Online courses directory (10358)

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. For example, the heat equation can be used to describe the change in heat distribution along a metal rod over time. PDEs arise as part of the mathematical modeling of problems connected to different branches of science, such as physics, biology, and chemistry. In these fields, experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. These connections must be exploited to find an explicit way of calculating the unknown quantity, given the values of the independent variables  that is, to derive certain laws of nature. While we do not know why partial differential equations provide what has been termed the “unreasonable effectiveness of mathematics in the natural sciences” (the title of a 1960 paper by physicist…

The study of “abstract algebra” grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted.  For example, we are familiar with the notion that real numbers are closed under multiplication and division (that is, if we add or multiply a real number, we get a real number).  But if we divide one integer by another integer, we may not get an integer as a resultmeaning that integers are not closed under division.  We also know that if we take any two integers and multiply them in either order, we get the same resulta principle known as the commutative principle of multiplication for integers.  By contrast, matrix multiplication is not generally commutative.  Students of abstract algebra are interested in these sorts of properties, as they want to determine which properties hold true for any set of mathematical objects under certain operations and which types of structures result when we perform certain o…

This course is a continuation of Abstract Algebra I: we will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms.  We will also take a look at ring factorization, which will lead us to a discussion of the solutions of polynomials over abstracted structures instead of numbers sets.  We will end the section on rings with a discussion of general lattices, which have both set and logical properties, and a special type of lattice known as Boolean algebra, which plays an important role in probability.  We will also visit an important topic in mathematics that you have likely encountered already: vector spaces.  Vector spaces are central to the study of linear algebra, but because they are extended groups, group theory and geometric methods can be used to study them. Later in this course, we will take a look at more advanced topics and consider several useful theorems and counting methods.  We will end the course by studying Galois theoryone of the most im…

This course is designed to introduce you to the rigorous examination of the real number system and the foundations of calculus of functions of a single real variable. Analysis lies at the heart of the trinity of higher mathematics algebra, analysis, and topology because it is where the other two fields meet. In calculus, you learned to find limits, and you used these limits to give a rigorous justification for ideas of rate of change and areas under curves. Many of the results that you learned or derived were intuitive in many cases you could draw a picture of the situation and immediately “see” whether or not the result was true. This intuition, however, can sometimes be misleading. In the first place, your ability to find limits of real-valued functions on the real line was based on certain properties of the underlying field on which undergraduate calculus is founded: the real numbers. Things may have become slightly more complicated when you began to work in other spaces. For instance, you may r…

Real Analysis II is the sequel to Saylor’s Real Analysis I, and together these two courses constitute the foundations of real analysis in mathematics. In this course, you will build on key concepts presented in Real Analysis I, particularly the study of the real number system and real-valued functions defined on all or part (usually intervals) of the real number line. The main objective of MA241 [1] was to introduce you to the concept and theory of differential and integral calculus as well as the mathematical analysis techniques that allow us to understand and solve various problems at the heart of sciencenamely, questions in the fields of physics, economics, chemistry, biology, and engineering. In this course, you will build on these techniques with the goal of applying them to the solution of more complex mathematical problems. As long as a problem can be modeled as a functional relation between two quantities, each of which can be expressed as a set of real numbers, the techniques used for real-value…

This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable.  Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable.  Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing.  Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear.  Simply put, you will be working with lines and sets and very specific functions on the complex planedrawing pictures of them and teasing out all of their idiosyncrasies.  You will again find yourself calculating line integrals, just as in multivariable calculus.  However, the techniques you learn in this course will help you get past many of the seeming dead-ends you ran up against in…

This course will introduce you to a number of statistical tools and techniques that are routinely used by modern statisticians for a wide variety of applications. First, we will review basic knowledge and skills that you learned in MA121: Introduction to Statistics [1]. Units 2-5 will introduce you to new ways to design experiments and to test hypotheses, including multiple and nonlinear regression and nonparametric statistics. You will learn to apply these methods to building models to analyze complex, multivariate problems. You will also learn to write scripts to carry out these analyses in R, a powerful statistical programming language. The last unit is designed to give you a grand tour of several advanced topics in applied statistics. [1] http://www.saylor.org/courses/ma121/…

This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling. Today, the theory of probability has found many applications in science and engineering. Engineers use data from manufacturing processes to sample characteristics of product quality in order to improve the products being produced. Pharmaceutical companies perform experiments to determine the effect of a drug on humans and use the results to make decisions about treatment of illnesses, while economists observe the state of the economy over periods of time and use the information to forecast the economic future. In this course, you will learn the basic terminology and concepts of probability theory, including random experiments, sample spaces, discrete distribution, probability density function, expected values, and conditional probability. You will al…

This course is designed to provide you with a simple and straightforward introduction to econometrics.  Econometrics is an application of statistical procedures to the testing of hypotheses about economic relationships and to the estimation of parameters.  Regression analysis is the primary procedure commonly used by researchers and managers whether their employments are within the goods or the resources market and/or within the agriculture, the manufacturing, the services, or the information sectors of an economy. Completion of this course in econometrics will help you progress from a student of economics to a practitioner of economics.  By completing this course, you will gain an overview of econometrics, develop your ability to think like an economist, hone your skills building and testing models of consumer and producer behavior, and synthesize the results you find through analyses of data pertaining to market-based economic systems.  In essence, professional economists conduct studies that combine…

This course will introduce students to the field of computer science and the fundamentals of computer programming.  It has been specifically designed for students with no prior programming experience, and does not require a background in Computer Science.  This course will touch upon a variety of fundamental topics within the field of Computer Science and will use Java, a high-level, portable, and well-constructed computer programming language developed by Sun Microsystems, to demonstrate those principles.  We will begin with an overview of the topics we will cover this semester and a brief history of software development.  We will then learn about Object-Oriented programming, the paradigm in which Java was constructed, before discussing Java, its fundamentals, relational operators, control statements, and Java I/0.  The course will conclude with an introduction to algorithmic design.  By the end of the course, you should have a strong understanding of the fundamentals of Computer Science and the Java p…

This course is a continuation of the first-semester course titled Introduction to Computer Science I (CS101 [1]).  It will introduce you to a number of more advanced Computer Science topics, laying a strong foundation for future academic study in the discipline.  We will begin with a comparison between Javathe programming language utilized last semesterand C++, another popular, industry-standard programming language.  We will then discuss the fundamental building blocks of Object-Oriented Programming, reviewing what we learned last semester and familiarizing ourselves with some more advanced programming concepts.  The remaining course units will be devoted to various advanced Computer Science topics, including the Standard Template Library, Exceptions, Recursion, Searching and Sorting, and Template Classes.  By the end of the class, you will have a solid understanding of Java and C++ programming, as well as a familiarity with the major issues that programmers routinely address in a professional setting.

Learn about the most effective machine learning techniques, and gain practice implementing them and getting them to work for yourself.

This class is offered as CS7641 at Georgia Tech where it is a part of the [Online Masters Degree (OMS)](http://www.omscs.gatech.edu/). Taking this course here will not earn credit towards the OMS degree. Machine Learning is a graduate-level course covering the area of Artificial Intelligence concerned with computer programs that modify and improve their performance through experiences. The first part of the course covers Supervised Learning, a machine learning task that makes it possible for your phone to recognize your voice, your email to filter spam, and for computers to learn a bunch of other cool stuff. In part two, you will learn about Unsupervised Learning. Ever wonder how Netflix can predict what movies you'll like? Or how Amazon knows what you want to buy before you do? Such answers can be found in this section! Finally, can we program machines to learn like humans? This Reinforcement Learning section will teach you the algorithms for designing self-learning agents like us!

Why write programs when the computer can instead learn them from data? In this class you will learn how to make this happen, from the simplest machine learning algorithms to quite sophisticated ones. Enjoy!

Machine Learning is the basis for the most exciting careers in data analysis today. You’ll learn the models and methods and apply them to real world situations ranging from identifying trending news topics, to building recommendation engines, ranking sports teams and plotting the path of movie zombies.

Major perspectives covered include:

• probabilistic versus non-probabilistic modeling
• supervised versus unsupervised learning

Topics include: classification and regression, clustering methods, sequential models, matrix factorization, topic modeling and model selection.

Methods include: linear and logistic regression, support vector machines, tree classifiers, boosting, maximum likelihood and MAP inference, EM algorithm, hidden Markov models, Kalman filters, k-means, Gaussian mixture models, among others.

In the first half of the course we will cover supervised learning techniques for regression and classification. In this framework, we possess an output or response that we wish to predict based on a set of inputs. We will discuss several fundamental methods for performing this task and algorithms for their optimization. Our approach will be more practically motivated, meaning we will fully develop a mathematical understanding of the respective algorithms, but we will only briefly touch on abstract learning theory.

In the second half of the course we shift to unsupervised learning techniques. In these problems the end goal less clear-cut than predicting an output based on a corresponding input. We will cover three fundamental problems of unsupervised learning: data clustering, matrix factorization, and sequential models for order-dependent data. Some applications of these models include object recommendation and topic modeling.

Machine learning is a type of artificial intelligence (AI) that provides computers with the ability to learn without being explicitly programmed. This area is also concerned with issues both theoretical and practical.

In this course, we will present algorithms and approaches in such a way that grounds them in larger systems as you learn about a variety of topics, including:

• statistical supervised and unsupervised learning methods
• randomized search algorithms
• Bayesian learning methods
• reinforcement learning

The course also covers theoretical concepts such as inductive bias, the PAC and Mistake‐bound learning frameworks, minimum description length principle, and Ockham's Razor. In order to ground these methods the course includes some programming and involvement in a number of projects.
 
By the end of this course, you should have a strong understanding of machine learning so that you can pursue any further and more advanced learning. 

This is a three-credit course.

6.867 is an introductory course on machine learning which gives an overview of many concepts, techniques, and algorithms in machine learning, beginning with topics such as classification and linear regression and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course will give the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how, why, and when they work. The underlying theme in the course is statistical inference as it provides the foundation for most of the methods covered.

Do you want to build systems that learn from experience? Or exploit data to create simple predictive models of the world?

In this course, part of the Data Science MicroMasters program, you will learn a variety of supervised and unsupervised learning algorithms, and the theory behind those algorithms.

Using real-world case studies, you will learn how to classify images, identify salient topics in a corpus of documents, partition people according to personality profiles, and automatically capture the semantic structure of words and use it to categorize documents.

Armed with the knowledge from this course, you will be able to analyze many different types of data and to build descriptive and predictive models.

All programming examples and assignments will be in Python, using Jupyter notebooks.

Machine Learning is a growing field that is used when searching the web, placing ads, credit scoring, stock trading and for many other applications.

This data science course is an introduction to machine learning and algorithms. You will develop a basic understanding of the principles of machine learning and derive practical solutions using predictive analytics. We will also examine why algorithms play an essential role in Big Data analysis.

Have you ever wanted to build a new musical instrument that responded to your gestures by making sound? Or create live visuals to accompany a dancer? Or create an interactive art installation that reacts to the movements or actions of an audience? If so, take this course!

In this course, students will learn fundamental machine learning techniques that can be used to make sense of human gesture, musical audio, and other real-time data. The focus will be on learning about algorithms, software tools, and best practices that can be immediately employed in creating new real-time systems in the arts.

Specific topics of discussion include:

• What is machine learning?

• Common types of machine learning for making sense of human actions and sensor data, with a focus on classification, regression, and segmentation

• The “machine learning pipeline”: understanding how signals, features, algorithms, and models fit together, and how to select and configure each part of this pipeline to get good analysis results

• Off-the-shelf tools for machine learning (e.g., Wekinator, Weka, GestureFollower)

• Feature extraction and analysis techniques that are well-suited for music, dance, gaming, and visual art, especially for human motion analysis and audio analysis

• How to connect your machine learning tools to common digital arts tools such as Max/MSP, PD, ChucK, Processing, Unity 3D, SuperCollider, OpenFrameworks

• Introduction to cheap & easy sensing technologies that can be used as inputs to machine learning systems (e.g., Kinect, computer vision, hardware sensors, gaming controllers)