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Course Criteria
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3.00 Credits
This course provides a systematic study of the most common and useful rings and groups; integers, rational numbers, real numbers, complex numbers, residue classes, polynomials, and matrices. Both computational and structural aspects are treated. Three lecture hours per week. Not open to students who have received credit for MAT303.
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3.00 Credits
A systematic study of vector spaces and linear transformations including the algebra of matrices, determinants, inner products, eigenvalues, and eigenvectors. Three lecture hours per week. Prerequisite: MAT214 or MAT221.
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3.00 Credits
An introduction to divisibility theory, prime numbers, congruences, Diophantine equations, number-theoretic functions, primitive roots and indices, and quadratic residues. Three lecture hours per week. Prerequisite: MAT303.
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3.00 Credits
Topics studied: linear equations and inequalities, convex regions, the simplex algorithm, duality and minimax theorems, matrix games, transportation and assignment problems. Experience is provided in the computer solution of linear programming problems and in applications to business and the sciences. Three lecture hours per week. Prerequisite: MAT210 or MAT220 or equivalent.
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3.00 Credits
Topics include finite-state machines, feedback, partially ordered sets, lattices, recursion and iteration, with applications to logic, circuit design, and computer systems. Three lecture hours per week. Prerequisite: MAT303.
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3.00 Credits
A survey of combinatorial methods, including graphs, trees, networks, permutations and combinations, partitions, and enumeration theory. Three lecture hours per week. Prerequisite: MAT214 or MAT221.
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4.00 Credits
An introduction to two and three dimensional analytic geometry and an extension of the ideas of calculus to both real-valued functions of several variables and vector-valued functions. Topics include polar, cylindrical and spherical coordinates, vectors in two and three dimensions, limits, derivatives and integrals of functions of several variables and vector-valued functions. Offered each fall. Four lecture hours per week. Required of all mathematics majors. Prerequisite: MAT221.
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3.00 Credits
A study of numerical methods. Topics include root finding for nonlinear equations, polynomial interpolation, series methods, numerical integration, finite differences, and solutions of linear systems. Efficiency, accuracy and roundoff and truncation errors are considered. Computer implementation of selected methods is included. Three lecture hours per week. Prerequisite: MAT221.
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3.00 Credits
Topics include normal subgroups, ideals, morphisms of groups and rings, fields and field extensions with examples and applications. Three lecture hours per week. Not open to students who have received credit for MAT404. Prerequisite: MAT303.
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3.00 Credits
A study of topics in advanced geometry from three perspectives: synthetic, analytic, and transformational. Topics include advanced results in Euclidean geometry, axiomatic development of Euclidean and non-Euclidean geometries, the use of coordinates, transformations, and symmetries. Writing, primarily in the form of mathematical proof, is an essential component of the course. Three lecture hours per week. Required of all Mathematics majors with a Secondary Education minor. Not open to students who have received credit for MAT405. Prerequisite: MAT304A.
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