The user provided a lengthy transcript that appears to be a detailed account of their undergraduate math courses. The summary of the provided text is as follows:
The user reflected on their undergraduate math degree and the question of what comes after calculus. They then proceeded to give a brief summary of 22 math courses they took during their undergraduate studies. These courses covered a wide range of topics, including linear algebra, mathematical structures, differential forms, real analysis, abstract algebra, ordinary differential equations, introduction to mathematical structures, complex analysis, number theory, probability, advanced linear algebra, and various independent research projects. They delved into each course's content and their experiences with them, including challenging aspects and highlights.
Please let me know if you would like more specific information about any of these courses or have any other questions.
Here are the key facts extracted from the text:
1. The author reflected on their math degree for a couple of months.
2. They self-studied multivariable calculus.
3. They planned to take 27 math courses, but five were cut due to a family situation.
4. Linear algebra was their first math course in undergrad.
5. They covered matrix operations, linear transformations, and more in linear algebra.
6. They took a course on proof methods and logic, including topics like tautologies and cardinality.
7. Differential forms and vector calculus were part of their coursework.
8. They studied real analysis, focusing on the rigor of calculus.
9. The author learned Euclid's elements in the original Greek.
10. They took a course on abstract algebra, covering groups, rings, and fields.
11. Ordinary differential equations covered harmonic oscillators.
12. Introduction to mathematical structures involved proofs and logic.
13. They learned about complex analysis, including conformal mapping.
14. Number theory included topics like modular arithmetic and the Chinese remainder theorem.
15. Advanced linear algebra focused on vector spaces and abstract concepts.
16. Probability covered combinatorial probability and coding in R.
17. The author's senior comprehensive project focused on topological entropy.
18. They did independent research on one-dimensional symbolic dynamics and substitutions.
These are the key factual points without opinions or additional commentary from the author.