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Course Criteria
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3.00 Credits
10S: Arrange Provides some applications of number theory and algebra. Specific topics will vary; two possibilities are cryptology and coding theory. The former allows for secure communication and authentication on the Internet, while the latter allows for efficient and error-free electronic communication over noisy channels. Students may take Math 75 for credit more than once. Offered in alternate years. Prerequisite: Mathematics 25 or 22/24 or Math 31/71, or permission of the instructor. Dist: QDS.
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3.00 Credits
09W: 10A 10W: Arrange The numerical nature of twenty-first century society means that applied mathematics is everywhere: animation studios, search engines, hedge funds and derivatives markets, and drug design. Students will gain an in-depth introduction to an advanced topic in applied mathematics. Possible subjects include digital signal and image processing, quantum chaos, computational biology, cryptography, coding theory, waves in nature, inverse problems, information theory, stochastic processes, machine learning, and mathematical finance. Prerequisite: Mathematics 22, 23, or permission of the instructor. Dist: QDS. Rockmore.
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3.00 Credits
08F: 10, 11, 12 09W: 12, 2 09S: 11 09F, 10W, 10S: Arrange This course is a sequel to Mathematics 3 and is appropriate for students who have successfully completed an AB calculus curriculum in secondary school. Roughly half of the course is devoted to topics in one-variable calculus: techniques of integrations, areas, volumes, trigonometric integrals and substitutions, numerical integration, sequences and series including Taylor series. The second half of the course generally studies scalar valued functions of several variables. It begins with the study of vector geometry, equations of lines and planes, and space curves (velocity, acceleration, arclength). The rest of the course is devoted to studying differential calculus of functions of several variables. Topics include limits and continuity, partial derivatives, tangent planes and differentials, the Chain Rule, directional derivatives and applications, and optimization problems including the use of Lagrange multipliers. Prerequisite: Mathematics 3 or equivalent. Dist: QDS. Weber, Vatter, Vatter (fall), Elizalde, Vatter (winter), Mainkar (spring).
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3.00 Credits
09W: 9L 10W: Arrange This course is the second term of the basic algebra sequence begun in Mathematics 71. While the content of this course varies somewhat from year to year, the topics treated will usually be chosen from among permutation groups, Sylow theory, factorization theory in commutative rings, Galois theory, modules, Wedderburn-Artin theory of semi-simple rings, Noetherian rings, integral extensions, and Dedekind domains. Prerequisite: Mathematics 71. In general, Mathematics 31 is not 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. Elizalde.
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3.00 Credits
Not offered in the period from 08F through 10S From its beginnings in the eighteenth century, Fourier analysis has branched in many directions that are central to applied mathematics. The core of the course consists of the main ideas of one-dimensional Fourier analysis of both periodic and non-periodic phenomena, coupled with an introduction to Lebesgue integration sufficient for understanding the contemporary foundations of the subject. Additional topics are drawn from such areas as signal processing, probability limit laws, and number theory. Offered in alternate years. Prerequisite: Mathematics 63. In general, Mathematics 35 is not an acceptable prerequisite, however, in consultation with the instructor, Mathematics 35 together with some out side reading should be adequate preparation for the course. Dist: QDS.
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3.00 Credits
08F: 11 09F: Arrange Financial derivatives can be thought of as insurance against uncertain future financial events. This course will take a mathematically rigorous approach to understanding the Black-Scholes-Merton model and its applications to pricing financial derivatives and risk management. Topics may include: arbitrage-free pricing, binomial tree models, Ito calculus, the Black-Scholes analysis, Monte Carlo simulation, pricing of equities options, and hedging. Prerequisites: Mathematics 20/60 and Mathematics 23, as well as some programming experience (e.g., Computer Science 5). Dist: QDS. Chu.
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3.00 Credits
All terms: Arrange Advanced undergraduates occasionally arrange with a faculty member a reading course in a subject not occurring in the regularly scheduled curriculum.
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3.00 Credits
Not offered in the period from 08F through 10S From time to time a section of Mathematics 88 may be offered in order to provide an advanced course in a topic which would not otherwise appear in the curriculum. Consult the advisor to majors for details about topics to be covered. Dist: QDS.
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3.00 Credits
10W: Arrange A study of selected topics in logic, such as model theory, set theory, recursive function theory, or undecidability and incompleteness. Offered in alternate years. Prerequisite: Mathematics 39 or 69. Dist: QDS.
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3.00 Credits
09F: Arrange Sections of Mathematics 8 for students who have been invited by the Department Chair based on their record in high school or exceptional work in Mathematics 3. Dist: QDS.
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