Lectures related to Hermite-Minkowski Theorems: Number Fields and Ideal Classes

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

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

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Explores embeddings of number fields, types, signatures, lattices, and determinants.

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

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

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

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

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.