Some of my research interests include studying problems that arise from or involve materials. I have studied composite materials using multiple scales analysis to study problems related to conductivity over heterogeneous electrode surfaces. This work required a deep analysis of the partial differential equations (PDEs) modeling the phenomena using asymptotic scales as well as a rigorous numerical solution of the PDEs. Another field of my research includes modeling and analyzing data using a data mining/machine learning approach based on spectral graph theory methods, probability and statistics. Large data sets are modeled on manifolds using a graph Laplacian approach. My recent work in this area involves using a graph theory based learning algorithm to perform a pattern analysis of synaptic activity induced by seizurelike events as well as using spectral graph theory based dimension reduction algorithms to analyze simulated radar and ladar data.
keywords
partial differential equations, asymptotics, numerical analysis, graph theory, probability and statistics
Teaching
courses taught
APPM 1340  Calculus 1 with Algebra, Part A
Primary Instructor

Fall 2019
Studies selected topics in analytical geometry and calculus: rates of change of functions, limits, derivatives and their applications. This course and APPM 1345 together are equivalent to APPM 1350. The sequence of this course and APPM 1345 is specifically designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for APPM 1350. For more information about the math placement referred to in the Enrollment Requirements, please contact your academic advisor.
APPM 1345  Calculus 1 with Algebra, Part B
Primary Instructor

Spring 2020
Continuation of APPM 1340. Studies selected topics in calculus: derivatives and their applications, integration, differentiation and integration of transcendental functions. Algebraic and trigonometric topics are studied throughout, as needed. Degree credit not granted for this course and APPM 1350 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330.
APPM 1350  Calculus 1 for Engineers
Primary Instructor

Spring 2018 / Spring 2019
Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the Enrollment Requirements, contact your academic advisor. Degree credit not granted for this course and APPM 1345 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330.
APPM 3170  Discrete Applied Mathematics
Primary Instructor

Spring 2018 / Fall 2018
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, wellordering; 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 3310  Matrix Methods and Applications
Primary Instructor

Summer 2018 / Summer 2019
Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Degree credit not granted for this course and MATH 2130 and MATH 2135.
APPM 3570  Applied Probability
Primary Instructor

Fall 2018
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as STAT 3100.
APPM 4350  Methods in Applied Mathematics: Fourier Series and Boundary Value Problems
Primary Instructor

Fall 2019
Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions. Same as APPM 5350.
APPM 4570  Statistical Methods
Primary Instructor

Spring 2019
Covers basic statistical concepts with accompanying introduction to the R programming language. Topics include discrete and continuous probability laws, random variables, expectation and variance, central limit theorem, testing hypothesis and confidence intervals, linear regression analysis, simulations for validation of statistical methods and applications of methods in R. Same as APPM 5570.
APPM 5570  Statistical Methods
Primary Instructor

Spring 2019
Covers basic statistical concepts with accompanying introduction to the R programming language. Topics include discrete and continuous probability laws, random variables, expectation and variance, central limit theorem, testing hypothesis and confidence intervals, linear regression analysis, simulations for validation of statistical methods and applications of methods in R. Same as APPM 4570.
STAT 3100  Applied Probability
Primary Instructor

Fall 2018
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as APPM 3570.
STAT 4000  Statistical Methods and Application I
Primary Instructor

Spring 2019
Introduces exploratory data analysis, probability theory, statistical inference, and data modeling. Topics include discrete and continuous probability distributions, expectation, laws of large numbers, central limit theorem, statistical parameter estimation, hypothesis testing, and regression analysis. Considerable emphasis on applications in the R programming language. Same as STAT 5000.
STAT 5000  Statistical Methods and Application I
Primary Instructor

Spring 2019
Introduces exploratory data analysis, probability theory, statistical inference, and data modeling. Topics include discrete and continuous probability distributions, expectation, laws of large numbers, central limit theorem, statistical parameter estimation, hypothesis testing, and regression analysis. Considerable emphasis on applications in the R programming language. Same as STAT 4000.