Seeking reading material before jumping into a master's in applied math...

July 15, 2007 4:57 PM

Starting this fall, I plan on taking some preparatory undergrad coursework with the intention of eventually applying to a master's program in applied mathematics. I am seeking suggestions for reading material concerning the field of mathematics in general, both as a refresher and as insight into current focus areas and work being done. As a working engineer, my situation and background might be a bit different from most considering this route...

I have a bachelor's degree in computer engineering, as well as a master's in the same that was earned while working full time. I continue to work full time, though I have reason to believe that both the school to which I'm applying and my employer will be accommodating. The master's was recently completed, but it has been five years since my undergrad work. Unfortunately, my undergrad coursework is far more relevant than the coursework I've recently taken.

This undergrad coursework largely covers the prerequisites I need for grad study -- core calculus, a class in differential equations, some proofs through a discrete math course, linear algebra, etc. I'm already in contact with advisors regarding further coursework to be taken before applying to a formal grad program and trust their advice. I'm not really seeking additional input concerning this. However, I would definitely consider advice on approaching the mathematics field from an engineering background.

That said, my primary inquiry concerns specific reading material about the field in general. I'm looking for something a bit above pop-science level, but not quite textbook level. I'm by no means afraid of a bit of dense reading; However, I also don't expect to attempt to master the field before entering. Naturally, I already intend to break out my old textbooks, so that's covered. What I'm really seeking is material to give a taste for parts of the field that I wouldn't have been introduced to in an undergrad engineering program. Although probably not a perfect example, I'm looking for something a bit like Knuth's 'The Art of Computer Programming' is to the computer science field, if that's familiar to anyone answering this.

Anyway, I'll attempt to monitor this and answer clarifying questions as they come up. Thanks in advance!

posted by Bugg to education (2 comments total)

A background in proofs will serve you well compared to your engineering and CS buddies. That's one of the spots where most of that ilk tend to struggle in math. Another big leap is analysis. If you can find an advanced calculus textbook (check local used bookstores; they'll be cheap and there's little difference between publishers) it's a start. For analysis it never hurts to do a little advanced reading. I had a friend give me Kolmogorov and Fomin's Real Analysis as a good starter in the subject as an undergrad pure math major and it was quite helpful. The canonical texts in analysis are Rudin's Real Analysis and Real and Complex Analysis, affectionately Baby and Papa Rudin respectively, along with Royden's Real Analysis. I'd only recommend the first (Baby) for you, and even that may be more than you need. In my experience teaching math to engineers and scientists there's no deficiency in calculation, algebra, etc. The difficulty lies in the ability to be creative in the use of the tools they've already got. Analysis is a good place to learn that, as was your Discrete Math course. You might also grab a GRE study guide to just skim through.
posted by monkeymadness at 8:07 PM on July 15, 2007 [1 favorite]

As an engineer, much of the material may already be familiar, but you should still check out Steven Strogatz's Non-Linear Dynamics and Chaos. It's one of the most interesting and readable textbooks I've ever encountered, and it will certainly get you thinking about calculus and differential equations.

I found that the key hurdle in going back to grad school (in physics) after time away from school wasn't that I needed to review material, it was that I needed to get back into the habit of problem solving. Practice working problems in Strogatz or similar texts and you'll probably gain more than if you try to learn or relearn things that you'll probably just end up looking up in books when you need them anyhow.
posted by dseaton at 8:06 AM on July 16, 2007