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.
Best Answer
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.