This fall I am teaching Mathematical aspects of data analysis and Numerical linear algebra.
As an undergraduate and masters student at MIT and a graduate student at RPI, I have been a teaching assistant for many courses. These courses are listed with the descriptions taken verbatim from the RPI and MIT course catalogs.TA for Methods of Partial Differential Equations of Mathematical Physics: RPI Department of Mathematics, Spring 2019
TA for Advanced Calculus: RPI Department of Mathematics, Fall 2018
TA for Complex Variables with Applications: RPI Department of Mathematics, Spring 2016
TA for Foundations of Applied Mathematics: RPI Department of Mathematics, Fall 2015
TA for Introduction To Differential Equations: RPI Department of Mathematics, Spring 2015
TA for Multivariable Calculus and Matrix Algebra: RPI Department of Mathematics, Fall 2014
TA for Unified Engineering: Mechanics and Structures: MIT Department of Aeronautics and Astronautics, Fall 2013
Instructor for Introduction to Existentialism: MIT Junction Program, Summer 2010
TA for Multivariable Calculus: MIT Experimental Studies Group, Fall 2009-Spring 2012
An intermediate course serving to introduce both the qualitative properties of solutions of partial differential equations and methods of solution, including separation of variables. Topics include first-order equations, derivation of the classical equations of mathematical physics (wave, potential, and heat equations), method of characteristics, construction and behavior of solutions, maximum principles, energy integrals.
A course emphasizing advanced concepts and methods from calculus. Topics include: multivariable integral theorems (Green’s, divergence, Stokes’, Reynolds transport), extrema of multivariable functions (including Taylor’s theorem and Lagrange multipliers), the calculus of variations (Euler–Lagrange equations, constraints, principle of least action), and Cartesian tensors (calculus, invariants, representations).
An introduction to the theory and applications of complex variables. Topics include analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residues, conformal mapping, harmonic functions, and Laplace transforms. Applications will be to problems in science and engineering such as fluid and heat flow, dynamical systems, and electrostatics.
Mathematical formulation of models for various processes. Derivation of relevant differential equations from conservation laws and constitutive relations. Use of dimensional analysis, scaling, and elementary perturbation methods. Description of basic wave motion. Examples from areas including biology, elasticity, fluid dynamics, particle mechanics, chemistry, geophysics, and finance.
First-order differential equations, second-order linear equations, eigenvalues and eigenvectors of matrices, systems of first-order equations, stability and qualitative properties of nonlinear autonomous systems in the plane, Fourier series, separation of variables for partial differential equations.
Directional derivatives, maxima and minima, double integrals, line integrals, div and curl, and Green’s Theorem; matrix algebra and systems of linear equations, vectors and linear transformations in R^n, eigenvectors and eigenvalues, applications in engineering and science.
Presents fundamental principles and methods of materials and structures for aerospace engineering, and engineering analysis and design concepts applied to aerospace systems. Topics include statics; analysis of trusses; analysis of statically determinate and indeterminate systems; stress-strain behavior of materials; analysis of beam bending, buckling, and torsion; material and structural failure, including plasticity, fracture, fatigue, and their physical causes. Experiential lab and aerospace system projects provide additional aerospace context
This is an introductory course on existentialism for high school students. After a brief motivation of existentialism, the course discusses the philosophy of Albert Camus, Kierkegaard, Nietzsche and Sartre. Central works of these philosophers are discussed. In addition, we will watch movies with existential theme “The Seventh Seal”, “Waiting for Godot”, “Run Lola Run” and “Ikiru”. Through a diverse coverage of existential philosophy, movies and literature, the course aims to give a comprehensive introduction to existentialism.
Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green’s theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes’ theorem; applications.