# Essential courses to take for research in OR with applications to Finance

 3 2 I'm currently the 2nd-year MS student in Applied Mathematics. As I'm planning for which classes to take the next semester, I would love to hear your feedback about my selection. The reason is because I'm almost completing the M.S program (this one is my second-to-last semester) before I apply to the PhD programs in Operation Research and/or Applied Math next Fall. As you probably realize, I want to hedge my bet by applying for both OR and Applied Math programs, most of which allow to specialize in interdisciplinary fields like OR or Finance, not necessarily Physics or Biology. To prepare for an intense competition in top PhD programs in OR/Applied Math, I think I would need to display stronger interest in OR, as I'm only taking 2 OR Grad courses in Linear and Nonlinear Programming (I got both As in them, and love NLP's materials quite a lot. LP is also fine, but it gave me impression that there is not much to do heavy research in this topic). I currently wonder if the best way to show a true interest in OR is to either take more OR grad courses, or to do some research with my OR professor(s) who taught me in the two OR courses above. The reason for my concern is that I'm afraid I overkilled with math courses (I still find my knowledge in Math is so little, considering how steep the learning curve is for PDEs, but my time is running out). My main interests in OR include 3 areas: optimal dynamic pricing for manufactured products and its impacts on a business's top + bottom line, derivatives pricing /asset allocation/portfolio optimization, and optimal routing/production scheduling in manufacturing and logistics. Now, the major problem is that I can only take at most $8$ more courses, and $2$ of them I have decided to be on Measure Theory and Stochastic Differential Equations (book by M. Steele) , I still have 2 more classes to choose for next semester, and below is my potential course to take (ranked from most to least important): Integer Programming - Applied Integer Programming - Modeling and Solution by Chen Dynammic Programming - Models + Application book by Eric Denardo Regression and Time Series - Econometrics Model + Economics Forecast book by Pindyck Numerical Solutions of Differential Equations (purely Finite Difference method) - A first course in Numerical Analysis of DEs (Cambridge Series Textbook) Complex Analysis I - no book decided yet My current temporary pick is the first two on the list, but that might be completely wrong. Needless to say, Integer programming is quite useful when applying for OR/Applied Math programs. But this is just my thought, and I don't really have that much experience, so please help offer your insight/suggestion/new courses proposal for me. I sincerely appreciate your time and help. asked 18 Dec '15, 03:42 ghjk 63●6 accept rate: 0%

 1 @Ehsan: My current choice is Numerical DEs + Dynamic Programming, although I'm still not sure whether Time Series or Queuing Theory would be better choice than DP? I'm more interested in Financial Engineering than Operation Management, but I don't want to keep my focus too narrow to avoid not having enough professors who match my interest at the schools I applied for (like Columbia, Cornell, UT-Austin's IROM, UMD's AMSC, UPenn's ACMS, etc.). Below is the syllabus for each course: Time Series and Regression: Mathematics of regression, exponential smoothing, time series, and forecasting Book: Econometric Models + Economic Forecast - Pindyck Dynamic Programming: (Deterministic DP) Dynamic Programming Networks and the Principle of Optimality. Formulating dynamic programming recursions, Shortest Path Algorithms, Critical Path Method, Resource Allocation (including Investments). Knapsack Problems, Production Control, Capacity Expansion, and Equipment Replacement. Infinite Horizon Optimization including Equipment Replacement over an Unbounded Horizon. Infinite Decision Trees and Dynamic Programming Networks. (Stochastic DP) Stochastic Shortest Path Problems with examples in Inventory Control. Markov Decision Processes, value and policy iteration for discounted cost criteria. MDP with examples in Equipment Replacement and inventory problems. Semi-Markov Decision Process. Book: Dynamic Programming: Models and Applications by Eric Denardo Queuing Theory: Introduction to queueing theory Review of Poisson processes, Markov chains, Little’s law, Simulation of queueing models, Fluid models, Simple Markovian queues, Advanced Markovian queues, Queueing networks, Models with general distributions. Book: Fundamentals of Queueing Theory by John Shortle I'm sorry if I bore you with my questions, but since I only have 2 semesters to go before grad application to top OR/Applied Math, it's very important for me to take a right course to show the admission that I have substantial background for doing research/passing the qual. answered 23 Dec '15, 23:53 ghjk 63●6 accept rate: 0% 1 If you want to keep your options open, take DP as it's a core OR technique. Forecasting (TS and Reg.) could be not necessary for an optimization-focused research in either FE or OM. The same goes for QS in OM. Please note that both TS and QS are useful for practice and you should eventually know them if you want to be successful in these fields. (25 Dec '15, 15:53) Ehsan ♦ @Ehsan: thanks a lot! I decided to go ahead with Numerical DEs + DP. Hopefully I won't regret later on. Btw, what is QS? Did you mean "Queuing Theory?" (25 Dec '15, 23:53) ghjk 1 I meant queueing theory, but I mistyped. QS stands for Queueing Systems, which was the name of a similar course I took when I was a graduate student. Sorry for the confusion. Good luck. (26 Dec '15, 07:55) Ehsan ♦
 0 Nobody minds giving me some advice on which course to take? It's quite a hard choice to choose between Complex Analysis, Regression and Time series, and Integer programming. Anyone has experienced this situation (professors @Andy, @Matthew, @Mark, @Michael, may you please give your thoughts here?) A little bit more about my previous courses in Math and OR: I took Advanced Linear Algebra, Fourier Analysis, Linear Analysis, Nonlinear Functional Analysis, Numerical Analysis, PDE + ODE, Topology, Linear & Nonlinear Programming, and received A/A+ in all of them. Hopefully this information is somewhat helpful to you. answered 19 Dec '15, 16:34 ghjk 63●6 accept rate: 0%
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Asked: 18 Dec '15, 03:42

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Last updated: 26 Dec '15, 07:55

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