Category theory for scientists

David Spivak

Research Scientist
Department of Mathematics
MIT

Office: 2-230
Email: dspivak--math/mit/edu

18-S996,  Spring 2013:
Category theory for scientists

General information

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.


Homework

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 dateReadingTo turn in
1.Feb 13Read Intro through 2.2. All exercises in sections 2.1, 2.2. (10 total).
2.Feb 19Read 2.3 through 2.5.Sections 2.3, 2.4, 2.5, your choice of four exercises in each section (12 total).
3.Feb 25Read 2.6 through 3.1.Sections 2.6, 2.7, 3.1, your choice of four exercises in each section (12 total).
4.Mar 6Read 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 13Read 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 20Read 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 3Read 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 12Read 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 22Read 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 26Read 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 1Read 5.3. Section 5.3: your choice of three exercises. (3 total).
Finish up your final project.
12.May 13Read 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.


Perhaps also of interest

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.


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