General Information
Content varies widely.
In Spring 2027, there will be two sections of Math 495:
- Section 01: Topological Quantum Computation and the Foundations of Quantum Mechanics
Instructor: Prof. Echeverria <>
Course Description: A syllabus will be posted here shortly.
Prerequisites: Math 251 and Math 250, but Webreg lists Calc IV = Math 244/252 and Math 250 as the prerequisites. If you are missing Calc IV but have taken the true prerequisites (Math 251 and Math 250), please fill out the Prerequisite Override Form for assistance with registration.
Note: The time for this section will likely be changed from Monday/Thursday mornings to Tuesday/Thursday evenings (5:40-7pm) on Livingston. We hope to update the schedule of classes with the new times and location in the next week or so. - Section 02: Euclidean Distance Geometry and Applications
Instructor: Prof. Suresh <>
Course Description: This course provides a concise introduction to metric geometry with a strong emphasis on classical and modern Euclidean distance geometry and its applications to data science. The central problem is to reconstruct a finite point cloud from its pairwise distances, up to Euclidean isometries. We investigate this problem under different lights and explore the possibility and stability of reconstruction when measurements are - for instance - noisy, incomplete, or unlabeled. The course develops the necessary tools to tackle this question from linear algebra and convex optimization, through the study of Gram/PSD matrices - which naturally leads to the topics such as Euclidean distance matrices, Procrustes alignments, low-rank matrix completions and multidimensional scaling. All topics will be studied in conjunction with applications such as data visualization, recommender systems, and reconstruction through echoes (LiDAR, SLAM etc.). The course concludes by extending these ideas to general metric spaces, introducing Hausdorff and Gromov–Hausdorff distances, and discussing what it means to approximate and compare geometric objects in a general setting. A syllabus will be posted here shortly with additional details.
Prerequisites: Math 251 and Math 250, but Webreg lists Calc IV = Math 244/252 and Math 250 as the prerequisites. If you are missing Calc IV but have taken the true prerequisites (Math 251 and Math 250), please fill out the Prerequisite Override Form for assistance with registration. - Section 03: Logical Foundation of Mechanized Reasoning
Instructor: Prof. Calderoni <>
Topics: Propositional logic, first-order logic, natural deduction, resolution, Lean as a proof assistant, SAT and SMT solvers, beyond first order logic.
Course Description: In the first part of the course, we will learn syntax and semantics of propositional and first-order logic. The focus will be on deduction systems such as natural deduction and resolution. In the second part, we will implement the logical syntax in a functional programming language called Lean. We will discuss the use of Lean as a proof assistant and see logic in action.
Prerequisites: A grade of C or better in 640:300 Intro Math Reasoning or 198:205 Discrete Structures I. If you have taken Math 300/CS 205 but are missing some of the official prerequisites listed in Webreg (Math 250 and Calc IV = Math 244/252), please fill out the Prerequisite Override Form for assistance with registration.
In Fall 2026, there were two sections of Math 495:
- Section 01: AI Tools for Mathematics
Instructor: Prof. Carbone <>
Course Description: see Syllabus
Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning or equivalent is required. Graduate students in CS and ECE may receive an exemption with instructor permission. Programming experience will be beneficial but is not essential.
If you have taken Math 300 but are missing some of the official prerequisites listed in Webreg (Math 250 and Calc IV = Math 244/252), please fill out the Prerequisite Override Form for assistance with registration. - Section 02: Multilinear Algebra and Tensor Networks
Instructor: Prof. Echeverria <>
Course Description: see Syllabus
Prerequisites: Math 251 and Math 250, but Webreg lists Calc IV = Math 244/252 and Math 250 as the prerequisites. If you are missing Calc IV but have taken the true prerequisites (Math 251 and Math 250), please fill out the Prerequisite Override Form for assistance with registration.
In Spring 2026, there were three sections of Math 495:
- Section 01: AI Tools for Mathematics
Course Description: see Syllabus
Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning is strongly recommended. Programming experience will be beneficial but is not essential. - Section 02: Combinatorial Game Theory
Course Description: A combinatorial game is ordinarily a two-player game with no hidden information, ending when there are no possible moves remaining. These games have a tendency to break down into smaller pieces, which can be analyzed independently. Dots and Boxes is perhaps a familiar example; one core objective of this course is to seek awesomeness at Dots and Boxes. Combinatorial Game Theory has also been applied to Go, but that is way beyond the scope of this course.
This course will cover both impartial games (in which both players have the same options) such as Nim, and partizan games, such as Hackenbush. A balance will be sought between deep dives on specific games (such as Sprouts or Hey! That's My Fish!) and general theory. The space of combinatorial games has a rich structure, with many surprising connections.
(Please note that this topic is essentially disjoint from "game theory", as studied by von Neumann, Nash, etc. No one will earn a Nobel prize based on knowledge from this course.)
Prerequisites: Math 300 or Math 428 or Math 454, but the website will list 244 and 250 as the prerequisites. In such case, please fill out the Prerequisite Override Form for assistance with registration. - Section 03: Introduction to Topological Data Analysis
Course Description: see Syllabus
Prerequisites: Math 251 and Math 250, but the website will list 244 and 250 as the prerequisites. In such case, please fill out the Prerequisite Override Form for assistance with registration.
In Fall 2025, there were three sections of Math 495:
- Section 01: AI Tools in Mathematics
Course Description: see Syllabus
Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning is strongly recommended. Programming experience will be beneficial but is not essential. - Section 02: Tensor Networks as a bridge between Neural Networks and Quantum Physics
Course Description: see Syllabus
Prerequisites: Linear Algebra (Math 250) is the only prerequisite for this course, - Section 03: An Introduction to Machine Learning
Course Description: see Syllabus
Prerequisites: A course in Linear Algebra
In Spring 2025, there were two sections of Math 495:
- Section 01: A Mathematical Invitation To Machine Learning
Course Description: This mathematics course covers topics related to machine learning. Some of these are multivariable calculus applications in neural networks, linear regression, principal component analysis and support vector machines. Emphasis will be on the mathematics aspects and connections.
Textbooks: The pre-print versions of both textbooks are freely available for download for personal use. The primary textbook: "Mathematics For Machine Learning" by Deisenroth, Faisal, Ong. (Cambridge University Press). Secondary textbook: "Foundations of Data Science" by Blum, Hopcroft, Kannan. (Cambridge University Press).
Pre-requisites: Math 152 or equivalent. Further courses such as linear algebra, multivariable calculus, probability or statistics, are a plus. Prior exposure to machine learning is not required. (If you have completed Math 152 but not the official prerequisite courses Math 244/252 and Math 250, fill out the Prerequisite Override Form for assistance with registration.) - Section 02: From Gravitational Waves to Supersonic Flows: An Introduction to Hyperbolic PDEs
Course Description: The sonic boom of jets, the rippling of ocean waves, and even the gravitational waves detected by astronomers are all described by Hyperbolic Partial Differential Equations (PDEs). This course offers an introduction to the mathematical theory of hyperbolic PDEs, focusing on simplified models in fluid dynamics and linear wave propagation. While the emphasis will be on mathematical rigor, no prior knowledge of PDEs will be assumed.
Textbook: Hyperbolic Partial Differential Equations, Serge Alinhac.
Pre-requisites: Multivariable calculus (Math 251), elementary ODE theory (Math 244/252), intro linear algebra (Math 250).
Assignments: Final presentation on a topic of the students' choosing (a list of suggested topics will be provided). Optional weekly homework will be available for extra credit.
In Spring 2024, there were two sections of 495:
- Section 01: Proofs from THE BOOK
Prerequisites - Math 300
Syllabus - Section 02: Mathematical Adventures in One-Dimensional Physics
Prerequisites - (244 or 252 or 292) (ODEs) and (250 or 291) (Lin. Alg.)
Syllabus
See the archives for details.
Archives
- Spring 2009: Connections Seminar, Prof. Cohen
- Spring 2008: Connections Seminar, Prof. Retakh
- Fall 2007 Financial Mathematics, Professor Rodriguez.
- Spring 2007
- Fall 2006 (Financial Mathematics)