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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:
-
Matrix Analysis for Scientists and Engineers by
Alan Laub, SIAM Publisher 2005 (required)
- Matrix
Analysis and Applied Linear Algebra by Carl Meyer,
SIAM Publisher 2000 (optional)
Course assistant and office hours:
- Salil Goyal () Office hours on Canvas
- Hamish Blair
() 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, Margot Hutchins (margothutchins at stanford.edu), 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, October 22, 10:30-11:50
a.m., Building 370, Rm 370
- Final: Thursday, December 12, 3:30-6:30
p.m.. This date is in accordance
with University scheduling of end-quarter
examination.
- We will have an open-notes exam in the sense
that you will be able to come to class with up to 50 pages of notes (printed or handwritten), which can be anything you like.
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. Please do this as this is very important and requires taking some action.
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."
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