The lectures will be a (very) gentle introduction to some simple ideas in mathematics and their applications. We will discuss what mathematics is, when it can be used to deepen our understanding, how one might go about doing so, and what the limitations of such analyses are. We also hope, through examples from many subfields within mathematics, to cultivate an appreciation for the elegance, economy, and clarity of mathematical thinking.
Here are some topics I hope to discuss: the shapes of surfaces and knotted pieces of string; elementary results in the theory of numbers; what proofs are and where definitions come from; wordless or picture-perfect proofs; counting, games, and probabilities; the infinitely big and infinitesimally small in mathematics.
Meetings: Wednesdays and Fridays (1500–1630) in AC-04-LR-005
Grading: 60% class tests + 30% final exam + 10% attendance
Office Hours: Thursday (0900–1200) by appointment.
For more details, please see the course information sheet.
03/23 — Your final exam will be held on 29th April between 1730–1930 in AC-02-LR-007.
02/17 — You can come check your grades for the first test on Friday, 20th February, between 5–7 PM.
02/11 — Your second class test will be held on 25th February, 2026.
01/30 — Your first class test will be held on 11th February, 2026.
01/23 — Your first assignment has been posted. Please bring attempts at solutions to all the questions in the assignment to your respective DSs.
Your take-home assignment is available here.
19. Hamiltonian Paths and Complexity — 04/01
18. Graphs — 03/28
17. Conditional Probability and Statistics — 03/27
16. Probability — 03/25
15. Permutations and Combinations — 03/18
14. Kleiber Scaling and Fractal Networks — 03/13
13. Dimensional Analysis and Scaling Laws — 03/11
12. Infinite Series and Primes — 02/27
11. Primitive Ideas of Calculus — 02/25
10. Continuity and Calculus — 02/20
9. Relations and Functions — 02/18
8. Countability and Correspondences — 02/13
7. The Infinite — 02/11
6. Induction and Primes — 02/06
5. Numbers — 02/04
4. Knots — 01/30
3. The Poincaré-Hopf Index Theorem — 01/28
2. The Euler Characteristic — 01/23
1. Introduction — 01/21
Below you'll find some reading material that is referenced in the classroom. Reading these, or even just dipping into them, will enrich your experience of the course immeasurably. For those texts without links, I trust you'll find a way to get hold of a copy.
An Intuitive Explanation of Bayes' Theorem by Eliezer S. Yudkowsky.
A Philosophical Essay on Probabilities by Pierre-Simon Laplace.
Discrete Thoughts: Essays on Mathematics, Science, and Philosophy by Mark Kac, Gian-Carlo Rota, and Jacob T. Schwartz.
Life's Universal Scaling Laws by Geoffrey B. West and James H. Brown.
On Being The Right Size by J. B. S. Haldane.
Prime Obsession by John Derbyshire.
The Historical Development of the Calculus by C. H. Edwards, Jr.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner
Avatars of the Tortoise and The Library of Babel by Jorge Luis Borges
The Infinite by A. W. Moore
The Presocratic Philosophers by Jonathan Barnes
Enriching Divisibility: Multiple Proofs and Generalizations by Benjamin Dickman
Why Isn't the Fundamental Theorem of Arithmetic Obvious? and Proving The Fundamental Theorem of Arithmetic by Timothy Gowers
Knots: Mathematics with a Twist by Alexei Sossinsky.
Why Space Has Three Dimensions by Henri Poincaré.
Proofs and Refutations by Imre Lakatos.
Funes the Memorious by Jorge Luis Borges.
A Mathematician's Lament by Paul Lockhart.
This is a first course in mathematical methods — both analytic and numerical — often used in physics. Here are some topics I hope to discuss: linear algebra and vector spaces; simple ordinary differential equations; elementary Fourier analysis; vector calculus; and some computational techniques including numerical solutions to algebraic and differential equations.
Meetings: Wed and Fri (1150–1320) in AC-04-LR-004
Grading: 45% class tests + 15% coding challenges + 30% final exam + 10% attendance
Office Hours: Thursday (0900–1200) by appointment.
For more information, please see the course information sheet.
03/25 — Your take-home assignment has been posted below. Please submit your solutions in class on April 1st.
03/23 — Your final exam will be held on 5th May between 1730–1930 in AC-04-LR-005.
02/19 — Your first coding challenge has been uploaded. The deadline for submission is 11th March.
02/18 — Your next class test will be on 25th February.
02/04 — Please note that Question 4 of Assignment 2 has been modified!
02/04 — Your first class test will be on 11th February.
01/23 — Your first assignment has been posted. Please bring attempts at solutions to all the questions in the assignment to your respective DSs.
19. More Second-Order Linear Differential Equations — 04/01
18. Second-Order Linear Differential Equations — 03/28
17. More First-Order Linear Differential Equations — 03/27
16. First-Order Linear Differential Equations — 03/25
15. Dirac Delta Functions — 03/18
14. Curvilinear Coordinates and Stokes' Theorems — 03/13
13. Stokes' Theorems — 03/11
12. Taylor Expansions and Jacobians — 02/28
11. Integrals in Two and Three Dimensions — 02/26
10. Curls and Product Rules — 02/20
9. Multivariable Calculus, Gradients, and Divergences — 02/18
8. Review of Differential Calculus + Curves and Surfaces — 02/13
7. Eigenvalues and Eigenvectors — 02/11
6. Linear Functionals and Derivations — 02/06
5. Algebras and Linear Transformations — 02/04
4. Inner Product Spaces — 01/30
3. Vector Spaces II — 01/28
2. Vector Spaces — 01/23
1. Introduction — 01/21
Below you'll find some reading material that is referenced in the classroom.
Introduction to Electrodynamics by David J. Griffiths
The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner.