Help me mathemaster
September 16, 2008 6:31 PM   Subscribe

Please suggest a learning plan for learning upper level math?

I am a year and a half removed from college. Freshman year I majored in biology and took the required two semesters of calculus. My courses were geared towards bio students and may or may not have been dumbed down to some degree. I ended up ditching the bio degree, however, and majoring in economics.

In college I took a graduate level macroeconomics course as well as a more advanced course in Econometrics. This was all really interesting, but one of my regrets is that I was always highly focused on graduating with a good GPA but still being able to have extensively good times; as a result I ended up deliberately not taking any other courses in mathematics.

I am interested in learning more about the field--the types of things that undergraduate math majors end up learning about beyond the first two semesters of calculus. Reading Overcoming Bias, many graduate economics papers I pick up, and in many other areas a disgusting math illiteracy on my part.

I guess the obvious caveat first and foremost is that my remembrance of calculus is slim--I would need a refresher I am sure.

But I ask you to submit to me a learning plan as well as perhaps textbooks geared towards the autodidact. When suggesting textbooks obviously the most important thing is how well the material is presented, but also please try to keep in mind price (free is good, but if there are cheap copies widely available for resale that is good too).
posted by prunes to Education (9 answers total) 15 users marked this as a favorite
Ian Stewart's Calculus is very popular today, for good reasons. I think you could sit down and work your way through the whole of it and be pretty much done.
posted by phrontist at 6:43 PM on September 16, 2008

Ideally I would like to be at a point where the Wikipedia math articles make sense. What really sparked this for me was when I picked up a copy of David MacKay's Information Theory, Inference, and Learning Algorithms and realized that I would not be able to even pretend that I knew what he was talking about.
posted by prunes at 6:54 PM on September 16, 2008

Which articles?
posted by phrontist at 7:40 PM on September 16, 2008

Check out Open Courseware. Also, many of the Wikipedia math articles don't actually make sense. A better goal might be to learn enough to fix them.
posted by martinX's bellbottoms at 9:00 PM on September 16, 2008 [1 favorite]

If you want an introduction to the mathematician's calculus (a.k.a. analysis), you may find it in Spivak's classic text Calculus. This is a world away from Stewart's book. In Stewart, you learn useful rules and some intuition; in Spivak you understand the foundation.

Also, you may find Polya's How to Solve It helpful when you are faced with proofs (well, not just then).

Note: if you are reading a math book on your own, you should be doing the exercises.
posted by parudox at 9:21 PM on September 16, 2008 [1 favorite]

I had to brush up on some specific math topics (especially linear algebra, which is not exactly what you're after, I think) for my graduate program and I asked some friends in the math PhD program, who recommended this book: All the Mathematics You Missed: But Need to Know for Graduate School. I bought it cheaply (used paperback online) and have found it very well suited to how I needed to learn, which is to say, on my own. There will definitely be chapters you'll want to skip, but it should bring you up to speed on what interests you.
posted by tractorfeed at 9:30 PM on September 16, 2008 [1 favorite]

I agree with parudox: Stewart is not very rigorous. That's the one thing I've gained from my college classes.
posted by phrontist at 10:48 PM on September 16, 2008

Seconding Spivak. It's what I learned Calculus from. The exercises are glorious. It covers pretty much all the Math you need for the core concepts in MacKay.
posted by Coventry at 4:34 AM on September 17, 2008

For autodidacts or those simply struggling with textbooks, schaum's outline guides are the best way to learn (tons of solved examples) any math or science subject, bar none.
posted by adamrobinson at 6:43 PM on October 4, 2008

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