https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-3 In the first and second articles in the series we looked at the courses that are taken in the first half of a four-year undergraduate mathematics degree - and how to learn these modules on your own. In the first year we discussed the basics - Linear Algebra, Ordinary Differential Equations, Real Analysis and Probability. In the second year we built on those basics, studying Metric Spaces, the Riemann Integral, Group Theory and calculus on Vector Spaces. In the third year of a four-year masters-level course, especially one with an applied focus that will be of interest to quants, we need to begin thinking about more abstract concepts that will prepare us for study of Stochastic Calculus, Probabilistic Machine Learning and Bayesian Econometrics. With that in mind it is essential that we study topics such as Measure Theory and Linear Functional Analysis. ...
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