Courses tagged with "Customer Service Certification Program" (208)

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.

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• Lecture Videos by Professor Arthur Mattuck.
• Course Notes on every topic.
• Practice Problems with Solutions.
• Problem Solving Videos taught by experienced MIT Recitation Instructors.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
• A full set of Exams with Solutions, including practice exams to help you prepare.

Content Development

In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

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.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• A complete set of Lecture Videos by Professor Gilbert Strang.
• Summary Notes for all videos along with suggested readings in Prof. Strang's textbook Linear Algebra.
• Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Java® Demonstrations to illustrate key concepts.
• A full set of Exams with Solutions, including review material to help you prepare.

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

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. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

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.

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

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.

This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools for explaining and predicting the behavior of iterative decoding algorithms, including EXIT charts and Density Evolution.

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.