Blog

Education and popular science
  1. Newton's laws in relativity
  2. "Calculus-based physics"
  3. The era of Einstein
  4. Why are calculus and linear algebra taught early?
  5. "In space, there's no up or down."
  6. Applied math and mathematical models (waves, walls, particles, noise, vector spaces) 
  7. Against moral thought experiments and for problem-solving
  8. Tips on learning and thinking (making connections, e.g. changing discrete to continuous; geometric interpretations -- sum of things invariant ==> ellipse, pythagorean invariant ==> like spacetime; find vector spaces in everything -- and find other things in everything) ... used to come up with various heuristics like "you need to write/teach what you learn", "you need to make connections", "you need to play with it", "you need to have a geometrical interpretation", "you need to skim through and fill in the gaps for yourself/discover for yourself" ... but fundamental points of learning are: honesty, having a mental framework, abstraction, original/creative thinking ("asking questions", experimenting, trying to fit various frameworks onto it, etc.) ... and on a more "human" note, confidence, figuring out what to emphasize.
Academia and sociology of science
  1. What even are pure and applied math, anyway?
  2. Positive vs normative social science
  3. Why do people conflate philosophy with psychology?
  4. What does it mean to "lie with statistics" (also: "lying with rationality", etc.)  
  5. Aesop's studies (square smiley face, eyes, etc.)
Short topics
  1. Multiplicative calculus: Probability of immorality for a transhuman being
  2. Filters and hyperreal numbers: [abhimanyu.iogithub 1, github 2]
  3. Fractional calculus: [arXiv paper 1, arXiv paper 2]
  4. Generalised determinants: [arXiv paper]
  5. Fractals
Special things (functions, numbers, polynomials, sequences, etc.)
  1. Gamma, Bessel, Elliptic, Hypergeo, numbers and sequences
  2. Special polynomials
  3. Riemann hypothesis related stuff
Probability puzzles and "paradoxes"
Also see the actual Statistics courses.
  1. Why the Monty Hall problem is completely boring
  2. Born on a Tuesday
  3. Sex ratio puzzle
  4. Bertrand's paradox
  5. Two-envelopes problem: beyond the Bayesian explanation
  6. Anthropic principle and multiple pathways
Other interesting math problems
  1. Pi and collisions (the 3blue1brown problem)
  2. A curious infinite sum arising from an elementary geometric argument
Tricks
  1. Using graphs to create images 
  2. Using Fourier series to create images
  3. Gridded cartograms
Miscellaneous

No comments:

Post a Comment