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Course Criteria
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3.00 Credits
Every two years. Spring 2008. THE DEPARTMENT. Topology studies properties of geometric objects that do not change when the object is deformed. The course covers knot theory, surfaces, and other elementary areas of topology. Prerequisite: Mathematics 181.
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3.00 Credits
Every other spring. Spring 2007. THE DEPARTMENT. A study of optimization problems arising in a variety of situations in the social and natural sciences. Analytic and numerical methods are used to study problems in mathematical programming, including linear models, but with an emphasis on modern nonlinear models. Issues of duality and sensitivity to data perturbations are covered, and there are extensive applications to real-world problems. Prerequisite: Mathematics 181.
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3.00 Credits
Every other year. Fall 2006. STEVE FISK. A standard course in elementary number theory which traces the historical development and includes the major contributions of Euclid, Fermat, Euler, Gauss, and Dirichlet. Prime numbers, factorization, and number-theoretic functions. Perfect numbers and Mersenne primes. Fermat's theorem and its consequences. Congruences and the law of quadratic reciprocity. The problem of unique factorization in various number systems. Integer solutions to algebraic equations. Primes in arithmetic progressions. An effort is made to collect along the way a list of unsolved problems.
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3.00 Credits
Every other fall. Fall 2007. THE DEPARTMENT. The differential and integral calculus of functions of a complex variable. Cauchy's theorem and Cauchy's integral formula, power series, singularities, Taylor's theorem,Laurent's theorem, the residue calculus, harmonic functions, and conformal mapping. Prerequisite: Mathematics 171.
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3.00 Credits
Fall 2008. THE DEPARTMENT. An introduction to statistical modeling techniques with an emphasis on applications. Deals first with regression analysis: least square estimates of parameters; single and multiple linear regression; hypothesis testing and confidence intervals in linear regression models; and testing of models, data analysis, and appropriateness of models. Follows with a focus on time series: linear time series models; moving average, autoregressive, and ARIMA models; estimation, data analysis, and forecasting with time series models; and forecast errors and confidence intervals. Prerequisite: Mathematics 155 or 165 or permission of the instructor.
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3.00 Credits
Spring 2008. THE DEPARTMENT. An introduction to the theory and application of numerical analysis. Topics include approximation theory, numerical integration and differentiation, iterative methods for solving equations, and numerical analysis of differential equations. Prerequisite: Mathematics 201 (formerly Mathematics 222) or permission of the instructor.
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3.00 Credits
Every other spring. Spring 2007. THE DEPARTMENT. A survey of modern approaches to Euclidean geometry in two and three dimensions. Axiomatic foundations of metric geometry. Transformational geometry: isometries and similarities. Klein's Erlangen Program. Symmetric figures. Scaling, measurement, and dimension. Prerequisite: Mathematics 171 or permission of the instructor.
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3.00 Credits
Every other spring. Spring 2007. THE DEPARTMENT. An introduction to combinatorics and graph theory. Topics to be covered may include enumeration, matching theory, generating functions, partially ordered sets, Latin squares, designs, and graph algorithms. Prerequisite: Mathematics 200, 262 or 263, or permission of the instructor.
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3.00 Credits
Spring 2007. THE DEPARTMENT. A study of the basic arithmetic and algebraic structure of the common number systems, polynomials, and matrices. Axioms for groups, rings, and fields, and an investigation into general abstract systems that satisfy certain arithmetic axioms. Properties of mappings that preserve algebraic structure. Prerequisite: Mathematics 200 and 201 (formerly Mathematics 222), or permission of the instructor.
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3.00 Credits
Fall 2006. REBECCA FIELD. Emphasizes proof and develops the rudiments of mathematical analysis. Topics include an introduction to the theory of sets and topology of metric spaces, sequences and series, continuity, differentiability, and the theory of Riemann integration. Additional topics may be chosen as time permits. Prerequisite: Mathematics 181 and 200, or a 200-level Mathematics course approved by the instructor.
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