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, random tree evolutions
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 3850  Seminar in Guided Mathematics Instruction
Primary Instructor

Spring 2019
Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to learning assistants in Math.
MATH 4520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2018 / Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023 / Summer 2023
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 4820  History of Mathematical Ideas
Primary Instructor

Fall 2020 / Fall 2021 / Fall 2022 / Spring 2024
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820.
MATH 5520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2020 / Spring 2022
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. Recommended prerequisite: previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510; minimum grade of C for all. Same as STAT 4520 and MATH 4520 and STAT 5520.
MATH 5820  History of Mathematical Ideas
Primary Instructor

Fall 2020 / Fall 2021 / Fall 2022
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended requisite: completion of upper division Written Communication requirement. Same as MATH 4820.
MATH 6320  Introduction to Real Analysis 2
Primary Instructor

Spring 2021 / Spring 2022 / Spring 2023 / Spring 2024
Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the RadonNikodym and Fubini theorems. Presents the general theory of differentiation on the real line and the Fundamental Theorem of Lebesgue Calculus. Recommended prerequisite: MATH 6310. Instructor consent required for undergraduates.
MATH 6534  Topics in Mathematical Probability
Primary Instructor

Spring 2020 / Fall 2024
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.
STAT 4520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023 / Summer 2023
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.
STAT 5520  Introduction to Mathematical Statistics
Primary Instructor

Spring 2020 / Spring 2022 / Spring 2023
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. Recommended prerequisite: previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510; minimum grade of C for all. Same as STAT 4520 and MATH 4520 and MATH 5520.