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Course Criteria
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4.00 Credits
An introduction to the mathematics most relevant for the physical sciences and physical problems that demonstrate its need. Topics include vector analysis, including line and surface integrals, complex differentiable functions, and partial differential equations and Sturm-Liouville problems. Prerequisites: MTH 302 or MTH 304; PHY 231; or permission of instructor.
Prerequisite:
Prerequisites: MTH 302 or MTH 304; PHY 231; or permission of instructor.
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3.00 Credits
Complex arithmetic derivatives and integrals of functions of a complex variable. Infinite series. Residue calculus. Applications to real integration and fluid flows. Prerequisites: MTH 203 and either MTH 204 or MTH 302.
Prerequisite:
Prerequisites: MTH 203 and either MTH 204 or MTH 302.
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3.00 Credits
Numerical methods in solving equations of a single variable, matrix algebra, numerical differentiation and integration, numerical solution to differential equations, polynomial approximations, and error estimates. Offered fall semester. Prerequisites: Either CIS 161 or CIS 162 or EGR 112, and either (MTH 202 and MTH 204) or (MTH 302).
Prerequisite:
Prerequisites: Either CIS 161 or CIS 162 or EGR 112, and either (MTH 202 and MTH 204) or (MTH 302).
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3.00 Credits
A theoretical presentation of linear algebra incorporating a proof-based study of vector spaces, inner product spaces, bases, linear transformations, isomorphisms, canonical forms, and applications to topics such as wavelets, quadratures, and Fourier transforms. Prerequisites: MTH 205 and (MTH 210 or (MTH 225 and MTH 325)).
Prerequisite:
Prerequisites: MTH 205 and (MTH 210 or (MTH 225 and MTH 325)).
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3.00 Credits
The goal of this course is to develop the intuitive and theoretical foundations necessary to study differentiation of real-valued functions. Topics include Cauchy sequences, convergence of sequences, series, limits, continuity, and construction of the real numbers. Students will extend and apply proof techniques from previous courses. Offered every year. Prerequisites: MTH 203 and one of the following (MTH 315, MTH 331, MTH 350, or MTH 431) or (MTH 210 and permission of instructor).
Prerequisite:
Prerequisites: MTH 203 and one of the following (MTH 315, MTH 331, MTH 350, or MTH 431) or (MTH 210 and permission of instructor).
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3.00 Credits
This course is an in-depth study of differentiation and integration, with additional topics such as sequences and series of functions, measure theory, and metric spaces. Prerequisite: MTH 408.
Prerequisite:
Prerequisite: MTH 408.
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1.00 Credits
Elementary math seminar to support student teachers as they critique and reflect upon their mathematical instruction. Emphasis is on assessment-driven instruction; communicating with children, caregivers, and communities; and effective use of instructional materials to support children's mathematics learning. Supported by current research in mathematics education. Corequisite: EDI 430.
Corequisite:
EDI 430
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3.00 Credits
A critical examination of several nonEuclidean geometries, including finite geometries, hyperbolic geometry, and spherical geometry; their relationships to Euclidean geometry; and the historical and philosophical significance of the development of Non-Euclidean geometries. Prerequisites: MTH 210 and either MTH 331 or permission of the instructor.
Prerequisite:
Prerequisites: MTH 210 and either MTH 331 or permission of the instructor.
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3.00 Credits
An introduction to the fundamental concepts of topology. The topology of the real number system and its generalizations to metric spaces and topological spaces. Topics include subspaces, neighborhood spaces, open and closed sets, interior and boundary of sets, continuity and homeomorphisms, connected and locally connected spaces, compact sets and spaces. Prerequisites: MTH 203, MTH 210, and MTH 204.
Prerequisite:
Prerequisites: MTH 203, MTH 210, and MTH 204.
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3.00 Credits
An introduction to groups, including homomorphisms and isomorphisms, Larange's Theorem, quotient groups, finite groups, and the Sylow Theorems. Additional topics from ring theory including polynomial rings, ideals, and quotient rings. Prerequisite: MTH 350.
Prerequisite:
Prerequisite: MTH 350.
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