What You Will Learn

Linear Algebra studies the solution of (possibly very large) systems of linear algebraic equations. It is an integral part of many scientific and engineering applications including page ranking in search engines, machine learning, artificial intelligence, predictive data analytics, optimization and linear programming, data encoding, signal analysis, computer graphics, image processing and face recognition, quantum computing, engineering calculations (such as deformations or electromagnetics fields, …), and many others.

But why should we be the ones explaining the importance of Linear Algebra when there is Stack Exchange? Here is a sample answer to “Why study Linear Algebra?”:

“Having studied Engineering, I can tell you that Linear Algebra is fundamental and an extremely powerful tool in every single discipline of Engineering. If you are reading this and considering learning Linear Algebra then I will first issue you with a warning: Linear Algebra is mighty stuff. You should be both maniacally excited and scared by the awesome power it will give you!!!!!!”      user1158559

Recommended Background

To succeed in this course, you should know basic high school math including arithmetic, working with fractions, relations, and functions. You should also know trigonometric functions, exponentials, and logarithms. Later we will work with inner products of polynomials which requires a basic knowledge of integration.

Note on Proofs

There are two types of Linear Algebra users – those who use it mechanically, and those who understand it. Proofs of theorems are optional, meaning that you can do well in this course without reading them. But if you want to understand Linear Algebra, read the proofs and try to understand them. If you are able to follow a proof, it means that you understand the concepts that you have learned.

Course Structure and Length

This course is an equivalent of a full semester three-credit course. It consists of five Units. Each Unit has five Sections, and each Section has around 10 Levels. Each Section is equivalent to one lecture plus the corresponding homework. You will go through the course at your own pace, one Level at a time. After each Level you will have an opportunity to test yourself and see if you have mastered the topic. Quizzes can be retaken after 12 hours, one time only. The 12-hour delay is designed to make sure that you have a chance to really understand the material before the next attempt. A quiz can be retaken any time before the end of the course (even after several weeks). The better score counts. Each Section will take 3-4 hours of your time.

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