Department of Mathematics

MIT

Email: dspivak--math/mit/edu

Category theory for scientists

Units: | 12 |

Room: | 2-131 |

Meeting times: | MWF 10am -- 11 |

First class: | Wednesday, February 6 |

Workload: | Weekly homework and a final project. |

Syllabus. | Includes basic information about what students can expect from the course and what I expect from students. |

Book. "Category theory for scientists" |
This static
version will remain constant once the semester starts.
(Dynamic
version.) Here is a sample .tex file and its .pdf output, in case you want to emulate the diagrams, etc. from the book, which was written using LaTeX. |

Google doc. | Any typos, comments, or suggestions about the book should be recorded here. |

History and plan. | See what we've covered and what we plan to cover. |

Student submissions. | See what other students have contributed. |

All homework will assume numbering to come from the static version of the book. If you prefer to work from the dynamic version, please summarize the problem before giving your solution. |

# | Due date | Reading | To turn in |
---|---|---|---|

1. | Feb 13 | Read Intro through 2.2. | All exercises in sections 2.1, 2.2. (10 total). |

2. | Feb 19 | Read 2.3 through 2.5. | Sections 2.3, 2.4, 2.5, your choice of four exercises in each section (12 total). |

3. | Feb 25 | Read 2.6 through 3.1. | Sections 2.6, 2.7, 3.1, your choice of four exercises in each section (12 total). |

4. | Mar 6 | Read 3.2 through 3.4. | Sections 3.2 (dynamic), 3.3, 3.4, your choice of four exercises in each section (12 total). |

5. | Mar 13 | Read 3.5 through 4.1. | Section 3.5: your choice of 4 problems; Section 4.1: your choice of 8 problems (12 total). |

6. | Mar 20 | Read 4.2. | Section 4.1, after 4.1.2.24: your choice of 4 problems. Section 4.2: your choice of 8 problems. (12 total). |

7. | Apr 3 | Read 4.3 through 4.5.1. | Sections 4.3, 4.4, 4.5.1: your choice of four exercises in each.(12 total). |

8. | Apr 12 | Read 4.5. Literature review: find past work on your proposed topic. | Sections 4.5.2, 4.5.3: your choice of four
exercises in
each. (8 total). Begin research on your final project. |

9. | Apr 22 | Read 4.6.1 through 5.1.3. | Sections 4.6, 5.1 (up through 5.1.3): your choice of
three
exercises in
each. (6 total). Make progress on your final project. |

10. | Apr 26 | Read 5.1.4 through 5.2. | Sections 5.1.4, 5.2: your choice of
three
exercises in
each. (6 total). Make progress on your final project. |

11. | May 1 | Read 5.3. | Section 5.3: your choice of
three exercises. (3 total). Finish up your final project. |

12. | May 13 | Read 5.4. | Section 5.4: your choice of
two exercises. Also, summarize your experience in this class. (2 total +
summary). |

13. | May 16 | (None.) | Written projects due by midnight. |

Weinstein
article: (1996) "Groupoids: unifying internal and external symmetry". |
In this short tour, mathematician Alan Weinstein discusses groupoids in terms of the tiling pattern on a bathroom floor. |

Gromov article: (2012) "In a search for a structure, Part 1: On Entropy". | In this talk, physicist Misha Gromov explains that category theory is the appropriate language for describing entropy. (Also available on Gromov's website.) By the end of this course, students will be able to understand the mathematics herein. |

Baez, Stay: (2009) Physics, topology, logic, and computation: a rosetta stone". |
The title pretty much says it all. The authors use monoidal categories to discuss important phenomena in each of these four fields, such as Feynman diagrams, cobordisms, and the lambda calculus. |

This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.