| source Harvard (X) |
level |
department Applied Mathematics (X) |
Sets, subsets, and partitions; mappings, operations, and equivalence relations; groups, rings, and fields, polynomials, encryption, computer coding, application of modular arithmetic, combinatorial designs, lattices, application of trellis representation of lattices, fast algorithms; selected readings.
Score: 10.4259615 Details | Listing | Web page
An algorithmic approach to topics in matrix theory which arise frequently in applied mathematics: linear equations, pseudoinverses, quadratic forms, eigenvalues and singular values, linear inequalities and optimization, linear differential and difference equations.
Score: 10.4259615 Details | Listing | Web page
Introduction to abstract algebra and its applications. Sets, subsets, and partitions; mappings, operations, and equivalence relations; groups, rings, and fields, polynomials, encryption, computer coding, application of modular arithmetic, combinatorial designs, lattices, application of trellis representation of lattices, fast algorithms.
Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
Complex Analysis: complex numbers, functions, mapping, differentiation, integration, branch cuts, series expansions, residue theory. Fourier Analysis: Fourier series, Fourier and Laplace transforms, applications to differential equations and data analysis.
Score: 10.4259615 Details | Listing | Web page
An introduction to functional analysis and its applications: metric, Banach and Hilbert spaces; linear operators, spectral theory; differentiation and integration.
Score: 10.4259615 Details | Listing | Web page
Introduction to geometrical concepts used to model physical phenomena. Coordinate and coordinate-free geometrical objects, fields, flows, calculus on manifolds, metrics, connections, integrability, symmetry and continuous group structures, gauge fields. Applications: mechanics and field theories.
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Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Specific topics taken from graph theory, enumeration techniques, optimization theory, combinatorial algorithms, and discrete probability.
Score: 10.4259615 Details | Listing | Web page
Introduction to the problems and issues of applied mathematics. This will be accomplished both through the reading of papers that use mathematical arguments to have substantial impact on some field of human activity, as well as guest lecturers from around Harvard to discuss how mathematics is used in their field.
Score: 10.4259615 Details | Listing | Web page
Principles and techniques of numerical analysis, synthesis and computation: interpolation and approximation, numerical quadrature and differentiation, linear and nonlinear equations, optimization, differential and integral equations.
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Introduction to basic mathematical ideas and computational methods for solving deterministic and stochastic optimization problems. Topics covered: linear programming, integer programming, branch-and-bound, branch-and-cut, Markov chains, Markov decision processes, queuing theory. Emphasis on modeling. Examples from business, society, engineering, sports, e-commerce. Exercises in AMPL, complemented by Maple or Matlab.
Score: 10.4259615 Details | Listing | Web page
Many complex physical problems defy simple analytical solutions or even accurate analytical approximations. Scientific computing can address certain of these problems successfully, providing unique insight. This course introduces some of the widely used techniques in scientific computing through examples chosen from physics, chemistry, and biology. The purpose of the course is to introduce methods that are useful in applications and research and to give the students hands-on experience with these methods.
Score: 10.4259615 Details | Listing | Web page
Complex numbers. Multivariate calculus: partial differentiation, directional derivatives, techniques of integration and multiple integration. Vectors: dot and cross products, parameterized curves, line and surface integrals. Vector calculus: gradient, divergence and curl, Green's, Stokes' and Gauss' theorems, including orthogonal curvilinear coordinates. Applications in electrical and mechanical engineering.
Score: 10.4259615 Details | Listing | Web page
Linear algebra: matrices, determinants, eigenvalues, eigenvectors, Markov processes. Optimization and least-squares analysis. Ordinary differential equations. Infinite series and Fourier series. Orthogonality and completeness. Introduction to partial differential equations. Applications in electrical and mechanical engineering.
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Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from mechanics, biology, economics and the behavioral sciences.
Score: 10.4259615 Details | Listing | Web page
Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from mechanics, biology, economics and the behavioral sciences.
Score: 10.4259615 Details | Listing | Web page
An introduction to nonlinear dynamical phenomena, covering the behavior of systems described by ordinary differential equations. Topics include: stability; bifurcations; chaos; routes to chaos and universality; approximations by maps; strange attractors; fractals. Techniques for analyzing nonlinear systems are introduced with applications to physical, chemical, and biological systems such as forced oscillators, chaotic reactions, and population dynamics.
Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page
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Score: 10.4259615 Details | Listing | Web page