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March 24th, 2015, 01:54 PM   #1
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Advice on renewing my math education

I am a 35 year old with an undergrad and masters in an engineering discipline. I have always been fascinated with math since I was a kid but I never really pursued it. I wanted to renew my math education as I am at a point in my life where I can learn for enjoyment. The problem is that I don't know where to start. I have studied applied math but I am interested in pure math. I was thinking of buying a book on set theory, numbers and functions and real analysis. I was wondering if I could be given some advice on this matter. Are these the right topics to build a foundation? I would be very thankful if someone can advise me. Thanks.

Last edited by skipjack; March 24th, 2015 at 05:03 PM.
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March 24th, 2015, 05:14 PM   #2
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Of the pure mathematics you must have done at school, how much do you remember, and of what you can remember, which parts were most interesting and enjoyable?
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March 24th, 2015, 10:41 PM   #3
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I enjoyed permutations and combinations, complex numbers and sets. Also, engineering involved a lot of probability hence various distributions, so through this I enjoyed functions. also, I took a career in partial differential equations which I really liked. Since all this was 15-20 years ago, I cannot say I remember a lot. However, I am reasonably confident of my aptitude and the time I can devote to these topics. I appreciate you taking the time to reply.
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March 25th, 2015, 09:28 AM   #4
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Most pure mathematics topics get difficult quite rapidly one you get past the introductory stuff, but try number theory or group theory just to find out how you get on.
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March 25th, 2015, 09:32 AM   #5
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Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Linear algebra (matrix algebra, not the high-school stuff!) would be a nice subject to learn, as it doesn't really have any prerequisites and is fun and useful. Since you say you liked PDEs you might consider a refresher course on differential equations and then a more advanced course depending on how things go.

Personally I enjoy number theory and related topics, but tastes may vary on this point.
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March 25th, 2015, 01:01 PM   #6
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Thanks. I have a few ideas know. Here are a steps I am planning to take. I found this book on How to Think about analysis by Alcock, which sets out certain guidelines. Also, saw a book on intro to pure math, which seems to offer a little bit various topics. I also thought that for getting some fundamentals straight, I should look at functions, so found a book called numbers and functions by RP Burn. From there if I am still feeling passionate, I will start to learn about number theory/linear algebra/complex analysis (complex numbers always fascinated me and we used them in engineering). I understand this is a vastly ambitious task, but I am going to give it a shot. I would like to know if someone thinks I am delusional!
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March 25th, 2015, 03:22 PM   #7
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Quote:
Originally Posted by prakashmscf View Post
I understand this is a vastly ambitious task, but I am going to give it a shot. I would like to know if someone thinks I am delusional!
Sounds good to me.

I should remark that complex analysis is about the calculus of complex numbers (or, really, meromorphic functions); you learn about basic arithmetic and algebra with complex numbers much earlier.
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