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Course Criteria
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3.00 Credits
Prerequisite: MATH 4150 or MATH 3040 or consent of instructor. Topics from groups, rings, and fields. Subgroups, cyclic groups, permutation groups, normal subgroups, homomorphisms, Cayley's and Lagrange's Theorems, factor groups, abelian groups, direct products.Introduction to rings and fields.
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3.00 Credits
Prerequisite: MATH 4081. Continuation of MATH 4081 with emphasis on rings and fields. Rings, integral domains, and fields. Vector spaces, extension fields, finite fields.
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3.00 Credits
Prerequisite: MATH 4081. Lattices, Boolean algebras, semigroups, binary group codes, binary relations, and graphs. Special emphasis is placed on applications.
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3.00 Credits
Prerequisite: MATH 2262. Elementary properties of integers including divisibility, unique factorization, progressions and prime numbers. Linear congruences and residue classes, complete and reduced residue systems, Chinese Remainder Theorem, quadratic residues, law of quadratic reciprocity, Theorems of Fermat and Wilson, Fibonacci and perfect numbers, sums of squares, elementary theory of continued fractions.
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3.00 Credits
Prerequisites: Either MATH 2150 and MATH 3040 or consent of instructor. Introduction to the theory of vector spaces, with emphasis on finite-dimensional vector spaces, linear systems, matrices, linear transformations, eigenvalues, and related subjects.
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3.00 Credits
Prerequisite: Grade of "C" or higher in either MATH 3162 or MATH 3180 or permission of instructor. An in-depth study of concepts and processes underlying the P-8 school mathematics curriculum, with special emphasis on informal and formal mathematical reasoning. Problem solving and historical context serve as unifying strands. The analysis and remediation of student errors manifested in the application of conceptual and procedural mathematical knowledge will also be addressed.
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3.00 Credits
Prerequisites: MATH 3040 or consent of instructor or MATH 2263 with a grade of ? ?" or "B.? ?A study of the principles of mathematical analysis; point set topology in Euclideanand metric spaces, numerical sequences and series, continuity, differentiation, integration, sequences and series of functions.
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3.00 Credits
Prerequisite: MATH 2263. Introductory study of the algebraic and geometric properties of the complex number system and functions of a complex variable. Limits, continuity, and differentiation of complex functions. Analytic functions and the Cauchy-Riemann conditions. Integration of complex functions; Cauchy-Goursat theorem; Cauchy integral formula; the theorems of Morera and Liouville. Taylor and Laurent series expansions. Residues and poles with applications to integration. Conformal mappings.
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3.00 Credits
Prerequisite: MATH 3040. The study of point set topology in metric and topological spaces. Open and closed sets, compactness, connectedness, topological mappings, separation, product and functions spaces.
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3.00 Credits
Prerequisites: MATH 2263 and MATH 3600. Distributions of random variables, conditional probability and stochastic independence, multivariate and some special distributions, and distributions of functions of random variables.
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