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Course Criteria
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4.00 Credits
Studies ordinary differential equations from both the quantitative and qualitative points of view: first-order equations and systems, second-order equations, analytic solution techniques, numerical methods and visualization (through computer labs), and applications to mechanical and electrical oscillations. Emphasizes the dynamical systems approach including instances of chaos.
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4.00 Credits
Uses the Gauss-Jordan elimination algorithm to analyze and find bases for subspaces such as the image and kernel of a linear transformation. Covers the geometry of linear transformations: orthogonality, the Gram-Schmidt process, rotation matrices, and least squares fit. Examines diagonalization and similarity, and the spectral theorem and the singular value decomposition. Is primarily for math and science majors; applications are drawn from many technical fields. Computation is aided by the use of software such as Maple or MATLAB, and graphing calculators.
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4.00 Credits
Provides an introduction to statistical techniques, including multisample statistics and regression. Offers an opportunity to learn to choose appropriate statistical data analysis methods for applications in various scientific fields and to learn to use a statistical package to implement the data analysis. Topics include descriptive statistics, elementary probability theory, parameter estimation, confidence intervals, hypothesis testing, analysis of variance, and regression. May also include optimal design.
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1.00 Credits
Intended for math majors who have completed their second co-op assignment. Its goal is to examine the mathematical problems encountered on the job, and relate them to courses already taken and to the student's future program. Faculty members and other guests contribute to the discussion. Grades are determined by the student's participation in the course.
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4.00 Credits
Introduces number theory. Topics include linear diophantine equations, congruences, design of magic squares, Fermat's little theorem, Euler's formula, Euler's phi function, computing powers and roots in modular arithmetic, the RSA encryption system, primitive roots and indices, and the law of quadratic reciprocity. As time permits, may cover diophantine approximation and Pell's equation, elliptic curves, points on elliptic curves, and Fermat's last theor
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4.00 Credits
Introduces techniques of mathematical proofs including mathematical induction. Explores various techniques for counting such as permutation and combinations, inclusion-exclusion principle, recurrence relations, generating functions, Polya enumeration, and the mathematical formulations necessary for these techniques including elementary group theory and equivalence relations.
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4.00 Credits
Presents an experimental study using simple mathematical models of chaotic behavior in dynamical systems. (Such systems are frequently found in science and industry.) Goals include the development of skills of experiment and inquiry, integration of visual and analytical modes of thought, and appreciation of issues of problem formulation and representation.
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1.00 Credits
Retired August 31, 2006. Offers additional intermediate academic experience by exploring course-related topics in greater depth with the professor. Available only to courses approved by the University Honors Program.
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1.00 Credits
Retired August 31, 2006. Offers additional intermediate academic experience by exploring course-related topics in greater depth with the professor. Available only to courses approved by the University Honors Program.
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1.00 Credits
Retired August 31, 2006. Offers additional intermediate academic experience by exploring course-related topics in greater depth with the professor. Available only to courses approved by the University Honors Program.
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