April 24, 2008

Curious George A while back I saw a link on Reddit (I think) to a picture that was a map of various mathematical objects. In the center of that map was a group of connected boxes labeled "Integers", "Rational Numbers", "Real Numbers", "Complex Numbers" and a circle around them going to a note that said "You are here". The rest of the map outside the circle were more esoteric mathematical objects and their relationships showed by linking lines, as well as their links to the "YAH" group. Well now I can't find that. Can a million monkeys with keyboards bang out the url or google search terms I can use to find that again?

Also, I've been thinking that I'd like to learn more about math. Years ago when I was pursuing my (sadly never completed) bachelor's in Electrical Engineering I got through Differential Equations, and also a Linear Algebra course and Discrete Math course. I also did some tutoring in algebra, trig, and calculus, so I felt pretty solid on those. It's been a while, though, so I'd kinda like to go back and brush up on the basics, reacquaint myself with the more advanced math I once learned, and then expand my knowledge from there. Basically what I'd like to do is design a personal long term self study plan to give myself the equivalent of a Masters in math. I'd like to be able to say to myself "yeah, I get math", so that even the parts I didn't know I'd have some sense of what they were and how I'd learn about them if I wanted to. So, what I'm looking for is a sort of overview of all of math. Hence my original question, but also I want a lot more than that little whimsical joke reddit post.

posted by ReverendJohn 16 years ago
  • Mathworld by Wolfram is a fantastic resource. A full list of Wolfram's resources here. I'll look at some of my bookmarks and see what else I have.
  • Mathworld does look like a wonderful resource if you know what you're looking for. I'm kinda looking more for a general overview and a guide that can help me find my way from pretending that I know almost nothing to having a fairly broad understanding of math as a whole, with some depths in the areas that interest me. I'm contemplating diving into a few different books. Some possibilities are Euclid's Elements, as I've seen some nice versions of that online, Silvanus Thompsons "Calculus Made Easy", since I remember Feynman talking about it in his biography, "Elementary Calculus: An Approach Using Infinitesimals" by Keisler is available online for free and seems to take an interesting approach to the subject, I once browsed a book called "A Tour of the Calculus" that seemed to take a bit of a topical and historical overview of some subjects in math, and I've got some curiousity about "Godel, Escher, and Bach". But all of these things are very scattershot. I want some help getting an idea of where I should start, and an overview of the places I could go and how they're connected.
  • There was a nicely made introductory course I looked at online a while back, but I can't find it now. This looks interesting, especially the bit about: There are nearly 100 free math courses available through MIT's innovative OpenCourseWare project. Most of the courses consist of lectures, slides, problem sets, assignments and other resources to assist in self-study. Registration is not required. There's a nice book called "The History of Zero" that you could add to your list.
  • Screw math. It's hard.
  • Hi. No luck with googling that map. It sure sounds like something from xkcd, though. I'll second the open courseware recommendation. I haven't looked at anything from the math department, but I've been through a few of the biology lectures and they are awesome. It looks like most of the math classes are lecture notes only, but there are a bunch of video lectures. I'd also recommend that if you're serious, you may need what the diet books call "lifestyle changes". Get out your old Thomas Calculus book and stick it on a shelf in your bathroom and read a small section every morning. Give yourself a math problem to solve and then solve it; doesn't matter what but it should be harder than you are comfortable with and take a fair amount of time and be personally interesting -- calculating satellite orbits or entering the Netflix recommendation challenge with some novel math approach, whatever. And hang around with other math nerds, online and in reality. To the point where you start to feel vaguely comfortable thinking of yourself as a math guy (or girl as appropriate). Which in the end is all a university degree really is.
  • You may like this math concept map, although it's not quite the same as what you described.
  • ough: I do like that, thanks! And you were closer than you thought. The blog posting which contained that math concept map you referred to also showed a "Tree of Knowledge" map of the relationships between various sciences. This tree of knowledge map is credited to Max Tegmark who created the original map that I was looking for, as posted on reddit. The image that I was thinking of is actually a modified version referenced in the comments of that article and posted here. I'm pretty sure the modified version was the version I originally saw and was thinking of and was actually posted as its own article a while back. So, thanks for the good info all around everyone!
  • *runs screaming from the math*
  • *hides behind GramMa*
  • eix = cos x + i sin x booga booga!