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  • Mathematics 42: Differential Geometry I

    3.00 Credits
    Dartmouth College

    09W: 2 This course will cover curves and surfaces in Euclidean 3-dimensional space. Topics include curvature and torsion of curves, the Frenet-Serret equations, Gaussian and mean curvature of surfaces, geodesics and parallel transport, isometries and Gauss's Theorem Egregium, the Riemann Curvature tensor. One or more of the following topics will be studied if time permits: vector fields, tangent bundles, hypersurfaces, connections, and curvature. Offered in alternate years. Prerequisite: Mathematics 22 or permission of the instructor, and Mathematics 23. Dist:QDS. Pauls.
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  • Mathematics 43: Functions of a Complex Variable

    3.00 Credits
    Dartmouth College

    09S: 10 10S: Arrange This course covers the differential and integral calculus of complex variables including such topics as Cauchy's theorem, Cauchy's integral formula and their consequences; singularities, Laurent's theorem, and the residue calculus; harmonic functions and conformal mapping. Applications will include two-dimensional potential theory, fluid flow, and aspects of Fourier analysisPrerequisite: Mathematics 13. Dist: QDS. Williams.
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  • Mathematics 46: Introduction to Applied Mathematics

    3.00 Credits
    Dartmouth College

    09S: 2 10S: Arrange Develops tools to analyze phenomena in the physical and life sciences, from cell aggregation to vibrating drums to traffic jams. Focus is on applied linear and nonlinear partial differential equations: methods for Laplace, heat and wave equations (Fourier transform, Green's functions, eigenfunction expansions), Burger's and reaction-diffusion equation. Further topics may include linear and integral operators, nonlinear optimization, linear programming, asymptotics, boundary layers, or inverse problems. Students will develop numerical skills with a package like MATLAB/Octave.Prerequisite: Mathematics 22 and 23, or permission of the instructor. Dist: TAS. Barnett.
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  • Mathematics 5: Exploring Mathematics

    3.00 Credits
    Dartmouth College

    08F: 10 09W: 10 09F, 10W: Arrange In 08F, The Mathematics of Music and Sound. Sound and music are integral parts of all cultures and are critical to human and animal communications. The production, transmission, and perception of sound is woven through with mathematics. With the goal of expanding both scientific and artistic horizons, we explore vibration, resonance, waves, musical instruments, the human ear, speech, architectural acoustics, harmony and dissonance, tuning systems, and musical composition. Hands-on project work may include time-frequency analysis, sound synthesis, inventing and building a new instrument. Prerequisite: high-school physics. Familiarity with musical notation or an instrument will help. Dist: QDS. Barnett. In 09W, A Matter of Time ( Identical to Comparative Literature 65 in 09W). Everybody knows about time. Our everyday language bears witness to the centrality of time with scores of words and expressions that refer to it as a measure, a frame of reference, or an ordering factor for our lives, feelings, dreams, and histories. Playing with time has been a favorite game in works of high culture-from the Greek sophists to cubism-and in popular culture-from H.G. Wells to Monty Python. And time is at the center of one of the most revolutionary scientific theories of all time: Einstein's Theory of Relativity. In this course we will use mathematics, literature, and the arts to travel through history, to explore and understand Time as a key concept and reality in the development of Western culture and in our own twentieth century view of ourselves and the wor ld. Dist: Q DS. Lahr, Pasto
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  • Mathematics 50: Probability and Statistical Inference

    3.00 Credits
    Dartmouth College

    09W: 2A 10W: Arrange Introduction to continuous probability and statistical inference for data analysis. Includes the theory of estimation and the theory of hypothesis testing using 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. Analysis of explicit data sets and computation are an important part of this hands-on statistics course. Prerequisite: Mathematics 13 and 20, or permission of the instructor. Dist: QDS. Demidenko.
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  • Mathematics 53: Chaos!

    3.00 Credits
    Dartmouth College

    09F: Arrange Chaotic dynamical systems are everywhere: weather patterns, swinging pendula, population dynamics, even human heart rhythms. With a balance of theory and applications, this course will introduce: flows, fixed points, bifurcations, Lorenz equations, Lyapunov exponent, one-dimensional maps, period-doubling, Julia sets, fractal dimension. Optional topics may include: Hamiltonian systems, symbolic dynamics. Numerical explorations will involve a package like MATLAB/Octave, and students will present a final project investigating a related topic. Offered in alternate years. Prerequisite: Mathematics 22 and 23, or permission of the instructor. Dist: QDS.
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  • Mathematics 54: Topology I

    3.00 Credits
    Dartmouth College

    09X: Arrange This course begins with the definitions of topological space, open sets, closed sets, neighborhoods, bases and subbases, closure operator, continuous functions, and homeomorphisms. The course will study constructions of spaces including subspaces, product spaces, and quotient spaces. Special categories of spaces and their interrelations will be covered, including the categories defined by the various separation axioms, first and second countable spaces, compact spaces, and connected spaces. Subspaces of Euclidean and general metric spaces will be among the examples studied in some detail. Prerequisite: Mathematics 13 and 22. Dist: QDS.
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  • Mathematics 56: Numerical Analysis

    3.00 Credits
    Dartmouth College

    Not offered in the period from 08F through 10S This course introduces the student to the concepts of modern numerical analysis. The main emphasis will be on developing effective numerical methods to solve problems in ordinary and partial differential equations. Other topics will be chosen from optimization, approximation, Fourier Transform, and Monte Carlo methods. The specific content will depend in part on the instructor. Offered in alternate years. Prerequisite: Mathematics 33 and Computer Science 5 or 14, or permission of the instructor. Dist: QDS.
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  • Mathematics 6: Introduction to Finite Mathematics

    3.00 Credits
    Dartmouth College

    09S: 9L 09X, 10S: Arrange This course is designed for students whose interests lie outside the physical sciences. The course includes an introduction to sets and logic, elementary counting techniques, an introduction to probability, and topics in matrix algebra including the solution of systems of equations and matrix inverses. Illustrative examples and problems will be chosen from the social, managerial, and biological sciences. Computing may be used to illustrate concepts and solve problems. No background in computer programming is assumed. The course is appropriate for the student who plans to take no advanced courses in mathematics. Dist: QDS. The staff.
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  • Mathematics 60: Probability

    3.00 Credits
    Dartmouth College

    10S: Arrange This course is a more theoretical introduction to probability theory than Mathematics 20. In addition to the basic content of Mathematics 20, the course will include other topics such as continuous probability distributions and their applications. Offered in alternate years. Prerequisite: Mathematics 13, or permission of the instructor. Dist: QDS.
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