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Applied Mathematics: course recommandation?

Hi guys, long lurker here, first actual post! I'm currently in the first semester of my Applied math masters programs, and I'm having a hard time choosing my next courses. My background is a Math major with Actuarial science minor, so I did a lot of probability/stats, but also did all the typical bachelor math stuff such as Real Analysis. My goal is to work as a Quantitative researcher, preferably in HFT.

So as for now I only took two courses in my masters:

  • Probability (measure theory based)
  • Univariate Time Series
And I am looking to take those courses for my next semesters, all courses are from the math department unless it's stated otherwise:

  • Stochastic calculus
  • [COMP SCI] Dynamic programming/Mathematical programming (which one to choose?)
  • [COMP SCI] Fundamentals of Machine Learning
  • Geometrical Data Analysis (half of the course is about Topological Data Analysis)
  • Scientific computing (numerical analysis)
  • Dynamical Systems
  • Advanced Statistical Inference Methods
Some courses that seemed interesting but will need to replace one of the above list, though I could maybe add one course at most:

  • [COMP SCI] Probabilistic Graphical Models
  • [COMP SCI] Advanced Structured Prediction and Optimization (PGMs would be a prerequisite)
  • Combinatorics (advanced Graph Theory)
  • Numerical methods for PDEs
  • Algebraic Topology
  • Groups Theory
  • Lie Group Theory
  • [COMP SCI] Cryptography
  • [COMP SCI] Introduction to Quantum computing
  • [COMP SCI] Deep Learning: Advanced Topics
Am I missing any fields that would be necessary for working in the HFT field? From what I gathered online (here notably), HFT does not really rely on the classical mathematical finance theory that is based more on probability and stochastic calculus. I still think they're necessary, but I believe that I should not develop an edge on those subjects and maybe focus more on Numerical Analysis/ML/Statistical inference. It also seems to me that HFT is a lot about networks, so Graph Theory/Cryptography would be useful.

Feel free to ask for more details about any courses! Thanks in advance for any help you could provide!
 
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Geometric Data Analysis, Fundamentals of ML, Adv. Statistical Inference, Probabilistic Graphical Models, Adv. Structured Prediction and Optimization, Deep Learning: Adv. Topics are what I would look more into. Assuming you're relatively strong with your undergrad real analysis, linear algebra, and measure-theoretic probability, you can self-study stochastic calculus, dynamical systems, and mathematical programming. As you alluded to, if you want to work in HFT, you don't really need courses like numerical methods for PDEs or even stochastic calculus. Combinatorics, Algebraic Topology, Group Theory, Lie Groups ... not useful for you imo -- advanced graph theory can mean different things depending on whom it comes from; personally, I think PGMs would be a more useful, resume-enhancing, course. I'd look into whether you can take a course in NLP as well.
 
Geometric Data Analysis, Fundamentals of ML, Adv. Statistical Inference, Probabilistic Graphical Models, Adv. Structured Prediction and Optimization, Deep Learning: Adv. Topics are what I would look more into. Assuming you're relatively strong with your undergrad real analysis, linear algebra, and measure-theoretic probability, you can self-study stochastic calculus, dynamical systems, and mathematical programming. As you alluded to, if you want to work in HFT, you don't really need courses like numerical methods for PDEs or even stochastic calculus. Combinatorics, Algebraic Topology, Group Theory, Lie Groups ... not useful for you imo -- advanced graph theory can mean different things depending on whom it comes from; personally, I think PGMs would be a more useful, resume-enhancing, course. I'd look into whether you can take a course in NLP as well.

Thanks for the input, much appreciated. So basically you're suggesting that a computational machine learning profile would be more appropriated for HFT and/or Quant research positions? What's your take on Numerical Analysis ("scientific computing" to use my course's title)? Also, even though your answer is very clear -thanks a lot- I'm curious about what you think of Dynamical Dynamic programming?
At first it seemed to me like an essential, from my undergrad derivative class I learned it's for example used to price american options, but from reading on forums it seems it's only used to answer leetcode-type questions in interviews and not much used in research positions. I'm aware one has to be more nuanced, but considering the list I have to choose from I guess it would be in the bottom positions?
 
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By and large, absolutely. Though not strictly pertinent to HFT, and slightly dated (2017), this page gives some good high-level details on what skills are important for modern quant research: Quantitative Researcher - Citadel . Numerical analysis is definitely good as well, though my opinion of whether you should take it depends on the number of elective courses you can squeeze. I'd put numerical behind the ML/advanced stats courses, only because I feel it would be an easier subject to learn on your own given your background + less eye-popping. I'm not sure what dynamical programming entails. Perhaps it is dynamic programming, which I know very little about from cs friends in undergrad. I'm sure some other people here can give more detail on this.

I didn't mean to disparage stochastic calculus, it is certainly essential; however, one standalone course in stochastic calculus has considerably less value than adding another ML/advanced stats to your locker (if you only have 3-5 elective courses, you want to make the most of them by making sure each enhances the value of one or more of the others). Here's a great book showing some elementary applications of stochastic calculus + calc of variations (optimization of functions defined on function spaces) to market making and HFT: The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making . Even though the industry has certainly shifted to embrace data science, I like to think books like this are still useful for the idea generation phase of quant research.
 
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By and large, absolutely. Though not strictly pertinent to HFT, and slightly dated (2017), this page gives some good high-level details on what skills are important for modern quant research: Quantitative Researcher - Citadel . Numerical analysis is definitely good as well, though my opinion of whether you should take it depends on the number of elective courses you can squeeze. I'd put numerical behind the ML/advanced stats courses, only because I feel it would be an easier subject to learn on your own given your background + less eye-popping. I'm not sure what dynamical programming entails. Perhaps it is dynamic programming, which I know very little about from cs friends in undergrad. I'm sure some other people here can give more detail on this.

I didn't mean to disparage stochastic calculus, it is certainly essential; however, one standalone course in stochastic calculus has considerably less value than adding another ML/advanced stats to your locker (if you only have 3-5 elective courses, you want to make the most of them by making sure each enhances the value of one or more of the others). Here's a great book showing some elementary applications of stochastic calculus + calc of variations (optimization of functions defined on function spaces) to market making and HFT: The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making . Even though the industry has certainly shifted to embrace data science, I like to think books like this are still useful for the idea generation phase of quant research.

Thanks again for the input and the references, much appreciated! I will look into this and add the Market Liquidity book on my list. And yes I meant Dynamic Programming -edited this on my posts.
 
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