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I am a math major and I am trying to figure out what math classes I want to take next semester. My question is what industries are Stochastic Processes and Combinatorics useful for?

I haven't decided what career/industry I am going to go into once I graduate so any information of what careers these classes would help me be great at would be helpful.

Last semester I took Probability and Real-Analysis, currently I am taking linear algebra and financial mathematics. Also how difficult are stochastic processes and combinatorics when compared to real-analysis because I want to know what I am getting myself into and Real-Analysis was the only math class thus far that I would say was very difficult.

My other option for next semester is statistics of mathematics, differential equations won't be offered in fall 2016 so I'll have to take that spring 2017.

I am not asking for you to decide what I am going to take, just some information or advice about what these classes have to offer.

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    $\begingroup$ stochastic processes are used in finance to model and price derivatives.. you need at least some notion of stochastic calculus if you want to do that, the more the better :) $\endgroup$ – Ant Mar 11 '16 at 1:14
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    $\begingroup$ What you'll learn in stochastic processes will much better translate into real-life applications because stochastic processes are everywhere - finance, actuary, queuing, gambling, network analysis, etc. It will help you think of uncertainty and get some feel for long-term behaviour of model systems. Combinatorics is "purer" and while it certainly has plenty of applications, they are not so close to the surface beyond the most basic combinatorics (where probability and combinatorics mix strongly). $\endgroup$ – A.S. Mar 11 '16 at 1:14
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    $\begingroup$ If you're interested in mathematical finance then you should definitely take a course in stochastics. $\endgroup$ – Math1000 Mar 11 '16 at 1:26
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    $\begingroup$ If it is a single "Stochastic processes and combinatorics", the above still applies because as I said on low levels these things mix strongly. Real analysis is considerably more abstract/conceptually new than what I perceive would the the level of stochastic processes you'll get. Statistics of mathematics sounds a lil too artificial but it's impossible to gauge the content based on such a name. $\endgroup$ – A.S. Mar 11 '16 at 1:38
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    $\begingroup$ I see - it's "mathematical statistics". I never took a course in this subject (picked up it on my own as needed) but the concepts don't seem as fundamental and important as stochastic processes - especially if you actually want to do some modeling yourself. To me, it makes the most sense to learn more theoretical foundations of probability/stochastic processes in class and later on delve into statistical issues as specific issues/applications arise. I'd prioritize Stochastic processes but can't factor in your own interests (imp), quality of profs teaching, books used (less essential factors). $\endgroup$ – A.S. Mar 11 '16 at 3:41
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Without knowing you personally or the curriculum at your school, it is not possible to give responsible advice on what you should take next term. You need to discuss this with an adviser. You should be clear that you are currently planning on a career in industry rather than academia. Perhaps ideas arising on this page could be included in that discussion.

Most beginning courses in stochastic processes include Markov chains and some simple queueing processes. Usually an introductory course in probability is a prerequisite. Material in a stochastic processes course is used in other parts of applied probability modeling: relaibility theory, sequential statistical analysis, modern computational methods such as Markov Chain Monte Carlo (MCMC), and many other topics (including those in the Comments).

If you are serious about an industrial career, I think you should study some basics of computer science and get acquainted with a computer language. Among my colleagues, it is debated whether this is best done in classes or by self study. I suspect many people benefit by learning the basics in a class. The first computer language you learn may soon be out of fashion, but basic principles won't

Also, please read to explore the connections among pure mathematics, statistics, probability, and computation. These days one reads a lot about uses 'big data', 'data science', 'machine learning', and 'data mining' in industry and national security. These are emerging interdisciplinary subjects. Standards for what methods and results are useful are still being established, but I think it is already clear that some of the ideas will turn out to be very important.

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