Lectures related to Gauss's lemma (polynomials)

Ramified Extensions: Eisenstein Polynomials

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Gaussian Lemma III: Irreducibility and Primitive Polynomials

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Algebraic Closure of Qp

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

Built-In Self-Test (BIST): Techniques and Implementations

Explores Built-In Self-Test (BIST) techniques in VLSI systems, covering benefits, drawbacks, implementation details, and the use of Linear Feedback Shift Registers (LFSRs) for test pattern generation.

Algebraic Extensions

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Algebraic Geometry

Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Finite Extensions of Qp: Local Constancy

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Residue Fields and Quadratic Forms

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

Polynomial Factorization over a Field: Eigenvalues

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Algebraic Geometry: Rings and Bodies

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Ramification and Structure of Finite Extensions

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Finite Fields: Construction and Properties

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Euclidean Division: Uniqueness and Remainder

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.