I’ve been asked variants of this question a number of times. So here’s a thorough answer for everyone: Where should I start reading mathematics if I never got far with it in school?
First, some well-written books on topics that interest me:
- Roger Penrose’s The Road to Reality if you’re interested in physics.
- Cosma Shalizi’s blog bactra.org
- John Baez’s blog
- Matthen’s tumblr and demonstrations.wolfram.com
- John Stillwell’s stroll through the historical development of mathematics
- Jan Koenderink’s book about weird shapes
- Tristan Needham’s book about complex numbers
- When you’re ready to take it to the next level and really understand stuff, watch Gilbert Strang’s lectures on linear algebra (MIT OCW).
- Tony Robbin’s book about the fourth dimension
- Bill Lawvere & Steve Schanuel’s book about categorial thinking.
My interests are like economics / philosophy / probability / trying-to-understand-the-universe, so that’s what I gravitate toward.
Second, some personalisation advice: Read anything mathematical that talks about something you’re interested in.
- If you are into weather / fluids, check out MIT OCW’s courses from the atmospheric science department (free pdf’s).
- If you’re into the philosophy of quantum mechanics, try Itamar Pitowsky’s book or the Stanford Encyclopedia of Philosophy (it will get into hilbert spaces soon enough).
- I haven’t read it, but Doug Hofstadter’s Gödel Escher Bach seems to have inspired a lot of people.
- Are you into puzzles? computer graphics? metaphysics? linguistics? liquids? animals? music theory? morality? interpersonal relationships? the function of cells? systems theory? how the body moves? There are mathematical takes on all of those.
- Scott, I can see from your blog that you’re a Rubyist. Google “Dominic Verity category theory part 2”, he explains category theory to Haskellers who like functional programming. You might also want to explore Wikipedia / google on “discrete math”? Posets and graph theory are programming related. Just guessing here.
I’ve seen speech-pathology students with bad-mathematics syndrome take off like a fish in water when they do mathematics that relates to what they know—building sawtooth waves, just intonation, EQ’s. You know, ear stuff.
I recommend starting from what you know and using mathematics as a bridge to other things. (“Hey, I didn’t realise audio engineering gets me trigonometry for free!”)
Finally: I try to aim this blog at people who didn’t do the whole calc 1-2-3-4, ode, real analysis thing. In an ideal world, my writing would come out well enough that an artist or writer with no mathematical confidence could parse it and be inspired with a new thought-shape.
That’s for the original posts, and I also try to make people aware of things that are well-known in my circles but not well-known in general. For example, did you know that some guy was actually able to define complexity?
There are three ways to explore this blog:
- http://isomorphismes.tumblr.com/tagged/economics groups together posts.
- http://isomorphismes.tumblr.com/search/quasicrystals lets you search.
- http://isomorphismes.tumblr.com/archive lets you browse the site backwards from today.
- http://isomorphismes.tumblr.com/archive/2010/12 lets you browse the site backwards from December 2010.