MATH 518

Fall 2026 All Classes

All Classes

Differentiable Manifolds I

Credit: 4 hours.

Definitions and properties of differentiable manifolds and maps, (co)tangent bundles, vector fields and flows, Frobenius theorem, differential forms, exterior derivatives, integration and Stokes' theorem, DeRham cohomology, inverse function theorem, Sard's theorem, transversality and intersection theory.

Prerequisite: MATH 423 or MATH 481, or consent of instructor.

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MATH 518 class schedule data for fall 2026
	Status		CRN	Type	Section	Time	Day	Location	Instructor	Section Details
			52652	Lecture-Discussion	X1	2:00PM -2:50PM	MWF	303 English Building	Tolman, S	Availability: Open (Restricted) Part of Term: 1 Date Range: 08/24/26-12/09/26 Section Info: Undergraduates seeking approval to enroll should obtain permission from the Math Undergrad Director by filling out the webform located at https://forms.illinois.edu/sec/1209343045. Students from the following programs must contact the Director of Graduate Studies in Mathematics <math-grad@illinois.edu> to request permission to register for the course: MS:Economics:Policy Econ -UIUC or MS: Financial Engineering. Restricted to Graduate - Urbana-Champaign. Not intended for MS:Economics:Policy Econ -UIUC, MS:Economics:Policy Econ -UIUC, MS: Financial Engineering, MENG:Mechanical Enginerng-UIUC, MENG:Elec & Computer Eng-UIUC, or MENG:Engineering:Comp Eng-UIUC Restriction(s): Restricted to Graduate - Urbana-Champaign. Not intended for MS:Economics:Policy Econ -UIUC, MS:Economics:Policy Econ -UIUC, MS: Financial Engineering, MENG:Mechanical Enginerng-UIUC, MENG:Elec & Computer Eng-UIUC, or MENG:Engineering:Comp Eng-UIUC.