Lectures related to Algebraic number

Algebraic Geometry

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

Purely Inseparable Decompositions

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Intersection: Sets and Properties

Explores the intersection of sets, defining it and discussing its properties.

Algebraic Operations on Limits: Indeterminate Forms and Fundamental Limits

Covers algebraic operations on limits, indeterminate forms, and fundamental limits.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Algebraic Operations and Taylor Expansions

Explores algebraic operations on Taylor expansions and the development of various functions.

Algebraic Closure of Qp

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

Operations on Limits

Explores algebraic operations on limits of sequences and discusses the uniqueness of limits and properties of convergent and divergent sequences.

Complex Numbers: Applications and Representations

Explores the origin, applications, and representations of complex numbers in crystallography and materials science, including their graphical, polar, and exponential forms.

Error-Correcting Codes: Hamming Distance and Polynomial Multiplication

Covers error-correcting codes, Hamming distance, and polynomial multiplication in algebraic fields.

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.

Algebraic Operations

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Mathematical Notations: Recap and Rational Numbers

Covers a recap on mathematical notations and introduces rational numbers and basic algebraic operations.

Taylor Polynomial: Order, Development, and Limits

Explores Taylor polynomials, including order, development, limits, and algebraic operations.

Integer Factorization: Quadratic Sieve

Explores integer factorization using the quadratic sieve method and the challenges of working with algebraic number fields.

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Étale Motives and the Hodge Conjecture

Explores étale motivic cohomology and the Hodge conjecture with a focus on counter-examples.

Completion of a Field: Algebraic Closure

Covers the completion of a field, focusing on algebraic closure and function convergence.