Cressy from the temple of Wafei
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Linear algebra is too abstract to learn? It doesn't matter, three scholars from Sweden have brought us immersive tutorials.
From vectors to matrices, from concepts to operations, almost every knowledge point is equipped with a picture that can be interacted with.
Moreover, some of the supporting cases are fully combined with reality, and the professional concepts are explained clearly with life scenarios.
As for the reasons for this format, the authors say in the preface that they have always believed that pictures can convey information more concisely and effectively than words:
A picture says more than a thousand words.（一图胜千言。 ）
This tutorial builds on this, and the interactive learning process further enhances the learning experience compared to static illustrations.
This has also made it known as the "ceiling of linear algebra textbooks" by netizens, and the founder of the game company Odd Tales also commented that it is "pure gold".
Of course, it is not enough to only have a novel form, this tutorial is also quite informative in terms of content, so let's learn about it together!
Interactive learning, with practical examples
First of all, this textbook can be said to be very beginner-friendly, and a chapter is dedicated to the beginning of the book to quickly review trigonometric functions and other knowledge points.
After quickly evoking this knowledge reserve, it is time to move on to formal learning.
This tutorial uses vectors as a starting point to explain the concept of vectors with a small game of arkanoid.
Other chapters are also accompanied by such simple examples at the beginning, and the author explains that just by memorizing these examples, it is easy to understand the topic.
After the concept is clear, it is the basic operations such as addition, subtraction, and number multiplication, and the concepts of basis vectors and high-dimensional vector spaces are also introduced.
The next two chapters are also related to vector operations, covering the product of quantities (inner product/dot product) and vector product (outer product/cross product) respectively.
It is worth mentioning that the tutorial is also equipped with practical examples, such as the part of point multiplication, which describes how to use vectors to explore the reflection laws of light in physics.
After learning (re)learning these vector knowledge, it is time to move on to more complex matrices.
Before that, however, there is an important tool to be understood, the Gaussian elimination element, which is used to solve systems of linear equations, which are the basis for understanding and using matrices.
In introducing Gaussian elimination, the author uses nearly 9,000 words and gives a very cutting-edge example – computer vision, in which the creation of 3D models is related to solving systems of linear equations.
The next five chapters are all related to matrices, including basic concepts, determinants, ranks, linear programming, eigenvalues, and eigenvectors.
About the Author
All three authors are from Sweden.
Tomas Akenine-Möller and Kalle Åström are professors at Lund University, teaching in the Department of Computer Science and the Department of Mathematics, respectively.
Tomas was hired as an assistant professor at Lund University in 2004 and promoted to professor in 2007, and since 2008 has been a part-time graphics researcher at Intel and NVIDIA.
Another author, Jacob Ström, who is now a principal researcher at Ericsson, a Swedish telecommunications equipment manufacturer, also has a past experience with Lund University.
As for the purpose of creating this tutorial, the authors have this to say:
After 20 years of using linear algebra, the three of us came up with the idea of writing a textbook to make it easier to learn and teach linear algebra.
At the same time, internet technology has also reached a certain threshold, allowing the book to be presented in a very new and innovative way.
If you approve of the system and learning style, you might as well arrange it for yourself, and the portal is down there.
Portals:
https://immersivemath.com/ila/