Studying Pure Math in LA - Where to Start?

[Bamboo_banga]

So I'm 29, and thinking of going back to school to study pure math. With the hopes of being a professor.
I know Terrence Tao works at UCLA, so he's an allstar of number theory. But that's also making UCLA super competitive in that field. Of course I'll still apply. And Caltech too.
But where are some other good places in the LA area I can go?

I have my undergrad in engineering and my masters in IT. I would probably need to enter an masters in math program first, then head to PhD after that. I still need to *brush* up on a lot of my old calc...
Thanks

 

[qspeechc]

Are you saying you think you will go straight into masters? Do you already have an honours degree in maths? And by calc you mean real analysis? Perhaps you need to enter as an undergrad.

 

[Bamboo_banga]

Are you saying you think you will go straight into masters? Do you already have an honours degree in maths? And by calc you mean real analysis? Perhaps you need to enter as an undergrad.

I have my undergrad in Electrical engineering. So I taken plenty of calc, but that was 8 years ago! I also have a master's in IT. I want my PhD in pure math, but I think I'd have to enter a master's program first. That's just what I thought...

 

[Vanadium 50]

I'm afraid a BSEE really doesn't cover the typical undergraduate curriculum of a math major going on to graduate school. Particularly if you are interested in pure math. I don't want to dissuade you from your goals, but I do want to make sure you understand realistically what you need to do to catch up.

 

[Bamboo_banga]

I'm afraid a BSEE really doesn't cover the typical undergraduate curriculum of a math major going on to graduate school. Particularly if you are interested in pure math. I don't want to dissuade you from your goals, but I do want to make sure you understand realistically what you need to do to catch up.

I much prefer the honesty, thank you. So I'd need to learn BA in math material? Are there any good online programs/courses good for that?

 

[Moonbear]

I'm afraid a BSEE really doesn't cover the typical undergraduate curriculum of a math major going on to graduate school. Particularly if you are interested in pure math. I don't want to dissuade you from your goals, but I do want to make sure you understand realistically what you need to do to catch up.

But isn't that usually to go straight into a Ph.D. program? I don't know how math departments work, so maybe they're different than other programs. Usually a master's is a good stepping stone for someone who has their B.A. or B.S., but needs some more coursework and a bit of research experience to be properly prepared to enter a Ph.D. program. Yes, it would be a steep learning curve for someone from a different background, but that's the point, to get that advanced education so you're ready by the time you start a Ph.D.

 

[Vanadium 50]

Moonbear, I agree - my point is that there is going to have to be some additional work before the OP is even ready for MS-level work. Just as an example, an undergraduate class in abstract algebra is something most BSEE's don't have, but every graduating math BS will have had.

 

[Howers]

I much prefer the honesty, thank you. So I'd need to learn BA in math material? Are there any good online programs/courses good for that?

You should jump right into junior year studies.

Here is what I recommend:

Linear Algebra: Book by Insel & Friedberg (Linear Algebra)

Real Analysis: Books by Rudin (Principles of Math Anal.) or Pugh (Real Analysis). If you are unaccumstomed to proofs get Spivak Calculus and the answer book. Velleman's How to Prove it will also get you used to rigorous math.

Complex Analysis: Get Ahlorfs (Complex Analysis)

Topology by Munkres

Abstract Algebra by Dummit & Foote (only get through Part 1 of the book)

I don't know how much PDE you know, Strauss is at a good level. Some differential geometry would also be useful. Going through these books and a good amount of exercises should take about 2-3 years depending on how much time you have. This will make you ready to study math in grad school.

Math is not something one can easily play "catch up" with. And it requires strong fundamentals in upper courses. And I hate to say it, but at your age, becoming a professor is not a likely thing.

 

[JasonJo]

You should jump right into junior year studies.

Here is what I recommend:

Linear Algebra: Book by Insel & Friedberg (Linear Algebra)

Real Analysis: Books by Rudin (Principles of Math Anal.) or Pugh (Real Analysis). If you are unaccumstomed to proofs get Spivak Calculus and the answer book. Velleman's How to Prove it will also get you used to rigorous math.

Complex Analysis: Get Ahlorfs (Complex Analysis)

Topology by Munkres

Abstract Algebra by Dummit & Foote (only get through Part 1 of the book)

I don't know how much PDE you know, Strauss is at a good level. Some differential geometry would also be useful. Going through these books and a good amount of exercises should take about 2-3 years depending on how much time you have. This will make you ready to study math in grad school.

This is ideal. I don't see any of the schools Bamboo mentioning accepting him without this kind of background. UCLA is a great math program, they probably WILL NOT accept someone who just took a calculus sequence. They want to see all of the classes that Howers mentioned.

Also keep in mind UCLA, Caltech have numerous applicants that have taken GRAD courses in all those subjects.

I would like to reiterate what Howers and V50 said: get a more thorough understanding of mathematics. Calculus isn't going to cut it.

You might be able to jump into some school's masters program/take a mixture of undergrad and masters classes. It is definitely possible. I am not trying to poo poo your goal of being a math phd. It is absolutely possible.

BUT, for your own good, you must at least learn abstract algebra, linear algebra, real analysis, complex analysis, topology, and ideally some differential geometry and PDE's.

Math PhD admissions are super competitive, it's probably with physics, the most competitive graduate field to enter. So it's better you be prepared and then get into a PhD program than try to get in without any prep.

 

[mathwonk]

in linear algebra, insel and friedberg is indeed a thorough and well written book, but if you want a shorter one, try my notes for math 4050 on my web page. assuming you know how to do gaussian reduction on a matrix, they cover as much or more than friedberg and insel in about 300 fewer pages. or use them as a guide to what is explained more fully in friedberg and insel.

 

[Vid]

You could probably get into the masters program for a much smaller school than UCLA (maybe UCSB or UC Davis, I don't know much about Cali schools but those both have good programs.) Your first year will probably be just undergrad classes, but you don't need to take anything but math classes so you should be able to catch up. A year of undergrad analysis and algebra plus whatever other electives sound good (maybe topology or advanced LA or anything that interests you really) will pretty much catch you up. A class on PDE's probably won't be too helpful. I don't really know what goes on in an EE curriculum, but I'm sure you learned to solve a bunch of PDEs. Undergrad PDE classes are usually about methods of solution with not too much theory. However, a PDE class at the level of Fritz John will definitely be required for anything in applied math, but that will most likely come from a graduate course. You probably won't have much funding during a masters and definitely not during your first year when your playing catch up so that's another thing to think about.

 

[thewhills]

If he is well read in Computer Science, I don't think a Math degree would be a problem.
Plenty of people go to Math from CompSci and Math to CompSci.

 

[Howers]

I don't know, the computer scientists in some of my analysis courses seemed pretty hung up on math. They were logically trained, that's for sure, but math scared them to the point of considering dropping. Maybe they were just more open about it? I certainly agreed with a lot of what they said. But I'm a lousy mathematician (actually more of a physicist who thinks he's a mathematician) so go figure