PHYSICS 017
Linear Algebra for Quantum

Course Information

• Lecture:
  MWF 4:00pm - 4:50pm, Physics 2111 [CRN: 69513]

• Discussion: (we will be using this)
  Wed 2:00 - 2:50pm, Physics 2111 [CRN: 69514]

• Office Hours: by appointment (ask your physics questions in class!)

• Syllabus (pdf, updated 30 March 26) | Canvas Page (not used)

Linear algebra is the mathematics of vector spaces and is a pillar of modern physics. This class teaches the tools of linear algebra that elucidate the structure of relativity and quantum mechanics. Topics include:

• Using index notation to indicate how physical quantities transform under symmetries. Rotation matrices and their complex generalizations.

• The difference between space and time in special relativity. Inner products, metric spaces.

• Quantum mechanics as linear algebra. Eigenvectors, eigenvalues, Hermitian and symmetric operators, diagonalizing (complex) matrices. 

• Spectral techniques in function space: differential equations as linear algebra, Fourier analysis, the origin of your favorite special functions in physics.

• Special topics on the linear algebra of quantum computing, machine learning, or general relativity depending on the interest of the students.

This course is strongly recommended for students taking quantum mechanics (Physics 156) next year. Students will also be prepared to take Mathematical Methods of Theoretical Physics (Physics 231) next fall.

Pre-requisites: While there are no strict pre-requisites, we expect students to have:

• a firm grasp of single variable calculus (Math 9). 

• and the first-year physics sequence (Physics 40 or 41). This is mainly to understand the physical motivation of our work.

Not having the formal preparation can be made up for with an enthusiasm to take time to dig into the material. If you have concerns about meeting the pre-requisites, please email Prof. Tanedo.

Why should I take this course? Physics 017 bridges a gap between Math 10/31/46 and the math used in quantum mechanics (Physics 156). Unlike Math 31, which focuses on engineering applications, Physics 017 focuses on complex vector spaces and advanced applications in physics.

Homework 

• Weekly short homework (24%): assigned Monday, due Friday of the same week.

• Every-two-weeks long homework (30%): assigned Monday of odd-numbered weeks, due on Monday of the next odd-numbered week (e.g. assigned Monday week 1, due Monday Week 3).

• Explainer video (30%): assigned on Monday of odd-numbered weeks, due Wednesday Friday of the next odd-numbered week (e.g. assigned Monday week 1, due Wednesday Friday Week 3). Videos are 5~minute pedagogical explanations of one problem from the long homework to be explained to your classmates. 

  • Each discussion section two students will present their explainer video works-in-progress on the board. (Aim for 10 minutes or less, but discussion time is welcome.)

• Peer review (15%): Submit online. Due Friday of the week after the explainer videos are submitted. 

• Final assessment (1%). Submit online. We will not be using our final exam slot.