Linear Algebra: Problems and Methods

The goal of the course is explain the fundamental ideas of linear algebra and how to use them to find easy solutions of hard problems.

Linear Algebra: Problems and Methods
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Linear algebra is an area of mathematics which studies linear functions and linear equations. If this sounds too simple, notice that the arguments and values of linear functions can be not only numbers, but also vectors, and this leads to very beautiful structures which we are going to study in this course. Moreover, linear algebra allows to study some nonlinear objects, such as quadratic forms!

Linear algebra has applications in almost any field one can imagine: physics, computer science, chemistry, economics, engineering and many, many others. It is also deeply connected to the other areas of mathematics, such as calculus, probability, group theory, differential equations etc. Ultimately, linear algebra is very exciting on its own: it allows to use geometry when algebra gets very complicated, and vice versa!

What is the best way to study linear algebra? As many other areas of mathematics, linear algebra has some building blocks:

  • key concepts,
  • main results,
  • common tricks;

The number of such building blocks is many times less than the number of pages in a typical textbook on linear algebra. At the same time, once you know these building blocks, you are ready to use linear algebra!

Программа курса:

  1. Welcome to the Linear Algebra course at Stepik
  2. Concept of linear space
  3. Coordinates of vectors and linear maps
  4. Systems of linear equations
  5. Structure of linear spaces
  6. Lesson by Emil Wiedemann
  7. Quick reference