Lecture Notes in Lie Groups

TL;DR

These lecture notes provide a comprehensive introduction to Lie groups, covering their mathematical foundations and applications across physics, engineering, and biology, suitable for advanced students.

Contribution

They offer an accessible, interdisciplinary overview of Lie groups with practical examples, bridging pure mathematics and applied sciences.

Findings

Rigorous foundation for modern dynamics and gauge theories

Includes physical and medical applications of Lie groups

Accessible to students with advanced calculus and linear algebra

Abstract

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. We give both physical and medical examples of Lie groups. The only necessary background for comprehensive reading of these notes are advanced calculus and linear algebra.