Teaching Notes

The following are my lectures notes from the courses that I taught at Yale University

Linear Algebra: click here!

This course covers proofs and standard linear algebra subjects including fields, vector spaces, linear maps, matrix algebra, determinants, systems of linear equations, and eigenvalues/eigenvectors. The linear algebra portion follows Linear Algebra (5th ed.) by Friedberg, Insel, and Spence (Pearson), though I deviate from the text during the chapter on determinants.

Analysis I: click here! (Lecture 1 are slides)

This course covers construction of the real numbers, limits and continuity, metric space topology, single variable differential and integral calculus, and Taylor polynomials/series. The last third of the course follows portions of Advanced Calculus 2^nd Ed by Gerald Folland, which one can find at the author’s homepage here.

Vector Analysis and Integration on Manifolds: click here!

This course is a continuation of Analysis I above and develops differential and integral calculus in several variables, inverse/implicit function theorem, embedded submanifolds of Euclidean space, tensor algebra and differential forms, culminating in the generalized Stokes’ Theorem. Roughly the first 70% of the course follows portions of Advanced Calculus 2^nd Ed by Gerald Folland, which one can find at the author’s homepage here.