Math 104
Applied Matrix Theory
Winter 2024



Instructor
Emmanuel Candes
144 Sequoia Hall

   

Lectures
Tuesday, Thursday
10:30-11:50 a.m.
Bishop Auditorium

 

Home

Handouts

Homework


Canvas: We will use for Canvas for the course. All handouts, homework assignments, and solutions will be posted on Canvas.

What's below is merely a placeholder with our syllabus and course information.

Course survey: Please fill the course survey sent by email.

Description: The aim of this course is to introduce the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and merely all quantitative fields of science and engineering. While the choice of topics is motivated by their use in various disciplines, the course will emphasize the theoretical and conceptual underpinnings of this subject, just as in other (applied) mathematics course.


Prerequisite:
Math 51, CS 106, and either Math 52 or Math 53. We expect all students to be familiar with the following notions:

  • vector operations: dot product, cross product
  • matrix operations: matrix-matrix and matrix-vector multiplications
  • partial derivatives and the chain rule of vector calculus
  • definition of eigenvalue and eigenvector
  • 3-by-3 determinants


Syllabus:

  • Matrices, vectors and their products (review)
  • Matrices as linear transformations
  • Rank of a matrix, linear independence and the four fundamental subspaces of a matrix
  • Orthogonality and isometries
  • The QR decomposition
  • Eigenvalues and the spectral decomposition of symmetric matrices
  • The singular value decomposition and its applications
  • The conditioning of a matrix
  • Least squares problems
  • Algorithms for solving systems of linear equations and least-squares problems
  • Iterative methods for solving linear systems: the method of conjugate gradients
  • Applications (mostly to data science): e.g. multivariate linear regression and principal component analysis


Textbooks:

  1. Matrix Analysis for Scientists and Engineers by Alan Laub, SIAM Publisher 2005 (required)
  2. Matrix Analysis and Applied Linear Algebra by Carl Meyer, SIAM Publisher 2000 (optional)

Course assistant and office hours:

  • Salil Goyal () Office hours on Canvas
  • Aman Malhotra () Office hours on Canvas
  • Ghadi Nehme () Office hours on Canvas
  • Jiyun Park () Office hours on Canvas

SUMO tutoring: The Stanford University Mathematical Organization (SUMO) is offering tutoring for Math 104, please see their website for information. Please email the tutoring coordinator, Yuzu Ido for general tutoring-related questions and comments.

Homework assignments:

  • Homework assignments will generally be distributed on Thursdays and are due in class the following Thursday.
  • Late homeworks will NOT be accepted for grading (medical emergencies excepted with proof).
  • There will be about 7 assignments; the lowest score will be dropped in the final grade.
  • It is encouraged to discuss the problem sets with others, but everyone needs to turn in a unique personal write-up.

Exams:

  • Midterm: Tuesday, February 6, 10:30-11:50 a.m., Bishop Auditorium
  • Final: Thursday, March 21, 3:30-6:30 p.m.. This date is in accordance with University scheduling of end-quarter examination.
  • We will have open-book, open-notes exams in the sense that you will be able to use your textbook, your class notes, and all the handouts we provided.

Grading:
Your final grade will be the maximum of the following two weightings:

  • 40% x (average homework) + 30% x (midterm exam) + 30% x (final exam)
  • 40% x (average homework) + 15% x (midterm exam) + 45% x (final exam)
Once again, your lowest homework grade will be dropped when computing your average homework score.

Course policies:
Use of sources (people, chatGPT, books, internet and so on) without citing them in homework sets results in failing grade for course.

Access and Accommodation:
Please check the syllabus on Canvas for information.

Stanford Math Department on Piazza (official line):
"Stanford Math Department does not use Piazza or similar platforms in its courses. This decision is based on a careful review of a variety of issues. We strongly encourage students working with and assisting one another, as well as with TA's and instructors. But we believe that (despite FERPA compliance) Piazza does not sufficiently protect student privacy, and there are other potentially adverse effects that give us additional concern."