# Archive

Sorted by categories. Here’s the archive page sorted by tags or by date.

## Research

## Maths

- A circle and a hyperbola living in one plot
- Taylor series raised to a power
- Alternate notation for topology
- The Gudermannian
- A physical interepertation of trigonometric substitution
- Using matrices to understand polynomials
- Visualising bifurications
- Visualising linear dynamical systems directly
- Visualising invertibility and diagonalisability of matrices
- Partial derivatives of the radius
- Understanding the hyperbolic plane with refraction
- Understanding potential wells
- Understanding Green's theorem
- Another visualization of the second fundamental theorem of calculus
- Calculus of inverse functions: Inverse function theorem and the Legendre transformation (Part I)
- Graph sketching techniques
- Generalising function plots to topological spaces
- Pedagogically weaker notions of continuity
- Constructing homotopies using gravity
- Geometry of curves and projectile motion
- Euclidean algorithm and GL(2, Z)
- Understanding the dual space
- Understanding linear fractional transformations
- Understanding the Jordan Normal Form
- Visualising composition series
- Visualising the group isomorphism theorems
- Three ways of thinking about matrix multiplication
- Levi-Civita Symbol (Part II)
- Structures closed under unions
- Levi-Civita Symbol (Part I)
- Structures closed under intersections
- Extending sequences into smooth functions using trignometric functions
- Interiors, closures and boundaries of topological spaces
- Compilation of miscellaneous ideas
- HKDSE Physics and M2 (Part III)
- HKDSE Physics and M2 (Part II)
- HKDSE Physics and M2 (Part I)
- Euler's formula and compound angle formulae
- Showing preservation of properties under multiplication via difference of squares
- Another example of pointwise but not uniform convergence

## Tools

## Non-Technical Maths

- Introduction to symmetries and its applications
- Playing with the real projective plane
- LEON Discounts

## Tech

- Stock Game
- Font sizes from 4px to 99.9px
- Calculator Programming
- Effort vs Quality
- Using Zoom / Google Meet with OBS

## Career

- Opportunities learning maths beyond the syllabus in HK
- Tackling Oxford Mathematics Interviews (Undergraduate)
- Making a mathematics personal statement personal
- Tackling the Oxford MAT
- Choosing a college at Oxford (Undergraduate)
- Applying to Oxford Mathematics (Undergraduate)

## Life

- Third Easter in Oxford
- Eighth Term at Oxford
- Third Christmas in Oxford
- Seventh Term at Oxford
- Second Summer in Oxford
- Second Year at Oxford
- Second Easter in Oxford
- Fifth Term at Oxford
- Second Christmas in Oxford
- DIY Pin Board of Tools and More
- Fourth Term at Oxford
- First Summer in Oxford
- First Year at Oxford
- Second Term at Oxford
- First Term at Oxford

## Personal

## Reviews

- From Immigrant to Inventor - Mihajlo Pupin
- A Brighter Summer Day
- Perfect Days
- The Creative Act - Rick Rubin
- Networking to network - Phil Agre
- I Want to be a Mathematician - Paul Halmos
- The Art of Doing Science and Engineering - Richard Hamming