Math 403 Course Webpage

Advanced Linear Algebra

Spring 2021, Duke University

General information | Course description | Lecture notes | Lecture and video policies | Assignments | Homework schedule | Grading | Links | Fine print

General information

Lectures: Tuesday and Thursday, 12:00 – 13:15, Physics Building 154


Online resources:

Contact information for the Instructor

Name: Professor Ezra Miller
Address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Course webpage: you're already looking at it... but it's
Sakai site: available to registered students via Duke NetID
Zoom links: available to registered students via Sakai
Office hours: Monday, 16:15 – 17:15 on Zoom
                        Thursday, 13:15 – 14:30 on Zoom from Physics 209 or outside

Course description

This course covers topics in linear algebra beyond those in a first course. The main themes of the course are Abstraction refers to the setting of general vector spaces, with finite dimension or not, with given basis or not, over an arbitrary field. Approximation asks for best answers to linear systems when exact solutions either don't exist or are not worth computing to arbitrary precision. This is related to variation of subspaces or of entries of matrices: what kind of geometric space is the set of all k-dimensional subspaces? And what happens to the eigenvalues of a matrix when the entries of the matrix are wiggled? Positivity refers to the entries of a matrix or to the eigenvalues of a symmetric matrix; both have interesting, useful consequences. Convexity stems from the observation that a real hyperplane H splits a real vector space into two regions, one on either side of H. Intersections of regions like this yield familiar objects like cubes, pyramids, balls, and eggs, the geometry of which is fundamental to many applications of linear algebra. Throughout the course, motivation comes from many sources: statistics, computer science, economics, and biology, as well as other parts of mathematics. We will explore these applications, particularly in projects (paper plus oral presentation) on topics of the students' choosing.

Students will continue to develop their skills in mathematical exposition, both written and oral, including proofs.

Course content:

Prerequisites: Fluency with a first course (Math 218 or 221) will be assumed. Notions from calculus will also be crucial: limits, continuity, derivatives, and so on; thus solid knowledge of multivariable calculus (Math 211 or 222) will also be required.

Lecture notes

All lectures in one PDF file

Lecture, attendance, and video policies


Check here two weeks before each homework is due, or one week before each exam is due, for the specifics of the assignments. If an assignment hasn't been posted and you think it should have been, then please do email the instructor. Sometimes I encounter problems (such as, for example, the department's servers going down) while posting assignments; other times, I might simply have neglected to copy the assignment into the appropriate directory, or to set the permissions properly. (I do try to check these things, of course, but sometimes web pages act differently for users inside and outside the Math department so I don't notice.)

Assignment Due Date Problems
Homework #1
Tue.   9 February in PDF or LaTeX
Homework #2
Tue. 23 February in PDF or LaTeX
Midterm 1 Tue.   2 March in PDF or LaTeX
Homework #3
Tue. 16 March in PDF or LaTeX
Homework #4
Tue. 30 March in PDF or LaTeX
Homework #5
Tue. 13 April in PDF or LaTeX
Midterm 2 Tue. 20 April in PDF or LaTeX
Final project Fri.  23 April, noon

Policies regarding homework and midterms

Grading scheme

Final course grades: Participation in class discussion and office hours can contribute to your homework score.


University academic links Departmental links

The fine print

I will do my best to keep this web page for Math 403 current, but this web page is not intended to be a substitute for attendance. Students are held responsible for all announcements and all course content delivered in class.
Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage many years ago.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.
Wed Apr 7 04:23:15 EDT 2021