Commutation Groups: Euler's Totient Function

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Covers commutative groups and their significance in cryptography.

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Covers the concept of the Cartesian product, emphasizing the order of elements in pairs.

Explores two definitions of group action on a set, focusing on properties and applications.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.

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

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.