Spring 2025 Course Announcement
MATH 345 (Topics in Undergraduate Mathematics)—“Linear Algebra and Optimization”
- Instructor: Sebastien Roch
- Lecture: MWF 9:55-10:45 AM in Van Vleck B239
- Credits: 4
- Prerequisites: MATH 222 and COMP SCI 200, 220, 300, 310, 320, or placement in COMP SCI 300. Not open to students with credit for MATH 320, 340, 341, or 375.
Are you interested in AI, machine learning, data science etc., but have not taken linear algebra yet? This may be the class for you. In Spring 2025, MATH 345 will serve as a pilot for a new “Linear Algebra and Optimization” course developed by the Mathematics Department. It will cover introductory linear algebra concepts (similarly to MATH 320, 340) as well as aspects of differential calculus in several variables and basic optimization theory (partly covered in MATH 234) — combining in a unified coverage two major pillars of modern data-driven and computational fields. Python implementations will help bring the mathematical material to life by connecting it with selected applications.
This class will meet for three 50-minute class periods and one 50-minute discussion period each week over the semester. (There are two discussion sections available. They both meet on Tuesdays. One meets 9:55-10:45 AM and the other meets 11-11:50 AM.)
Notes on related courses
- MATH 331, which covers probability as well as aspects of integral calculus in several variables, may serve as a good complementary course for students who will not take MATH 234.
- MATH 340 or MATH 341 (instead of Linear Algebra and Optimization) is recommended for students who have taken or plan to take MATH 234.
- Formal techniques in mathematical argument will not be covered in this class; interested students should instead consider MATH 341.
Major Requirements
If you are declared in (or plan to declare) any of the following majors and take this pilot course, it will count toward your major’s linear algebra requirement:
- Computer Sciences
- Data Science
- Mathematics (including all of the named options)
- MATH 341, 340, or 320 is recommended since Mathematics majors will take MATH 234.
- Statistics
- MATH 340 or MATH 341 is recommended since Statistics majors will take MATH 234.
All of these programs have officially approved the pilot to count toward their linear algebra requirement, but DARS updates to handle this are still in progress. Please ask a major advisor if you have questions. (Students may count at most one introductory linear algebra course, including Linear Algebra and Optimization, toward most of these programs’ major/certificate requirements. Students who take Linear Algebra and Optimization, you should not take MATH 320, 340, 341, or 375 in the future.)
Use in Prerequisites
You will also be able to use Linear Algebra and Optimization to satisfy the “MATH 320, 340, 341, or 375” portion of a prerequisite for any course taught by the Departments of Computer Sciences, Mathematics, or Statistics. The exact details of how this will be implemented are being determined, but want to ensure that students can enroll in further courses relying on this foundational linear algebra content.
More About the Course
Topics in linear algebra: vectors, analytic geometry, matrices, linear functions, linear independence, orthogonality, inverses, eigenvalues and eigenvectors. Topics in multivariable differential calculus and basic optimization theory: partial derivatives, gradients, Taylor approximation, gradient descent, Lagrange multipliers, multivariable Chain Rule. Applied topics: clustering, regression, classification. Implementations in Python.
Required texts
Stephen Boyd and Lieven Vandenberghe, Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, Cambridge University Press, 2018. Available free online
[SH] Strang, G., & Herman, E. (2016). Calculus Volume 3. OpenStax. Available free online
Questions?
- Contact Prof. Roch if you have questions about the course content.
- Contact a CS, DS, Math, or Statistics major advisor if you have questions about how this course applies to those major requirements.
- Contact Dr. Keller if you have questions about possibly applying the course to other majors.