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On my pursuit to sharpen my thinking and increase my personal toolkit, I’ll be speedrunning a math degree and figured it would be beneficial to write up the curriculum. The goal for this is to be self-followable so anyone who’s also interested in speedrunning a math degree at their own pace would be able to.


Why not? Well, to be truthful, I wanted to go for a pure math degree when I went to school but, since the university I went to didn’t offer a program for it, I opted for computer science. Ended up staying a semester before figuring it’d be better to grow through five years in the industry than five years scrambling for a diploma so here I am now.


For this, I will be going with MIT’s Applied Math program and their equivalents in OpenCourseWare for the courses that were available (a common misconception is that all courses are listed on OCW but not all of them actually have lectures/notes or other materials to work off of).



This is what the “freshman year” equivalent will be and a place to brush up on prereqs

Description Link
Calc 1 Khanacademy Calc 1
Calc 2 Khanacademy Calc 2
Multivar Calc Khanacademy Multivar Calc

For each of these, there’s a Course Challenge available that you can take to verify your knowledge after completing or take in place of going through the whole session

Summer between Freshman and Sophomore

Things to do to lock down some of that new calc knowledge or just a way to pass by the time

Description Link
Integration Bee https://www.youtube.com/results?search_query=integration+bee

Integration Bees are like spelling bees but for solving an integral with an allotted time against an opponent and a good way to develop some pattern matching for working with non-trivial antiderivatives


These are the first courses that are actually with some nitty gritty math

Course ID Name Links
18.03 Differential Equations Fall 2011
18.04 Complex Variables with Applications 37 Spring 2018
18.06 Linear Algebra Spring 2010
18.200 Principles of Discrete Applied Mathematics Fall 2004
18.300 Principles of Continuum Applied Mathematics Spring 2009, Spring 2006, Spring 2003


These courses deviate from general math requirements in other programs

Course ID Name Links
18.212 Algebraic Combinatorics Spring 2019, Spring 2009
18.410 Introduction to algorithms Fall 2005
18.424 Information Theory Spring 2016
18.600 Probability and random variables Fall 2019


Some fun stuff to finish off the ‘degree’

Course ID Name Links
18.303 Linear partial differential equations Fall 2006
18.330 Introduction to numerical analysis Spring 2004, UCLA Remote Lectures Spring 2020
18.353 Nonlinear dynamics I Fall 2012
18.354 Nonlinear dynamics II Spring 2015


Some additional courses that seemed of interest

Course ID Name Links
(Harvard) Math 122 Abstract Algebra Video Lectures Course Page
18.S097 Applied Category theory January 2019
15.070 Advanced Stochastic Processes Fall 2013


One of the pitfalls of a self-studied curriculum is that there isn’t a way to verify the learning of some material so, as a solution to this, I’ve devised a shortlist of project ideas that would be fun to work on. Not all of these are immediate applications to the materials in the degree but seem interesting nonetheless