Concept
Cauchy's theorem (group theory)
Related lectures (15)
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Orbit-Stabilizer Theorem: Conjugacy Classes and Direct Products
Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.
Symmetric Group and Group Actions
Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.
Symmetric Group and Cycle Decomposition
Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Convergence of Fourier Series
Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.
Finite Abelian Groups & Rings
Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.
Symmetric Matrices: Eigenvalues and Diagonalization
Covers symmetric matrices, eigenvalues, and diagonalization process for spectral theorem applications.
Vector Spaces: Properties and Operations
Covers the properties and operations of vector spaces, including addition and scalar multiplication.