Teaching
This semester (Autumn 2025) I'm
teaching Math 265 "Linear Algebra" at Purdue University
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 2nd 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 2nd Ed by Gerald
Folland, which one can find at the author's homepage here.