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Academic Guidance Academic Guidance - Academic guidance for those pursuing a college degree... what college? Grad school? PhD help?

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February 25th, 2010, 10:51 AM   #11
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Re: How to begin advancing in mathematics?

Originally Posted by croesoswallt
Would I be a fool to consider getting a 'Maths for Dummies' type of book?
No. But you may find that an 'off-the-beaten-path' approach is more fun. I think if you come across a subject within math that you really enjoy, it will encourage you to shore up whatever basics you missed so you can go further with that. For me, the subject was number theory -- and it's certainly approachable to someone at your level. (There are used textbooks for under 7; I have Dudley's, for example.) For others, it's graph theory -- also an approachable subject with little background needed initially. (I don't have a textbook recommendation on that one, but there are lots out there.) A nice mind-bending approach might be sampling non-Euclidean geometry; I expect there are books aimed at your level though I haven't seen any. If you can handle not-hard-but-very-tedious transformations, you can learn a *ton* about logic and set theory through (introduction).

But if you want to soldier through and re-learn the algebra -- certainly beneficial no matter which way you end up going -- you're going to have to find a good book or someone to help you through a less-good book. Unfortunately I don't know what's out there; anyone have advice on this point?
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February 26th, 2010, 08:39 AM   #12
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Re: How to begin advancing in mathematics?

Originally Posted by croesoswallt
I would be lying if I said I wasn't still confused, in fact I may be more confused than ever.
Trying to figure out what all math there is to learn is a really great way to confuse the hell out of yourself.

Is discrete maths what I want to be looking at?
It's certainly a good start. I like CRG's suggestion to find an area that seems interesting, and then spend time learning the background you need; on the other hand, "discrete math" provides a really nice background of a number of areas in math, so it may be a good way to find out what areas seem interesting.

I've been getting definitions off wikipedia, which of course is known to be less than reliable.
Actually, wikipedia is a fantastic reference for math... the one problem is sometimes the articles are written at a high level, or with no thought of trying to give intuition.

The problem is, as I think Pseudonym may have described (I was confused) that to understand one idea I must read on several other ideas, which in turn require me to read on several more, in an endless branching out of ideas.
That's one of the most fascinating things about math-- as you delve deeper into something, all sorts of other structures and ideas begin to show up. This also makes learning math very daunting, and sometimes even discouraging: there is just soooo much that needs to be understood. At the same time, it makes it very rewarding and exciting to understand a new, deeper connection-- especially when you start to notice things showing up in unexpected places.

Would I be a fool to consider getting a 'Maths for Dummies' type of book?
To repeat CRG: certainly not. That will really help to build an intuition for and understanding of the basic ideas; from there, the more advanced and "deeper" results will be much easier to understand and to appreciate.
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