Lectures related to The Discriminant and Ideal Class Group in Mathematics

Ideal Class Group Relations

Covers the relations between the ideal class group and proper fractional ideals.

Concept of Proof in Mathematics

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

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Logarithmic Embedding in Number Fields

Explores the properties and applications of logarithmic embeddings in number fields.

Stability of Networked Control Systems

Explores the stability analysis of Networked Control Systems under stochastic packet dropouts, emphasizing mean-square stability and practical implications.

Hermite-Minkowski Theorems: Number Fields and Ideal Classes

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Coq: Introduction

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

Propositions and Proofs

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

Short Coq Tutorial

Offers a tutorial on Coq, covering inductive definitions, recursive functions, propositions, theorems, and tactics.

Mathematical Induction: Basics and Applications

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Discrete Mathematics: Logic, Structures, Algorithms

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

Linear Algebra: Sets and Propositional Language

Covers sets, propositional language, reading, writing, containment, and cardinality.

Number Fields: Embeddings and Ideal Classes

Covers the embeddings of number fields and ideal classes with proofs and examples.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, focusing on logic, structures, and algorithms for computer systems.

Dedekind Rings: Theory and Applications

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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Predicate Logic: Basics and Applications

Covers the basics and applications of predicate logic, including quantifiers, predicates, and propositional functions.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Discrete Mathematics: Logic & Structures

Covers propositional logic, truth tables, and problem-solving strategies in discrete mathematics.