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Course Criteria
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3.00 Credits
Staff. Elementary applications of decision analysis, game theory, probability and statistics to issues in accounting, contracting, finance, law, and medicine, amongst others.
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3.00 Credits
Staff. Corequisite(s): Math 104, 114 or 240. This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying real and complex numbers, sequences, series, continuity, differentiability and integrability. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill- sharpening.
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3.00 Credits
Staff. Corequisite(s): Math 104, 114 or 240. This course focuses on the creative side of mathematics, with an emphasis on discovery, reasoning, proofs and effective communication, while at the same time studying arithmetic, algebra, linear algebra, groups, rings and fields. Small class sizes permit an informal, discussion-type atmosphere, and often the entire class works together on a given problem. Homework is intended to be thought-provoking, rather than skill-sharpening.
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3.00 Credits
Staff. Prerequisite(s): Math 114, Math 115 or equivalent. This course counts as a regular elective for both the Mathematics Major and Minor. Style: the course will center around a sequence of case studies and projects rather than go systematically through a textbook. Many of these topics will be drawn from current events in the world. The class will be divided into small teams that will carry out work on each topic, perform whatever mathematical analysis is appropriate according to the mathematical topics being discussed. Internet. An important ingredient in the course will be to learn to present interactive material on the Web using a computer language such as Perl. No special computer background is presumed; learning it is part of the course. Topics: Some probability/statistics (including Markov chains), mathematical modeling (including differential equations). Many of the topics will use calculus and matrices.
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3.00 Credits
Staff. Prerequisite(s): Calculus II. Linear algebra: vectors, matrices, systems of linear equations, eigenvalues and eigenvectors. Vector calculus: functions of several variables, vector fields, line and surface integrals, Green's, Stokes' and divergence theorems. Series solutions of ordinary differential equations, Laplace transforms and systems of ordinary differential equations. Use of symbolic manipulation and graphics software.
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3.00 Credits
Staff. Prerequisite(s): MATH 240. St urm-Liouville problems, orthogonal functions, Fourier series, and partial differential equations including solutions of the wave, heat and Laplace equations, Fourier transforms. Introduction to complex analysis. Use of symbolic manipulation and graphics software. (MATH412) Linear Algebra. (M) Staff. Prerequisite(s): MATH 240. Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Mathematics majors are advised that MATH 312 cannot be taken to satisfy the major requirements. ( CIS 313, MATH513) Computational Linear Algebra. Staff. Prerequisite(s): Math 114 or 115, and some programming experience. Students who have already received credit for either Math 370, 371, 502 or 503 cannot receive further credit for Math 312 or Math 313/513. Students can receive credit for at most one of Math 312 and Math 313/513. Many important problems in a wide range of disciplines within computer science and throughout science are solved using techniques from linear algebra. This course will introduce students to some of the most widely used algorithms and illustrate how they are actually used. Some specific topics: the solution of systems of linear equations by Gaussian elimination, dimension of a linear space, inner product, cross product, change of basis, affine and rigid motions, eigenvalues and eigenvectors, diagonalization of both symmetric and non-symmetric matrices, quadratic polynomials, and least squares optimazation. Applications will include the use of matrix computations to computer graphics, use of the discrete Fourier transform and related techniques in digital signal processing, the analysis of systems of linear differential equations, and singular value deompositions with application to a principal component analysis. The ideas and tools provided by this course will be useful to students who intend to tackle higher level courses in digital signal processing, computer vision, robotics, and computer graphics.
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3.00 Credits
Staff. Prerequisite(s): MATH 240 or concurrent and ability to program a computer, or permission of instructor. Students will use symbolic manipulation software and write programs to solve problems in numerical quadrature, equation-solving, linear algebra and differential equations. Theoretical and computational aspects of the methods will be discussed along with error analysis and a critical comparison of methods.
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3.00 Credits
Staff. Prerequisite(s): MATH 320. Continuation of MATH 320. (LGIC210) Discrete Mathematics I. (M) Staff. Prerequisite(s): MATH 114 or Math 115 or permission of the instructor. Topics will be drawn from some subjects in combinatorial analysis with applications to many other branches of math and science: graphs and networks, generating functions, permutations, posets, asymptotics. (LGIC220) Discrete Mathematics II. Staff. Prerequisite(s): Math 340/Logic 210 or permission of the instructor. Topics will be drawn from some subjects useful in the analysis of information and computation: logic, set theory, theory of computation, number theory, probability, and basic cryptography.
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3.00 Credits
Staff. Congruences, Diophantine equations, continued fractions, nonlinear congruences, and quadratic residues.
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3.00 Credits
Staff. Prerequisite(s): MATH 240. Syllabus for MATH 360-361: a study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
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