PROMYS Minicourse: Triternions? [2019-07-30]
We have complex numbers being two dimensional over \(\mathbb{R}\). You might have also heard of quaternions. Why are there no tri-ternions? This article is a mostly self-contained survey. This is a talk given at PROMYS, a high school level summer math program.
Tiling with Unfolded Cubes [2018-02-22]
You unfold a cube into 6 connected squares by cutting along its edges. Can you tile the plane with tiles of that shape?
Intro to Pseudorandomness [2020-07-26]
Applications of randomness; motivations for pseudorandomness; a usable definition.
Sublinear Time Algorithms [2020-07-21]
Several notions of efficient algorithms; motivations of sublinear time algorithms; examples of sublinear property tester (list monotonicity, homomorphism).
When is P=NP? [2020-07-19]
Introduction to time complexity of algorithms; P vs NP and related open problems; finite state automata and Turing machine.
\(\mathbb{Z}\) is the Initial Object in the Category of Rings [2020-07-17]
Last year, one of my student at PROMYS proposed a description of \(\mathbb{Z}\) as the ring with a unique ring homomorphism to every other ring. We start with our intuition with \(\mathbb{Z}\) and morph it into categorical language. [full.tex has \pause]
Chip-firing Games [2020-07-16]
We analyze Spencer's original chip-firing game on a one dimensional line and touches on the more general game. The bulk of the talk come from Anne Kelley's paper. Corry and Perkinson has an introduction on this subject.
Fun Objects in Analysis [2020-07-13]
This talk goes over a few notions of small sets and discuss some functions that behaves unexpectedly even if it is only "bad" on a small set. This talk is inspired by Gelbaum and Olmsted's book Counterexamples in Analysis.
How to Catch a Frisbee [2020-07-10]
We discuss how to catch a point-like Frisbee in 2D space in reminiscing of the Friday evening games in Ross/Ohio. I learned this from a lecture at MathILy in summer 2014. To read more, look up the "lion and man" problem.
Slaying Hydras - The Arithmetic of Infinities [2020-07-06]
Cut off a head of a hydra, and \(n\) copies of the injured branch grow back at the grandparent node - it may be counterintuitive that you can always kill it. I learned this from Vivian Kuperberg's math club talk on Oct 17, 2016.
Ross: Equidistribution Review Session W/ James Leng.
Session 1 [2020-07-01] - Riemann/Lebesgue measure (James) and polynomial version of Weierstrass Approximation Thm.
Session 2 [2020-07-05] - Weierstrass Approximation Thm w/ trig; concept of metric spaces, point-set topology, Cantor set.
Session 3 [2020-07-08] - Measure 0, Cantor set (Hausdorff dimension).
Session 5 [2020-07-15] - The \(n\) dimensional torus \(\mathbb{R}^n/\mathbb{Z}^n\); every dense sequence in \([0,1]\) has a U.D. rearrangement.
Session 6 [2020-07-18] - Measure 0, (un)countable, Monotone and Dominated Convergence theorem for Riemann and Lebesgue integrals, \(L^1\) and \(L^2\) norm, \(L^2(\mathbb{T})\) as a Hilbert space.
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Last modified 2020-07-05 by Jiazhen Tan
Cornell '20
Math Club | MSC
Email: jt699 cornell edu, but insert @ and .