About Mathemaniac

---

Hi, I am Trevor. This channel is dedicated to promoting Maths and help people generate interest in Maths by showing a more fun side of Mathematics, as well as the elegance of Math. It takes a different turn from the traditional textbook Maths, and go much more in-depth, making the journey of Math more rewarding. This channel contains both highly visual mathematical topics like integration, graph theory and group theory, but also some less visual topics including some algebraic tricks which are equally amazing.

For those who are wondering, I don't use coding to produce my videos, and while stylistically similar to 3Blue1Brown, I don't use Manim (Grant's mathematical animation Python library) to produce my videos. I actually use PowerPoint, GeoGebra and (sometimes) Mathematica to produce my videos.

SUBSCRIBE!! I try to upload at least monthly, but no guarantee on this.

What is Lie theory? Here is the big picture.

Part 4: (Work in progress, but it will be THE most important video of the series) A bird's eye view on Lie theory, providing motivation for studying Lie algebras and Lie brackets in particular. Basically, Lie groups are groups and manifolds, and thinking about them as manifolds, we know that we w…

---

How to rotate in higher dimensions? Complex dimensions? | Lie groups, algebras, brackets #2

Part 3: https://youtu.be/ZRca3Ggpy_g Around 11:50, can't imagine that this error got in - it should have been SU(n) = {U in U(n), det U = 1}. Orthogonal and unitary groups. Rotational symmetries, real and complex, are particularly useful in the field of Lie theory, because their (complexified) Li…

---

Why study Lie theory? | Lie groups, algebras, brackets #1

Next video: https://youtu.be/erA0jb9dSm0 Lie’s theory of continuous symmetries was originally for differential equations, but turns out to be very useful for physics because symmetries are manifest in many physical systems. This is the start of a series on Lie groups, Lie algebras, and Lie bracket…

---