Teaching

In this spring, I am teaching Math 223 (Calculus III) , Math 247 (Linear Algebra I) and Math 611 (Measure Theory). In 2017~2021 fall, I taught Math 492W (Mathematics Capstone Experience), where students write math biographies, work on mini-projects, and write up the final project reports on RSA Cryptography, Google Page Rank, and Deep Learning. In 492W, besides calculus and linear algebra, there are excursions to number theory, discrete math, combinatorial games and differential equations to cover interesting math ideas/techniques. The free open-source mathematics software SAGE is used to aid the exploration. We also round up the picture by presenting global views on mathematics of great mathematicians. The course webpages are on D2L.

In the past, I have taught standard undergraduate courses including Math 115 (Precalculus), Math 121 & 122, Math 234 (Calculus I, II, III), Math 247 & Math 447/547 (Linear Algebra I & II), Math 321 (Ordinary Differential Equations), and Abstract Algebra I. I have also lead seminars of projective geometry and real analysis.

Besides undergraduate courses, recently I have taught the following graduate courses:

  1. Math 611 Measure Theory (2018, 2022 spring): This is a continuing course of Real Analysis I and II. We cover Lebesgue measure and integration theory, integral and differentiation theorems, classic Banach spaces, with topics in Baire category, probability, Fourier analysis and general measure theory.
  2. Math 692 Topology (2017, 2021 spring): This is a first course for point set topology and algebraic topology. We first introduce topological spaces and their constructions (subspace, product, quotient topologies), continuity, connectivity, compactness, separation properties, metric spaces. Then we introduce the winding number and Euler number, and give many classic applications. After that, we refine these invariants to the fundamental group and homology group, and connect them to recent applications: persistence homology in topological data analysis.
  3. Math 680 Nonlinear Dynamics (2016 fall): This is a first course on nonlinear dynamics and chaos. We use analytical methods, concrete examples, and geometric intuition to develop the basic theory of dynamical systems. We cover many sections of Strogatz’s book “Nonlinear Dynamics and Chaos”, including phase plane study, bifurcation analysis, limiting cycles, perturbation methods, index theorems, discrete dynamics, with many applications to physics, biology and engineering.