Honors courses in Mathematics are for highly motivated and mathematically talented students who are interested in mathematics, engineering, and sciences. The courses rapidly introduce students to the rigorous and abstract thought processes of higher mathematics.
Students in honors courses enjoy small classes and close contact with research-active faculty from the very first day. And most students develop close working relationships with classmates because they study together for up to four semesters.
Honors Courses
Math 424. Honors Real Analysis (3 hours)
Continuity, compactness, completeness, connectedness and uniform convergence are developed in the metric space setting, and are then applied to rigorously establish the fundamentals of calculus, including the theory of differentiation, Riemann-Darboux integration, sequences and series of functions, and interchange of limiting operations.
Math 425. Honors Advanced Analysis (3 hours)
This course provides a theoretical treatment of differential and integral calculus in higher dimensions. Topics include inverse and implicit function theorems, submanifolds, the theorems of Green, Gauss and Stokes, differential forms, and applications.
Math 427. Honors Abstract Algebra (3 hours)
Group theory elucidates structures ranging from elementary clock arithmetic to symmetries in theoretical physics. This abstract algebra course displays the power and also the beauty of groups, covering counting formulae, factorization, and modules, with applications to the structure of Abelian groups and linear operators.
Math 428. Honors Topics in Mathematics (3 hours)
A capstone course whose topic can vary. Possibilities include geometric analysis, algebraic geometry, and computational algebra.
Entry requirements for Honors Courses
| Course | Approval Criteria |
|---|---|
| MATH 241H | One of the following:
|
| MATH 314H | One of the following:
Strongly recommended: Coursework using proof-based mathematics |
| MATH 416H | One of the following:
|
| MATH 424 |
|
| MATH 425 | Grade of A- or higher in MATH 424 or MATH 447 |
| MATH 427 |
|
| MATH 428 |
|
Registering for Honors Courses
To request approval for an honors course, please fill out this form: https://forms.illinois.edu/sec/1782500582
Requirements satisfied by Honors Courses
Honors courses count toward the mathematics major and minor.
Students in other majors can consult the following list to determine how honors courses might count towards their degree requirements:
- Math 424 meets any requirement for Math 447.
- Math 425 does not relate to any specific requirement.
- Math 427 meets any requirement for Math 417.
- Math 428 does not relate to any specific requirement.
Further Information
To learn more about the honors courses, or to ask advice on how to fit it into your course of study, please contact the mathematics advising team.