**Education and popular science**

- Newton's laws in relativity
- "Calculus-based physics"
- The era of Einstein
- Why are calculus and linear algebra taught early?
- "In space, there's no up or down."
- Applied math and mathematical models (waves, walls, particles, noise, vector spaces)
- Against moral thought experiments and for problem-solving
- 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**

- What even are pure and applied math, anyway?
- Positive vs normative social science
- Why do people conflate philosophy with psychology?
- What does it mean to "lie with statistics" (also: "lying with rationality", etc.)
- Aesop's studies (square smiley face, eyes, etc.)

**Short topics**

- Multiplicative calculus: Probability of immorality for a transhuman being
- Filters and hyperreal numbers: [abhimanyu.io, github 1, github 2]
- Fractional calculus: [arXiv paper 1, arXiv paper 2]
- Generalised determinants: [arXiv paper]
- Fractals

**Special things (functions, numbers, polynomials, sequences, etc.)**

- Gamma, Bessel, Elliptic, Hypergeo, numbers and sequences
- Special polynomials
- Riemann hypothesis related stuff

**Probability puzzles and "paradoxes"**

Also see the actual Statistics courses.

- Why the Monty Hall problem is completely boring
- Born on a Tuesday
- Sex ratio puzzle
- Bertrand's paradox
- Two-envelopes problem: beyond the Bayesian explanation
- Anthropic principle and multiple pathways

**Other interesting math problems**

- Pi and collisions (the 3blue1brown problem)
- A curious infinite sum arising from an elementary geometric argument

**Tricks**

- Using graphs to create images
- Using Fourier series to create images
- Gridded cartograms

**Miscellaneous**

## No comments:

## Post a Comment