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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.
 
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.
where are courses like numerical methods for PDE used in quant?
 
i am going to be studying the math aspect of these topics once i start an ms applied math degree this fall. however, i have only a little bit of experience in python and none in c++. how can i reach the level that is needed to take your online courses
Mostly PDE/FDM pricing libraries in C++ for speed and versatility.
I give all these online courses.
 

Daniel Duffy

C++ author, trainer
i am going to be studying the math aspect of these topics once i start an ms applied math degree this fall. however, i have only a little bit of experience in python and none in c++. how can i reach the level that is needed to take your online courses
The Quantnet C++ course assumes no prior knowledge of C++, A wise decision was to do a couple C modules. In fact, quite a few students had never programmed before.

 

Daniel Duffy

C++ author, trainer
I tried it out. while i understood the video lectures, i found the homework problems too hard to solve
Did you try programming them or just reading?

The point is you get support from TAs which cannot be encapsulated in a book. Hands-on is what matters.

Like learning martial arts, you need trainer.
 
yes i did. it felt like too much of a leap from the lectures for me and i didnt get very far

is there a more gradual approach i can take and then join the course?
Much of the early-on material is ad-hoc -- they are meant to force one to think about the basic syntax. The lectures cover the concepts but the trivial syntax (i.e. how to use printf) is meant to explore and implement independently. Levels 1&2 are a lot of information, with loose connection between the concepts. It is normal to struggle a bit through the exercises; it is kind of like working out a muscle that one has never used before. This is where the course forum is extremely useful -- there is a wealth of information there from our many previous students who faced similar struggles early on. Plus, you are always able to post your own questions/confusions on the forums where TAs or other students help guide you through. Once you submit your code, TAs provide you with very detailed feedback.

Levels 3+ start to become more pedagogic and things should start to click into place -- the material becomes a lot more intuitive and applicable, and by that time your new 'muscles' have started to gain some definition.
 
okay... i will give it another shot. thank you.
also,
I am going to start my MS applied math degree in fall 2021
Is my degree a disadvantage for quant roles?
I do not know what kind of quant role i want to be in.. can anyone suggest which courses i should focus on during my degree?
 

Daniel Duffy

C++ author, trainer
At the end of the day, programming entails 2-3 fundamental activities

1. Variables
2. Functions

3. Creating algorithms that use 1 and 2. Maybe C is too rough just yet, but a good way might be VBA in Excel.

file:///C:/Users/DATASI~1/AppData/Local/Temp/VBAPrimer.pdf

Nice thing about Excel is input-output is easy and useful.

just an idea.

I know the problem; how to get a handle on 1 and 2 without getting bogged down in nasty syntax, at least not just yet.

As APalley said, getting them muscles going is part of the game: no pain, no gain.
 
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