# Never too late

### From enfascination

I meet many people who stopped paying attention in Math, anywhere between 4th and 12th grade and, years later, got their interest piqued again. This happened to me too, and I know the feeling that it is too late. And I know that it isn't, particularly with the resources of the web. I'm posting an email I wrote to a friend. It is a post-calculus curriculum. If you made it as far as 11th grade before fading out, you can start here. You'll pick up the trig again as a result of getting back in, sort of piecemeal, the rest you can get guided through in the courses. This is more of a roadmap through MIT's OCW. OCW is the complete coursework of every MIT course that is or has been taught. A great effort to make knowledge haveable. Everything is there: HW, tests, lectures, slides, readings (or books to buy) and answers to all the HW and tests. If you haven't made it as far as calc but want a roadmap through everything up to it, let me know and I'll put something together.

Here is the letter:

" Lucky you, OCW not only has a complete linear algebra class, but it has full video lectures AND it is taught by the amazing Gilbert Strang. He is the Mr. Roger's of Linear algebra. I took Numerical Methods with him at MIT and he started the course off talking about his 4 favorite matrices. When I was taking linear algebra at Berkeley, having never even heard of the guy, friends were watching these lectures to help them understand what was going on in the local class which was taught entirely differently.

Watching the lectures will be nice enough, but to really benefit from this stuff, you should do the HW

http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm

Here are all the math class, with all the All Class on the left sidebar. http://ocw.mit.edu/OcwWeb/Mathematics/index.htm

It is lucky that you learned, back in the day, 'everything up to' calculus, because there isn't really a one stop shop for full pre-calculus courses. MIT assumes precalc and all that trig. Though you have likely forgotten your trig and a bunch of your algebra, it won't be prohibitive to pick up again, and you can ask me to clarify steps, and the internet Does have all the bits and pieces scattered about. http://mathworld.wolfram.com/ is a great resource. Wolfram is an important egomaniac who has done some cool stuff.

Given a foundation just up to calc, I prescribe the following four-unit plan to Catching You Up. The goal is to give you the fairly conventional ladder up to taking courses with proofs. That is when you really start seeing the beauty of mathematics, and when equations stop having numbers in them. The first three units form a sort of bottle neck, with intertwined prereqs, after that, you can branch off in all kinds of directions: more applied or more abstract or more fun. If you want to skip straight to courses with proofs, you can do that, just let me know and I'll revise this to take out all the courses that use numbers in their equations, though you should give this a try. If you want a Unit 0, just to get you psyched and ease you in, take 18.781 Theory of Numbers . Number Theory was my favorite math.

Unit 1 18.01 Single Variable Calculus (or 18.013) 18.06 Linear Algebra

Unit 2 18.02 Multivariable Calculus 18.03 Differential Equations

Unit 3 18.05 Introduction to Probability and Statistics 18.100A Analysis I

Unit 4 pretty much whatever you'd like. Everything below is in math, but from here you can learn Real Physics and Engineering of all kinds. Physics tends to start as three courses: Classical Mechanics, E&M (electricity and magnetism) and then Quantum (which MIT teaches concurrently with statistical mechanics, which is excellent). None of these requires all of the above prereqs, but just the process of doing them all is great preparation for all of these, and, importantly, all of the above are considered a minimal foundation (though I haven't taken analysis and have never had a proper DE (Diff Eq)(differential equations) course. Recommendations: 18.781 Theory of Numbers (Great!!) 18.04 Complex Variables with Applications 18.100B Analysis I 18.152 Introduction to Partial Differential Equations 18.353J Nonlinear Dynamics I: Chaos 18.901 Introduction to Topology 18.950 Differential Geometry "