Lectures related to Modular Arithmetic: Introducing Z/mZ

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Covers the basics of group theory, including definitions, examples, and isometries.

Covers the properties of subtraction and the distributivity of multiplication.

Covers addition properties and operations in the set of integers Z.

Covers commutative groups and their significance in cryptography.

Explores division in rational numbers and the extension of addition from integers.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

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

Explains the definition and properties of integer multiplication in various scenarios.

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

Covers the concept of natural numbers, including properties like commutativity and associativity.

Introduces Cartesian product and induction for proofs using integers and sets.

Explores polynomial operations, properties, and subspaces in vector spaces.

Covers the construction of integers through equivalence relations and their properties in mathematics.

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.

Covers basic properties of natural numbers, including order relations and inverses.

Introduces matrix algebra operations and their properties, including commutativity and distributivity.

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Explains the importance of parentheses in simplifying mathematical operations and notations.