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Lecture
Multiplication: Properties and Definitions
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Properties of Rational Multiplication
Covers the properties of rational multiplication through fractions and simple calculations, leading to the resolution of division problems.
Subtraction: Properties and Definitions
Covers the properties and definitions of subtraction using addition and multiplication as a basis.
Vector Spaces: Properties and Examples
Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.
Integrity in Algebra
Explores the properties of commutative rings and integral domains in algebra.
Abstract Concepts: Semi-Ring
Explores the concept of a commutative semi-ring based on set theory properties.
Auxiliary Assertions in Stainless
Showcases the use of assertions in Stainless to prove properties of fractions.
Commutative Groups: Foundations for Cryptography
Covers commutative groups and their significance in cryptography.
Physics 1: Vectors and Dot Product
Covers the properties of vectors, including commutativity, distributivity, and linearity.
Q is a Field
Covers the properties of rational numbers and introduces the concept of an ordered field in Q.