Undergraduate Courses

• MATH 438 Mathematical Foundation of Deep Learning: Mathematical methods for Deep Learning, Regression Types, Perceptron Models, Shallow Networks, Universal Approximation Theorem, Feedforward NN, SGD Convergence Analysis, Backpropagation, Regularization, L2 and L1 Penalties, Mathematical Intuition of RNNs, Application of CNNs.

• MATH 457 Methods of Mathematical Economics: Introduction to linear programming. Examples from economics, the transportation problem, the diet problem, Chebyshev approximation. Representations of linear programs. Graphical solution. The Simplex method. Brief review of some linear algebra. The simplex tableau. Convergence of the simplex method. Linear programming in matrix form. Duality. Duality for linear programs in canonical form. The dual of a linear program in general form. Complementary slackness. The separating hyper plane theorem. Perturbations and parametric programming. Zero-sum matrix games. Multi objective linear programming. Integer linear programming: Gomory’s method. Network flows. Assignment and shortest-route problems.

• MATH 494 Mathematical Methods for Data Analysis: Linear regression, Logistic regression, Overfitting, Regularization, and model validation techniques, Support Vector Machines (SVM), Clustering, Principal Component Analysis (PCA), Feedforward Neural Networks, Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN).

Graduate Courses

• MATH 504 Computational Number Theory and Modern Cryptography: As an introduction, the course will provide a brief overview of major public-key cryptographic systems, including RSA encryption, the Diffie-Hellman key exchange protocol, ElGamal encryption and digital signatures, and elliptic curve cryptography. The focus will then shift to the factorization problem and the discrete logarithm problem, which form the basis of the security of these algorithms. In addition, the course will cover primality tests such as divisibility, the Miller-Rabin test, elliptic curve tests, and the AKS test; factorization algorithms such as the rho method, the quadratic number field sieve, and the generalized number field sieve; and discrete logarithm algorithms including Pollard's rho method, the index calculus method, and the elliptic curve index calculus method. These topics constitute the core content of the course.

• MATH 545 Mathematical Fundamentals of Gauge Theories: Introduction to topology and differentiable manifolds. Vector fields and differential forms. Fibre bundles and connections. Yang-Mills fields and gauge formulation of general relativity.

• MATH 550 Mathematical Methods of Quantum Gravity: Linear Hamiltonian systems, Quantum fields on curved manifolds, Canonical quantization of gauge theories, mathematical formulations of general relativity, Hilbert space of quantum geometries.

• MATH 551 Mathematical Fundamentals of Advanced Quantum Gravity: Geometry of connections and gauge theory, holonomy-flux algebra, spin-networks and representation theory, topological field theory with defects and covariant formulation of loop quantum gravity.