Applied Lectures on the geometric anatomy of theoretical physics

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Dr. Frederic Schuller's series of 28 lectures at the University of Twente covers advanced topics in mathematics, particularly focusing on Lie theory and related concepts. The lectures range from foundational topics like logic and set theory to complex subjects such as Lie groups, their algebras, and applications in quantum mechanics and symmetries. The quality of the lectures is highly praised, especially lectures 13 to 18, which delve into Lie groups and representation theory. There is a desire among viewers for supplementary materials, specifically problem sheets referenced during the lectures. The series is noted for its engaging content, with viewers reporting that the lectures maintain their interest and provide substantial educational value. Links to the lecture series and additional resources related to Dr. Schuller are shared for further exploration.
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I stumbled across this series of 28 lectures by Dr Frederic Schuller of the university of Twente whilst searching for lectures about Lie theory. Having watched through lectures 13 to 18, I think they are simply superb (of course I'm assuming the rest are of similar quality). I only wish he would also publish the problem sheets he keeps referring to... :oldeyes:

Lecture 01 - Introduction/Logic of Propositions and Predicates
Lecture 02 - Axioms of Set Theory
Lecture 03 - Classification of Sets
Lecture 04 - Topological Spaces - Construction and Purpose
Lecture 05 - Topological Spaces - Some Heavily Used Invariants
Lecture 06 - Topological Manifolds and Manifold Bundles
Lecture 07 - Differential Structures: Definition and Classification
Lecture 08 - Tensor Space Theory I: Over a Field
Lecture 09 - Differential Structures: the Pivotal Concept of Tangent Vector Spaces
Lecture 10 - Construction of the Tangent Bundle
Lecture 11 - Tensor Space Theory II: Over a Ring
Lecture 12 - Grassmann Algebra and deRham Cohomology
Lecture 13 - Lie Groups and Their Lie Algebras
Lecture 14 - Classification of Lie Algebras and Dynkin Diagrams
Lecture 15 - The Lie Group SL(2,C) and its Lie Algebra sl(2,C)
Lecture 16 - Dynkin Diagrams from Lie Algebras, and Vice Versa
Lecture 17 - Representation Theory of Lie Groups and Lie Algebras
Lecture 18 - Reconstruction of a Lie Group from its Algebra
Lecture 19 - Principal Fibre Bundles
Lecture 20 - Associated Fibre Bundles
Lecture 21 - Connections and Connection 1-Forms
Lecture 22 - Local Representations of a Connection on the Base Manifold: Yang-Mills Fields
Lecture 23 - Parallel Transport
Lecture 24 - Curvature and Torsion on Principal Bundles
Lecture 25 - Covariant Derivatives
Lecture 26 - Application: Quantum Mechanics on Curved Spaces
Lecture 27 - Application: Spin Structures
Lecture 28 - Application: Kinematical and Dynamical Symmetries

Here is the playlist:

 
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Likes andresB, robphy, PhDeezNutz and 1 other person
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Thanks for sharing! They look very substantive and interesting.

I’ve watched the first thirty minutes so far and haven't gotten lost and didn't fall asleep so I think that’s a good sign.
 
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By looking around, it seems like Dr. Hassani's books are great for studying "mathematical methods for the physicist/engineer." One is for the beginner physicist [Mathematical Methods: For Students of Physics and Related Fields] and the other is [Mathematical Physics: A Modern Introduction to Its Foundations] for the advanced undergraduate / grad student. I'm a sophomore undergrad and I have taken up the standard calculus sequence (~3sems) and ODEs. I want to self study ahead in mathematics...

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