My research area is in the realm of computational methods for data analytics. I use spectral graph theory, computational harmonic analysis, applied probability, and machine learning to design algorithms for extracting information from complex datasets.
APPM 3170 - Discrete Applied Mathematics
Primary Instructor
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Fall 2019 / Fall 2021 / Fall 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 4515 - High-Dimensional Probability for Data Science
Primary Instructor
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Fall 2020 / Fall 2022 / Fall 2024
Provides students with an exposition of the most recent methods of high-dimensional probability for the analysis of high dimensional datasets. Applications include randomized algorithms and high-dimensional random models of datasets. Same as APPM 5515.
APPM 4720 - Open Topics in Applied Mathematics
Primary Instructor
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Fall 2019
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 15 total credit hours. Same as APPM 5720.
APPM 5440 - Applied Analysis 1
Primary Instructor
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Fall 2023 / Fall 2024
Discusses the elements of basic real and complex analysis, Banach spaces, Lp spaces and many relevant inequalities. Includes applications of existence and uniqueness of solutions to various types of ordinary differential equations, partial differential equations, and integral equations. Department enforced prerequisites: APPM 4440 and APPM 4450.
APPM 5450 - Applied Analysis 2
Primary Instructor
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Spring 2024
Continuation of APPM 5440. Department enforced prerequisite: APPM 5440.
APPM 5515 - High-Dimensional Probability for Data Science
Primary Instructor
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Fall 2020 / Fall 2022 / Fall 2024
Provides students with an exposition of the most recent methods of high-dimensional probability for the analysis of high dimensional datasets. Applications include randomized algorithms and high-dimensional random models of datasets. Same as APPM 4515. Recommended prerequisites: APPM 3310 and APPM 3570, or equivalent.
APPM 5720 - Open Topics in Applied Mathematics
Primary Instructor
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Fall 2019
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 6 total credit hours. Same as APPM 4720.
APPM 6560 - Measure-Theoretic Probability
Primary Instructor
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Spring 2024
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 6950 - Master's Thesis
Primary Instructor
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Fall 2021 / Spring 2022
May be repeated up to 6 total credit hours.
ECEN 4632 - Introduction to Digital Filtering
Primary Instructor
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Spring 2018 / Fall 2018 / Fall 2019
Covers both the analysis and design of FIR and IIR digital filters. Discusses implementations in both software and hardware. Emphasizes use of the FFT as an analysis tool. Includes examples in speech processing, noise canceling, and communications.
ECEN 5322 - Data and Network Science
Primary Instructor
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Spring 2019
The course covers the theory and design of algorithms that are used to model, analyze, and extract information from large scale datasets and networks. The course includes a project. Same as ECEN 4322.
ECEN 5632 - Theory and Application of Digital Filtering
Primary Instructor
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Spring 2018 / Fall 2018 / Fall 2019
Digital signal processing and its applications are of interest to a wide variety of scientists and engineers. The course covers such topics as characterization of linear discrete-time circuits by unit pulse response, transfer functions, and difference equations, use of z-transforms and Fourier analysis, discrete Fourier transform and fast algorithms (FFT), design of finite and infinite impulse response filters, frequency transformations, study of optimized filters for deterministic signals.
STAT 4000 - Statistical Methods and Application I
Primary Instructor
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Spring 2021
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 4610 - Statistical Learning
Primary Instructor
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Spring 2020
Consists of applications and methods of statistical learning. Reviews multiple linear regression and then covers classification, regularization, splines, tree-based methods, support vector machines, unsupervised learning and Gaussian process regression. Same as STAT 5610.
STAT 4630 - Computational Bayesian Statistics
Primary Instructor
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Spring 2021
Introduces Bayesian statistics, normal and non-normal approximation to likelihood and posteriors, the EM algorithm, data augmentation, and Markov Chain Monte Carlo (MCMC) methods. Additionally, introduces more advanced MCMC algorithms and requires significant statistical computing. Examples from a variety of areas, including biostatistics, environmental sciences, and engineering, will be given throughout the course. Recommended prerequisite: prior programming experience. Same as STAT 5630.
STAT 5000 - Statistical Methods and Application I
Primary Instructor
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Spring 2021
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. Recommended prerequisites of APPM 1360 or MATH 2300 or equivalent. Same as STAT 4000.
STAT 5610 - Statistical Learning
Primary Instructor
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Spring 2020
Consists of applications and methods of statistical learning. Reviews multiple linear regression and then covers classification, regularization, splines, tree-based methods, support vector machines, unsupervised learning and Gaussian process regression. Recommended prerequisite: previous coursework equivalent to that of STAT 3400 or STAT 4010 or STAT 5010; minimum C- grade for all. Same as STAT 4610.
STAT 5630 - Computational Bayesian Statistics
Primary Instructor
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Spring 2021
Introduces Bayesian statistics, normal and non-normal approximation to likelihood and posteriors, the EM algorithm, data augmentation, and Markov Chain Monte Carlo (MCMC) methods. Additionally, introduces more advanced MCMC algorithms and requires significant statistical computing. Examples from a variety of areas, including biostatistics, environmental sciences, and engineering, will be given throughout the course. Recommended prerequisite: prior programming and basic statistical modeling experience is required. Same as STAT 4630.
