I recently applied for and was accepted to WorldQuant University’s Master of Science in Financial Engineering (MScFE) program! So far I’m enjoying the experience and the online courses fit my lifestyle perfectly.

With some of the math heavy courses coming up I have been reflecting on the entrance exam, their Quantitative Proficiency Test. I found this test extremely hard to study for. First, I graduate almost 6 years ago, and this sort of math is not a part of my everyday work. Second, the topic list is extensive and fails to provide any details on how deep into each subject one should go. The Official Guidance:

“The Mathematics section comprises 20 questions, covering differential calculus, integral calculus, matrices and linear algebra, set theory, differential equations, complex numbers, sequences and series, logic and proofs, multivariate calculus, convergence of sequences and functions, and partial differential equations.
The Statistics section comprises 20 questions, covering exploratory data analysis, elementary probability, univariate random variables, bi-variate random variables, generating functions, statistical estimation theory, hypothesis testing and confidence intervals, and simple linear regression.”

WQU 2019

I figured I would share how I studied and hopefully this will give you a starting point.

I wanted to get a high-level overview and inspired so I started by watching and taking notes of the “Essence” series on YouTube by 3Blue1Brown.
Essence of Calculus
Essence of Linear Algebra
These two series are incredibly well put together, I found them genuinely entertaining, and a great place to start. NO these will not replace doing actual problems.

My next stop was practice problems and I turned to Khan Academy. Khan Academy seems to offer problems up to a first year of undergraduate university level or so. What I like about Khan Academy is that you can work through problems quickly, if you get stuck they have worked solutions, and they offer quizzes to test where you are. For me this meant that I could quickly hone in on specific areas I was weak on and cover these topics before getting into more difficult problems.
For each of the subjects linked here you can do the Course Challenge at the bottom. When you pass it you are ready to move on.
Differential Calculus
Integral Calculus
Multivariate Calculus
Linear Algebra
Differential Equations
Statistics and Probability

At this point I would say you are mostly ready to go. You’ve covered most of the topics and techniques you will need to know to do okay on the test.
BUT the test questions are certainly a level-harder than what I was seeing on Khan Academy. So at this point I would recommend heading over to MIT’s OpenCourseWare.
Here the topic list pretty much follows the same outline as that for Khan Academy, but the problem sets are much harder. If you have all the basics covered from Khan Academy you can do the mid-terms and exams from MIT right away. Then determine which lectures you need to review to get you through the more difficult problems.
Single Variable Calculus
Multivariable Calculus
Linear Algebra
Differential Equations
Introduction to Probability and Statistics
Probabilistic Systems Analysis and Applied Probability

Full Disclosure :
I gave myself two full weeks to review these topics and that was barely enough time for me. I was truly only able to get through all the Khan Academy material and was in the process of doing mid-terms and going deeper on each of the MIT courses when I wrote the test.
The exam I wrote (I assume they draw from a random bank of questions) had one question on differential equations, so the fact that I hadn’t gotten there yet wasn’t too bad.
Also, half the test is on statistics and probability, so logically you should spend half your study time on those topics if possible.

Hope this helps you get studying!