Lectures related to The inhomogeneous Ising chain

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Propositions and Proofs

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

Fourier Transform: Properties and Applications

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Jordan Curve Theorem

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Variety Defined as the Closure of VCA

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

Kernel Regression: Basics and Applications

Explores kernel regression, the curse of dimensionality, and random features in neural networks.

Initial Problem Solutions

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Hensel's Lemma Application

Discusses the application of Hensel's lemma in determining nth roots and elements that are nth powers.

Derivatives and Solutions

Explores differentiability, propositions evaluation, and solutions to equations using derivatives.

Linear Algebra: Systems and Subspaces

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Linear Applications: Kernel

Introduces the kernel of a linear application and its properties.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Coq: Introduction

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Linear Algebra: Rank Theorem

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.

Linear Algebra: Rank Theorem

Covers the Rank Theorem in linear algebra, focusing on vector spaces and linear applications.

Isometries and Group Homomorphisms

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, including logic, structures, and algorithms.

Coordinate Calculations: Scalar Product in Coordinates

Covers the calculation of scalar products in coordinates and extends the concept to three-dimensional space.

Subgroups Criteria: Propositions and Examples

Covers the criteria for subgroups and provides examples and proofs.