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Office Camera

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. You can read more about the setup here. If you know of anyone else with a similar setup, please let me know.

Notebook and Image File Structure

MAT A29 Course Layout

The Spacing Effect

Here is a wonderful interactive essay about the spacing effect: How to Remember Anything Forever~ish. I also really like this paper about how we’ve failed to apply this result to education:

Test of new office-camera

This is $ \LaTeX $.

Alex Teeter: Manifolds

This is my friend Alex Teeter, manifold explorer.

Fitch Cheney Ordering

Raw photo


This is my friend, Paco Estrada.

A Designer Graph

The designer graph on the first term test for MAT A29 Winter 2022.

MAT B41 Exam Coverage (Draft)

Backup System Flowchart

This is the current layout of my Backup System. It shows how:,, and work. The Syncthing and Tailscale connections are not shown for the sake of clarity.

Plan for Final Exam Study

Volume in Conical Tank at t = 5 min

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 $dV/dt = 1 m^3 / min$.

MAT A29 Exam Coverage

Jordan Form and Organization

Pre-Exam To-Do

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

Integration by parts

Convergence and Divergence

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

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

My friend Hooman

Partial fractions with repeated factor

Dihedral calculator: sts

Rows and Columns in Elimination

Rows and Columns in Elimination

The (0,2n+1) Puzzle

A22: Proofs in A22 (Part 1)

A22: Proofs in A22 (Part 2)

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

A linearly dependent set

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

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

Puzzle: Sums of Reciprocals

Proof Structure

Puzzle: Sum of Reciprocals (continued)

A System with a Particular Solution Set

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

In Shuffles and Out Shuffles

MAT A22 Term Test Content (draft)

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

Visualizing F(R)

Hitting and Missing a Span

Missing a Span: The Details

The Fastest Intro to Derivatives

Why do we care about the extension lemma?

Dimension Examples

Linear Independence Calculation

Malhar's Puzzle

Hello Twitter!

Reading Week A22 Todo

Subspaces and Their Sums (Part 1)

Subspaces and Their Sums (Part 2)

Subspaces and Their Sums (Part 3)

Subspaces and Their Sums (Part 4)

Subspaces and Their Sums (Part 5)

Subspaces and Their Sums (Part 6)

Subspaces / Image / Kernel / Bases (Part 1)

Subspaces / Image / Kernel / Bases (Part 2)

Subspaces / Image / Kernel / Bases (Part 3)

Subspaces / Image / Kernel / Bases (Part 4)

Subspaces / Image / Kernel / Bases (Part 5)

Subspaces / Image / Kernel / Bases (Part 6)

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

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

The Null Space as a Linear System

Dimension of the Space of nxn Symmetric Matrices

Dimension of the Space of nxn Skew Matrices

Square Wave Setup

The Idea of a Surface Integral

A Quarter of an Annulus

A22 Final Exam Draft

MathEd vs Math Researcher Career Trajectories

Changing Coords TO the Standard Basis

Linear System with Prescribed Solution Set

Eigenvectors and Linear Independence

Diagonalization and Powers

Diagonalization and Invertibility

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

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

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

Nilpotent Transformations Are Not Invertible

The Smallest Vectors with Integer Entries

Transpose a Matrix

Projections are Never Invertible

The Matrix of Transposition

Diagonalizing Transposition (Part 1)

Diagonalizing Transposition (Part 2)

CN Tower Stair Climb Times

Attitude, Skills, Knowledge

Lives vs the Universe

Zombies vs Humans (via Diagonalization)

WolframAlpha Calculation

Boxes and Spheres in n-Dimensional Space

XOR and Nimbers

Adding Nimbers

2023-05-05 @ 16:35:41

Mira colours!

My daughter Mira came in to the office this afternoon and coloured.

To-do list stuff

Canonical Start of A Linear Sequence

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.

Nim and Nimbers

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

Nim Winning Strategy Lemmas

How does string figure calculus act on linear sequences?

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

Ideals and Principal Ideals

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

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

Dedekind Cuts and Completeness of R

Juggling State Machine

When to apply for gradschool or jobs?

Putnam B4 2005

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 $|x_1|+|x_2|+ \cdots +|x_n| \leq m$.

Fake Crossings in Knots

Formal Grammar for Linear Sequences and Calculus

Duck and Dog: The Dog's Strategy

The Heart Groupoid and String Figures Calculus

D92: Possible Projects

D92: Possible Projects

Alexander and Markov's Theorems

From a Markov Sequence to a Heart Sequence

Yulong's Wrapped L1

2023-10-16 @ 09:13:37

Alfredo's Opening A

Yulong's O.A Construction

Paco: Terms from Graphics Programming / Half-Second Star

Family Halloween

From Markov to A Heart Sequence Redux

For another discussion of this, see: From a Markov Sequence to a Heart Sequence.

Yulong's Braid Word Reduction

Mira Doodles: vvbnm,,.//

Mira Doodles: Part II

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

This photo has a sketch of an embedding $\heartsuit_n \leq B_{2n}$.

Bessel's Inequality

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.

The Calculus of Heart Sequences

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

Loop Manipulation Nomenclature

Three loop manipulations are shown. What should we call them?

The Braid Group

A quick peek at the braid group $B_3$

Loop Manipulation Generators

Labelled generators of $H_{n} \subseteq B_{2n}$.


Solving 2/x - 9 greater than 0

About the Office Camera

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.

A22 Term Test 1 Attendance Numbers

ES-Potential for 4^2

ES Potential for 4^2 (with monotonicity)

2022 / 08 / 23 @ 10:06:16



Tic-Tac-Tree (Induction)

3b and 4b siteswaps

Knots and 3-Manifolds

Range of x/(x^2-16)

Composition of sqrt(x) and x+9

Level Curves of Planes

Reading Week Todo

End of Reading Week To-Do

Probability of (Mentally) Choosing a Card

Chain and Power Rule

Leibniz Notation (Part 1)

Leibniz Notation (Part 2)

Leibniz Notation (Part 3)

Leibniz Notation (Part 4)

Leibniz Notation (Part 5)

Leibniz Notation (Part 6)

Taylor Series B41

Taylor Series: The True Formula (Multi-Indices)

The (Boring) Structured Essay

Optimization Doodles and Dave's Amazing Summation (Redo)

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!

Mira draws!

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