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Introduction to Group Representations Theory
Introduces group representations theory in quantum physics, covering symmetries, perturbation theory, and energy state degeneracy.
Density Theorem: Endomorphisms of Simple Modules
Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.
Schur Lemmas, Part 1
Explores Schur Lemmas, group representations, and stability properties in group theory.
Orthogonality and Characters
Explains group representation, character, and theory, emphasizing orthogonality and equivalence.
Group Representations: Matrices and Symmetry
Explores group representations using matrices, discussing reducible vs. irreducible representations and the Great Orthogonality Theorem.
Generators of Groups
Explains the concept of generators of groups and their mathematical properties.
Machine Learning at the Atomic Scale
Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.
Group Theory: Characters and Representations
Covers the concepts of group characters, representations, and character tables.
Modeling: Principles and Applications
Explores the basics of modeling in systems neuroscience and the importance of experimental data analysis.
Constant Integration and Vector Equations
Covers constant integration, vector equations, and applying physical laws to solve movement problems.