Brief Introduction
This course is an introduction to linear algebra. You will discover the basic objects of linear algebra – how to compute with them, how they fit together theoretically, and how they can be used to solve real problems.
Description
Linear algebra is at the core of all of modern mathematics, and is used everywhere from statistics and data science, to economics, physics and electrical engineering. However, learning the subject is not principally about acquiring computational ability, but is more a matter of fluency in its language and theory.
In this course, we will start with systems of linear equations, and connect them to vectors and vector spaces, matrices, and linear transformations. We will be emphasizing the vocabulary throughout, so that students become comfortable working with the different aspects.
We will then introduce matrix and vector operations such as matrix multiplication and inverses, paying particular attention to their underlying purposes. Students will learn not just how to calculate them, but also why they work the way that they do.
We willdiscuss the key concepts of basis and dimension, which form the foundation for many of the more advanced concepts of linear algebra.
The last chapter concerns inner products, which allow us to use linear algebra for approximating solutions; we will see how this allows for applications ranging from statistics and linear regression to digital audio.
Coaching
If you are enrolled in the verified track (paid track) in any course that is a part of a MicroBachelors program, including this course, you are eligible for coaching at no additional cost. Please note that coaching is only available via SMS to U.S. phone lines.
Our coaches (real humans) are ready to help you with career exploration, navigating resources, staying motivated, and solving problems along the way to your goals.
Learn more about the value of coaching directly from one of our coaches, Erin.
Knowledge
- The relationships between linear equations, matrices, and linear transformations; the principles of vector and matrix operations; the significance of basis and dimension of a vector space; the applications of inner products and orthogonality.
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