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Course Criteria
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2.00 - 3.00 Credits
3795H. Topics in Mathematics PIC Math. The study of a mathematical topic or the development of a special area of mathematics. May be repeated once. Prereq.: MATH 1570 or MATH 1571 or MATH 2623 or MATH 2651. 2-3 s.h.
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3.00 Credits
4822. Abstract Algebra 2. A continuation of MATH 3721 with special emphasis on fields. Additional topics in pure or applied algebra. Prereq.: MATH 3721 or equivalent. 3 s.h.
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3.00 Credits
4823. Abstract Algebra 3. This course introduces advanced topics in field theory. Topics may include principal ideal domains, irreducibility, quotient rings, algebraic extensions, finite fields, splitting fields, and the Galois group. Prereq.: MATH 4822. 3 s.h.
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3.00 Credits
4830. Foundations of Geometry. The development of Euclidean and non-Euclidean geometries from postulate systems. Prereq.: MATH 3715. 3 s.h.
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3.00 Credits
4832. Euclidean Transformations. General properties of functions and transformations; isometries and transformations of the Euclidean plane; the complex plane, its geometry and subfields; transformational, analytical, and vector approaches to Euclidean geometry; connections to other branches of mathematics and applications. Prereq.: MATH 3720 and MATH 4830. 3 s.h.
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3.00 Credits
4855. Ordinary Differential Equations. A second course in differential equations with emphasis on nonlinear problems and qualitative methods or on boundary value problems. Topics are chosen from: proofs of fundamental theorems, phase plane analysis, limit cycles and the Poincare-Bendixon theorem, biological models, stability via Liapunov functions, asymptotic methods, and boundary value problems. Prereq.: MATH 3705 and MATH 3720. 3 s.h.
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3.00 Credits
4857. Partial Differential Equations. Introduction to partial differential equations (PDE) including solution techniques and applications. Classifications of the basic types of PDE's (hyperbolic, parabolic and elliptic) and dependence on boundary and initial conditions. Topics include Fourier series, integral transforms (Fourier, Laplace), and applications in vibrations, electricity, heat transfer, fluids or other selected topics. Prereq.: MATH 3705 and MATH 3720. 3 s.h.
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3.00 Credits
4869. Functions, Calculus, and Applications for Middle School Teachers. Polynomial and exponential functions, limits, derivatives, integrals, and applications. Interpretation of slope and area in graphs of functions from applied settings. Applications of limits to the derivations of geometric formulas. Relations between tables, graphs, and the symbolic representation of functions. Prereq.: MATH 3767 or consent of instructor. 3 s.h.
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3.00 Credits
4870. Mathematics Concepts for Middle School Teachers. Problem solving from a broad spectrum of mathematics topics (Number Sense and Operations; Algebra, Functions, and Calculus; Measurement and Geometry; Statistics, Probability, and Discrete Mathematics) designed to prepare future middle school mathematics teachers to address Common Core Standards. May be repeated 2 times. Prereq.: MATH 1564, 2665, MATH 3767, MATH 3768, MATH 4869, and either STAT 2601, STAT 2625 or STAT 2625C. 3 s.h.
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3.00 Credits
4875. Complex Variables. Complex numbers and their geometric representation, analytic functions of a complex variable, contour integration, Taylor and Laurent series, residues and poles, conformal mapping. Prereq.: MATH 3751 or equivalent. 3 s.h.
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