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DeMeo, William J Visiting Asst Professor

Positions

Research Areas research areas

Research

research overview

  • William DeMeo specializes in universal algebra, or more specifically, the exploration and discovery of general algebraic and relational structures and equational theories. When not proving properties of these structures or investigating their applications, Dr. DeMeo works with computer algebra systems and proof assistants to gain deeper insights and make new discoveries in general algebra. Sometimes the latter activity leads to the production of useful software or to advances in algorithms and complexity theory.

keywords

  • universal algebra, lattice theory, algebraic logic, complexity theory, model theory, category theory, functional programming, theoretical computer science

Teaching

courses taught

  • MATH 2001 - Introduction to Discrete Mathematics
    Primary Instructor - Fall 2018 / Spring 2019
    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. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).
  • MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
    Primary Instructor - Spring 2018
    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 3140 - Abstract Algebra 1
    Primary Instructor - Fall 2018
    Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
  • MATH 6000 - Model Theory
    Primary Instructor - Spring 2018
    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.

International Activities