Teaching

U.S. Naval Academy

• SM122S, Calculus II, fall 2013, fall 2014, fall 2015, fall 2016, fall 2017, fall 2019. The course gives students hands-on experience with physics and engineering applications of integrals, infinite series, and three-dimensional vectors. The course also helps students build algebraic skills and geometrical intuition required for any STEM discipline.

• SM221, Calculus III, fall 2012, spring 2014, spring 2015. This course deals with multidimensional integration and differentiation. It is an interesting, yet challenging course. It helps students develop a spatial visualization ability. Analytical concepts such as line integrals, surface integrals, fluxes, etc. are illustrated on applied problems.

• SM212P, Differential Equations, spring 2013, spring 2016, spring 2019. In this course students learn to recognize various classes of differential equations and apply the right technique to solve them. A big part of the course is devoted to the discussion of various application problems such as population dynamics, resonance in mechanical and electrical systems, oscillators, sound reverberation in electronic music as well as mathematical ideas and equations behind them.

• SM291, Fundamentals of Mathematics, spring 2017, spring 2018, spring 2020. The aim of this course is to facilitate a smooth transition from courses designed to develop computational skills and problem-solving abilities to courses which emphasize logical reasoning, theorem proving and mathematical writing.

• SM333, Sequences and Series, fall 2015. The course revolves around the concepts of real numbers, convergence, and continuity, which are fundamental to mathematics. This course helps students develop technical writing and communication skills.

• SM464, Topology, fall 2015, fall 2019. This course is focused on the global structure of spaces (surfaces, domains, intervals, etc.) that are preserved under “continuous stretching”.

Ohio State University

• Calculus and Analytic Geometry III, spring 2011. The learning goals of the course is similar to those of USNA’s SM122. This course was a part of the Fundamentals of Engineering for Honors Program at OSU and was coordinated between Departments of Physics, Mathematics, and Engineering. Each class had more than 80 students.

• Calculus and Analytic Geometry IV, fall 2009, fall 2010, fall 2011. The syllabus of the course is similar to that of SM221.

• Ordinary and Partial Differential Equations, winter 2010, spring 2010, winter 2011, spring 2012. The syllabus of the course is similar to that of SM212. Each class had more than 100 students.

• Probability Theory, fall 2011, winter 2012. In this two-quarter series, the students learned the concepts of random variables, random walks, central limit theorems, and related results and concepts. The course was tailored for graduate math and engineering students. Proofs were included. I used the book “Probability Theory and Examples” by Rick Durrett.

• Ergodic Theory, winter 2011. We used the book “An Introduction to Ergodic Theory” by Peter Walters. The class revolved around such concepts as ergodicity, time and space averages, mixing, and entropy.

• Real Analysis, fall 2010, a recitation session. This course covers Lebesgue integration, modes of convergence and set theory.