Online courses directory (418)

This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001).

Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

In this course, you will learn how to formalize information and reason systematically to produce logical conclusions. We will also examine logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.

Learn how to apply mathematical methods to philosophical problems and questions.

This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms.

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.

The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.

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.

Improve your understanding of data and learn how to develop graphs and charts so you can use this information to make better decisions.

We are surrounded by information, much of it numerical, and it is important to know how to make sense of it. Stat2x is an introduction to the fundamental concepts and methods of statistics, the science of drawing conclusions from data.

The course is the online equivalent of Statistics 2, a 15-week introductory course taken in Berkeley by about 1,000 students each year. Stat2x is divided into three 5-week components. Stat2.1x is the first of the three.

The focus of Stat2.1x is on descriptive statistics. The goal of descriptive statistics is to summarize and present numerical information in a manner that is illuminating and useful. The course will cover graphical as well as numerical summaries of data, starting with a single variable and progressing to the relation between two variables. Methods will be illustrated with data from a variety of areas in the sciences and humanities.

There will be no mindless memorization of formulas and methods. Throughout Stat2.1x, the emphasis will be on understanding the reasoning behind the calculations, the assumptions under which they are valid, and the correct interpretation of results.

FAQ

• What is the format of the class?
  • Instruction will be consist of brief lectures and exercises to check comprehension. Grades (Pass or Not Pass) will be decided based on a combination of scores on short assignments, quizzes, and a final exam.
• How much does it cost to take the course?
  • Nothing! The course is free.
• Will the text of the lectures be available?
  • Yes. All of our lectures will have transcripts synced to the videos.
• Do I need to watch the lectures live?
  • No. You can watch the lectures at your leisure.
• Can I contact the Instructor or Teaching Assistants?
  • Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.
• Do I need any other materials to take the course?
  • If you have any questions about edX generally, please see the edX FAQ.

Statistics 2 at Berkeley is an introductory class taken by about 1,000 students each year. Stat2.3x is the last in a sequence of three courses that make up Stat2x, the online equivalent of Berkeley's Stat 2. The focus of Stat2.3x is on statistical inference: how to make valid conclusions based on data from random samples. At the heart of the main problem addressed by the course will be a population (which you can imagine for now as a set of people) connected with which there is a numerical quantity of interest (which you can imagine for now as the average number of MOOCs the people have taken). If you could talk to each member of the population, you could calculate that number exactly. But what if the population is so large that your resources will not stretch to interviewing every member? What if you can only reach a subset of the population?

Stat 2.3x will discuss good ways to select the subset (yes, at random); how to estimate the numerical quantity of interest, based on what you see in your sample; and ways to test hypotheses about numerical or probabilistic aspects of the problem.

The methods that will be covered are among the most commonly used of all statistical techniques. If you have ever read an article that claimed, "The margin of error in such surveys is about three percentage points," or, "Researchers at the University of California at Berkeley have discovered a highly significant link between ...," then you should expect that by the end of Stat 2.3x you will have a pretty good idea of what that means. Examples will range all the way from a little girl's school science project (seriously – she did a great job and her results were published in a major journal) to rulings by the U.S. Supreme Court.

The fundamental approach of the series was provided in the description of Stat2.1x and appears here again: There will be no mindless memorization of formulas and methods. Throughout the course, the emphasis will be on understanding the reasoning behind the calculations, the assumptions under which they are valid, and the correct interpretation of results.

Statistics 2 at Berkeley is an introductory class taken by about 1000 students each year. Stat2.2x is the second of three five-week courses that make up Stat2x, the online equivalent of Berkeley's Stat 2.

The focus of Stat2.2x is on probability theory: exactly what is a random sample, and how does randomness work? If you buy 10 lottery tickets instead of 1, does your chance of winning go up by a factor of 10? What is the law of averages? How can polls make accurate predictions based on data from small fractions of the population? What should you expect to happen "just by chance"? These are some of the questions we will address in the course.

We will start with exact calculations of chances when the experiments are small enough that exact calculations are feasible and interesting. Then we will step back from all the details and try to identify features of large random samples that will help us approximate probabilities that are hard to compute exactly. We will study sums and averages of large random samples, discuss the factors that affect their accuracy, and use the normal approximation for their probability distributions.

Be warned: by the end of Stat2.2x you will not want to gamble. Ever. (Unless you're really good at counting cards, in which case you could try blackjack, but perhaps after taking all these edX courses you'll find other ways of earning money.)

The fundamental approach of the series was provided in the description of Stat2.1x and appears here again: There will be no mindless memorization of formulas and methods. Throughout the course, the emphasis will be on understanding the reasoning behind the calculations, the assumptions under which they are valid, and the correct interpretation of results.

FAQ

• What is the format of the class?
  • Instruction will be consist of brief lectures and exercises to check comprehension. Grades (Pass or Not Pass) will be decided based on a combination of scores on short assignments, quizzes, and a final exam.
• How much does it cost to take the course?
  • Nothing! The course is free.
• Will the text of the lectures be available?
  • Yes. All of our lectures will have transcripts synced to the videos.
• Do I need to watch the lectures live?
  • No. You can watch the lectures at your leisure.
• Will certificates be awarded?
  • Yes. Online learners who achieve a passing grade in a course can earn a certificate of achievement. These certificates will indicate you have successfully completed the course, but will not include a specific grade. Certificates will be issued by edX under the name of BerkeleyX, designating the institution from which the course originated.
• Can I contact the Instructor or Teaching Assistants?
  • Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.
• Do I need any other materials to take the course?
  • If you have any questions about edX generally, please see the edX FAQ.

This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.

In questo corso imparerete i Principi che stanno alla base della Fisica del XX secolo, cioè della Relatività e la Meccanica Quantistica, e come sia cambiata la nostra visione del mondo.

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.

This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with 18.06 Linear Algebra, more emphasis is placed on theory and proofs.

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.