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Course Criteria
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3.00 Credits
Pr. grade of at least C in 292 or 303 or permission of instructor Hours count toward teacher licensure but do not count toward degree requirements for a mathematics major. Primarily for students seeking teacher certification. Includes properties and algebra of real numbers; analytic geometry; polynomial, rational, exponential, logarithmic, and trigonometric functions; complex numbers; concept of limits of functions. This course cannot be applied toward the requirements for the M.A. degree in Mathematics. (Spring)
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3.00 Credits
Pr. grade of at least C in 292 Study of the historical development of mathematics, not a history of persons involved in development. This course cannot be applied toward the requirements for the M.A. degree in Mathematics. (Fall)
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3.00 Credits
Pr. grade of at least C in 311 or permission of instructor An introductory course to both multiplicative and additive number theory. Divisibility, prime numbers, congruencies, linear and nonlinear Diophantine equations (including Pell's equation), quadratic residues, number-theoretic functions, and other topics.
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3.00 Credits
Pr. grade of at least C in 253 or 311 or permission of instructor Formal languages, recursion, compactness, and effectiveness. First-order languages, truth, and models. Soundness and completeness theorems. Models of theories. (Odd Spring)
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3.00 Credits
Pr. grade of at least C in 311 Rings, integral domains, fields, division algorithm, factorization theorems, zeros of polynomials, greatest common divisor, relations between the zeros and the coefficients of a polynomial, formal derivatives, prime polynomials, Euclidean rings, the fundamental theorem of algebra.
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3.00 Credits
Pr. grade of at least C in 311 Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated Abelian groups.
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3.00 Credits
Pr. grade of at least C in 311 or 395 The axioms of set theory, operations on sets, relations and function, ordinal and cardinal numbers.
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3.00 Credits
Pr. grade of at least C in 311 or 395 Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity.
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3.00 Credits
Pr. grade of at least C in 311 or 395 Fifth postulate, hyperbolic geometries, elliptic geometries, consistency of non-Euclidean geometries, models for geometries, elements of inversion.
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3.00 Credits
Pr. permission of instructor Transformation groups and projective, affine and metric geometries of the line, plane, and space. Homogeneous coordinates, principles of duality, involutions, cross-ratio, collineations, fixed points, conics, ideal and imaginary elements, models, and Euclidean specializations.
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