An introduction to quantum theory from a mathematical perspective. On the physics side we’ll cover quantum computing, time-dependent and -independent quantum systems, wave-particle duality, harmonic oscillators, quantum algorithms, spin, particle statistics, and path integral formalism. To discuss these formally, we’ll introduce Hilbert spaces, L^{2} space, unitary and Hermitian operators, functional analysis, the spectral theorem, Fourier transforms, Pontryagin duality, Lie algebras, spin groups, and more. The exact topics covered will depend on the background and interests of the participants.

**Prerequisites:** Introductory courses in linear algebra and in real analysis. No physics background required.**Lectures:** Sundays 8:00pm - 10:00pm ET and Tuesdays/Thursdays 8:30pm - 10:30pm ET, on Zoom

Please contact me with any questions.

**Important dates:**

- June 27: First class
- August 1-5: Presentations
- August 5: Last class
- August 12: Final papers due

**Textbooks:** The main textbook for this course is

- Brian Hall,
*Quantum Theory for Mathematicians*.

For much of the course, we will not follow this book closely. The following books should address the topics we cover which are not explained in Hall.

- Michael Nielsen and Isaac Chuang,
*Quantum Computation and Quantum Information*. - Klaas Landsman,
*Foundations of Quantum Theory*.

**Final project:** Final presentations will be given in the last week of class. The final paper will be due **August 12 at 11:59pm ET**.

Potential final project ideas

- Homework 1, due July 17 at 11:59pm ET
- Homework 2, due August 10 at 11:59pm ET
- Homework 3, due August 21 at 11:59pm ET