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Course Criteria
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1.00 - 3.00 Credits
1-3 s.h. Individual studies or research activities carried out under the direction of appropriate departmental faculty. ( LA) Prerequisites: SoS and permission of department.
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3.00 Credits
3 s.h. Studies the development of mathematics as a part of our intellectual and cultural heritage. Emphasizes the more fundamental aspects of mathematics. ( LA) Prerequisites: MATH 174, MATH 205 and successful completion of the CWE.
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3.00 Credits
3 s.h. Primes, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions. ( LA) Prerequisites: MATH 174 and MATH 205.
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3.00 Credits
3 s.h. each Introductory concepts of modern algebra and their applications to the solution of polynomial equations over various fields. Elementary properties of groups, rings, integral domains, fields, and vector spaces; introductory Galois theory and applications including Abel's theorem and compass-straightedge constructions. ( LA) Prerequisites: MATH 174 and MATH 205 for 321, 321 for 322.
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3.00 Credits
3 s.h. Finite dimensional vector spaces; linear transformations and their matrix representations; eigenvalues; rational and Jordan canonical forms; inner product spaces; quadratic and bilinear forms; applications. Prerequisite: MATH 174 and MATH 205, MATH 323 is required for MATH 324. ( LA)
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3.00 Credits
3 s.h. For description see MATH 326. ( LA) Prerequisite: MATH 174 and MATH 205.
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3.00 Credits
3 s.h. Introduction to theory of groups, including the Sylow theorems and the fundamental theorem of abelian groups, the theory of rings and modules, especially modules over a principal ideal domain; field extensions, and an introduction to Galois theory. ( LA) Prerequisite: MATH 325.
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3.00 Credits
3 s.h. Sets, binary relations, induction, partially ordered sets, weak orders, Boolean algebra, switching circuits, finite state machines, state diagrams, formal languages, context-free languages, groups, semigroups, permutations, group codes, modular arithmetic. Additional topics may include linear machines, Turing machines, finite fields, automata, latin squares, and block design. ( LA) Prerequisites: JrS and MATH 174 and MATH 205.
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3.00 Credits
3 s.h. For description see MATH 336. ( LA) Prerequisite: MATH 174 and MATH 205.
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3.00 Credits
3 s.h. A postulational approach to some Euclidean and non-Euclidean geometries. Topics include incidence and separation properties of planes and space, constructions with compass and straightedge, geometric inequalities, the parallel postulate, similarity theorems, circles, properties of triangles, and metric relationships. ( LA) Prerequisite: MATH 335.
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