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DSpace at MIT (104.280 recursos)

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Mathematics (18) - Archived

Mostrando recursos 1 - 20 de 107

  1. 18.905 Algebraic Topology, Fall 2006

    Lawson, Tyler
    This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

  2. 18.785 Number Theory I, Fall 2016

    Sutherland, Andrew
    This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

  3. 2.062J / 1.138J / 18.376J Wave Propagation, Fall 2006

    Mei, Chiang; Rosales, Rodolfo; Akylas, Triantaphyllos
    This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a...

  4. 2.062J / 1.138J / 18.376J Wave Propagation, Fall 2006

    Mei, Chiang; Rosales, Rodolfo; Akylas, Triantaphyllos
    This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a...

  5. 18.783 Elliptic Curves, Spring 2015

    Sutherland, Andrew
    This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.

  6. 18.783 Elliptic Curves, Spring 2015

    Sutherland, Andrew
    This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.

  7. 18.785 Number Theory I, Fall 2015

    Sutherland, Andrew
    This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

  8. 5.95J / 6.982J / 7.59J / 8.395J / 18.094J / 1.95J / 2.978J Teaching College-Level Science and Engineering, Fall 2012

    Rankin, Janet
    This participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. This course is designed for graduate students interested in an academic career, and anyone else interested in teaching. Topics include theories of adult learning; course development; promoting active learning, problem-solving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Students research and present a relevant topic of particular interest. The subject is appropriate for both novices and those with teaching experience.

  9. 18.405J / 6.841J Advanced Complexity Theory, Fall 2001

    Spielman, Daniel
    The topics for this course cover various aspects of complexity theory, such as  the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved.

  10. 6.042J / 18.062J Mathematics for Computer Science, Spring 2005

    Leiserson, Charles; Lehman, Eric; Devadas, Srinivas; Meyer, Albert R.
    This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.

  11. 6.042J / 18.062J Mathematics for Computer Science, Spring 2010

    Meyer, Albert R.
    This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in Computer Science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.

  12. 18.466 Mathematical Statistics, Spring 2003

    Dudley, Richard
    This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.

  13. 18.785 Analytic Number Theory, Spring 2007

    Kedlaya, Kiran
    This course is an introduction to analytic number theory, including the use of zeta functions and L-functions to prove distribution results concerning prime numbers (e.g., the prime number theorem in arithmetic progressions).

  14. 18.103 Fourier Analysis - Theory and Applications, Spring 2004

    Melrose, Richard
    18.103 picks up where 18.100B (Analysis I) left off. Topics covered include the theory of the Lebesgue integral with applications to probability, Fourier series, and Fourier integrals.

  15. 18.304 Undergraduate Seminar in Discrete Mathematics, Spring 2006

    Kleitman, Daniel
    This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

  16. 18.443 Statistics for Applications, Spring 2009

    Dudley, Richard
    This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics. Note: Please see the syllabus for a description of the different versions of 18.443 taught at MIT.

  17. 18.310C Principles of Applied Mathematics, Fall 2007

    Shor, Peter; Kleitman, Daniel
    Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world. This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing.

  18. 18.311 Principles of Applied Mathematics, Spring 2009

    Kasimov, Aslan
    This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation.

  19. 18.303 Linear Partial Differential Equations: Analysis and Numerics, Fall 2010

    Johnson, Steven G.
    This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

  20. 18.783 Elliptic Curves, Spring 2013

    Sutherland, Andrew
    This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.

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