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Kearnes, Keith A

Professor

Positions

Research Areas research areas

Research

research overview

  • Dr. Kearnes' research interests include the classification of equational theories, structure theory for finite algebras, and applications of combinatorics and model theory to algebra.

keywords

  • associative algebras, commutative ring theory, finite group theory, universal algebra, lattice theory, model theory, combinatorics

Publications

selected publications

Teaching

courses taught

  • MATH 2001 - Introduction to Discrete Mathematics
    Primary Instructor - Spring 2019 / Spring 2021 / Fall 2021 / Fall 2023
    Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
  • MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
    Primary Instructor - Spring 2021
    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 - Fall 2018 / Fall 2019
    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 4730 - Set Theory
    Primary Instructor - Fall 2019 / Fall 2023
    Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic and other topics chosen by the instructor. Same as MATH 5730.
  • MATH 4820 - History of Mathematical Ideas
    Primary Instructor - Fall 2024
    Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820.
  • MATH 5730 - Set Theory
    Primary Instructor - Fall 2019 / Fall 2023
    Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic and other topics chosen by the instructor. Same as MATH 4730.
  • MATH 6000 - Model Theory
    Primary Instructor - Spring 2020 / Spring 2024
    Proves the compactness theorem, showing the essential finiteness of logical implication. Proves many basic properties of theories, showing how the syntactic form of statements influences their behavior w.r.t., different models. Finally, studies properties of elements that cannot be stated by a single formula (the type of the element) and shows it can be used to characterize certain models.
  • MATH 6020 - Category Theory
    Primary Instructor - Fall 2024
    Studies categories, functors, natural transformations, adjoints, and universal constructions. Special topics may include monads and their algebras, abelian categories, Kan extensions, or sheaves in geometry and logic. Instructor consent required for undergraduates.
  • MATH 6150 - Commutative Algebra
    Primary Instructor - Fall 2020
    Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals and Noetherian rings. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
  • MATH 6270 - Theory of Groups
    Primary Instructor - Fall 2021
    Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
  • MATH 6730 - Set Theory
    Primary Instructor - Spring 2023
    Presents cardinal and ordinal arithmetic, and basic combinatorial concepts, including stationary sets, generalization of Ramsey's theorem, and ultrafilters, consisting of the axiom of choice and the generalized continuum hypothesis. Department enforced prerequisites: MATH 4000 or MATH 5000 and MATH 4730 or MATH 5730. Instructor consent required for undergraduates.
  • MATH 8714 - Topics in Logic 1 and 2
    Primary Instructor - Fall 2018
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