Calculus

Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations. All the features of this [...]

This course continues your study of calculus by focusing on the applications of integration. The applications in this section have many common features. First, each is an example of a quantity that is computed by evaluating a definite integral. Second, the formula for that application is derived [...]

This course continues your study of calculus by introducing the notions of series, sequences, and integration. These foundational tools allow us to develop the theory and applications of the second major tool of calculus: the integral. Rather than measure rates of change, the integral provides a means [...]

This course continues your study of calculus by focusing on the applications of integration to vector valued functions, or vector fields. These are functions that assign vectors to points in space, allowing us to develop advanced theories to then apply to real-world problems. We define line integrals, which [...]

In this course, we build on previously defined notions of the integral of a single-variable function over an interval. Now, we will extend our understanding of integrals to work with functions of more than one variable. First, we will learn how to integrate a real-valued multivariable function over different [...]

This course serves as an introduction to the physics of rotational motion and gravitation. Upon completion, learners will have an understanding of how mathematical laws and conservation principles describe the motions and interactions of objects all around us. They will gain experience in solving physics problems with [...]

This course introduces you to additional topics in Machine Learning that complement essential tasks, including forecasting and analyzing censored data. You will learn how to find analyze data with a time component and censored data that needs outcome inference. You will learn a few techniques for Time Series Analysis [...]

This course introduces you to two of the most sought-after disciplines in Machine Learning: Deep Learning and Reinforcement Learning. Deep Learning is a subset of Machine Learning that has applications in both Supervised and Unsupervised Learning, and is frequently used to power most of the AI applications that we [...]