This course covers both the basic theory and applications of Vector Calculus. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about multidimensional integration and curvilinear coordinate systems. The fourth week covers line and surface integrals, and the fifth week covers the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem and Stokes’ theorem. These theorems are needed in core engineering subjects such as Electromagnetism and Fluid Mechanics. Instead of Vector Calculus, some universities might call this course Multivariable or Multivariate Calculus or Calculus 3. Two semesters of single variable calculus (differentiation and integration) are a prerequisite. The course contains 53 short lecture videos, with a few problems to solve following each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of five weeks to the course, and at the end of each week there is an assessed quiz. Download the lecture notes: http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Watch the promotional video: https://youtu.be/qUseabHb6Vk

Have you ever heard that computers "think"? Believe it or not, computers really do not think. Instead, they do exactly what we tell them to do. Programming is, "telling the computer what to do and how to do it." Before you can think about programming a computer, you need to work out exactly what it is you want to tell the computer to do. Thinking through problems this way is Computational Thinking. Computational Thinking allows us to take complex problems, understand what the problem is, and develop solutions. We can present these solutions in a way that both computers and people can understand. The course includes an introduction to computational thinking and a broad definition of each concept, a series of real-world cases that illustrate how computational thinking can be used to solve complex problems, and a student project that asks you to apply what they are learning about Computational Thinking in a real-world situation. This project will be completed in stages (and milestones) and will also include a final disaster response plan you'll share with other learners like you. This course is designed for anyone who is just beginning programming, is thinking about programming or simply wants to understand a new way of thinking about problems critically. No prior programming is needed. The examples in this course may feel particularly relevant to a High School audience and were designed to be understandable by anyone. You will learn: -To define Computational Thinking components including abstraction, problem identification, decomposition, pattern recognition, algorithms, and evaluating solutions -To recognize Computational Thinking concepts in practice through a series of real-world case examples -To develop solutions through the application of Computational Thinking concepts to real world problems

As data collection has increased exponentially, so has the need for people skilled at using and interacting with data; to be able to think critically, and provide insights to make better decisions and optimize their businesses. This is a data scientist, “part mathematician, part computer scientist, and part trend spotter” (SAS Institute, Inc.). According to Glassdoor, being a data scientist is the best job in America; with a median base salary of $110,000 and thousands of job openings at a time. The skills necessary to be a good data scientist include being able to retrieve and work with data, and to do that you need to be well versed in SQL, the standard language for communicating with database systems. This course is designed to give you a primer in the fundamentals of SQL and working with data so that you can begin analyzing it for data science purposes. You will begin to ask the right questions and come up with good answers to deliver valuable insights for your organization. This course starts with the basics and assumes you do not have any knowledge or skills in SQL. It will build on that foundation and gradually have you write both simple and complex queries to help you select data from tables. You'll start to work with different types of data like strings and numbers and discuss methods to filter and pare down your results. You will create new tables and be able to move data into them. You will learn common operators and how to combine the data. You will use case statements and concepts like data governance and profiling. You will discuss topics on data, and practice using real-world programming assignments. You will interpret the structure, meaning, and relationships in source data and use SQL as a professional to shape your data for targeted analysis purposes. Although we do not have any specific prerequisites or software requirements to take this course, a simple text editor is recommended for the final project. So what are you waiting for? This is your first step in landing a job in the best occupation in the US and soon the world!

In this 2-hour long project-based course, you will learn the game theoretic concepts of Two player Static and Dynamic Games, Pure and Mixed strategy Nash Equilibria for static games (illustrations with unique and multiple solutions), Example of Axelrod tournament. You will be building two player Nash games and analyze them using Python packages Nashpy and Axelrod, especially built for game theoretic analyses. Also, you will gain the understanding of computational mechanisms related to the aforementioned concepts. Note: This course works best for learners who are based in the North America region. We’re currently working on providing the same experience in other regions.

An introduction to physics in the context of everyday objects.

Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements? In the online course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself. Prerequisites: 1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity. 2. Basic programming knowledge is necessary as some quizzes require programming in Python.

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 from Riemann sums. Rather than measure rates of change as we did with differential calculus, the definite integral allows us to measure the accumulation of a quantity over some interval of input values. This notion of accumulation can be applied to different quantities, including money, populations, weight, area, volume, and air pollutants. The concepts in this course apply to many other disciplines outside of traditional mathematics. We will expand the notion of the average value of a data set to allow for infinite values, develop the formula for arclength and curvature, and derive formulas for velocity, acceleration, and areas between curves. Through examples and projects, we will apply the tools of this course to analyze and model real world data.

This first course on concepts of single variable calculus will introduce the notions of limits of a function to define the derivative of a function. In mathematics, the derivative measures the sensitivity to change of the function. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. This fundamental notion will be applied through the modelling and analysis of data.

The course provides an introduction to quantum information at a beginning graduate level. It focuses on the fundamental understanding of how information is processed with quantum systems and how the quantum properties apply to computing and communication tasks. The course begins by presenting quantum theory as the framework of information processing. Quantum systems are introduced with single and two qubits. Axioms of quantum theory such as states, dynamics, and measurements are explained as preparation, evolution, and readout of qubits. Quantum computing and quantum communication are explained. Entanglement is identified as a key resource of quantum information processing. Manipulation and quantification of entangled states are provided.  Quantum information processing opens an avenue to new information technologies beyond the current limitations but, more importantly, provides an approach to understanding information processing at the most fundamental level. What is desired is to find how Nature performs information processing with the quantum and classical systems. The ultimate power of Nature in computing and communication may be found and understood. The course provides a modest step to learn quantum information about how physical systems can be manipulated by the laws of quantum mechanics, how powerful they are in practical applications, and how the fundamental results make quantum advantages.

This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications. The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.