Intermediate Maths Primers?

Magospietato on 20/1/2011 at 23:19

Does anyone have any suggestions for resources I can use to get up to speed with mid-level mathematics?

Sadly, for someone in my late 20s, I only have an intermediate GCSE-level maths education, and nothing beyond.

So I'm looking for something to educate me in more advanced geometry, calculus; that type of thing.

Most importantly, I find I need to know why the magical formulae that seem to make up maths are actually provable.

Thinking about it, a small refreshed on basic algebra might be useful too...

Suggestions appreciated.

Scots Taffer on 20/1/2011 at 23:43

Consider looking at syllabuses for University courses and suggested reading materials?

Xorak on 20/1/2011 at 23:56

I would also recommend either buying university textbooks or even auditing a university course if you felt you needed some help with it. If there is a university around, just go and look in their bookstores. Maybe start with the materials for a Finite math/Algreba course and then move up to Calculus.

I don't get what you mean by, "Most importantly, I find I need to know why the magical formulae that seem to make up maths are actually provable." This sounds like how Pythagoras built an actual religion upon the premise that numbers are physical and corporeal objects.

Briareos H on 21/1/2011 at 06:43

If you're really interested in why there is provability rather than how to prove, getting into epistemology, history of science and philosophy will bring you more answers than straight-up math theory. Maybe start with (http://www.amazon.com/Philosophy-Quest-Louis-P-Pojman/dp/0195156242/ref=sr_1_8?s=books&ie=UTF8&qid=1295592128&sr=1-8) something like that (allegedly good, haven't read it).

Chimpy Chompy on 21/1/2011 at 10:01

If you want introductory calculus, look for an A-level textbook I guess. University stuff might go over your head, although that might depend if it's "maths for mathematicians" or "maths for people who just use it as a tool, like engineers".

Brian The Dog on 21/1/2011 at 12:14

The book we recommended to our first-year engineers and scientists at uni as a revision book would be Stroud's (http://www.amazon.com/Engineering-Mathematics-K-Stroud/dp/0831133279/ref=sr_1_1?ie=UTF8&qid=1295611798&sr=8-1) Engineering Mathematics. The covers everything from basic arithmetic up to differential equations, matrices and complex numbers, so everything up to stuff required for engineering courses at university.

A bit more advanced is Kreyszig's (http://www.amazon.com/Engineering-Mathematics-K-Stroud/dp/0831133279/ref=sr_1_1?ie=UTF8&qid=1295611798&sr=8-1#reader_0831133279) Advanced Engineering Mathematics, which was my recommended Maths book throughout my undergrad course. I'd start with Stroud's though.

Rug Burn Junky on 21/1/2011 at 13:45

If you're going to self-study, the (http://www.amazon.com/Princeton-Companion-Mathematics-ebook/dp/B003AUTEKO/ref=wl_it_dp_o?ie=UTF8&coliid=I1Q5RCEIRX314Q&colid=3F15FE0MF9Q70) The Princeton Companion to Mathematics is one of the best overviews I've ever come across. From what I've seen, it's pretty accurate, knowledgeable AND, most importantly, accessible.

Academic textbooks tend to be a bit too narrowly focused, sometimes making it difficult to leap into if you're more of a dilettante.

Shug on 21/1/2011 at 15:39

Quote Posted by Rug Burn Junky

dilettante.

New word of the month, ty