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Mathematics

4 min read

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

  1. SV Calc
  2. MV Calc
  3. Linear Algebra
  4. Algebra I, Algebra II
  5. Real Analysis, Analysis, Real Analysis: 18-100C
  6. Calculus with theory, DiffEq, Analysis II
  7. Lie Groups and Lie Algebra I, Lie Groups and Lie Algebra II
  8. Topology
  9. Algebraic topology I, Algebraic topology II
  10. Fourier Analysis
  11. Differential Analysis I, Differential Analysis II
  12. Probability and Random Variables, Probabilistic Systems Analysis and Applied Probability
  13. Introduction to Stochastic Processes

Calculus & Real Analysis

  1. Linear Algebra, Precalculus, Trignometry
  2. Stewart, Calculus or any Calculus I, II lecture and PS and Spivak, Calculus: Intro to real analysis
  3. Apostol, Calculus Vol. II
  4. Abbot, Understanding Analysis or Pugh, Mathematical Analysis
  5. Measure Theory:
  6. Functional & Convex Analysis
  7. Fourier Analysis
  8. ODE/PDE

Prob & Stats & StochProc

  1. PreReq: LA, Calc, RA
  2. Probability: Blitzstein & Hwang or Bertsekas & Tsitsiklis or Ross First course in probability or MIT 18.05 and MIT 18.440
  3. Statistics: Wasserman (All of Statistics)
  4. Processes: Grimmett and D. R. Stirzaker or Durrett (Essentials of Stochastic Processes) or Ross, Stochastic Processes or MIT 18.175
    1. Syllabus | Fundamentals of Probability | Electrical Engineering and Computer Science | MIT OpenCourseWare
  5. HD probability: Vershynin, Wainwright
  6. Learning theory: Mohri et al. or Shalev-Shwartz & Ben-David
  7. Optimization: Boyd & Vandenberghe
  8. Info theory (optional but great): Cover & Thomas

Courses

  • 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
  • Probability and Statistics and Distributions and Random processes
  • 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:

syllabus

Graph View

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