The essential mathematics necessary for Data Science can be acquired with these 15 MOOCs, with a strong emphasis on applied algebra & statistics.
Most of the mathematics required for Data Science lie within the realms of statistics and algebra, which explains the disproportionate number of these courses listed below. A few other areas are included to round out the list, including calculus, finite mathematics, and a few more advanced offerings; however, the essence of the skills on parade here are statistical and algebraic in nature.
Statistics, in particular, is at the very foundation of Data Science and is the collection of tools which helps us separate significance from randomness. Algebra is quite often at the heart of the analysis itself. The further quantitative skills facilitate intuition, which is essential in analytics.
Whether you lack formal quantitative education or are simply looking to brush up on these skills, the following MOOCs can help you achieve your goals.
Getting in the Mood
These courses can help lay the foundation for quantitative thinking.
Description excerpt: Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures.
Description excerpt: This course is a basic introduction to Logic. It shows how to formalize information in form of logical sentences. It shows how to reason systematically with this information to produce all logical conclusions and only logical conclusions. And it examines logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.
These courses progress from introductory to real-world applications of algebra.
Description excerpt: Algebra is an essential tool for all of high school and college-level math, science, and engineering. So if you're starting out in one of these fields and you haven't yet mastered algebra, then this is the course for you!
Description excerpt: Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors.
Description excerpt: This course is part 1 of a 2-part course. In this part, we'll learn the basics of matrix algebra with an emphasis on application. This class has a focus on computer graphics while also containing examples in data mining. We'll learn to make an image transparent, fade from one image to another, and rotate a 3D wireframe model. We'll also mine data; for example, we will find similar movies that one might enjoy seeing.
Description excerpt: This class has a focus on data mining with some applications of computer graphics. We'll discuss, in further depth than part 1, sports ranking and ways to rate teams from thousands of games. We'll apply the methods to March Madness. We'll also learn methods behind web search, utilized by such companies as Google. We'll also learn to cluster data to find similar groups and also how to compress images to lower the amount of storage used to store them.
An understanding of calculus can help the practitioner think in terms of understanding change.
Description excerpt: Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.
The mathematical meat of Data Science. These courses start with basic statistics topics and finish with some exploratory analysis in R.
Description excerpt: 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.
Description excerpt: 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.
Description excerpt: 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.
Description excerpt: Do you want to learn how to harvest health science data from the Internet? Or learn to understand the world through data analysis? Start by learning R Statistics! Learn how to use R, a powerful open source statistical programming language, and see why it has become the tool of choice in many industries in this introductory R statistics course.
A few slightly more advanced topics covering optimization and applied linear algebra.
Description excerpt: This class is an introduction to discrete optimization and exposes students to some of the most fundamental concepts and algorithms in the field. It covers constraint programming, local search, and mixed-integer programming from their foundations to their applications for complex practical problems in areas such as scheduling, vehicle routing, supply-chain optimization, and resource allocation.
Description excerpt: In this class, you will learn the concepts and methods of linear algebra, and how to use them to think about problems arising in computer science. You will write small programs in the programming language Python to implement basic matrix and vector functionality and algorithms, and use these to process real-world data.