What is mathematical analysis and/or discrete mathematics used for?

[mitcho]

I am starting a maths major and I will going to go into pure maths. I am going to specialize in either analysis or discrete maths. I understand that mathematical analysis has a very strong connection to calculus and that discrete mathematics is used mainly in the cryptography and security industry. What other areas are either of these two studies used in? Also, what area of mathematics would be used to predict trends in things like the stockmarket for example?
Any help would be appreciated.
Thanks.

 

[discrete*]

I am starting a maths major and I will going to go into pure maths. I am going to specialize in either analysis or discrete maths. I understand that mathematical analysis has a very strong connection to calculus and that discrete mathematics is used mainly in the cryptography and security industry. What other areas are either of these two studies used in? Also, what area of mathematics would be used to predict trends in things like the stockmarket for example?
Any help would be appreciated.
Thanks.

I'm curious; how does you know what you're going to specialize in if you don't even know what the fields are?

Analysis does have connections to Calculus. In the course of your bachelor's degree you'll probably take a course (or two) called Advanced Calculus. This is typically Calculus presented in a rigorous manner and usually functions as a bridge course to Real Analysis and the Theory of Functions of a Complex Variable (AKA: Complex Analysis).

That being said, Analysis is the mathematical study of theories of integration, differentiation, measure, functions etc. Informally, it's the mathematics of change. Analysis tends to break complex things into smaller parts and analyze those constituent parts.

Discrete Mathematics is a large field of mathematics that studies discrete models. What this means is that Discrete Math seeks to study noncontinuous objects. I wish I had a better way to describe it, because if you're not yet in some advanced courses, you probably don't know what I'm talking about. We can define Discrete Math, rather loosely, as the study of countable sets.

Discrete Mathematics has deep connections to Computer Science, and most (if not all) CS majors take the course. Discrete Math has some very interesting subfields. A few off the top of my head are Number Theory, Set Theory & Logic, Probability, Combinatorics...

There are many members here at the PF that can answer your last question much better than I can, but I'll give you what I can. To answer questions in finance, I believe Stochastic Calculus is very important. Anything that studies nonlinear functions would most likely have a use.

Both a very broad fields and very interesting subjects in their own right. You should get some coursework under your belt before you start thinking about specializing in any field. Good luck.

 

[mitcho]

Hey and thank you for the reply.
I am unsure at this stage what to specialize in for that reason; I don't yet understand what the two are. The reason I have decided on either one of these is because I have a keen interest in pure mathematics rather than applied simply because of its 'beauty' and I was under the impression that these fields are the two main fields in pure maths. Given the information that you have, do you know of any do you know any industries that would employ a discrete mathematician (apart from cryptography) or a mathematician specializing in analysis as I am worried about employment prospects for a pure mathematician outside of research.
Thanks.

 

[discrete*]

Hey and thank you for the reply.
I am unsure at this stage what to specialize in for that reason; I don't yet understand what the two are. The reason I have decided on either one of these is because I have a keen interest in pure mathematics rather than applied simply because of its 'beauty' and I was under the impression that these fields are the two main fields in pure maths. Given the information that you have, do you know of any do you know any industries that would employ a discrete mathematician (apart from cryptography) or a mathematician specializing in analysis as I am worried about employment prospects for a pure mathematician outside of research.
Thanks.

It really depends on what you study and what you take to doing research in while at university. For example, if you study and do research in Theoretical Computer Science (a subject under Discrete Mathematics) than you might be able to work for companies like Microsoft, IBM, Apple, etc... Now, you may be able to get a job with these companies with any specialization, but I would think that they'd look for persons with an interest in the theory of computing.

The techniques of Analysis are widely applied. Curiously, you've said that you want to work in pure maths, but then work in industry. Pure mathematics typically are not worked on by industry professionals. Perhaps if you get a government research position or something, but other than that, industry is looking for mathematicians that can apply their skills to real world problems.

I think you have a while before you have to worry about this type of stuff. Focus on doing well in all your maths and see what you like best along the way. When I first started I thought I'd be interested in Geometry, then I took a course on the Logic and Set Theory and found my niche so to speak. I never thought I'd study the Foundations, but it was a natural progression for me to choose that as a track for my masters, and soon my Ph.D, and I couldn't be happier. Take your time, and let the chips fall where they will.