• MATH 361: Mathematics Junior Seminar

  3.00 Credits

  Tusculum University

  
  This course will introduce students to the application of mathematics to solving independent research problems. Students will learn to develop research questions and to understand how research questions and solutions are formulated. Prerequisites: At least three mathematics courses at the MATH 190 level or higher or permission of the instructor.
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• MATH 390: Calculus III

  4.00 Credits

  Tusculum University

  
  Continuation of differential and integral calculus. Topics include parametric equations, vector geometry, curves and surfaces in space, partial derivatives and multiple integration. Calculator or computer lab projects will constitute a portion of the course. Prerequisite: MATH 290.
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• MATH 410: Partial Differential Equations

  3.00 Credits

  Tusculum University

  
  This course introduces students to the theory of boundary value and initial value problems for partial differential equations. Topics include Laplace's equation, heat equations, wave equations, Green's functions, Bessel functions and Laplace transforms. Prerequisites: MATH 310 or permission of the instructor.
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• MATH 420: Real Analysis

  3.00 Credits

  Tusculum University

  
  Rigorous treatment and in-depth exploration of fundamental concepts of calculus, including limits, continuity, derivatives, and Riemann integration. Prerequisite: Math 290 with a minimum grade of C- and either Math 220 or Math 225 with a minimum grade of C-, or permission of the instructor
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• MATH 430: Abstract Algebra

  3.00 Credits

  Tusculum University

  
  This course in abstract algebra (modern algebra) introduces the abstract concepts of mapping, operation, equivalence, congruence and divisibility. Rings and integral domains will be discussed briefly, and the fundamental concept of groups will be developed thoroughly. Examples (such as permutation and symmetry groups) will be used to illustrate abstract notions (such as subgroup, coset and isomorphism) as these are developed. The study of abstract ideas of number theory will be enhanced by analyzing concrete examples of abstract ideas. Prerequisite: MATH 190.
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• MATH 435: Intr to Complex Analysis

  3.00 Credits

  Tusculum University

  
  This course gives an introduction to the theory of functions of one complex variable. Central themes in the course are analytic and harmonic functions and their properties, power series and Laurent series, isolated singularities, Cauchy's integral theorem and residue calculus, the maximum principles, Schwarz lemma, and conformal mappings. Prerequisite: MATH 290.
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• MATH 440: Introduction to Topology

  3.00 Credits

  Tusculum University

  
  This course gives an introduction to topology. This course will cover the following topics: review of set theory, metric spaces, topological spaces, continuity, convergence, subspaces, product spaces, quotient spaces, connectedness, compactness, and simple connectedness. Prerequisite: MATH 220.
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• MATH 450: Independent Study in Math

  1.00 - 3.00 Credits

  Tusculum University

  
  A student-initiated request to study some aspect of mathematics not covered in-depth in a regular course. The work will be accomplished under the direction of an advisor and may terminate in a formal paper. Prerequisite: MATH 190.
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• MATH 460: Mathematics Seminar

  3.00 Credits

  Tusculum University

  
  This course will synthesize ideas from different areas of mathematics in topics of current interest. A portion of this course will involve presentation of original research to at least two mathematics professors and all students, addressing problem solving when appropriate. Students will prepare a cover letter and a resume or curriculum vitae for review by the instructor. Course may be repeated once, with a different topic, for a total of six semester hours. Prerequisite: At least three mathematics courses at the MATH 190 level or higher or permission of the instructor.
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• MATH 501: Fundamentals of Algebra and Trigonometry

  3.00 Credits

  Tusculum University

  
  This course provides content suitable for students intending to take the Praxis II Mathematics Content Knowledge examination. Topics include, but are not limited to, algebraic and trigonometric functions and their applications.
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