Yu-Jui Huang's research is focused on Mathematical Finance and the Mathematics for Machine Learning. It involves theories and techniques from stochastic analysis, stochastic control, optimal stopping, and viscosity solutions to fully nonlinear PDEs. Current projects involve optimization under time-inconsistent behaviors, systemic risk, and gradient-flow frameworks for machine learning.
APPM 1360 - Calculus 2 for Engineers
Primary Instructor
-
Fall 2019
Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Degree credit not granted for this course and MATH 2300.
APPM 3170 - Discrete Applied Mathematics
Primary Instructor
-
Spring 2020 / Spring 2022
Introduces students to ideas and techniques from discrete mathematics that are widely used in science and engineering. Mathematical definitions and proofs are emphasized. Topics include formal logic notation, proof methods; set theory, relations; induction, well-ordering; algorithms, growth of functions and complexity; integer congruences; basic and advanced counting techniques, recurrences and elementary graph theory. Other selected topics may also be covered.
APPM 4120 - Introduction to Operations Research
Primary Instructor
-
Spring 2021 / Spring 2023
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Same as APPM 5120 and MATH 4120 and MATH 5120.
APPM 4530 - Stochastic Analysis for Finance
Primary Instructor
-
Fall 2018 / Fall 2019 / Fall 2020 / Fall 2021 / Fall 2022 / Fall 2023
Studies mathematical theories and techniques for modeling financial markets. Specific topics include the binomial model, risk neutral pricing, stochastic calculus, connection to partial differential equations and stochastic control theory. Same as APPM 5530, STAT 4230 and STAT 5230.
APPM 5120 - Introduction to Operations Research
Primary Instructor
-
Spring 2021
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Recommended prerequisites: APPM 3310 OR MATH 2130 OR MATH 2135 or equivalent. Same as APPM 4120 and MATH 4120 and MATH 5120.
APPM 5530 - Stochastic Analysis for Finance
Primary Instructor
-
Fall 2018 / Fall 2019 / Fall 2020 / Fall 2021 / Fall 2022 / Fall 2023
Studies mathematical theories and techniques for modeling financial markets. Specific topics include the binomial model, risk neutral pricing, stochastic calculus, connection to partial differential equations and stochastic control theory. Recommended prerequisite: previous coursework equivalent to that of APPM 3310 and one of APPM 3570, STAT 3100 or MATH 4510; all with minimum grade of C-. Same as APPM 4530, STAT 5230 and STAT 4230.
APPM 6560 - Measure-Theoretic Probability
Primary Instructor
-
Spring 2022 / Spring 2023
Introduces a series of fundamental concepts and results in probability theory, using rigorous measure-theoretic language. Provides a solid foundation for further studies and research in probability, stochastic processes, statistics, and data science. Recommended prerequisites: Undergraduate analysis at the level of APPM 4440.
APPM 6570 - Stochastic Differential Equations
Primary Instructor
-
Spring 2021
Devoted to a comprehensive investigation of stochastic differential equations, as well as their important applications in Finance, Physics, and Engineering. Consists of three main topics: stochastic integration, the theory of stochastic differential equations (SDEs), and applications of SDEs. Recommended prerequisite: APPM 6560 or MATH/APPM 6550.
APPM 6950 - Master's Thesis
Primary Instructor
-
Fall 2021 / Spring 2022
May be repeated up to 6 total credit hours.
APPM 7400 - Topics in Applied Mathematics
Primary Instructor
-
Fall 2018 / Fall 2019
Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
MATH 4120 - Introduction to Operations Research
Primary Instructor
-
Spring 2021 / Spring 2023
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Same as APPM 5120 and APPM 4120 and MATH 5120.
