Maths / Physics - How to approach independent learning

[nhuang_88]

Hi everyone,

I know this subject has been broached before but would appreciate some extra help - I'm an English major in second year uni so I haven't done physics and maths for a while, but I have quite a lot of free time at the moment and would really love to get back into these subjects which have always fascinated me. The problem is I don't have a very strong basis in physics at all - did science from Grade 7-10 and only half a year of physics in Grade 11 (australian high school system). For maths I did it all the way up to Grade 12 but only at the second highest level (extension 1 or 3 unit in case anyone is familiar with the HSC) - so basically a calculus focused course but I don't know anything about complex numbers and things like that. And even my calculus would be pretty rusty now.

So my question is, how would you suggest I go about teaching myself maths and physics? I guess you need a solid maths grounding for physics so should I start with maths revision? Or would it be more constructive / complementary if I tried doing both at the same time? And what would be the best way to learn the basics of physics again - textbooks or using a teach yourself website? It's quantum physics which particularly interests me, how much groundwork would you recommend before I start focusing more specifically on that?

Thanks very much for your help.
Nikki

[Tac-Tics]

It sounds like a good endeavor!

Don't worry about your math skills. You can learn as you go. As long as you're familiar with the basics of calculus, you should be able to swallow a lot of physics. Learning both at the same time is very helpful. Each reinforces the other, although the language can be very different between the two subjects. Physics makes very heavy use of advanced calculus techniques in three dimensional space. But math is much broader than calculus.

If you're interested in math, you should look into set theory and analysis. Set theory is the foundation of the rest of mathematics. Analysis is basically rigorous calculus, where you focus on *proving* theorems you assumed to be true in school. It also sets up a formal definition for the real number (something you've taken for granted your whole life), and generalizes everything to linear spaces (so you can do calculus in three-dimensional space).

Quantum mechanics, in my experience, is a tough nut to crack. From what I understand, the theory developed very slowly over the course of about 30 years, and there are a lot of approaches to it both conceptually and mathematically. I'm still looking for a good, no-nonsense text or other resource, but so far I haven't found it =-( The mathematics is also pretty broad. Instead of working in R^3, where each point is a triplet of real numbers, you get to work in a space where each point is a complex-valued function.

However, if you're interested in approach from the other side, special relativity isn't too hard to understand. Einstein did a wonderful job coming up with the subject in an almost entirely pictorial way. Starting off with the assumption that each observer measures light to be moving at the same speed immediately leads to a number of paradoxes that are resolved when you abolish some intuitions you have over how time works.

Good luck!

[nhuang_88]

Thanks so much for the detailed reply! I must admit I've fallen a little behind in my plans with the end of the year approaching and now I feel reinspired to give it a go :)

[Vid]

I recommend the Road to Reality by Penrose.