Yi Ni

Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms, 2026-27. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence.
Instructors: Ni, Gherman, Flach, Song

Ma 151 abc. Geometry and Topology. 9 units (3-0-6); first, second, third terms, 2026-27. Prerequisites: Ma 109 abc or equivalent. Part a: Homology Theory. CW complexes, homology and calculation of homology groups, exact sequences, cohomology rings, Poincare duality. Part b: Homotopy Theory and K-theory. Fibrations, higher homotopy groups, and exact sequences of fibrations. Fiber bundles, Eilenberg-MacLane spaces, classifying spaces. K-theory, generalized cohomology theory, Bott periodicity. Part c: Basic Riemannian geometry: geometry of Riemannian manifolds, connections, curvature, Bianchi identities, completeness, geodesics, exponential map, Gauss's lemma, Jacobi fields, comparison theorems, relation between curvature and topology.
Instructors: Ni, Qin