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MATH 496: Selected Topics:Non-recurring
1.00 - 6.00 Credits
American University
Course Level: Undergraduate Topics vary by section, may be repeated for credit with different topic.
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MATH 496 - Selected Topics:Non-recurring
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MATH 501: Probability
3.00 Credits
American University
Course Level: Undergraduate/Graduate Algebra of sets; probability in discrete sample spaces; combinatorial analysis; random variables; binomial, Poisson, normal, and other distributions; and applications. Usually offered every fall. Prerequisite: MATH-313.
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MATH 501 - Probability
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MATH 503: Foundations of Mathematics
3.00 Credits
American University
Course Level: Undergraduate/Graduate An introduction to the proof-based methodology of advanced mathematics courses, with emphasis on the fundamentals of logic and set theory (truth-tables and quantifiers, Boolean operations, functions, relations, and cardinally); elementary number theory (mathematical induction and modular arithmetic), and structural properties of the fields of real and complex numbers. Usually offered every spring. Prerequisite: MATH-222.
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MATH 503 - Foundations of Mathematics
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MATH 504: Advanced Calculus of Several Variables
3.00 Credits
American University
Course Level: Undergraduate/Graduate Vector-functions of several variables, limits and continuity, differentials and tangent plane, implicit and inverse functions, line and surface integrals, gradient, divergent, curl, Stoke's and Green's theorems. Usually offered alternate springs. Prerequisite: MATH-310 and MATH-313 and MATH-503, or permission of instructor.
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MATH 504 - Advanced Calculus of Several Variables
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MATH 505: Mathematical Logic
3.00 Credits
American University
Course Level: Undergraduate/Graduate The mathematical study of the scope and limits of deductive reasoning with special attention to propositional and first order logic, leading to results concerning completeness, compactness, and the existence of decision procedures for various logical systems, culminating in the incompleteness theorems of Godel. Usually offered alternate falls. Prerequisite: MATH-503.
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MATH 505 - Mathematical Logic
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MATH 508: Automata,Languages,and Computability
3.00 Credits
American University
Course Level: Undergraduate/Graduate Introduction to the theoretical concepts underlying computing. Finite automata, push-down automata, and Turing machines. Regular, context-free, and phrase-structure languages. Computability and computational complexity. Usually offered every spring. Prerequisite: CSC-350 or permission of instructor.
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MATH 508 - Automata,Languages,and Computability
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MATH 510: Geometry
3.00 Credits
American University
Course Level: Undergraduate/Graduate Euclidean and non-Euclidean (spherical, elliptic and hyperbolic) geometries from axiomatic and analytic points of view. Includes isometrics, transformation groups, symmetry groups, quadratic forms, projective geometry, as well as some historical background. Usually offered alternate falls (even years). Prerequisite: MATH-310 or equivalent.
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MATH 510 - Geometry
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MATH 512: Introduction to Modern Algebra
3.00 Credits
American University
Course Level: Undergraduate/Graduate An introduction to the study of abstract algebraic structures. Includes groups, subgroup, quotient groups, homomorphisms, rings, ideals, fields, and group actions and Sylow theory. Usually offered every fall. Prerequisite: MATH-503.
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MATH 512 - Introduction to Modern Algebra
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MATH 513: Rings and Fields
3.00 Credits
American University
Course Level: Undergraduate/Graduate An advanced study of rings and fields with a focus on polynomials and their roots. Includes ring theory, factorization, polynomials, field theory, ruler and compass constructions, Galois theory, and solvability of polynomials. Usually offered alternate springs. Prerequisite: MATH-512 or permission of instructor.
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MATH 513 - Rings and Fields
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MATH 515: Number Theory
3.00 Credits
American University
Course Level: Undergraduate/Graduate Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Usually offered alternate falls(even years). Prerequisite: MATH-222.
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MATH 515 - Number Theory
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