Concept

Field of fractions

Related lectures (22)

Showcases the use of assertions in Stainless to prove properties of fractions.

Covers the properties of rational multiplication through fractions and simple calculations, leading to the resolution of division problems.

Flow Equations: Singular SPDEs and Quantum Field Theory

Covers recent research on singular SPDEs and their applications in quantum field theory.

Multiplication in Rational Numbers

Covers the extension of addition and multiplication operations in rational numbers.

Addition of Fractions

Covers the addition of fractions and properties of rational numbers, emphasizing associativity and summing fractions with the same denominator.

Lesson Design: Backwards Design

Explores designing lessons with a focus on learning goals and constraints.

Rational Numbers: Construction and Properties

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Euclidean Division and Simple Elements

Explains polynomial division, factor decomposition, and rational function simplification.

Decimal Numbers

Explains the conversion process from fractions to decimal numbers and vice versa.

Rational Numbers: Amplification and Simplification

Covers rational numbers, amplifying and simplifying fractions, and calculating values.

Fractions of Rings Log in to Mediaspace to watch this video

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Projective Plane Curves Log in to Mediaspace to watch this video

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Field of Fractions: Definition and Properties Log in to Mediaspace to watch this video

Covers the definition and properties of a field of fractions.

Field of Rational Functions Log in to Mediaspace to watch this video

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.

Decomposition of Fractions: Simple and Corollary Proof Log in to Mediaspace to watch this video

Covers the decomposition of fractions into simple terms and provides a corollary proof related to the convergence of integrals.

Morphisms between Affine Varieties Log in to Mediaspace to watch this video

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Local Noetherian Rings Log in to Mediaspace to watch this video

Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.

Division and Multiplication in Rational Numbers Log in to Mediaspace to watch this video

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Integers and Rings Log in to Mediaspace to watch this video

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Irreducible Polynomials and Finite Fields Log in to Mediaspace to watch this video

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