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Course Criteria
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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. Students may not take both Mathematics 35 and 63 for credit. Prerequisite: Mathematics 22 or 24, or Mathematics 13 and permission of the instructor. Dist: QDS. Chernov.
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3.00 Credits
09S: 12 This introductory course presents mathematical topics that are relevant to issues in modern physics. It is mainly designed for two audiences: mathematics majors who would like to see modern physics and the historical motivations for theory in their coursework, and physics majors who want to learn mathematics beyond linear algebra and calculus. Possible topics include (but are not limited to) introductory Hilbert space theory, quantum logics, quantum computing, symplectic geometry, Einstein's theory of special relativity, Lie groups in quantum field theory, etc. No background in physics is assumed. Offered in alternate years. Prerequisites: Mathematics 24, or Mathematics 22 and permission of the instructor. Dist: QDS. Webb.
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3.00 Credits
09F: Arrange This course covers the use of abstract algebra in studying the existence, construction, enumeration, and classification of combinatorial structures. The theory of enumeration, including both Polya Theory and the Incidence Algebra, and culminating in a study of algebras of generating functions, will be a central theme in the course. Other topics that may be included if time permits are the construction of block designs, error-correcting codes, lattice theory, the combinatorial theory of the symmetric group, and incidence matrices of combinatorial structures. Offered in alternate years. Prerequisite: Mathematics 28 and 31, or Mathematics 71, or permission of the instructor. Dist: QDS.
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3.00 Credits
09W: 11 This course begins with a study of relational systems as they occur in mathematics. First-order languages suitable for formalizing such systems are treated in detail, and several important theorems about such languages, including the compactness and Lowenheim-Skolem theorems, are studied. The implications of these theorems for the mathematical theories being formulated are assessed. Emphasis is placed on those problems relating to first-order languages that are of fundamental interest in logic. Offered in alternate years. Prerequisite: experience with mathematical structures and proofs, as offered by such courses as Mathematics 71, 54, or 24; or permission of the instructor. Dist: QDS. Groszek.
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3.00 Credits
Consult special listing
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3.00 Credits
Not offered in the period from 08F through 10S This course will be a continuation of the study of the theory of statistical inference that was begun in Mathematics 50. Topics will include the mathematical development of normal theory t-tests and nonparametric tests for means and medians, tests for variances, chi-square tests, and an introduction to the theory of the analysis of variance and regression analysis. Offered in alternate years. Prerequisite: Mathematics 50. Dist: QDS.
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3.00 Credits
08F: 10 09F: Arrange The sequence Mathematics 71 and 81 is intended as an introduction to abstract algebra. Mathematics 71 develops basic theorems on groups, rings, fields, and vector spaces. Prerequisite: Mathematics 22 or 24. Dist: QDS. Mileti.
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3.00 Credits
09S: 2 This course develops one or more topics in geometry. Possible topics include hyperbolic geometry; Riemannian geometry; the geometry of special and general relativity; Lie groups and algebras; algebraic geometry; projective geometry. Offered in alternate years. Prerequisite: Mathematics 71, or permission of the instructor. Depending on the specific topics covered, Mathematics 31 may not be an acceptable prerequisite; however, in consultation with the instructor, Mathematics 31 together with some outside reading should be adequate preparation for the course.. Dist: QDS. Gordon.
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3.00 Credits
09S: 10 10S: Arrange This course develops aspects of the general theory of differentiation and integration in Euclidean space. Primary topics include the Implicit and Inverse Function Theorems, differential forms, and Stokes' Theorem. Prerequisite: Mathematics 63. In general, Mathematics 35 is not an acceptable prerequisite; however in consultation with the instructor, Mathematics 35 together with some outside reading should be adequate preparation for the course. Dist: QDS. Webb.
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3.00 Credits
10S: Arrange This course develops one or more topics in topology. Possible topics include classification of surfaces, fundamental group and covering spaces, knot theory, combinatorial topology, and fixed point theory. Offered in alternate years. Prerequisite: Mathematics 31/71 and 54, or permission of the instructor. Dist: QDS.
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