The Mathematics Department teaches Honors sections of Mathematics 53, 54, 104, 110, 113 and 185 (denoted H53..., H185). These are for students with strong mathematical ability and interests, who wish to see a deeper and more rigorous development of the material, and be challenged by difficult problems.
In general H54 (Honors Linear Algebra & Differential Equations), H104 (Honors Introduction to Analysis) and H110 (Honors Linear Algebra) are offered in the Fall semester and H53 (Honors Multivariable Calculus), H113 (Honors Abstract Algebra) and H185 (Honors Complex Analysis) are offering in the Spring semester, but check the Course Offerings to be sure.
Honors courses satisfy the same course requirements as their non-honors equivalents.
Depending on your background and abilities, and on decisions made by the instructor as to what to include in the course, an honors course may be far more work for you than the corresponding non-honors course. (A GPA in previous math courses of at least 3.5 should be considered a minimum evidence of preparation.) If you are unsure of whether to take such a course, you should (a) meet with the instructor at or before the start of the Semester and discuss your background and the instructor's plans for the course, and (b) sit in on the first few days of the course, do the initial homework assignments, and see how successful you are with them.