O'Rourke, Sean Daniel

Research

keywords

probability theory, random matrix theory, random polynomials

Publications

selected publications

conference proceeding
- Optimal Subspace Perturbation Bounds under Gaussian Noise. 2601-2606. 2023
- Littlewood-Offord Theory and Controllability of Random Structures. Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & Control. 5195-5200. 2016
journal article
- ON RANDOM POLYNOMIALS WITH AN INTERMEDIATE NUMBER OF REAL ROOTS. Proceedings of the American Mathematical Society. 4933-4942. 2024
- SUMS OF RANDOM POLYNOMIALS WITH DIFFERING DEGREES. Transactions of the American Mathematical Society. 3325-3355. 2024
- The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 10189-10218. 2024
- Matrices With Gaussian Noise: Optimal Estimates for Singular Subspace Perturbation. IEEE Transactions on Information Theory. 1978-2002. 2024
- Spectrum of Levy-Khintchine Random Laplacian Matrices. Journal of Theoretical Probability. 933-973. 2024

Teaching

courses taught

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 distribution-free 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 distribution-free methods. Department enforced prerequisite: one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Same as STAT 4520 and MATH 4520 and MATH 5520.
FYSM 1000 - First Year Seminar
Primary Instructor - Fall 2018 / Fall 2020
Provide first year students with an immersive experience in an interdisciplinary topic that addresses current issues including social, technical and global topics. Taught by faculty from across campus, the course provides students with an opportunity to interact in small classes, have project based learning experiences and gain valuable communication skills. Seminar style classes focused on discussion and projects.
MATH 2400 - Calculus 3
Primary Instructor - Spring 2020
Continuation of MATH 2300. Topics include vectors, three-dimensional 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 3001 - Analysis 1
Primary Instructor - Spring 2021 / Spring 2022 / Spring 2024 / Fall 2024
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.

MATH 3850 - Seminar in Guided Mathematics Instruction
Primary Instructor - Spring 2020
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 2019
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 distribution-free methods. Same as MATH 5520 and STAT 4520 and STAT 5520.

MATH 4530 - Theoretical Foundations of Data Science
Primary Instructor - Spring 2024
Introduces theoretical concepts from mathematics, statistics, and computer science required to understand and analyze data. Topics include randomized algorithms, machine learning, streaming, sketching, clustering, random matrices and graphs, graphical models and compressed sensing.

MATH 5520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2019
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 distribution-free methods. Department enforced prerequisite: one semester calculus-based 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 6310 - Introduction to Real Analysis 1
Primary Instructor - Fall 2021
Develops the theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6320 - Introduction to Real Analysis 2
Primary Instructor - Spring 2018
Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the Radon-Nikodym 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 6350 - Functions of a Complex Variable 1
Primary Instructor - Fall 2020
Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6534 - Topics in Mathematical Probability
Primary Instructor - Fall 2023
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

STAT 4520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2019
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 distribution-free methods. Same as STAT 5520 and MATH 4520 and MATH 5520.

STAT 5520 - Introduction to Mathematical Statistics
Primary Instructor - Spring 2019
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 distribution-free methods. Department enforced prerequisite: one semester calculus-based 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.

... more

Background

education and training

Ph.D., University of California-Davis 2011
M.A., University of California-Davis 2008
B.S., California Polytechnic State Univ-San Luis Obispo 2006

awards and honors

Faculty Early Career Development Program (CAREER), conferred by National Science Foundation, 2022

VIVO

Positions

Research Areas

Research

keywords

Publications

selected publications

conference proceeding

journal article

Teaching

courses taught

Background

education and training

awards and honors

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