# Online courses directory (258)

In this college level Algebra course, you will learn to apply algebraic reasoning to solve problems effectively. You’ll develop skills in linear and quadratic functions, general polynomial functions, rational functions, and exponential and logarithmic functions. You will also study systems of linear equations. This course will emphasize problem-solving techniques, specifically by means of discussing concepts in each of these topics.

Content in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.

This 3 credit hour course satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.

College Algebra Prep will get you ready for College Algebra. We will cover the prerequisite algebra topics, study skills, success skills, and things you need to know about electronic homework systems, to be successful in college algebra. You will supply the drive and commitment to make this a successful course for you.

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.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

This course explored topics such as complex algebra and functions, analyticity, contour integration, Cauchy's theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals, multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms.

6.844 is a graduate introduction to programming theory, logic of programming, and computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself. Topics covered include: programming and computability theory based on a term-rewriting, "substitution" model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert's Tenth Problem.

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called "Mathematical Methods for Engineers I."

The modern data analysis pipeline involves collection, preprocessing, storage, analysis, and interactive visualization of data.

The goal of this course, part of the Analytics: Essential Tools and Methods MicroMasters program, is for you to learn how to build these components and connect them using modern tools and techniques.

In the course, you’ll see how computing and mathematics come together. For instance, “under the hood” of modern data analysis lies numerical linear algebra, numerical optimization, and elementary data processing algorithms and data structures. Together, they form the foundations of numerical and data-intensive computing.

The hands-on component of this course will develop your proficiency with modern analytical tools. You will learn how to mash up Python, R, and SQL through Jupyter notebooks, among other tools. Furthermore, you will apply these tools to a variety of real-world datasets, thereby strengthening your ability to translate principles into practice.

Concepts in Nanotechnology is a six-week introduction to nanotechnology. The course is designed at a pre-college level, with no college level chemistry, math, or physics experience required. You will learn what nanotechnology is and what it means for something to be a nanomaterial. You will also learn about the applications and commercial products that use nanotechnology. This is an exciting opportunity to delve into the nano-world. Prerequisites: The course is taught entirely in English and aimed at a U.S. high school level. You need to be familiar with the basic concepts of chemistry, such as the theory of atoms and the periodic table of elements. Basic algebra skills, such as how to deal with equations containing variables, fractions, and exponents is necessary. No prerequisite knowledge in nanotechnology, materials science, or physics is required.

Looking to get started with computer science while learning to program in Python?

This computer science course provides an introduction to computer science that’s both challenging and fun. It takes a broad look at the field of computer science through a variety of demonstrations and projects. We’ll cover both low- and high-level concepts, from how the circuits inside a computer represent data to how to design algorithms, as well as how all of this information affects the technology we use today. Additionally, we’ll teach the basics of Python programming, giving us a a way to put our new CS knowledge into practice.

No need to know any programming before starting the course; we’ll teach everything you need to know along the way. All you need to start is a good grasp of algebra, and you can fall in love with both the concepts and the practice of computer science.

This course is an introduction to linear algebra. It has been argued that linear algebra constitutes half of all mathematics. Whether or not everyone would agree with that, it is certainly true that practically every modern technology relies on linear algebra to simplify the computations required for Internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between. Linear algebra can be viewed either as the study of linear equations or as the study of vectors. It is tied to analytic geometry; practically speaking, this means that almost every fact you will learn in this course has a picture associated with it. Learning to connect the facts with their geometric interpretation will be very useful for you. The book which is used in the course focuses both on the theoretical aspects as well as the applied aspects of linear algebra. As a result, you will be able to learn the geometric interpretations of many of the algebraic concepts…

*This course is part of the MITx MicroMasters program in Data, Economics, and Development Policy (DEDP). To audit this course, click “Enroll Now” in the green button at the top of this page. *

*To enroll in the MicroMasters track or to learn more about this program and how it integrates with MIT’s new blended Master’s degree, go to MITx’s MicroMasters portal. *

This statistics and data analysis course will introduce you to the essential notions of probability and statistics. We will cover techniques in modern data analysis: estimation, regression and econometrics, prediction, experimental design, randomized control trials (and A/B testing), machine learning, and data visualization. We will illustrate these concepts with applications drawn from real world examples and frontier research. Finally, we will provide instruction for how to use the statistical package R and opportunities for students to perform self-directed empirical analyses.

This course is designed for anyone who wants to learn how to work with data and communicate data-driven findings effectively, but it is challenging. Students who are uncomfortable with basic calculus and algebra might struggle with the pace of the class.

Are you interested in pursuing a degree in Data Science, but unsure whether you have the necessary Math and Programming skills? This assessment will help you identify your current readiness in three core areas required for the study of Data Science; Calculus, Linear Algebra, and Programming.

You can take this assessment at your own pace and receive a private score report that identifies your readiness in each specific area. We will also provide, when necessary, recommendations for additional free online study.

This assessment is free, unproctored, and not offered for credit; it is designed for enrichment and self-assessment for anyone interested in pursuing data science as a career.

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed, though students who have taken an undergraduate course in databases are encouraged to attend.

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed, though students who have taken an undergraduate course in databases are encouraged to attend.

This course presents an example of how to apply a database application development methodology to a major real-world project.

All the database concepts, techniques and tools that are needed to develop a database application from scratch will be introduced along the way as you apply them to your own major class team project.

In addition to the development methodology, techniques and tools learned in this course will include the Extended Entity Relationship Model, the Relational Model, Relational algebra, calculus and SQL, database normalization, efficiency and indexing. Finally, techniques and tools for metadata management and archival will be presented.

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

Haynes Miller

Jeremy Orloff

Dr. John Lewis

Arthur Mattuck

## Other Versions

## Other OCW Versions

OCW has published multiple versions of this subject.