Mojtaba Tefagh – Teaching

Rigorous introduction to game theory and its applications to economics, political science, computer science, and biology. Topics include normal and extensive forms, dominant strategies, static and dynamic games of complete and incomplete information, repeated games and refinements, elements of evolutionary game theory, solution concepts such as Nash equilibrium, subgame-perfect equilibrium, and Bayesian equilibrium.

Computational thinking and programming code, data representation and data types, branching and iteration, recursion and bisection, string manipulation, tuples and lists, arrays and dictionaries, variables and immutable data structures, functions and methods, classes and objects, abstraction and interfaces, encapsulation and object-oriented programming, inheritance and polymorphism, overloading and overriding, testing and debugging, exceptions and assertions.

Frontiers in mechanism design and incentive engineering for cryptoeconomic systems such as decentralized finance (DeFi). This course focuses on both the systemic risks at the protocol level ranging from miner extractable value (MEV) to transaction fee price manipulation and the economic exploits on the incentive layer like malicious flash loan transactions and the horrors of the dark forest. Through a wide variety of examples of issues stemming from incentive misalignment, we will see the emergence of adversarial attacks by self-interested rational agents who behave strategically to optimize their own objectives and values.

Introduction to applied linear algebra with a focus on applications. Vectors, distance, and angle; applications to clustering (the k-means algorithm) and document analysis. Matrices, left and right inverses, QR factorization; applications to population and epidemic dynamics. Least-squares, constrained and nonlinear least-squares; applications to model fitting, regularization and cross-validation. Additional applications include but are not limited to time-series prediction, tomography, optimal control, and portfolio optimization.

Vector space, linear independence, dimension, duality, linear mappings, matrices, nonsingular matrices, kernel, determinant, trace, spectral theory, eigenvalues, eigenvectors, eigendecomposition, conjugacy, Cayley-Hamilton theorem, inner product space, orthonormal basis, euclidean structure, self-adjoint mappings, Hermitian matrices, unitary matrices, orthogonal matrices, diagonalizable matrices, semi-definite matrices, matrix inequalities, convexity, normed linear spaces, positive matrices, systems of linear equations, matrix decomposition, the Jordan canonical form.

This course discusses computational systems biology focusing on select topics in fluxomics in a well-balanced mixture of biology, mathematics, and computer science. We start by looking in detail at the mathematical underpinning of constraint-based analysis of genome-scale metabolic network reconstructions and provide a foundation for the analysis of optimization algorithms involved. Subsequently, we provide an overview of various papers and toolboxes from the literature in the remainder of the semester. Students will explore concepts through a research-oriented term project that will require them to define goals, success metrics, and deliverables for a computational challenge in systems biology and implement and evaluate a solution.

Least-squares, constrained and nonlinear least-squares; applications to model fitting, regularization and cross-validation. Convex sets and functions and the corresponding analytical conditions for recognition. The basics of convex analysis and theory of convex programming: Karush-Kuhn-Tucker (KKT) optimality conditions, complementary slackness conditions, duality theory (weak and strong duality theorems), sensitivity analysis, theorems of the alternatives including Farkas’ lemma. Linear and quadratic programming, semidefinite programming, and geometric programming.