Lectures related to P-adic Expansion: Unique Representations and Power Series

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Power Series and Taylor Series

Explores power series, Taylor series, convergence criteria, and applications in mathematics.

Hensel's Lemma and Field Theory

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Cauchy Sequences and Series

Explores Cauchy sequences, convergence, bottoms, and series with illustrative examples.

Dirichlet Series: Properties and Examples

Explores the properties and examples of Dirichlet series, highlighting their key characteristics and applications.

Variance Reduction Techniques

Covers variance reduction techniques in optimization, focusing on gradient descent and stochastic gradient descent methods.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Taylor Series: Convergence and Applications

Explores Taylor series, convergence criteria, and applications in calculus.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Norms and Valuations on Fields

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Taylor Series: Basics and Applications

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.

Deep Learning Building Blocks: Linear Layers

Explains the fundamental building blocks of deep learning, focusing on linear layers and activation functions.

Quantum Chemistry: Schrödinger Equation Solutions

Explores the solutions to the Schrödinger Equation in Quantum Chemistry, emphasizing wavefunction properties and energy quantization.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Online Lecturing: Integral Equations and Laplace Transform Methods

Explores integral equations, Laplace transform methods, and problem-solving techniques.

Group Operations and Homomorphisms in Abelian Groups

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.