I haven’t taken any formal education in mathematics and with more experience, I’ve come to realise, it’s the best thing you can do for your brain. Math is beautiful.
Initially, want to complete at least undergraduate level courses.
Improvements
- Write my own notation OR explain concepts formally on my own
- Solve more problems without looking at notes.
- Start making small hypothesis about next chapters/subtopics inside the chapters.
- Active learning than writing notes. Less and less notes from now on.
Syllabus
- Abstract algebra, Group Theory Problems
- Algebra I, Algebra II
- MA 231: Topology, Topology Problems, Topology
- Analysis II
- Introduction To Differential Geometry
- Lie Groups and Lie Algebra I, Lie Groups and Lie Algebra II
- Measure Theory Notes
- Introduction to Functional Analysis | Mathematics | MIT OpenCourseWare, 18.102 Intro to Functional Analysis
- Complex Analysis, Jan 2020
- PDE: Math 4340 (Advanced Engineering Mathematics), Summer II 2023 (online)
- Fourier Analysis
- Probability and Random Signals II: I don’t know many things inside this course, and it’s theory heavy too, going deep into measure theory, sigma-algebra, hilbert spaces.
- Algebraic topology I, Algebraic topology II
- Fourier Analysis
- Differential Analysis I, Differential Analysis II
- ODE
Problems
- real analysis: Problems and solutions: I should be very comfortable with these problems.
- Practice for Math PhD Prelims - TCU
- Darij Grinberg: Mathematical Problem Solving (Math 235), Fall 2020: Initial undergraduate course on problem solving with amazing putnam problem and notes
Courses
- MATH 185 Complex Analysis
- MATH 202A Introduction to Topology and Analysis
- MATH 202B Introduction to Topology and Analysis
- MATH 214 Differential Topology
- MATH 240 Riemannian Geometry
- MATH 250A Groups, Rings, and Fields
- MATH 250B Commutative Algebra
- MATH C218A/STAT C205A Probability Theory
- MATH 256A Algebraic Geometry
- MATH 256B Algebraic Geometry
- STAT 210B Theoretical Statistics
- CS 229A Information Theory and Coding
- EE 227BT Convex Optimization
Meta Learning so far
- Problem solving approach
- What previous axioms/statements/theorems do I need to solve this problem?
- What assumptions do I need to make to start solving?
- What auxiliary statements or assumptions do I need to create that simplify the problem?
- Can I backtrack the assumptions from the result?
- Avoid
- Looking at text many times during problem solving. Better to go back and read properly.
- Not designing the solution to completeness and doing hand-wavy solutions.
- Not analysing unsolvable problems after going through the solution.
- Not performing revision or spaced repetition.
- Examples. Examples that are not mentioned in the resource. Intuition is sometimes built using examples. If you can’t provide an example to 2 concepts from 2 different chapters instantly, you’re lacking understanding of the topic.
Interesting Approaches
- LLM prompt for further investigation into a topic:
can you give me a rabbit hole related to `x` that can allow me to explore something much deeper than it?
Resources:
- Math — Susan Rigetti
- Mathematics for the adventurous self-learner
- Amazing set of notes: Class Notes by Andrew Lin
- How to Become a Pure Mathematician (or Statistician)
- Art of Problem solving
- Math notes
- OSSU math
- MIT syllabus
- Caltech syllabus
- Oxford mathematics hub
- UCL maths modules
- Yale Mathematics major
- How to Learn Math and Physics - John Baez
- Math Major Guide | Warning: Nonstandard advice. - YouTube
- Mathematics Textbooks for Self Study --- A Guide for the Autodidactic
- Suggested Readings by Subject - Mathematics - Research Guides at University of Michigan Library
- Asteroids on a Donut – Infinity Plus One
- Problem Tags - Sachchidanand Prasad