I know there's a lot of "how do I learn maths" questions out there but I wanted to lay down my history and interest to possibly get a better approach.

When I was in secondary school ( high school ) I was excellent at maths. For instance I remember figuring out the energy needed to theoretically split a charged particle using an electromagnet. It was probably incorrect and impossible but I knew enough to take a stab at it.

Nowadays I can't even remember how to do algebra or long division. I want to re-learn to a high enough level that I can do some hobbyist work with particle physics or space ( think NASA coding competitions, calculating orbits, etc )

So what would you recommend to refresh my memory on the basics and where should I aim to go for these goals (with respect to types of maths)? I tried digging out my old maths books but they're designed to be done over 5 years and I lost the interest after a few weeks.

Ideally I would like a crash course in the basics followed by some entry level physics books and some puzzle books to keep my interest. Any suggestions?

TL:DR - Best way to refresh on high school maths and move on to understanding physics formulae, specifically used in particle physics, orbits, space propulsion, etc?


closed as too broad by Najib Idrissi, N. F. Taussig, SchrodingersCat, Silvia Ghinassi, jameselmore Jan 28 '16 at 14:36

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ For arithmetic and the real basics, I think Teach Yourself Mathematics: A Complete Introduction isn't bad. For algebra and geometry at the next level up, you could try Serge Lang's Basic Mathematics. Physics books can be divided into those that assume you know calculus and those that don't. If you want to get back to physics and can't wait for calculus, try PSSC Physics, which also has accompanying films, many of which can be found on Youtube. $\endgroup$ – David Jan 28 '16 at 16:52

Your two main topics of interest (space and particles) cover rather diverse areas of mathematics.

For the space part, why don't you take a stab at celestial mechanics? My favourite one is written from a hobbyist perspective, which might appeal to you: Jean Meeus, "Astronomical Algorithms," Willmann-Bell. After that you might want to visit more standard textbooks so that you understand how Newton, Lagrange etc. first came up with these formulas and algorithms.

For particles I would recommend advanced calculus with a stress on Hilbert spaces and operator theory. The four-volume "Methods of Modern Mathematical Physics" by Simon and Reed is not the first one you want to read but it offers a very useful bridge to the theoretical physics after you get past the advanced calculus. Another perspective, less rigourous but closer to modern insights in physics, would be David Griffiths, "Introduction to Elementary Particles".

For general maths at an elementary to first-year college level, assuming that you are a native English speaker the offer is so broad that I would not know where to begin. Since your comment contains the adverb 'quickly' let me try recommending the 'focused reading' approach:

(1) Pick a maths or mathematical physics book that solves a problem that you are genuinely interested in (could be, but does not have to be, one of the references above). Invest money in a paper copy. Start reading. A desk with blank paper is better than a commuter train.

(2) Now more likely than not you are bound to hit a snag soon, e.g., in the first chapter someone mentions a partial derivative and you do not even remember, or have never learned, what an ordinary derivative is. Read on a little bit further to see if you can get away with it, understanding the main points of the argument without knowing derivatives. If so: continue reading and repeat point 2. If not, see point 3.

(3) Use the internet to remind you of this particular unknown topic. In many cases Wikipedia is a reasonable starting point to get a feel for what it's about, but use google to find downloads of elementary lecture notes that cover your particular snag (derivatives or anything else).

(4a) Either get interested in derivatives for their own sake, which is nice: go back to step 1. Or

(4b) Quickly learn what partial derivatives mean and move on with your original quest in step 2.

  • $\begingroup$ Thank you very much for taking the time to answer, would you have any recommendations for self-learning books that cover the basics for general maths quickly but in an understandable manner? I mean geometry, long division, algebra, rational numbers, etc. $\endgroup$ – LiamRyan Jan 28 '16 at 11:29
  • $\begingroup$ General maths is so broad that it is not possible to reach any meaningful new understanding while repecting even the most relaxed interpretation of the word 'quickly.' I have added a section on focused reading. By the way, the 'derivatives' example is not chosen arbitrarily. An inordinate amount of 'applied mathematics' relies on basic calculus, especially on derivatives. $\endgroup$ – Justpassingby Jan 28 '16 at 12:43
  • $\begingroup$ Thanks again, I really appreciate the help $\endgroup$ – LiamRyan Jan 28 '16 at 12:46

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