Topology (in particular of stratified spaces), Global Analysis, Noncommutative Geometry, Deformation Quantization (in particular in the singular setting), Topological Data Analysis, Computational Algebraic Geometry, Mathematical Physics, Axiomatic Quantum Field Theory, Chemical Topology
MATH 2002 - Number Systems: An Introduction to Higher Mathematics
Primary Instructor
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Fall 2018 / Spring 2020 / Fall 2020 / Fall 2021 / Fall 2022 / Spring 2023 / Spring 2024 / Fall 2024
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 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
Primary Instructor
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Spring 2019
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 do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 3001 - Analysis 1
Primary Instructor
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Spring 2018 / Spring 2021 / 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 4001 - Analysis 2
Primary Instructor
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Fall 2023
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 4810 - Special Topics in Mathematics
Primary Instructor
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Summer 2018 / Summer 2019 / Summer 2020 / Summer 2021 / Summer 2022 / Summer 2023 / Summer 2024
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 5810.
MATH 5001 - Analysis 2
Primary Instructor
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Fall 2023
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 5810 - Special Topics in Mathematics
Primary Instructor
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Summer 2018 / Summer 2019 / Summer 2020 / Summer 2021 / Summer 2022 / Summer 2023 / Summer 2024
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 4810.
MATH 6220 - Introduction to Topology 2
Primary Instructor
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Spring 2020 / Spring 2021
Continuation of MATH 6210. Department enforced prerequisite: MATH 6210. Instructor consent required for undergraduates.
MATH 6230 - Introduction to Differential Geometry 1
Primary Instructor
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Spring 2022
Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001. Instructor consent required for undergraduates.
MATH 6260 - Geometry of Quantum Fields and Strings
Primary Instructor
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Fall 2021 / Fall 2023
Focuses on differential geometric techniques in quantum field and string theories. Topics include: spinors, Dirac operators, index theorem, anomalies, geometry of superspace, supersymmetric quantum mechanics and field theory and nonperturbative aspects in field and string theories. Department enforced prerequisites: MATH 6230 and MATH 6240 and PHYS 5250 and PHYS 7280. Instructor consent required for undergraduates. Same as PHYS 6260.
MATH 6280 - Advanced Algebraic Topology
Primary Instructor
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Fall 2018 / Fall 2022
Covers homotopy theory, spectral sequences, vector bundles, characteristic classes, K-theory and applications to geometry and physics. Department enforced prerequisite: MATH 6220. Instructor consent required for undergraduates.
