I'm bad at mathematics.
For all the years before my senior year in college, I feared mathematics, struggled with mathematics, and was anxious about all kinds of mathematical tests. Ironically, my program in college was half math and half computer, so I was forced to study many mathematical subjects. Even more ironically, after being forced to study such much mathematics, in the last year of college (2006), the year I was about to finish my student life, I suddenly started to like mathematics, but I didn't have much time to learn it.
For almost 20 years after graduating from college (I was writing this README file in 2023), I didn't have the courage to pick up mathematics again. But as years passed by, I gradually realized that re-learning mathematics is one of the achievements I want make before I die. I don't want to be "just drifting through the sea of life" (Save Me by Hanson). I want to build my life on top of a solid foundation.
The purpose of re-learning is twofold:
- 80% for personal interest.
- 20% for building a solid foundation for my career as a software developer.
This repository thus serves two purposes as well:
- I use it to track my progress of learning.
- I use it to put my learning notes.
For now (2023), I want to learn the following subjects:
- Foundations
- This part includes several subjects such as:
- Set theory
- Proof systems
- Propositional logic
- Graph theory
- Finite automata
- Turing machine
- Complexity theory
- This part includes several subjects such as:
- Linear algebra
- Real mathematical analysis
- Side note: I could have just learned calculus but I feel mathematical analysis is more appealing to me.
- Probability and statistics
As I was learning linear algebra and real analysis, I gradually realize I needed to refresh my memory on these fundamental subjects, too. I had learned various such subjects when I was in middle school, high school, or college, but that was two or three decades ago.
I'm primrily using all kinds of online resources to (re)learn the fundamental subjects:
As of 2023, I'm learning Linear Algebra Done Right. The notes (including exercises) are in the sub-directory Linear-Algebra-Done-Right.
While I'm learning linear algebra by reading a textbook, for real mathematical analysis I want to try a different approach: taking an open course online. I'm currently following the MIT 18.100A Real Analysis. The notes (including exercises) are in the sub-directory Real-Analysis-MIT-18100A.
(TODO)
- Open Logic Project: "The Open Logic Project is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments."
- GitHub link: OpenLogicProject/OpenLogic
- The built PDF documents for download: Open Logic Project Builds
- Math3ma: A math blog.
- Logic and Proof: Both this online textbook and the Lean theorem prover are new and ongoing projects.
- The PDF version is here.
- Theorem Proving in Lean
See LICENSE.