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March 24th, 2015, 01:54 PM  #1 
Newbie Joined: Mar 2015 From: London Posts: 3 Thanks: 0  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. 
March 24th, 2015, 05:14 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,063 Thanks: 1396 
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?

March 24th, 2015, 10:41 PM  #3 
Newbie Joined: Mar 2015 From: London Posts: 3 Thanks: 0 
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 1520 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.

March 25th, 2015, 09:28 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,063 Thanks: 1396 
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.

March 25th, 2015, 09:32 AM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Linear algebra (matrix algebra, not the highschool 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. 
March 25th, 2015, 01:01 PM  #6 
Newbie Joined: Mar 2015 From: London Posts: 3 Thanks: 0 
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!

March 25th, 2015, 03:22 PM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
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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