothing to me but I would say that to get a head start on linear algebra would be a good idea then you will sail through it when the time comes :)

Good luck sweetheart x

I would recommend taking the time off and enjoying yourself before starting college.  Plenty of time to work hard at school once there. But if you want to get a head start, something like differential equations would be a good one to get started on early.  Linear algebra is super easy, so no real need to get a head start on it.

I wish I could take more than one math course my first semester, but a lot of schools have their freshmen's time taken up with their cores, most of which I don't care about. I like diffiq. I'd probably be taking it the second semester of my first year.

I would look at prime numbers and encryption as fun over the summer, but I'm not sure how much there is exactly to know/learn about encryption.  Since the middle ground between math and philosophy is number theory, in my eyes, you could try to learn as much about it before next year.

Learn an instrument.  It will give you a whole new perspective on math and number theory.  I'd go for the piano, but, of course, I'm particular to it.  Start with Bach's stuff, and work your way through each period (Mozart - Classic, Beethoven, Chopin - Romantic, etc.).  Music is truly math with sound (of course, computers are just math with electronics and logic gates).

I guess these are more mundane applications of math, but music sure sounds good, and computers are real helpful, with darn near anything.  After all, what good is math unless we can apply it to something?

Of course, most of my ideas are just undirected thinking, so don't give them too much heed.  Perhaps, just sitting by the pool (or lake, or beach) and working on your tan would be a good way to spend the summer (with a little volleybal thrown in).  I agree with s7silver; life's too short.  Before you know it, you'll be as buzy as you wanna' be, and you will find life flying by at an enormous rate of speed.

Well, enough rambling.  Enjoy you summer vacation, and make sure to get some really good fireworks for the 4th.  They're good for studying the effects of gravity on hypothetical telemetry paths.

This is all very good advice. I have wanted to be a cryptanalyst for a while, and I was able to read a whole course book about cryptography over last summer. I unfortunately was turned off of the piano years ago due to the amount of practice I had to do. Later, I adopted the mentality that "everyone I know likes to play on the piano, and most things that are commonly liked are silly pursuits, so playing on the piano is a silly pursuit." incidentally I know a number theorist who employs this same philosophy about watching star wars (that is, he has never seen it and people told him he should, therefore he won't ever watch star wars). But I'll definitely try a computer science aspect in college, as it would probably be useful for my intended job.

Right now I fear I will have to retake math courses because the math profs. appear to be uncomfortable starting me on these classes. Which would be somewhat understandable if not for the fact that I got good college grades for all of these courses. But for example I might have to retake Calculus 3. First and foremost, that would be absolutely humiliating. Secondly, I would be bored. Thirdly, it would be a waste of my time and leave me two courses behind what I should have been taking. I will even have to take a calculus 2 final to give them a sense of placement. But I took Calculus 2 a while ago and I'm afraid I might make silly mistakes on a subject that I already know I have mastered. :(

Not quite sure I got the idea you were much older, strangequark. Maybe the breadth of your knowledge.

Anyhow, my thoughts, a little of:

• Topology
• Graph theory
• Category theory, if it clicks with you
• Whatever appeals to you

Thanks very much for your suggestions, Elroch.

The good news is that i get to skip calc 1,2,3, and the proof course that i took. I've never heard of category theory, sounds like something I should look up.

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That's not very good logic . First, not everybody likes to play on the piano. Most people don't, though it may be true that most of the people YOU know do like to play on the piano. The problem is that if you restrict yourself to the subset of people that you know (which is a tiny and extremely unrepresentative subset), you'll get nonsensical results. For example, if you go through the math major and go to grad school in math, then most of the people you know will love math (and probably music too, btw), which would make math a silly pursuit according to that logic.

Anyway, I agree with the people who say that you should relax and enjoy your time before the business of school begins, but you might also really enjoy some stimulating study and reading occasionally as well if it's fun. If it seems interesting, I would suggest a book like Spivak's Calculus, which will give you a deeper understanding of what you learned about Calculus so far, and more importantly, introduces you to the rigor of real mathematics that you'll need in your math courses at the college level, and gives you lots more practice in proofs (you can't have too much). It's also beautifully written and a real pleasure to read, so you won't find yourself slogging through something that's no fun during your last summer vacation before college.

If category theory seems interesting, this book is a good, gentle introduction.

I believe you should go on linear algebra. Although it might be easy, it is a field with overwhelming applications in more advanced fields (such as graph theory), and as such should be learned thoroughly.

I should know, because I wasn't serious enough and neglected my linear algebra studies (it was too boring!!!), and now I'm paying the price for it, having to study it all over again.

Elaboration on the applications of linear algebra: One of the more popular fields in research these days is the connection between the geometrical attributes of a graph and the algebric attributes of matrices that represent them.

Pardon my lame English, for I am no native speaker.