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Course Criteria
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1.00 - 3.00 Credits
An opportunity for more advanced courses than the usual offerings in number theory, modern geometry, complex variables, real analysis, algebra, differential equations or topology, this course is given when student interest and faculty time permit. May be repeated for credit with a different topic.
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3.00 Credits
A study of Euclidean spaces, general linear spaces and inner product spaces. Topics include linear independence and dependence; bases and linear transformations; matrices and determinants with application to linear systems; change of basis; and representation of linear transformation and inner products. Prerequisite: MAT 142.
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3.00 Credits
A study of differential equations. Topics included Fourier series and boundary value problems. Prerequisite: MAT 212. Offered in alternate years.
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3.00 Credits
An introduction to the basic concepts, including groups, rings and fields. Prerequisite: MAT 142 or permission of the instructor. Offered in alternate years.
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3.00 Credits
Numerical methods in solving equations, interpolation and numerical differentiation, approximation of integrals, systems of linear equations, approximation by spline functions, Monte Carlo methods, simulation and error analysis are studied. Topics include programmed solutions and computer methods. Prerequisite: MAT 142, CIS 135.
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3.00 Credits
An introduction to some areas of geometry, including cross ratio, inversion, poles and polars, dissection theory, projective and non-Euclidean geometry. Prerequisite: MAT 142 or permission of the instructor. Offered in alternate years.
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3.00 Credits
A study of basic topological concepts: mapping, continuity, connectivity, compactness, separation axioms and metric spaces. Prerequisite: MAT 212.
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3.00 Credits
A study of divisibility, congruences, quadratic reciprocity, number-theoretic functions and elementary Diophantine equations. Prerequisite: Permission of the instructor.
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3.00 Credits
Functions of a complex variable are studied. Topics include Laurent and Taylor series, residue theory, contour integration and conformal mapping. Prerequisite: MAT 212 or permission of the instructor.
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3.00 Credits
Topics covered include basic theorems of the field of real numbers, inequalities, sequential limits, function limits and the derivative. The student submits a comprehensive journal reflecting the material covered in this course. The journal should include the major definitions and theorems studied during the term with proofs of the theorems. Also included is all graded work from the course, solutions to assigned problems and interesting results discovered in outside readings or relevant computer work. Students are also required to conduct independent research on a level appropriate to a senior mathematics major and make an oral presentation on their topic. Prerequisite: MAT 212.
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