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O'Rourke, Sean Daniel

Associate Professor

Positions

Research Areas research areas

Research

keywords

  • probability theory, random matrix theory, random polynomials

Publications

selected publications

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
    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. 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. Same as STAT 4520 and MATH 4520 and MATH 5520.

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