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Week 1 • 02/02 - 02/06
Important: Welcome to the Spring 2026 edition of Symm4ML! Office hours start Wednesday.
Exercise Released: Numpy (optional)
Exercise Released: Groups Due 2/13
Lecture 1 Mon, 02/02
Course Overview and Intro to Finite Group Theory I
Readings: ☰☰☰◉
Lecture 2 Wed, 02/04
Intro to Finite Group Theory II
Readings: ☰☰☰◉
Week 2 • 02/09 - 02/13
Exercise Released: Linear Algebra and Group Representation I Due 2/23
Exercise Due 2/13: Groups
Lecture 3 Mon, 02/09
Linear Algebra: Vector spaces, nullspaces, orthogonality, and Kronecker product
Readings: ☰☰
Lecture 4 Wed, 02/11
Linear Algebra + Representations of Finite Groups I: Kronecker Sums, Change of Basis, Reps, Irreps, Schur's Lemma Part 1
Readings: ☰☰
Week 3 • 02/16 - 02/20
Important: Monday, Feb. 16 is Presidents' Day Holiday. Tuesday, Feb. 17 -- Monday schedule held
Exercise Released: Group Representations II Due 3/6
Lecture 5 Tue, 02/17
Representations of Finite Groups II: Schur's Lemma Part 2, Wonderful Orthogonality Theorem
Readings: ☰
Lecture 6 Wed, 02/18
Representations of Finite Groups III: Regular Representations and Characters
Readings: ☰☰
Week 4 • 02/23 - 02/27
Lecture 7 Mon, 02/23
Class Canceled
Lecture 8 Wed, 02/25
Representations of Finite Groups IV: Tensor Products and Decompose to Irreps
Readings: ☰☰☰☰☰☰
Week 5 • 03/02 - 03/06
Important: Office Hours on Friday 03/06 will be on Zoom
Exercise Released: Vibrational Modes Due 4/3
Exercise Due 3/6: Group Representations II
Lecture 9 Mon, 03/02
Vibrational Modes I
Readings: ☰☰☰
Lecture 10 Wed, 03/04
Vibrational Modes II: Recap and Projector Approach
Readings: ☰☰☰
Week 6 • 03/09 - 03/13
Important: Exam Practice Problems:
Exercise Released: Group Convolution Due 4/3
Lecture 11 Mon, 03/09
Group Convolution I
Lecture 12 Wed, 03/11
Group Convolution II
Week 7 • 03/16 - 03/20
Important: Exam Practice Problems: Office Hours on Wednesday 03/18 will be cancelled due to the exam.
Lecture 13 Mon, 03/16
Exam Logistics and Review of Lec. 1-10
Lecture 14 Wed, 03/18
Exam 1 (Lectures 1-10)
Readings: ☰
MIT Spring Break 3/23 - 3/27
Week 8 • 03/30 - 04/03
Exercise Due 4/3: Vibrational Modes
Exercise Due 4/3: Group Convolution
Lecture 15 Mon, 03/30
Steerable Convolution I — Basis Functions and the Tensor Product Structure of Filters
Lecture 16 Wed, 04/01
Steerable Convolution II — Equivariant Filters and Activations
Week 9 • 04/06 - 04/10
Exercise Released: Lie Groups Due 4/17
Lecture 17 Mon, 04/06
Intro to Lie Algebra
Readings: ☰☰
Lecture 18 Wed, 04/08
SO(2) and SO(3) and their Representations
Readings: ☰☰
Week 10 • 04/13 - 04/17
Important: Exam Practice Problems: Exam 2 Review is scheduled for Friday 04/17 from 4:00-5:30pm in 34-101. Office Hours on Friday 04/17 will be pushed to 5:30-6:30pm and will be on Zoom
Exercise Released: SO(3) and O(3) Due 5/1
Exercise Due 4/17: Lie Groups
Lecture 19 Mon, 04/13
O(3), Spherical Harmonics, and Branching
Readings: ☰☰
Lecture 20 Wed, 04/15
Cartesian Tensors and Point Group Symmetry
Readings: ☰☰
Week 11 • 04/20 - 04/24
Important: Exam Practice Problems: April 20 is Patriots' Day! No class and no office hours on Monday! Office hours on Wednesday will also be cancelled due to the exam.
No lecture this day
Lecture 21 Wed, 04/22
Exam 2 (Lectures 10-20)
Week 12 • 04/27 - 05/01 Current
Lecture 22 Mon, 04/27
Signals on Spheres and Fourier Transforms on Groups I
Readings: ☰☰▶▶▶
Lecture 23 Wed, 04/29
Signals on Spheres and Fourier Transforms on Groups II
Readings: ▶☰
Week 13 • 05/04 - 05/08
Lecture 24 Mon, 05/04
E(3) Equivariant Graph Neural Networks
Lecture 25 Wed, 05/06
Symmetry-Breaking
Week 14 • 05/11 - 05/15
Important: Exam Practice Problems:
Lecture 26 Mon, 05/11
Final Exam
No lecture this day