Lectures on the Geometric Anatomy of Theoretical Physics: Difference between revisions

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# [https://www.youtube.com/watch?v=V49i_LM8B0E Introduction/Logic of propositions and predicates]
# [https://www.youtube.com/watch?v=V49i_LM8B0E Introduction/Logic of propositions and predicates]
# Links to all of the lectures would be helpful...
# [https://www.youtube.com/watch?v=AAJB9l-HAZs&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=2 Axioms of set theory]
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# [https://www.youtube.com/watch?v=6EIWRg-6ftQ&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=3 Classification of sets]
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# [https://www.youtube.com/watch?v=1wyOoLUjUeI&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=4 Topological spaces: construction and purpose]
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# [https://www.youtube.com/watch?v=hiD6Tz06k30&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=5 Topological spaces: some heavily used invariants]
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# [https://www.youtube.com/watch?v=uGEV0Wk0eIk&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=6 Topological manifolds and manifold bundles]
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# [https://www.youtube.com/watch?v=Fa6SRAwY80Y&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=7 Differentiable structures: definition and classification]
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# [https://www.youtube.com/watch?v=4l-qzZOZt50&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=8 Tensor space theory I: Over a field]
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# [https://www.youtube.com/watch?v=UPGoXBfm6Js&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=9 Differential structures: The pivotal concept of tangent vector spaces]
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# [https://www.youtube.com/watch?v=XZcKSoI17r0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=10 Construction of the tangent bundle]
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# [https://www.youtube.com/watch?v=V0TPgeiyWCo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=11 Tensor space theory II: Over a ring]
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# [https://www.youtube.com/watch?v=QLnzIOGIvfo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=12 Grassman algebra and De Rham cohomology]
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# [https://www.youtube.com/watch?v=mJ8ZDdA10GY&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=13 Lie groups and their lie algebras]
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# [https://www.youtube.com/watch?v=Vlbcd_lPNMA&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=14 Classification of lie algebras and their dynkin diagrams]
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# [https://www.youtube.com/watch?v=H1D09cuFWlM&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=15 Lie group SL(2,C) and its algebra]
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# [https://www.youtube.com/watch?v=G9uVcit_VwY&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=16 Dykin diagrams from Lie algebras and vice versa]
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# [https://www.youtube.com/watch?v=h-d8TUg022A&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=17 Representation theory of lie groups and lie algebras]
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# [https://www.youtube.com/watch?v=7qO5y6Es9Ns&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=18 Reconstruction of a Lie group from its algebra]
# [https://www.youtube.com/watch?v=vYAXjTGr_eM Principal fibre bundles]
# [https://www.youtube.com/watch?v=vYAXjTGr_eM Principal fibre bundles]
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# [https://www.youtube.com/watch?v=q2GYZz6q3QI&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=20 Associated fiber bundles]
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# [https://www.youtube.com/watch?v=jFvyeufXyW0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=21 Connections and Connection 1 forms]
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# [https://www.youtube.com/watch?v=KhagmmNvOvQ&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=22 Local representations of a connection on the base manifold: Yang-Mills fields]
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# [https://www.youtube.com/watch?v=jGHaZc2fuX8&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=23 Parallel transport]
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# [https://www.youtube.com/watch?v=j36o4DLLK2k&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=24 Curvature and torsion on principal bundles]
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# [https://www.youtube.com/watch?v=ClIVG7ilm_Q&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=25 Covariant derivatives]
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# [https://www.youtube.com/watch?v=C93KzJ7-Es4&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=26 Application: Quantum mechanics on curved spaces]
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# [https://www.youtube.com/watch?v=Way8FfcMpf0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=27 Application: Spin structures]
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# [https://www.youtube.com/watch?v=F3oGhXNhIDo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=28 Application: Kinematical and dynamical symmetries]


== Lecture Notes ==
== Lecture Notes ==
2

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