Math 33x Series
Accelerated Honors Advanced Calculus
See the page on Honors Mathematics for course equivalencies and registration information if you are considering taking this series. Note that the honors series is transitioning to a new syllabus in 2027-2028 which will involve changes to content, name, and equivalencies so please pay attention.
Textbook
- Advanced Calculus by Gerald B. Folland (for Math 334 and Math 335)
Suggested Syllabus
Math 334
- Topology of Euclidean space, open sets, limits and continuity, completeness and compactness
- Bolzano-Weirstrass and Heine-Borel theorems, connectedness, uniform continuity
- Differentiation in several variables, the chain rule, mean value theorem, higher order differentiation
- Taylor's theorem, critical points, extremal problems and Lagrange multipliers
- The implicit and inverse function theorems, curves and surfaces in the plane and space
- Integration in several variables, multiple and iterated integrals, the change of variables formula
Math 335
- Integration over lines and surfaces: parametrizations
- Theorems of Green, Gauss (divergence), and Stokes
- Infinite series: absolute and conditional convergence, convergence tests
- Sequences and series of functions: uniform convergence, integration and differentiation
- Power series, complex exponential and trigonometric functions, the Gamma function
Math 336
In Spring 2027, Math 336 will cover Math 480 Functional Analysis. Functional analysis provides tools for studying linear and nonlinear problems on infinite-dimensional (normed) vector spaces. This framework underlies much of modern analysis, differential equations, and quantum mechanics. Topics covered include- Normed spaces, completeness, linear functionals
- Hahn-Banach Theorem, duality, operators
- Hilbert spaces
- Compact and self-adjoint operators
- The Spectral Theorem