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Course Criteria
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3.00 Credits
Not offered in the period from 08F through 10S This course provides an introduction to the most common model used in statistical data analysis. Simple linear regression, multiple regression, and analysis of variance are covered, as well as statistical model-building strategies. Regression diagnostics, analysis of complex data sets and scientific writing skills are emphasized. Methods are illustrated with data sets drawn from the health, biological, and social sciences. Computations require the use of a statistical software package such as STATA. Offered in alternate years. Prerequisite: Mathematics 10, another elementary statistics course, or permission of the instructor. Dist: TAS.
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3.00 Credits
08F: 12 09X, 09F: Arrange This course will provide an introduction to fundamental algebraic structures, and may include significant applications. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. Additional work will consist either of the development of further algebraic structures or applications of the previously developed theory to areas such as coding theory or crystallography. As a result of the variable syllabus, this course may not serve as an adequate prerequisite for Mathematics 81. Students who contemplate taking Mathematics 81 should consider taking Mathematics 71 instead of this course. Prerequisite: Mathematics 22. Dist: QDS. The staff.
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3.00 Credits
10W: Arrange Topics in intuitive geometry and topology, for example: how to turn a sphere inside out; knots, links, and their invariants; polyhedra in 2, 3, and 4 dimensions; the classification of surfaces; curvature and the Gauss-Bonnet theorem; spherical and hyperbolic geometry; Escher patterns and their quotients; the shape of the universe. Offered in alternate years. Prerequisite: Mathematics 22 or 24. Dist: QDS.
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3.00 Credits
Not offered in the period from 08F through 10S This course provides an overview of the mathematical tools used for analyzing common problems in science and engineering. Particular attention will be given to problems involving linear operators. Topics include partial differential equations, Fourier analysis, linear spaces and operators (in particular, matrix operators), and the calculus of variations. Both analytical and numerical methods will be covered. Prerequisite: Mathematics 23. Dist: TAS.
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3.00 Credits
09W: 12 10W: Arrange This course introduces the basic concepts of real-variable theory. Topics include real numbers and cardinality of sets, sequences and series of real numbers, metric spaces, continuous functions, integration theory, sequences and series of functions, and polynomial approximation. Some applications of the theory may be presented. Mathematics 63 presents similar material, but from a more sophisticated point of view. This course may not serve as an adequate prerequisite for either Mathematics 73 or 83. Students who contemplate taking one of these two advanced courses should consider taking Mathematics 63 instead of this course. Prerequisite: Mathematics 13 and permission of the instructor, or Mathematics 22. Dist: QDS. Lahr.
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3.00 Credits
08F: 2 09F: Arrange Disciplines such as anthropology, economics, sociology, psychology, and linguistics all now make extensive use of mathematical models, using the tools of calculus, probability, game theory, network theory, often mixed with a healthy dose of computing. This course introduces students to a range of techniques using current and relevant examples. Students interested in further study of these and related topics are referred to the courses listed in the Mathematics and Social Sciences program. Prerequisite: Mathematics 13, 20. Dist: TAS. Pauls.
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3.00 Credits
09S: 12 10S: Arrange The theory of graphs has roots in both practical and recreational mathematics. Today there are major applications of graph theory in management science (operations research) and computer science. This course is a survey of the theory and applications of graphs. Topics will be chosen from among connectivity, trees, and Hamiltonian and Eulerian paths and cycles; isomorphism and reconstructability; planarity, duality, and genus; independence and coloring problems, including interval graphs, interval orderings and perfect graphs, color-critical graphs and the four-color theorem; matchings; network flows, including applications to matchings, higher connectivity, and transportation problems; matroids and their relationship with optimization. Prerequisite: Mathematics 22 (or Computer Science 25 and permission of the instructor). Dist: QDS. Mileti.
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3.00 Credits
09F: Arrange This course begins with a brief treatment of sentential logic and then concentrates on first-order logic. Both proof theory and model theory are taken up. The course ends with a proof of the G del incompleteness theorem. Connections with the philosophy of mathematics are discussed. There is an honors version of this course: see Mathematics 69. Offered in alternate years. Prerequisite: one of Mathematics 22, 28, and 29, or Philosophy 10 by permission of the instructor. Dist: QDS.
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3.00 Credits
09W: 10A 10W: Arrange This course will establish the relevance of calculus to medicine. It will develop mathematical tools extending the techniques of introductory calculus, including some matrix algebra and solution techniques for first order differential equations. These methods will be used to construct simple and elegant models of phenomena such as the mutation of HIV, spread of infectious disease, and biological disposition of drugs and inorganic toxins, enzyme kinetics and population growth. Prerequisite: Mathematics 3. Note: This is a second-term calculus course, but it does not cover the same material as Mathematics 8, and does not serve as a prerequisite for Mathematics 13. There is a version of this course suitable for major credit: see Mathematics 27. Dist: QDS. Wallace.
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3.00 Credits
Not offered in the period from 08F through 10S This is a continuation of Mathematics 20 (60). The course studies probability models chosen from queueing theory, genetics, statistical physics, and gambling. Additional probability concepts such as continuous probability and stochastic processes will be discussed in the context of these models. Offered in alternate years. Prerequisite: Mathematics 13 and 20, or permission of the instructor. Dist: QDS.
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