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Course Criteria
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3.00 Credits
Implicit-function theorems, transformations and mappings, vectors and vector fields, differential calculus of vector-valued functions. Prerequisite: MAT 2533 and MAT 3410. Fall, odd years.
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3.00 Credits
Numerical computation techniques for solving non-linear and transcendental equations including Newton's method, bisection method, and secant method. Numerical solutions to polynomials, including synthetic division. Numerical interpolation, approximation, integration, and numerical solutions to ordinary differential equations. Prerequisite: MAT 3210, MAT 3310 or consent of instructor. Periodically. Offered on a limited basis in consultation with the department chair.
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3.00 Credits
Topics from the theory of groups, rings, and fields leading up to Galois theory. Prerequisite: MAT 2533, MAT 3210 and MAT 3410, or consent of instructor. Spring, odd years.
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3.00 Credits
The foundations of Euclidean geometry and an introduction to hyperbolic geometry. The historical and philosophical implications of the discovery of non-Euclidean geometry are examined as well as the contributions of Gauss, Hilbert, Saccheri, Bolyai, Lobachevsky and others. Prerequisite: MAT 3410. Spring, even years.
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2.00 Credits
This course is intended for pre-service teachers who are seeking to increase their understanding of mathematics. The course uses data collection and analysis to guide improvement in K-6 mathematics programs. The student will build on the knowledge gained in MAT 3020 to obtain a deeper understanding of mathematics as related to NCTM and the Vermont Framework guidelines. In this course, students will function as researchers by gathering data and analyzing data, as means of improving the curriculum and instruction in K-6 mathematics programs. As researchers, students are encouraged to ask questions, pose problems, and identify means of solving problems by using different strategies. Emphasis will be on student-centered instructional approach, with ample use of manipulatives and technology. Prerequisite: MAT 3020 and EDU 3330 or consent of instructor.
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1.00 - 3.00 Credits
Advanced topics in mathematics offered on a rotating basis. Examples of topics include: complex analysis, topology, Galois theory, number theory. Prerequisite: MAT 2533, MAT 3410, or consent of the instructor. Fall.
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1.00 - 3.00 Credits
An undergraduate research seminar. Students spend the first half of the semester studying and presenting undergraduate research in mathematics. In the second half, students investigate their own topic, prepare a written report, and present their research. Prerequisite: Math major, senior standing, or consent of the instructor. Fall.
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1.00 - 12.00 Credits
Signed contract required at time of registration.
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1.00 - 3.00 Credits
Open on a limited basis only and ordinarily restricted to students with upper-level standing. A personal interview with the Mathematics Department faculty is required prior to registration. Hours by arrangement. Prerequisite: Consent of department chair. NOTE: Computer related courses require payment of a materials charge.
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3.00 Credits
A listening course in which the student is introduced to the various elements of music such as melody, rhythm, and harmony. Emphasis is placed on the music of Bach, Mozart, Beethoven, Brahms, and Stravinsky, etc. No previous training required. Every semester.
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