Page 174 of Boston College 2006-2007 University Catalog by Boston College University

174 The Boston College Catalog 2006-2007 method, history of the parallel postulate, the Lobachevskian plane, Hilberts axioms for Euclidean geometry, elliptic and projective geometry, the trigonometric formulas, models, geometry and the study of physical space. MT 470 Mathematical Modeling (Fall: 3) Prerequisites: MT 202, MT 210, and familiarity with using a computer This is a course primarily for mathematics majors with the purpose of introducing the student to the creation, use, and analysis of a variety of mathematical models and to reinforce and deepen the mathematical and logical skills required of modelers. A secondary purpose is to develop a sense of the existing and potential roles of both small and large scale models in our scientific civilization. It proceeds through the study of the model-building process, examination of exemplary models, and individual and group efforts to build or refine models through a succession of problem sets, laboratory exercises, and field work. MT 475 History of Mathematics (Spring: 3) Prerequisites: MT 310 and MT 320, one of which may be taken concurrently. Offered Biennially Students must be familiar with abstract algebra (groups, rings, fields) and rigorous analysis (differentiation and integration of real valued functions, sequences and series of functions) This course studies the development of mathematical thought, from ancient times to the twentieth century. Naturally, the subject is much too large for a single semester, so we will concentrate on the major themes and on the contributions of the greatest mathematicians. The emphasis in the course will be on the mathematics. Students will follow the historical arguments and work with the tools and techniques of the period being studied. MT 480 Topics in Mathematics (Spring: 3) Offered Periodically Topics for this one-semester course vary from year to year according to the interests of faculty and students. With department permission it may be repeated. MT 860 Mathematical Logic (Fall: 3) Prerequisite: MT 310 or MT 320 or permission of the instructor Offered Biennially This course is a mathematical examination of the way mathematics is done and of axiom systems, logical inference, and the questions that can (or cannot) be resolved by inference from those axioms. Specific topics will include propositional calculus, first order theories, decidability, and Godels Completeness Theorem. MT 861 Foundations of Mathematics (Spring: 3) Prerequisite: MT 860 or equivalent Offered Biennially Topics to be treated in this course will be selected from one or more of the following areas: formal number theory, axiomatic set theory, effective computability, and recursive function theory. Graduate Course Offerings MT 580 Mathematics for Statistics (Fall: 3) Restricted to graduate students in the Interdisciplinary Statistics Minor Program. This course is an introduction to probability, calculus, and linear algebra for graduate students in the Statistics Minor Program having little or no formal training in these subjects. Topics include: counting methods, axioms and properties of probability, conditional probability, independence, Bayes rule, limits, infinite series, derivative and integral methods, vector and matrix operations, and computer methods. MT 801 Thesis Seminar (Fall: 3) Problems of research and thesis guidance, supplemented by individual conferences. MT 804 Analysis I (Fall: 3) Prerequisite: MT 320 or equivalent The MT 804-805 sequence is intended to emphasize the basic ideas and results of calculus and to provide an introduction to abstract analysis. The course begins with an axiomatic introduction to the real number system. Metric spaces are then introduced. Theoretical aspects of convergence, continuity, differentiation, and integration are treated carefully and are studied in the context of a metric space. The course includes an introduction to the Lebesgue integral. MT 805 Analysis II (Spring: 3) Prerequisite: MT 804 This course is a continuation of MT 804. MT 814 Theory of Functions of a Complex Variable I (Fall: 3) Prerequisite: MT 320 or equivalent Topics for the MT 814-815 sequence include: differentiation and integration of a function of a complex variable, series expansion, residue theory, entire and meromorphic functions, multiple-valued functions, Riemann surfaces, and conformal mapping problems. MT 815 Theory of Functions of a Complex Variable II (Spring: 3) Prerequisite: MT 814 This course is a continuation of MT 814. MT 816 Modern Algebra I (Fall: 3) Prerequisite: MT 310 or permission of instructor The MT 816-817 course sequence will study the basic structures of abstract algebra. Topics will include groups, rings, ideal theory, unique factorization, homomorphisms, field extensions, and Galois theory. MT 817 Modern Algebra II (Spring: 3) Prerequisite: MT 816 This course is a continuation of MT 816. MT 820 Measure and Integration (Fall: 3) Prerequisite: MT 804-805 or equivalent, or permission of instructor Offered Periodically This is a course in the classical theory of functions of a real variable. Topics include the Lebesgue integral, the classical Banach spaces, and integration in general measure spaces. MT 853 Topics in Modern Statistics (Spring: 3) Prerequisites: Calculus-based probability and statistics (e.g., MT 426-427, although some review will be included at the beginning of the semester). Offered Periodically This course introduces the student to intermediate level statistics using classical (parametric), non-parametric, permutation and bootstrap methods. Topics include analysis of variance, regression, and analysis of contingency tables, as well as specialized applications of computer-intensive methods from a wide variety of fields. Students interested in taking the course should consult with Professor Baglivo during the fall semester since it will be possible to tailor applications to the interests of the students. Computing experience helpful. Jenny A. Baglivo ARTS AND SCIENCES

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