Areas of mathematics to strengthen if interested in OR

Question

I realize that this question may be off-topic, but I do not know where else can I find a 'social media' where OR practitioners hang out. I am about to finish my math BSc. and about to do my masters. I am interested in learning more OR, so I would like to know which areas of mathematics are the most useful for OR?

Question: Which areas of mathematics should be strengthen in anticipation of doing OR? Strengthen can be understood as learning from a graduate text for subject X in the summer break.

Personally,:

• Linear Algebra. I haven't touched a more advanced linalg book, but I made a point to try to use it in my thesis. I don't have a more advanced knowledge but I know the undergraduate material pretty intimately by usage.
• Abstract Algebra. Took two courses, covered rigorously groups, rings, and fields.
• Graph theory. Fairly ahead of the standard graph theory classes math and cs students take (did ramsey theory, turan graphs), I just like the subject.
• Analysis. What you would expect to know of an undergraduate, rigorous single + multivar, rigorous real analysis, somewhat milder complex analysis (half of the class was complex analysis, the other half was intro to measure theory). In fact, I skipped a proper measure theory course, should I take this in my masters?
• Probability, statistics, stochastics. I did a course in each, and I am strong in them, but I don't know if they are that relevant to OR?

Answer 1

Already I think you have a sufficiently strong math background for someone going into OR. Among your cohort in your Master's program there are likely to be students who have an undergraduate degree in IE, who will know more about OR than you do but less about math. And there will likely be some math majors, who have a similar background as yours, and folks from totally unrelated fields as well. So I would not worry that you are deficient in math as you head into your Master's.

But to your specific question about which math fields are most relevant, I would say it's useful to have a solid understanding of the fundamentals of:

• Linear algebra (important for linear programming theory and algorithms)
• Graph theory (important for combinatorial optimization)
• Real analysis (important if you specialize in continuous optimization, but even if you don't, the mathematical maturity students typically gain in real analysis courses is useful throughout OR)
• Probability, stats, stochastics (all are heavily used in OR)

For a Master's program, a first course in each of these is usually sufficient, though of course having taken more won't hurt you.

You most likely won't use much abstract algebra or complex analysis, but again, it won't hurt you.

You didn't say much about your computing background, but if you haven't done too much coding, you might want to spend the summer improving your skills there instead of in math. Learn or improve your Python, MATLAB, Julia, etc.

Answer 2

I agree with Larry that you've already got most of what you need. I would suggest taking a look at numerical analysis. An understanding of convergence arguments for algorithms and, perhaps more importantly, how mathematics on a computer diverges from mathematics as taught in a math class can be helpful and at times critical.