This free 1-day workshop is designed specifically for students with some basic background in algebra, trigonometry and geometry. Participants will gain a geometric intuition of linear algebra and understand how matrices can be used to scale and rotate 3-dimensional objects. To bridge the gap between theoretical knowledge and practical application, the course includes step-by-step exercises that eventually build up to the final product of a spinning donut.
Part One is a refresher of the mathematics required for the project. This includes revision on trigonometry, cartesian equations and similar triangles. As a warmup, the concept of a vector is introduced. Participants will learn how to add, subtract and scale linear combinations of vectors. The dot product of two vectors is also introduced including how it relates top rojections. To ensure active understanding of these concepts, participants will be implementing these operations in Python. They will also start working on rendering the donut on a static screen using the concepts that were covered.
Part Two delves deeper into the subject and begins by introducing the mathematical object which is most central to linear algebra – the matrix through the lens of linear transformations.Participants will learn how each matrix corresponds to a certain transformation of space, such as translation, rotation, reflection, scaling, etc. Furthermore, they will be introduced to the idea of the determinant as a scaling factor for the transformation. These concepts will be reviewed and applied through practical coding sessions that implement these operations inPython. In this part, they will rotate the donut and render it on a static screen.
Part Three starts off by introducing matrix multiplication as how a usual class on linear algebra would, by defining it as a formula. Then, the geometric intuition of matrix multiplications as composing linear transformations will be introduced. Participants will learn how to appreciate the significance of matrix multiplication and why it is defined as such. In addition, they will start applying their knowledge of these concepts to finally animate the static donut which they have rendered.
Throughout the workshop, attendees will participate in a variety of hands-on activities, including worksheet exercises to ensure that they not only understand the theoretical aspects of linear algebra but also how to apply these concepts in real-world scenarios. Each session is designed to foster learning through interaction, discussion, and practical experimentation, supported by tools and resources for continued education beyond the workshop.
Objectives
● Understand the concept of a vector as a mathematical object, including the ideas behind vector addition, scalar multiplication and dot product
● Understand the idea of a linear combination of vectors and the span of a set of vectors
● Learn about matrices as a mathematical object and what it represents geometrically
● Understand the concept of linear transformations and how it is represented asa matrix
● Learn how to compose multiple linear transformations together using matrix multiplication
● Discover how these concepts can be applied to render an animation of a spinning donut
● Explore further learning resources including other areas where linear algebra is applied such as machine learning and computer vision
Target group
This workshop is an excellent opportunity for IT professionals, business analysts, and tech enthusiasts to explore the potential of Generative AI, enhance their technical skills, and prepare for the future of technology.
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