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Course Criteria
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3.00 Credits
Prerequisites: MATH 4200. Continuation of MATH 4200. Sampling distribution, estimation theory, properties of estimators, hypothesis testing, Neyman-Pearson Theorem, likelihood ratio tests, introduction of analysis of variance and linear models.? Basics of some nonparametric procedures.
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3.00 Credits
Prerequisites: MATH 2020, 2450, and ability to program in an upper-level language. Solutions of equations, interpolation and approximation, numerical differentiation and integration, and numerical solution of initial value problems in ordinary differential equations. Selected algorithms will be programmed for solution on computers.
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3.00 Credits
Prerequisite: MATH 4230 or consent of instructor. Topics chosen from: the numerical solution of systems of linear? equations; the eigenvalue/eigenvector problem; numerical solution of Partial Differential Equations (PDE); numerical solution of stiff Ordinary Differential Equations (ODE); boundary value problems; sparse matrix methods; approximation theory; optimization theory; digital filters; integral equations.
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3.00 Credits
Prerequisites: MATH 2020 and 4100. Methods for optimizing functionals and their application. The Euler-Lagrange condition. Hamilton's principle, two dimensional variational problems, and isoperimetric problems. Approximate methods for the solution of variational problems.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or consent of instructor. Properties of integers, multiplicative functions, congruences, primitive roots, and quadratic residues.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or consent of the department. Introduction to groups, rings, and fields, with emphasis on groups and rings.
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3.00 Credits
Prerequisites: CMP SCI/MATH 3000, MATH 2000 and MATH 2450. Topics selected from vector spaces, bases, linear transformations, matrices, canonical forms, eigenvalues, hermitian and unitary matrices, inner product spaces, and quadratic forms.
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1.00 - 10.00 Credits
Prerequisites: CMP SCI/MATH 3000, MATH 2000 and consent of instructor.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000. Advanced counting methods are introduced, including the use of generating functions for the solution of recurrences and difference equations. Additional topics may include: graphs and trees, combinatorial designs, combinatorial games, error-correcting codes, and finite-state machines.
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3.00 Credits
Prerequisite: CMP SCI/MATH 3000 and MATH 2000 or PHIL 4460. A study of the logic of mathematics by the axiomatic method, with a development of the propositional calculus and restricted predicate calculus emphasizing its application to the foundations of mathematics.
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