Discrete and continuous-time stochastic models, including Markov chains and Poisson processes. Examines stationarity, autocorrelation, and transition probabilities to analyze systems evolving over time.
This sequence bridges the gap between discrete mathematics and quantitative finance, focusing on the application of geometric series to asset valuation, loan amortization, and risk management. Graduate students will develop the mathematical foundations for pricing complex financial instruments and understanding market dynamics.
A graduate-level exploration of expected value through the lens of measure theory, covering Lebesgue integration, fundamental inequalities, convergence theorems, and conditional expectation using Sigma-algebras.
A graduate-level sequence exploring the gradient vector as the foundational tool for modern optimization. Students move from the geometric interpretation of multivariate derivatives to the implementation of stochastic algorithms used in machine learning.
An advanced graduate-level exploration of stochastic processes, covering discrete and continuous-time Markov chains, Poisson processes, and queueing theory. The sequence bridges theoretical rigor with computational application through simulations and real-world modeling.
An advanced graduate-level sequence exploring the mathematical foundations and computational applications of stochastic processes, from discrete-time Markov chains to Monte Carlo simulations.
A comprehensive introduction to Time Series Analysis for 12th-grade students, focusing on random processes, autocorrelation, stationarity, and smoothing techniques. Students move from basic random walks to understanding complex dependencies in temporal data.
