Concept

Absorbing element

Related lectures (28)

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

Numerical Modeling of Solids and Structures

Covers the basics of numerical modeling of solids and structures.

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Quotients of Groups by Relations of Equivalence

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

Operations in Z

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

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.

Trivial Group: Properties and Notation

Covers properties and notation of the trivial group and discusses the uniqueness of elements.

Group Theory: Definition and Examples

Covers the definition of a group, properties of symmetries, and group operations.

Recap of Group Theory

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

Element by element operations

Covers element by element operations in MATLAB and Octave for beginners.

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.

Polynomials and Endomorphisms

Covers the properties of rings, examples of rings, and polynomials.

Q is a Field

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

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

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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.

Infimum

Explains the concept of infimum in real numbers and its properties.

Reasoning about lists

Covers laws of list concatenation, proof by induction, referential transparency, and structural induction.