For full information on section offerings, see Course Explorer.
Some course information will vary by section. See section notes for more details.
Summer 2023 Courses
Please see notes on individual sections on the Summer 2023 timetable:
Fall 2023 Courses
Several undergraduate and graduate courses contain restrictions during the regular registration period, to ensure that students who have completed the registration requirements will have the best chance at successfully registering for their preferred courses. Some of these restrictions will be lifted later in the registration period.
- MATH 347: Major restrictions will be removed during business hours (8:30 a.m. or later) on April 20, 2023. Some seats are reserved for incoming students in programs requiring this course. Any remaining seats would be released on the Friday before fall classes begin. For information about the Honors section of MATH 347, see "Honors Courses" in the following section.
- MATH 412, 413, 416, 417, 441, 442, 444, 446, 447, 448, 466, 482, 484: Major restrictions will be removed during business hours (8:30 a.m. or later) on April 19, 2023. Some seats are reserved for incoming students in programs requiring these courses. Any remaining seats would be released on the Friday before fall classes begin.
- MATH 481: Restricted to those enrolled online Engineering MS programs. Please see the note at http://engineering.illinois.edu/online/courses.
The Merit Program provides an interactive group learning environment for selected students. For general information regarding the Merit Program, consult the Merit Program website.
Registration in Math Merit sections requires approval from the Math Merit Director (see contact information below). Concurrent enrollment for 1 hour of credit in the Merit Section of Math 199 is required for MATH 220, MATH 221, MATH 231, and MATH 241.
Jennifer McNeilly, Math Merit Program Director
326 Altgeld Hall
The department offers the three following honors mathematics courses to undergraduate students:
- Honors MATH 347
- Honors MATH 416
- MATH 425
Students interested in taking mathematics honors courses should have A grades in prior coursework and must obtain approval from the undergraduate advising team to register for honors courses. To express interest in registering for these courses, email firstname.lastname@example.org using the subject line “Honors course request: [347/416/425]” (please specify which course you'd like to take). In the same email, include your name, UIN, netID, the reason for your interest, and your qualifications for applying to the honors course.
Honors Section of Math 347
Enrollment in this honors section is restricted to students who have shown excellence in mathematics. Completion of Math 241 is typically expected as well. To request permission for this section please email email@example.com with name, UIN, and reason for interest. Students who have demonstrated excellence in mathematics may use this section for James Scholar credit, but the section is not restricted to James Scholars.
Undergraduate Topics Courses
Course offerings in undergraduate-level mathematics topics are as follows:
- MATH 199, Conversations in Mathematics (Undergraduate Open Seminar)
This course is for those who wish to experience mathematics through experimentation, reflection, intuition, and conversation. We will explore a number of provocative, interesting, and important ideas from the canon of mathematics. The goal of this course is to offer the student memorable, lifelong topics of conversations about math. Assessment will be through evaluation of student journal entries. For Chancellor's Scholars only; other may only enroll with the consent of the instructor and the Campus Honors Program.
- MATH 428, Honors Topics: Introduction to Fourier Analysis
Fourier analysis is one of the most influential fields in mathematics with applications in analysis, differential equations, number theory, geometry, quantum mechanics, signal processing and many others. This is an introductory course to Fourier analysis. It will focus on rigorous development of basic concepts in the area. Prerequisites are MATH 447 or equivalent such as MATH 424 or MATH 444. This course will also require some familiarity with complex numbers and basic linear algebra. Topics to be covered include:
Fourier series solutions of wave and heat equations
Properties of Fourier series: decay of coeffcients, uniqueness, convergence, summability
Fourier series of square integrable functions; Vector spaces and inner products; Parseval's and Placherel identities.
Some applications of Fourier series: Isoperimetric inequality, Weyl's equidistribution theorem
Fourier transform on R. Schwartz space. Fourier inversion. Poisson summation formula. Uncertainty principle
Further topics (if time permits): Fourier transform on Rd. Radial symmetry and Bessel functions. X-ray and Radon transforms
MATH 490, Quantum Information Theory
The goal of this course is to provide a rigorous introduction to the mathematical aspects of quantum information theory. The second postulate of quantum mechanics states that the dynamics of any closed (isolated) quantum system is determined by unitary evolution. Though, in reality, every system is open! And thus, there is always some interaction with an external system (the environment). Thus, disturbance of the state of our initial system is an occurrence which we must get used to and learn how to work with. Quantum channels may be defined via such processes. In particular, a quantum channel is a completely positive trace preserving map which changes the state of your system. The focus of the first half of term will be to study quantum channels and their properties. This includes the study of subclasses of quantum channels and unital channels, and various representation theorems for quantum channels. The next task will be to look at similarity and distance amongst states and channels. This includes quantum state and channel discrimination, the fidelity function, distance between quantum channels, and majorization. The focus of the second half of term will be on quantum error correction. Classical error correction is a very well understood, and well-developed field. For many years it was unknown if quantum error correction was possible. Three major hurdles are present when moving from classical error correction, to quantum error correction: in short 1) (quantum) errors are continuous 2) the no-cloning theorem 3) measurements destroy quantum information. Despite this, after the seminal work of Shor, Steane and others, exciting progress in the area of quantum error correction is happening every day! During this second half of term, we will learn the basics and touch on some important/foundational aspects of the theory. Such topics include Shor’s 9 qubit code, the stablilizer formalism, and the Knill-Laflamme subspace condition. Prerequisite: MATH 416 or equivalent proof-based linear algebra. No prior knowledge of quantum physics is expected.
Graduate Topics Courses
Course offerings in graduate-level mathematics topics are as follows:
- MATH 595 TV, .5 Toric Varieties – Prof. Sheldon Katz
- MATH 595 GAM, Geometric Analysis – Prof. Gabriele La Nave
- MATH 595 TQF, Topological Quantum Field Theory – Prof. Gabriele La Nave
- MATH 595 LTG, Lagrangian Torus Fibrations – Prof. Joey Palmer
- MATH 595 SM, Sieve Methods – Prof. Kevin Ford
- MATH 595 OS, Operator System Theory – Prof. Roy Araiza
- MATH 595 INC, Integrable Combinatorics – Prof. Philippe Di Francesco
- MATH 595 LC, Local Cohomology – Prof. Sankar Dutta
- MATH 595 QC, Quantum Channels – Prof. Felix Leditzky
Special Course Requests
Graduate Students May Request to Take a 400-Level Course for 4 Credits
Many 400-level MATH classes are offered as 3-credit sections by default, but some may have a 4-credit option available to graduate students, at the instructor’s discretion. Please note that the inclusion of a 4-credit section on the timetable does not guarantee that the instructor will be offering a 4-credit option.
Graduate students requesting the 4 credit hour section must first register for the 3 hour section. If the instructor is willing to offer extra work to graduate students for the 4-hour section, students can fill out the request form between the first day of the semester and the 8th week of the semester at this link: https://go.math.illinois.edu/3to4credit
Undergraduate Students May Request to Take a 500-Level Course
Undergraduate students who are interested in taking a graduate mathematics course should first have completed significant work at the 400-level with A or A+ grades. To request approval to take a graduate MATH course, please email firstname.lastname@example.org using the subject line “Undergraduate requesting a graduate course.” The same email should include your name, netID, UIN, the course you're requesting to take, the CRN of the course requested, and reason for your request.
Note that for some classes, including MATH 500 and MATH 540, review may be delayed to ensure that students in mathematics graduate programs are able to register for the classes they need. Review may also be delayed if the current semester’s class grades are needed for the review.