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?

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.

## How?

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).

## Syllabus

### Prelimary

#### 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

### Sophomore

#### 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 |

### Junior

#### 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 |

### Senior

#### 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 |

### Post-Senior

#### 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 |

## Projects

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

- Build/train a NN to learn XOR (as a simple introductory project to start on ML)
- Find a paper on some ML model and implement from scratch (ie node2vec)
- Contribute to a theorem prover (ie Lean)
- Using JS/WASM for in-browser privacy preserving machine learning
- Read a Twitter account to get insights on type of content etc
- As a platform, Twitter is becoming a place where people find connections/jobs so it would be nice to be able to get a breakdown of an account like you can get a breakdown of an individual on LinkedIn

- Comma.ai’s speed challenge
- Re-implementing something built by OpenAI