Please Help: The Road To Mathematics

[incomplete]

IN SUMMARY

How do I best go about becoming an amateur mathematician?

 

MORE SPECIFICALLY

I've been a computer consultant for a decade now. Math has always intrigued me. My knowledge and understanding is pretty good up through integral calculus. I'm new to differential equations. I'd like very much to become a mathematician. It won't be a career, but I look forward to it becoming one heck of a hobby.

 

My question is: How do I best go about becoming an amateur mathematician? For example, I have studied courses and text in pretty much the following order:

 

- Arithemtic

- Algebra

- Geometry

- Trigonometry

- Differential Calculus

- Integral Calculus

- Differential Equations

 

It may be a good start, but its far from where I need to be. Where do I go from here? What about vector and linear algebras, multi-variable calculus, non-euclidean geometry, number theory, and others? I'm unsure of what path to take, that is, which particular field leads to the next one(s). What habits should I develop to increase my results and success? Are there software programs I should use? And finally, how do I go about doing research?

 

This is a very broad inquiry and may be difficult to answer completely, but any advice or guidance you may have would be most appreciated.

 

Thanks in advance.

[ydoaPs]

IN SUMMARY

How do I best go about becoming an amateur mathematician?

learn math

[Mot]

I don’t have my math texts with me or I could give you a better answer, but here are my thoughts off the top of my head.

 

I will assume your understanding of the courses you listed is passable. If you want to learn more basic math try “What is Mathematics”. It is an old book, but it is still in print and will get you into some discrete math. You may want to consider looking into real analysis. As I have always said, all you need are the three R’s. Rudin, Royden and ‘rythmatic. Baby Rudin is tough but can be gotten through without a mentor and big Rudin and Royden will get you past what most people ever see in math except for Phds. I would advise you to find a mentor if possible. It doesn’t have to be someone who knows the math you wish to look at, but it should be someone who has a willingness to explore ideas and can handle subtle reasoning. You might be able to find a math club in your area by looking at ads, schools and internet. Be prepared to spend 2 months on background before you can get through one chapter of some of these books.

 

One other book that I love is “Introductory Functional Analysis With Applications” by Erwin Kreyszig.

 

All this should keep you busy for a few years or longer.

 

If you breeze through these, there is a whole bunch more. Game theory, combinatorics, tensors, etc...

 

My best advice is for you to follow your interests. If you are working out one proof and discover Bezel functions and they sound interesting, then go explore them. Have fun whatever you do.

 

Cheers,

Mot

 

PS Keep a good calculus book and a good ODE/PDE book around because sometimes you have to review basic concepts to understand what is in the harder books. Maybe E.T. Bell for some interesting not always true math history.

[Mot]

PPS Get a membership in the AMA (american mathematical association) or at least the magazines. You may be able to find them at the library. The essays and proofs will tend to be in the weeds for a laymen, but they may give you some ideas of what is on the cutting edge.

[cosine]

Not to contradict Mot, but I would like to suggest that you think about exploring some non-analysis math too. This isn't the order that I've fallen in love with math, but since you're already fairly deep into it, I would suggest you check out some things like elementary number theory, or combinatorics. There are many things in these topics you can teach yourself. Also, it may sounds like a dry suggestion, it gets fun to sort of read your way through Euclid's Elements. Its especially fun if you're reading one with a good commentary, like Sir Thomas Heath's translation. There are also translations on the interenet, with commentary. I suggest you search for "Euclid's Elements" and I'm sure you'll find something. Otherwise I would also suggest Arther T. Benjamin's "Proofs That Really Count." I saw him talk this summer at Math Fest, it was amazing. I would also suggest any of William Dunham's books. This should provide you with many things that you will definitely find interesting, as well as leading you to new topics. Good luck, and remember, have fun!

[Dave0x01]

IN SUMMARY

How do I best go about becoming an amateur mathematician?

 

MORE SPECIFICALLY

I've been a computer consultant for a decade now.

[snip]

 

I can't answer your question' date=' but what sort of math do you use in your profession (as [i']computer consultant[/i] could encompass a wide range of activites)?

 

sci.math is another place you might ask your question.