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Office Camera

About the Office Camera

Summary: There is a webcam in my office that I use to take photos of the whiteboard. This setup was inspired by Dror Bar Natan’s Blackboard Shots. [full page]

The Calculus of Heart Sequences: Passing a Loop Through and Returning It

The Calculus of Heart Sequences

Bessel's Inequality

Summary: We check a simple lemma leading up to Bessel’s Inequality. Suppose that ${e_n}$ is an orthonormal system of vectors, with a Hermititan inner product $\left\langle x,y \right\rangle$ inner product. [full page]

The Heart Group as A Subgroup of B_{2n}

Summary: This photo has a sketch of an embedding $\heartsuit_n \leq B_{2n}$. [full page]

Mira Doodles: Part II

Mira Doodles: vvbnm,,.//

Yulong's Braid Word Reduction

From Markov to A Heart Sequence Redux

Summary: For another discussion of this, see: From a Markov Sequence to a Heart Sequence. [full page]

Family Halloween

Paco: Terms from Graphics Programming / Half-Second Star

Yulong's O.A Construction

Alfredo's Opening A

2023-10-16 @ 09:13:37

Yulong's Wrapped L1

From a Markov Sequence to a Heart Sequence

Alexander and Markov's Theorems

D92: Possible Projects

D92: Possible Projects

The Heart Groupoid and String Figures Calculus

Duck and Dog: The Dog's Strategy

Formal Grammar for Linear Sequences and Calculus

Fake Crossings in Knots

Putnam B4 2005

Summary: For positive integers $m$ and $n$, let $f(m, n)$ denote the number of $n$-tuples $(x_1, x_2, \dots , x_n)$ of integers such that $|x_1|+|x_2|+ \cdots +|x_n| \leq m$. [full page]

When to apply for gradschool or jobs?

Juggling State Machine

Dedekind Cuts and Completeness of R

Ideals and Principal Ideals: Are all ideals in Z[x,y] actually principal?

Ideals and Principal Ideals: Are all ideals in Z actually principal?

Ideals and Principal Ideals

How does string figure calculus act on linear sequences?

Summary: I’m working with Eric Vandendriessche and Alfredo Braunstein to understand a bit about how the string figure calculus acts of canonical linear sequences. [full page]

Nim Winning Strategy Lemmas

Nim Playing (4,3,0,1) Part 1

Nim and Nimbers

Canonical Start of A Linear Sequence

Summary: The canonical start of a linear sequence is a point in nearest LFn string. In this simple example, there are three possible linear sequences (with the correct orientation) but only $L2, L5, R1$ has the correct start point. [full page]

To-do list stuff

Mira colours!

Summary: My daughter Mira came in to the office this afternoon and coloured. [full page]

2023-05-05 @ 16:35:41

Adding Nimbers

XOR and Nimbers

Boxes and Spheres in n-Dimensional Space

Zombies vs Humans (via Diagonalization)

Summary: WolframAlpha Calculation [full page]

Lives vs the Universe

Attitude, Skills, Knowledge

CN Tower Stair Climb Times

Diagonalizing Transposition (Part 2)

Diagonalizing Transposition (Part 1)

The Matrix of Transposition

Projections are Never Invertible

Transpose a Matrix

The Smallest Vectors with Integer Entries

Nilpotent Transformations Are Not Invertible

Diagonalize T(p(x)) = (x+1)p'(x) Part 2

Diagonalize T(p(x)) = (x+1)p'(x) Part 1

Diagonalize T(x,y) = (x,x)

Diagonalization and Invertibility

Diagonalization and Powers

Eigenvectors and Linear Independence

Linear System with Prescribed Solution Set

Changing Coords TO the Standard Basis

MathEd vs Math Researcher Career Trajectories

A22 Final Exam Draft

A Quarter of an Annulus

The Idea of a Surface Integral

Square Wave Setup

Dimension of the Space of nxn Skew Matrices

Dimension of the Space of nxn Symmetric Matrices

The Null Space as a Linear System

Finding a System with a Particular Solution Set (Part 2)

Finding a System with a Particular Solution Set (Part 1)

Subspaces / Image / Kernel / Bases (Part 6)

Subspaces / Image / Kernel / Bases (Part 5)

Subspaces / Image / Kernel / Bases (Part 4)

Subspaces / Image / Kernel / Bases (Part 3)

Subspaces / Image / Kernel / Bases (Part 2)

Subspaces / Image / Kernel / Bases (Part 1)

Subspaces and Their Sums (Part 6)

Subspaces and Their Sums (Part 5)

Subspaces and Their Sums (Part 4)

Subspaces and Their Sums (Part 3)

Subspaces and Their Sums (Part 2)

Subspaces and Their Sums (Part 1)

Reading Week A22 Todo

Hello Twitter!

Malhar's Puzzle

Linear Independence Calculation

Dimension Examples

Why do we care about the extension lemma?

The Fastest Intro to Derivatives

Missing a Span: The Details

Hitting and Missing a Span

Visualizing F(R)

sin(x) and cos(x) in the space of functions

MAT A22 Term Test Content (draft)

In Shuffles and Out Shuffles

A System with a Particular Solution Set

Summary: We find a linear system with solution set $\operatorname{Span}({ (1,0,2,3), (0,1,4,5)})$. [full page]

Puzzle: Sum of Reciprocals (continued)

Proof Structure

Puzzle: Sums of Reciprocals

Practice Quiz 1 Q2 : sin(x), sin(2x), sin(3x) : Solving the Linear System

Practice Quiz 1 Q2 : sin(x), sin(2x), sin(3x)

A linearly dependent set

A22: Proofs in A22 (Part 3): A Worked Proof

A22: Proofs in A22 (Part 2)

A22: Proofs in A22 (Part 1)

The (0,2n+1) Puzzle

Rows and Columns in Elimination

Rows and Columns in Elimination

Dihedral calculator: sts

Partial fractions with repeated factor

My friend Hooman

Partial fractions (x^2+4)/(x^2-4) and (2x+1)/(x+4)(x-1)

Does the integral of e^{-x^2} from x=1 to x=infty converge?

Convergence and Divergence

Integration by parts

Area bounded by y=6 - x^2 and y = |x|

Pre-Exam To-Do

Jordan Form and Organization

MAT A29 Exam Coverage

Volume in Conical Tank at t = 5 min

Summary: We find the height of water in a conical tank such that: $$ V = \frac{1}{3} \pi x^3 $$ given that water is flowing in at a rate $dV/dt = 1 m^3 / min$. [full page]

Plan for Final Exam Study

Backup System Flowchart

Summary: This is the current layout of my Backup System. It shows how: archive-servers.sh, offline-backup.sh, and offsite-backup.sh work. The Syncthing and Tailscale connections are not shown for the sake of clarity. [full page]

MAT B41 Exam Coverage (Draft)

A Designer Graph

Summary: The designer graph on the first term test for MAT A29 Winter 2022. [full page]

Paco!

Summary: This is my friend, Paco Estrada. [full page]

Fitch Cheney Ordering

Summary: Raw photo [full page]

Alex Teeter: Manifolds

Summary: This is my friend Alex Teeter, manifold explorer. [full page]

Test of new office-camera

Summary: This is $ \LaTeX $. [full page]

Mira draws!

Optimization Doodles and Dave's Amazing Summation (Redo)

Summary: Dave has an amazing summation: $\displaystyle \sum_{n=1}^\infty \frac{n^{13}}{e^{2\pi n} - 1} = \frac{1}{24}$ Moreover, this is exactly equal to the integral! [full page]

The (Boring) Structured Essay

Taylor Series: The True Formula (Multi-Indices)

Taylor Series B41

Leibniz Notation (Part 6)

Leibniz Notation (Part 5)

Leibniz Notation (Part 4)

Leibniz Notation (Part 3)

Leibniz Notation (Part 2)

Leibniz Notation (Part 1)

Chain and Power Rule

Probability of (Mentally) Choosing a Card

End of Reading Week To-Do

Reading Week Todo

Solving 2/x - 9 greater than 0

Summary: = 0" title="Solving 2/x - 9 >= 0" [full page]

Level Curves of Planes

Composition of sqrt(x) and x+9

Range of x/(x^2-16)

Knots and 3-Manifolds

3b and 4b siteswaps

Tic-Tac-Tree (Induction)

Testing?

Tic-Tac-Tree

2022 / 08 / 23 @ 10:06:16

ES Potential for 4^2 (with monotonicity)

ES-Potential for 4^2

A22 Term Test 1 Attendance Numbers

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