Advice for a newcomer to mathematics

[dmehling]

I have developed an interest in mathematics rather late in life since I am about finished with my professional education. I realize that it is too late for me to make a career out of mathematics, so it will probably remain a recreational or aesthetic activity. I'm wanting suggestions on how to make the most out of my mathematical studies. I've recently been studying mainly algebra and calculus, which is interesting enough, but most of the material I have been reading is mainly concerned with the mundane and procedural aspects. I'm wanting to understand mathematics more conceptually. I believe the ability to understand and develop mathematical proofs is a very important practice, but I don't seem to understand the assumptions and philosophy behind proofs. I feel rather confused and I'm beginning to wonder if mathematics is really something that would continue to interest me.

 

[Pinu7]

I know this is not the advice you are looking for, but don't use math equations to pick up girls; it ends badly.

I think everyone here can agree to that.

 

[dmehling]

I am being totally serious here. That's the least motivating factor for me.

 

[dx]

Maybe you could give an example of what you're having difficulty with. I can't quite tell from your post what exactly the problem is.

 

[dmehling]

Not really sure what the problem is either. Just a general uncertainty rather than something specific. I guess I'm really trying to figure out if I really am interested in mathematics for mathematics sake. Some of the more advanced topics that mathematicians explore are completely unknown to me. You don't really know what they're about until you get to them, so I fear I might not actually enjoy them. Maybe that is a question no one can answer, but I have to find out for myself.

 

[union68]

The first step to higher mathematics is usually a course in logic and proof. That would be where I start.

I read An Introduction to Mathematical Reasoning, by Eccles. It covers logic, proof, sets, functions, and even a little number theory. I also read Discrete Mathematics and Its Applications, by Rosen. It covers many of the same topics in addition to some combinatorics and other stuff. However, as the title suggests, it's very application-based.

You need to get a firm grounding in this sort of stuff if you ever hope to understand a book on analysis, topology, or abstract algebra.

 

[whs]

If this is just going to be a sort of 'hobby' then I'd just find lots of interesting problems to solve. The harder the problems get, the more math knowledge you will need to learn on your own, and then you will have something to show for it.

Otherwise, you will have to actually diligently study to learn more, and if you don't use it, you lose it.

Go to IBM's website and look at the 'ponder this' problems. They are hard, and fun to try to solve.

 

[VeeEight]

Assuming you haven't taken any other math courses than the ones you mentioned, I suggest a course on Into Analysis and Abstract Algebra. Into Analysis courses are usually quite rigorous and gives you the basic tools needed to study things like topology, measure theory, and complex analysis. Basic Abstract Algebra, such as an introduction to groups and rings, is important because it covers a wide array of material and sets you up for more rigorous courses in Group, Ring, and Field Theory.