Mathematics (18) - Archived
http://hdl.handle.net/1721.1/33995
Mathematics (18)2017-06-04T04:39:54Z18.785 Number Theory I, Fall 2015
http://hdl.handle.net/1721.1/109488
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.
2015-12-01T00:00:00Z18.06 Linear Algebra, Spring 2005
http://hdl.handle.net/1721.1/59010
18.06 Linear Algebra, Spring 2005
Strang, Gilbert
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
2005-06-01T00:00:00Z18.336 Numerical Methods of Applied Mathematics II, Spring 2005
http://hdl.handle.net/1721.1/56567
18.336 Numerical Methods of Applied Mathematics II, Spring 2005
Koev, Plamen S.
Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities. From the course home page: Course Description This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.
2005-06-01T00:00:00Z18.311 Principles of Applied Mathematics, Spring 2006
http://hdl.handle.net/1721.1/55891
18.311 Principles of Applied Mathematics, Spring 2006
Bazant, Martin Z.
Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modelling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world. From the course home page: Course Description This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow.
2006-06-01T00:00:00Z