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MTH 472: Introduction to Numerical Analysis II
3.00 Credits
University of Rhode Island
Numerical solution of ordinary differential equations, systems of linear equations, least squares, approximation, special topics. (Lec. 3) Pre: 243, CSC 201 or equivalent, or permission of instructor.
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MTH 472 - Introduction to Numerical Analysis II
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MTH 492: Special Problems
1.00 - 3.00 Credits
University of Rhode Island
Advanced work under the supervision of a faculty member arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.
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MTH 492 - Special Problems
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MTH 513: Linear Algebra
3.00 Credits
University of Rhode Island
Linear spaces and transformations, linear functionals, adjoints, projections, diagonalization, Jordan form of matrices, inner products; positive, normal, self-adjoint, and unitary operators; spectral theorem, bilinear and quadratic forms. (Lec. 3)
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MTH 513 - Linear Algebra
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MTH 515 ,516: Algebra I,II
3.00 Credits
University of Rhode Island
Groups, rings, modules, commutative algebra. (Lec. 3) Pre: 316. In alternate years.
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MTH 515 ,516 - Algebra I,II
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MTH 525: Topology
3.00 Credits
University of Rhode Island
Topological spaces, separation properties, connectedness, compactness, uniformities. Function spaces, spaces of continuous functions, and complete spaces. (Lec. 3) Pre: 425 or equivalent. In alternate years.
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MTH 525 - Topology
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MTH 535 ,536: Measure Theory and Integration
3.00 Credits
University of Rhode Island
Elements of topology and linear analysis. Lebesgue measure and integration in R, in Rn, and in abstract spaces. Convergence theorems. Bounded variation, absolute continuity, and differentiation. Lebesgue-Stieltjes integral. Fubini and Tonelli theorems. The classical Banach spaces. (Lec. 3) Pre: 435.
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MTH 535 ,536 - Measure Theory and Integration
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MTH 545 ,546: Ordinary Differential Equations I,II
3.00 Credits
University of Rhode Island
Existence and uniqueness theorems. Continuous dependence on parameters and initial conditions. Singularities of the first and second kinds, self-adjoint eigenvalue problems on a finite interval. Oscillation and comparison theorems. Introduction to delay and difference equations. Elements of stability theory of Lyapunov's second method. (Lec. 3) Pre: 435. In alternate years.
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MTH 545 ,546 - Ordinary Differential Equations I,II
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MTH 547: Combinatorics and Graph Theory )
3.00 Credits
University of Rhode Island
Enumeration: generating functions, recurrence relations, classical counting numbers, inclusion-exclusion, combinatorial designs. Graphs and their applications: Euler tours, Hamilton cycles, matchings and coverings in bipartite graphs, the four-color problem. (Lec. 3) Pre: 215 or equivalent. In alternate years.
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MTH 547 - Combinatorics and Graph Theory )
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MTH 548: Topics in Combinatorics )
3.00 Credits
University of Rhode Island
Topics such as Ramsey theory, Polya theory, network flows and the max-flow-mincut variations, applications in operations research; finite fields and algebraic methods; block designs, coding theory, other topics. (Lec. 3) Pre: 547 or permission of instructor. In alternate years.
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MTH 548 - Topics in Combinatorics )
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MTH 550: Probability and Stochastic Processes
3.00 Credits
University of Rhode Island
Review of probability theory. Generating functions, renewal theory, Markov chains and processes, Brownian motions, stationary processes. (Lec. 3) Pre: 437 or 435 and 451, or permission of instructor. In alternate years.
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MTH 550 - Probability and Stochastic Processes
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