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Video
Stanford Electrical Engineering Course on Convex Optimization.
- Course related:
- AMA4850 Optimization Methods
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical optimization Convex functions
- Resource Type:
- Video
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Others
Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.
- Course related:
- AAE3009 Operations Research and Computational Analytics in Air Transport Operations
- Subjects:
- Mathematics and Statistics
- Keywords:
- Linear programming
- Resource Type:
- Others
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Courseware
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.
- Course related:
- AMA1120 Basic Mathematics II
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Courseware
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Video
With calculus well behind us, it's time to enter the next major topic in any study of mathematics. Linear Algebra! The name doesn't sound very intimidating, but there are some pretty abstract concepts in this subject. Let's start nice and easy simply by learning about what this subject covers and some basic terminology.
- Course related:
- COMP4434 Big Data Analytics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Video
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Others
In these comprehensive video courses, created by Santiago Basulto, you will learn the whole process of data analysis. You'll be reading data from multiple sources (CSV, SQL, Excel), process that data using NumPy and Pandas, and visualize it using Matplotlib and Seaborn, Additionally, we've included a thorough Jupyter Notebook course, and a quick Python reference to refresh your programming skills.
- Course related:
- AMA1600 Fundamentals of AI and Data Analytics and AMA1751 Linear Algebra
- Subjects:
- Mathematics and Statistics and Computing
- Keywords:
- Computer programming Computer science Python (Computer program language)
- Resource Type:
- Others
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Others
We offer mathematics in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics
- Resource Type:
- Others
-
Video
Lecture videos from Gilbert Strang's course on Linear Algebra at MIT.
- Course related:
- AMA1120 Basic Mathematics II - Calculus and Linear Algebra
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Video
-
Video
This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
- Subjects:
- Mathematics and Statistics and Economics
- Keywords:
- Game theory
- Resource Type:
- Video
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MOOC
This course teaches the R programming language in the context of statistical data and statistical analysis in the life sciences. We will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R code. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research. Given the diversity in educational background of our students we have divided the course materials into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. We start with simple calculations and descriptive statistics. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.
- Subjects:
- Statistics and Research Methods and Mathematics and Statistics
- Keywords:
- Life sciences -- Statistical methods Mathematical statistics -- Data processing R (Computer program language)
- Resource Type:
- MOOC
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Others
Euclid’s Elements was a collection of 13 books about geometry originally written circa 300 BC. Shortly after the advent of the printing press, many editions and translations have been created over the centuries. Byrne’s 1847 edition of the first six books stands out for its unique use of colorful illustrations to demonstrate proofs rather than using letters to label angles, edges, and shapes. His edition was one of the first books to be published with such detailed use of colors and combined with its detailed diagrams makes it an impressive feat of publishing for the times and it stands out even today as a work of art. This site is a reproduction of Byrne’s Euclid by Oliver Byrne from 1847 that pays tribute to the beautiful original design and includes enhancements such as interactive diagrams, cross references, and posters designed by Nicholas Rougeux.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Euclid's Elements Elements (Euclid) Geometry
- Resource Type:
- Others
-
Video
Engineering Mathematics tutorial series covers aspects of applied mathematics including: multivariable calculus; vector field theory; differential equations; Laplace transforms and Fourier series.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Engineering mathematics
- Resource Type:
- Video
-
Courseware
This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Mathematical optimization
- Resource Type:
- Courseware
-
Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations
- Resource Type:
- Courseware
-
Courseware
The course is taught using the textbook by T. Apostol, "Calculus" Vol. I Second Edition (1967) and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Mathematical analysis
- Resource Type:
- Courseware
-
Courseware
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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Courseware
-
Video
In this video we look at how to decide for a given scenario (worded problem) if the distribution described is a Binomial distribution or Poisson distribution and whether its probability distribution function or its cumulative distribution function is required to calculate a specified probability.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Binomial distribution Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
-
Video
In this video we look at how to use statistical tables to calculate probabilities in a Binomial distribution. This includes an example of using the table for the probability density function to determine the probability the random variable takes a particular value and an example of using the table for the cumulative distribution function to determine the probability the random variable is less than or equal to a certain value and an example determining the probability it is greater than or equal to a certain value.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
-
Video
In this video we look at how to use statistical tables to calculate probabilities in a Poisson distribution. This includes an example of using the table for the probability density function to determine the probability the random variable is equal to particular value in a case where the average number of events per interval needs to be adjusted to match the units specified in the question and an example of using the table for the cumulative distribution function to determine the probability the random variable takes a value between two specified numbers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Binomial distribution Probabilities Distribution (Probability theory)
- Resource Type:
- Video
-
Video
In this video we look at how to use statistical tables to calculate probabilities in a Poisson distribution. This includes an example of using the table for the probability density function to determine the probability the random variable is equal to a particular value and an example of using the table for the cumulative distribution function to determine the probability the random variable is less than a certain value and an example determining the probability it is greater than or equal to a certain value.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
-
Courseware
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Stochastic partial differential equations Evolution equations
- Resource Type:
- Courseware
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