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Course Criteria
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4.00 Credits
Study of fields, systems of linear equations, matrices, vector spaces, subspaces, bases and dimension, linear transformations, isomorphism, representation of transformations by matrices, linear functionals, determinants, eigenvalues and eigenvectors, invariant subspaces, inner product spaces, stochastic matrices, matrix exponentials, and numerical methods. Prereq: MATH 270. Strongly recommended prereq: MATH 280 and/or COSC 200. Offered: Fall.
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4.00 Credits
Study of vector algebra in two and three dimensions, equations of lines in space, scalar products, orientation, vector products, triple scalar products, vector identities, tensors, vector valued functions, velocity, tangent vectors, acceleration, vector fields, gradients, divergence, curl, the Laplacian, line integrals, potentials, conservative fields, irrotational fields, surface integrals, volume integrals, divergence theorem, Green's formula, and Stoke's theorem. Applications to electrostatics,force fields, potential theory, fluid flow, heat flow, gravitation, and wave equations. Prereq: MATH 270. Strongly recommended prereq: MATH 280 and/or COSC 200; PHYS 203 and PHYS 204.
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4.00 Credits
Study of functions of a complex variable. Topics include analytic and harmonic functions, transformation and mapping, complex integration, power series, residues and poles, conformal mapping, and additional theory of functions. Prereq: MATH 270. Strongly recommended prereq: MATH 280 and/or COSC 200.
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4.00 Credits
Introduction to calculus-based probability theory and statistical inference. Topics include: probability measures, independence and conditional probability, discrete random variables, continuous random variables, distribution functions, expectations, multivariate distributions, correlations, binomial, Poisson, gamma, chisquare, normal distributions, sampling distributions, order statistics, moment-generating functions, functions of random variables, convergence of distributions, central limit theorem, point estimators, maximum likelihood, confidence intervals, hypothesis testing, sufficient statistics, Bayesian estimation, likelihood ratio tests, analysis of variance, linear regression, and nonparametric statistics. Prereq: MATH 270. Strongly recommended prereq: MATH 280 and/or COSC 200.
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4.00 Credits
Introduction to the theory of numbers. Topics include divisibility, factorization, prime numbers, congruencies, arithmetic functions, quadratic residues, and Diophantine equations. Additional topics may include primitive roots, continued fractions, cryptography, Fibonacci numbers, and numerical techniques. Prereq: MATH 280.
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4.00 Credits
Axiomatic, proof-oriented treatment of different geometries, including synthetic, metric, absolute, and Euclidean geometries. Other topics may include finite geometries, fractals, constructions, and specific non-Euclidean geometries. Prereq: MATH 280.
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4.00 Credits
Introduction to abstract algebra, groups, rings, and fields. Topics include: binary operations, groups, subgroups, cyclic groups, groups of permutations, cosets, finitely generated groups, homeomorphisms, isomorphisms, factor groups, rings, fields, and integral domains. Additional topics may include fields of quotients, rings of polynomials, factor rings, ideals, unique factorization domains, and the Sylow Theorems. Prereqs: MATH 340 or MATH 410.
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4.00 Credits
Proof-oriented introduction to topics in mathematical analysis. Topics include: field axioms of real numbers, completeness axiom, set theory, relations and functions, infinite sets, countable sets, open and closed sets, closure, limit points, Bolzano-Weierstrass theorem, limits and partial limits of sequences, monotone sequences, Cauchy sequences, limits of functions, continuity, extreme value theorem, intermediate value theorem, uniform continuity, differentiation, chain rule, mean value theorem, L'Hopital's rule, convergent series, tests for convergence ofseries, rearrangement of series, Riemann sums, Riemann integrability, Fundamental Theorem of Calculus, change of variables, sequences of functions, uniform convergence, and power series. Prereq: MATH 280.
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4.00 Credits
Survey of the fundamental concepts of general topology which depend upon the elementary properties of sets and functions. Includes topological spaces, subspaces, continuity, homeomorphisms, product spaces, connectedness, compactness, separation properties, and metric spaces. Prereq: MATH 280.
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1.00 - 4.00 Credits
Independent study arranged between a student (or students) and a faculty member. Topics vary. May be repeated for credit. Prereqs: At least one upper-level mathematics course.
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