Order theory

Related lectures (26)

Covers the operations in rings, ideals, classes, and quotient rings.

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Explores the construction of quotient rings and the properties of well-defined operations within rings.

Explores the concept of a commutative semi-ring based on set theory properties.

Covers the properties of subtraction and the distributivity of multiplication.

Explains the importance of parentheses in integer operations and how to simplify calculations using properties.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Explores Boolean algebra properties and optimization techniques using Karnaugh diagrams and De Morgan's theorems.

Explores properties of relations, monotonicity, semantics of local variables, and translation in programs.

Covers the concept of convolution and its properties in signal processing.

Explains how systems are composed in parallel or series.

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

Explains the cup and cap product in algebraic topology and their relation to homology groups.

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

Explores properties of matrices, endomorphisms, and linear applications in vector spaces.

Covers matrix multiplication, properties, and the identity matrix in algebraic operations.

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

Page 1 of 2