Manifolds (MATH-0285)

Fall 2023 · MATH 0285 · Tufts University · 3 credits · Undergraduate

Key examples of manifolds such as spheres, tori, projective spaces. Topics in manifolds, including quotients, submanifolds, regular level sets, Lie groups, and smooth maps between manifolds. Topics in tangent spaces, including differential and rank of a smooth map, regular level set theorem (implicit function theorem), vector fields, integral curves, and the Lie algebra of a Lie group. Topics in differential forms and integration, including: wedge product, pullback of forms, exterior derivatives, orientation, integral of an n-form, and Stokes’ theorem. Prerequisites: Math 135, Math 136, Math 145, and graduate standing; or permission of instructor.

Course codes: MATH-0285, MATH 0285, MATH0285, MATH-285, MATH 285, MATH285

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