Dr. Deeley's research involves the study of index theory and topological dynamical systems using operator algebras and noncommutative geometry/topology.
keywords
Operator algebras, Index theory, Topological dynamics, Ktheory
Teaching
courses taught
MATH 2002  Number Systems: An Introduction to Higher Mathematics
Primary Instructor

Spring 2019
Introduces the concepts of mathematical proofs using the construction of the real numbers from set theory. Topics include basic logic and set theory, equivalence relations and functions, Peano's axioms, construction of the integers, the rational numbers and axiomatic treatment of the real numbers. Credit not granted for this course and MATH 2001.
MATH 2135  Introduction to Linear Algebra for Mathematics Majors
Primary Instructor

Spring 2018 / Fall 2022
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 3001  Analysis 1
Primary Instructor

Spring 2018 / Fall 2018 / Fall 2020 / Spring 2022
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 4001  Analysis 2
Primary Instructor

Fall 2022
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 5001.
MATH 5001  Analysis 2
Primary Instructor

Fall 2022
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 4001.
MATH 6210  Introduction to Topology 1
Primary Instructor

Fall 2019 / Fall 2020
Introduces elements of pointset topology and algebraic topology, including the fundamental group and elements of homology. Department enforced prerequisites: MATH 2130 and MATH 3140 and MATH 4001. Instructor consent required for undergraduates.
MATH 8304  Topics in Analysis 1
Primary Instructor

Spring 2021
Presents advanced topics in analysis including Lie groups, Banach algebras, operator theory, ergodic theory, representation theory, etc. Department enforced prerequisites: MATH 8330 and MATH 8340. Instructor consent required for undergraduates.
MATH 8330  Functional Analysis 1
Primary Instructor

Fall 2018 / Fall 2021
Introduces such topics as Banach spaces (HahnBanach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations and spectral theorem for bounded selfadjoint operators) and Banach algebras (the Gelfand theory). Department enforced prerequisites: MATH 6310 and MATH 6320. Instructor consent required for undergraduates. See also MATH 8340.