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数学视频

Watch and Learn

• Fun Applications of Geometric Algebra! by Logan Lim
• Introduction to modular forms and elliptic curves by Kenny Li
• An Algebraic Proof of the Fundamental Theorem of Algebra by Blake Madill
• Math-Life Balance. K-Theory Wonderland.

Michael Baker seminar

• Notes: Young tableaux and representation theory
• Raymond Cheng. Hopf algebras, symmetric functions and representation theory. I.
• Raymond Cheng. Hopf algebras, symmetric functions and representation theory. II.
• Clifford algebras and spin representations I.
• Notes: Bundles, spheres, and Clifford algebras
• Representation of Lorentz Group and Clifford algebra-I
• Representation of Lorentz Group and Clifford algebra-II
• Eigenchris. Spinors for Beginners.
• Eigenchris. Tensors for Beginners. Also: Tensor Calculus. Relativity.

Watch and Relax

• Math-Life Balance. Interviews.
  • Interview with Max Karoubi.
  • Interview with Ravi Vakil.
  • Interview with Peter Scholze.

More Sources

Easy general

• Infinite Series
• Numberphile
• Mathologer

Talk collections

• Institute for Advanced Study: Mathematics
• Institute for Advanced Study
• Clay Mathematics Videos
• Oxford: The Secrets of Mathematics
• Max Planck Science Symplectic geometry, algebraic geometry, differential geometry
• Collected by Xuan Gottfried Yang
• Alexander Grothendieck channel
• Collected by "Graduate Mathematics" Number theory, Riemann hypothesis

Course collections

• Park City Mathematics Institute
• NPTEL videos, Alternate catalog
• MIT Open Courseware. Math Department.
• List of math class videos

College Math

• 3 blue 1 brown Linear algebra, Partial differential equations
• Academy of Khan
  • Tensor Calculus
  • Complex Variables and Functions

Overviews of Math

• Oliver Knill. Playlists. Great theorems.
• Oliver Knill. Media.

Lie theory preliminaries

• Algebraic topology
  • Curtis McMullen - Algebraic topology - The Geometry of 3 Manifolds
  • The Mystery of 3-Manifolds - William Thurston
• Federico Ardila
  • Coxeter groups
  • Polytopes
  • Hopf Algebras and Combinatorics, Index and Overview by Sara Billey

Lie theory

• Fredric Schuller: Lectures on Geometrical Anatomy of Theoretical Physics
• Continuous groups in physics
• Continuous Groups for Physicists
  • Video named "17". End of general theory of Lie group and Lie algebra.
  • "18" Classification of compact semisimple Lie algebras and Lie groups and their representation theory. Complexification. Direct sum of semisimple and solvable Lie algebras.
  • "19" root systems
  • "20" simple roots
  • "22" orthogonal, symplectic Lie algebras, table of their properties
  • "23" unitary Lie algebra An, exceptional algebras
  • "24" Representation theory, starting spinors
  • "25" Spinors
• Amritanshu Prasad: Representation Theory: A Combinatorial Viewpoint

Complex analysis, Riemann surfaces

• Complex Analysis P. A. S. Sree Krishna Course
  • Properties of Mobius Transformations
• Introduction to Riemann Surfaces and Algebraic Curves
  • The Idea of a Riemann Surface T.E.Venkata Balaji
• Advanced Complex Analysis Dr. T.E. Venkata Balaji

Physics

• DoctorPhys: Theoretical Physics including basic Lie theory
• DrPhysicsA: Particle Physics
• Leonard Susskind: The Theoretical Minimum
  • Quantum Mechanics
  • Leonard Susskind: General Relativity, Notes
  • Particle Physics 2: Standard Model
    • Group theory: Part 2
• The Mathematical Formalism of Quantum Mechanics
• Quantum Fields, Strings, and Black Holes: A Primer for Non Experts

Algebraic geometry preliminaries

• Daniel Chan Tensors, affine geometry, projective geometry, vector bundles, category theory, homological algebra, modules, algebraic geometry.
• Taylor Dupuy Model theory, mathematical logic, Grothendieck, algebraic geometry
  • Fiber bundles
• Harpreet Bedi Homology, cohomology, etc.
• Introductory homological algebra by Rishi Vyas

Algebraic geometry, classical

• Basic Algebraic Geometry: Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity
• ML Baker on Elliptic curves and modular forms
• Miles Reid. Algebraic surfaces.
• Assorted Geometry videos

Category theory

• The Catsters and Catsters overview, Another overview.
• Applied Category Theory David Spivak, Brendan Fong On Youtube
• David Spivak. Seven Sketches in Compositionality

Grothendieck theory

• Nickolas Rollick: Algebraic Geometry: Sheaves
• What is a Motive? Pierre Deligne
• Peter Arndt. Motivic Verona.

Topos theory

• Toposes in Como. Olivia Caramello et al
• Daniel Murfet: Topos theory
• André JOYAL - 1/4 A crash course in topos theory : the big picture

Other branches

• Field theory
  • 3.2 Properties of finite fields
• Analytic Combinatorics - Robert Sedgewick

Original thinkers

• An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky
• The Problem of Modelling the Mathematical Mind
• Mikhael Gromov - 2/6 Probability, symmetry, linearity, In a Search for a Structure, Part 1: On Entropy. Misha Gromov.

Math podcasts

List of podcasts

• Math podcasts

Talks with mathematicians

• My Favorite Theorem
• Numberphile
• Travels in a Mathematical World
• Breaking Math Podcast
• Relatively Prime
• Mathematical Moments from the American Mathematical Society
• Women in Math: The Limit Does Not ExistPro Unlimited

Previously watched

Physics

• John Baez. Unsolved Mysteries in Fundamental Physics.