Trivial Group: Properties and Notation

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Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.

Group Theory: Properties and Examples

Introduces the concept of a group and its properties through illustrative examples.

Properties of Rational Multiplication

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

Q is a Field

Covers the properties of rational numbers and introduces the concept of an ordered field in Q.