# Teaching Philosophy

My approach to teaching is focused on making the best use of class time by having students work together, actively doing math. I accomplish this in a wide variety of courses, class sizes, and settings, using active learning techniques adapted to the particular class.

I'm always interested in discussing approaches to teaching and how best to implement them. I'm eager to incorporate new types of activities into my classes, in order to retain students' interest, and to accomodate students with a variety of learning styles.

Below, I include a list of courses which I've taught.

# Teaching Experience

I have taught as an instructor for the following courses at the University of Minnesota:

- Math 1471. UMTYMP Calculus 1. Functions of one variable; limits; continuity; derivatives, including geometric interpretation of first and second derivatives; extended mean value theorem, optimization; Newton’s method; proofs of major results, such as the product rule, chain rule, and L’Hospital’s rule.
- Math 1472. UMTYMP Calculus 1. Sequences/series, vector functions, differentiation in multivariable calculus. Introduction to first-order systems of differential equations. Emphasizes concepts/explorations.
- Math 2471. UMTYMP Calculus 2. Theoretical course in linear algebra, including Euclidean space and general vector spaces; eigenvalues and systems of differential equations.
- Math 2472. UMTYMP Calculus 3. Multivariable calculus through differentiation. Focuses on proofs and formal reasoning.
- Math 2473. UMTYMP Calculus 3. Multivariable integration, vector analysis, nonhomogeneous linear equations, nonlinear systems of equations. Emphasizes concepts/explorations.
- Math 5248. Cryptology and Number Theory. Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probabilistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves.
- Math 5251. Error-Correcting Codes, Finite Fields, and Algebraic Curves. Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves.

I have taught as a workshop leader for the following courses at the University of Minnesota:

- Math 1471. UMTYMP Calculus 1. Functions of one variable; limits; continuity; derivatives, including geometric interpretation of first and second derivatives; extended mean value theorem, optimization; Newton’s method; proofs of major results, such as the product rule, chain rule, and L’Hospital’s rule.
- Math 1472. UMTYMP Calculus 1. Sequences/series, vector functions, differentiation in multivariable calculus. Introduction to first-order systems of differential equations. Emphasizes concepts/explorations.
- Math 2471. UMTYMP Calculus 2. Theoretical course in linear algebra, including Euclidean space and general vector spaces; eigenvalues and systems of differential equations.
- Math 2472. UMTYMP Calculus 3. Multivariable calculus through differentiation. Focuses on proofs and formal reasoning.
- Math 2473. UMTYMP Calculus 3. Multivariable integration, vector analysis, nonhomogeneous linear equations, nonlinear systems of equations. Emphasizes concepts/explorations.

I have taught as an instructor for the following courses at UCLA:

- Math 1. Precalculus. Functions. Linear and polynomial functions and their graphs, applications to optimization. Inverse, exponential, and logarithmic functions. Trigonometric functions.
- Math 31A. Differential and Integral Calculus. Differential calculus and applications; introduction to integrals.

I have served as a teaching assistant for the following courses at UCLA. More detailed course descriptions can be found **here**.

- Math 3A. Calculus for Life Sciences Students. Techniques and applications of differential calculus.
- Math 3B. Calculus for Life Sciences Students. Techniques and applications of integral calculus, introduction to differential equations and multivariable differential calculus.
- Math 31A. Differential and Integral Calculus. Differential calculus and applications; introduction to integration.
- Math 110A. Algebra. Ring of integers, integral domains, fields, polynomial domains, unique factorization.
- Math 110B. Algebra. Groups, structure of finite groups.
- Math 115A. Linear Algebra. Techniques of proof, abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory.
- Math 120A. Differential Geometry. Curves in 3-space, Frenet formulas, surfaces in 3-space, normal curvature, Gaussian curvature, congruence of curves and surfaces, intrinsic geometry of surfaces, isometries, geodesics, Gauss/Bonnet theorem.
- Math 210C. Algebra. Commutative algebra, non-commutative algebra, representation theory.
- PIC 10A. Introduction to Programming. Basic principles of programming, using C++; algorithmic, procedural problem solving; program design and development; basic data types, control structures and functions; functional arrays and pointers; introduction to classes for programmer-defined data types.
- PIC 10B. Intermediate Programming. Abstract data types and their implementation using C++ class mechanism; dynamic data structures, including linked lists, stacks, queues, trees, and hash tables; applications; object-oriented programming and software reuse; recursion; algorithms for sorting and searching.

Also at UCLA, I served as an instructor and teaching assistant for the Summer Bridge and Academic Excellence Workshops run by UCLA Engineering's Center for Excellence in Engineering and Diversity. In these roles, I gave lectures and ran problem sessions designed to help entering students excel in their first calculus course (Math 31A) at UCLA. More information about these CEED programs can be found **here**.