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Course Criteria
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3.00 Credits
Introductory course with emphasis on applications of calculus. Topics include: first order equations, higher order linear equations, undetermined coefficients, variation of parameters, linear systems, bifurcation analysis, series solutions, Laplace transforms, numeric and qualitative techniques, mathematical modeling and applications, and computational technology. Additional topics selected from linear and nonlinear systems as time permits. Prerequisites: MATH 122, 123, 223, 231 or permission from the instructor.
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3.00 Credits
Topology of the real line, measure and integration on the real line, function spaces and their topologies.
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3.00 Credits
Geometric interpretation of the complex plane, analytic functions and power series representations, introduction to Riemann Surfaces, the Cauchy Integral Theorem and Intergral Formula, calculation of integrals by residues, application to potential theory.
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3.00 Credits
An introduction to rings and fields: rings; integral domains; fields; charactersistic of a ring; subrings; ideals; factor rings; ring homomorphisms; polynomial rings; introduction to Galois theory as time permits.
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3.00 Credits
Study of selected applications of abstract algebra. Topics selected from: identification numbers, symmetry, applications to combinatorics, coding theory, cryptography.
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3.00 Credits
Topics selected from: congruence relations; arithmetic functions; primitive roots; quadratic reciprocity; sums of squares; continued fractions; Farey sequences; factoring and primality testing; analytic and additive number theory. The course relates directly to the following N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, numbers and numeration, and patterns/functions.
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3.00 Credits
The addition, multiplication and pigeonhole principles. Permutations and combinations, partitions and distributions; the binomial and multinomial theorems. Generating functions; recurrence relations; principle of inclusion-exclusion; combinatorial algorithms or designs as time permits. The course relates directly to the following N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, modeling/multiple representation, and pattern/functions.
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3.00 Credits
Graph models; graph structure and representation; trees; connectivity; graph traversals; graph colorings; other topics as time permits. The course relates directly to the N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, modeling/multiple representation, and pattern/functions.
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3.00 Credits
Neutral geometry; Euclidean geometry; comparison of various models of Euclidean geometry, such as that of Hilbert and the SMSG; comparison of Euclidean geometryto various finite geometries and non-Euclidean geometries; geometry of circles and triangles; other topics such as analytic and transformational geometry as time permits.
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3.00 Credits
Neutral geometry; hyperbolic geometry; elliptic geometry; various models of hyperbolic and elliptic geometry; comparison of results to those of Euclidean geometry.
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