Dr. Englander's research concerns spatial branching particle systems and superprocesses, and their relationship to nonlinear partial differential equations. Special focus is on interactions and random environments. Furthermore, some nonclassical random walks and inhomogeneous Markov chains are studied.
keywords
Spatial branching processes, superprocesses, nonlinear partial differential equations, random environments, interacting particle systems, nonclassical random walks, inhomogeneous Markov chains
APPM 4520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2018
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distributionfree methods. Same as STAT 5520 and MATH 4520 and MATH 5520.
APPM 5520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2018
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distributionfree methods. Department enforced prerequisite: one semester calculusbased probability course, such as MATH 4510 or APPM 3570. Same as STAT 4520 and MATH 4520 and MATH 5520.
APPM 6550  Introduction to Stochastic Processes
Primary Instructor

Fall 2019
Systematic study of Markov chains and some of the simpler Markov processes including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560 or instructor consent. Same as MATH 6550.
MATH 2400  Calculus 3
Primary Instructor

Spring 2019
Continuation of MATH 2300. Topics include vectors, threedimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis. Department enforced prerequisite: MATH 2300 or APPM 1360 (minimum grade C). Degree credit not granted for this course and APPM 2350.
MATH 4520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2018 / Spring 2020
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distributionfree methods. Same as MATH 5520 and STAT 4520 and STAT 5520.
MATH 5520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2018 / Spring 2020
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distributionfree methods. Department enforced prerequisite: MATH 4510 or MATH 5510 or APPM 3570. Same as MATH 4520 and STAT 4520 and STAT 5520.
MATH 6534  Topics in Mathematical Probability
Primary Instructor

Spring 2020
Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains and Brownian motion. Department enforced prerequisite: MATH 6310. Instructor consent required for undergraduates
MATH 6550  Introduction to Stochastic Processes
Primary Instructor

Spring 2018 / Fall 2019
Systematic study of Markov chains and some of the simpler Markov processes, including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Department enforced prerequisite: MATH 4001 or MATH 4510 or APPM 3570 or APPM 4560. Instructor consent required for undergraduates. Same as APPM 6550.