How to best prepare for MFE?

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I finished a MS in pure math in 2022 and will be attending a MFE program this September. I'm a bit lost on how to best prepare over the next 6 months. Am I better served solidifying math fundamentals like stochastic processes and measure theory (topics I don't know very well) or am I better off diving right into a book on options (eg. Hull) and working through it in parallel to focus on coding/implementation? More generally should I focus more on theory or practice? I keep being told my math background is "good" but looking at the curriculum it kinda feels not good enough (stochastic calculus is most intimidating). I don't know if this feeling is warranted or imposter syndrome.

Here is my program's curriculum (research paper option).
 
Here are the elective course recommendations provided by my mentor:

1. Mathematics:
- Compulsory Courses: Linear Algebra, Calculus, Ordinary Differential Equations.
- Recommended Elective Courses: Stochastic Processes (particularly crucial for roles in sales, covering Ito's Lemma, martingales, stochastic integrals, Brownian motion, etc.), Stochastic Analysis (stochastic calculus), Numerical Analysis (scientific computing). Additionally, if time permits, consider courses in Real Analysis, Functional Analysis, and Measure Theory. Bonus courses could include Partial Differential Equations, Convex Optimization, Complex Analysis, and Topology.

2. Statistics:
- Compulsory Courses: Probability Theory and Mathematical Statistics.
- Recommended Elective Courses: Opt for courses related to financial statistics or those with titles involving linear regression, time series analysis, or econometrics.

3. Computer Science:
Learn an object-oriented programming language such as C++ and a procedural programming language like Python. Also, delve into Data Structures and Algorithms. Consider elective courses in Artificial Intelligence, Machine Learning, and Deep Learning.

4. Finance:
Explore relevant subjects like Financial Mathematics/Engineering, Financial Derivatives, Monetary Banking (Principles of Finance/Money and Banking), Investment Management, Fixed Income Securities, and Option Pricing.

Please note that I am a third-year undergraduate student and may not be familiar with the specific admission requirements for the MFE program you are considering. This is merely a reference and I hope it proves helpful to you!
 
1. Stochastic process and probability -> u need it for interviews. Super impt since apps start the moment u reach lol. Good revision nonetheless
2. John C Hull’s bible of options -> learn to discuss BS model
3. Programming too in Python

Depends on where you want but HFT loves probability and brain teasers
 
1. Stochastic process and probability -> u need it for interviews. Super impt since apps start the moment u reach lol. Good revision nonetheless
2. John C Hull’s bible of options -> learn to discuss BS model
3. Programming too in Python

Depends on where you want but HFT loves probability and brain teasers
Thank you for the insightful suggestions! I appreciate the guidance on key areas for interviews.
 
1. Stochastic process and probability -> u need it for interviews. Super impt since apps start the moment u reach lol. Good revision nonetheless
2. John C Hull’s bible of options -> learn to discuss BS model
3. Programming too in Python

Depends on where you want but HFT loves probability and brain teasers
You'l only have a summer, so don't do much of Hull other than being able to draw simple option payoffs to recreate more complex positions and then maybe cram in a bunch of BS model knowledge. Otherwise, start learning to code very well. Stochastic processes I agree with as well.
 
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