Lectures related to Sets and Functions

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Relations: Reflexive, Symmetric, Antisymmetric, Transitive

Explains binary relations on a set and their properties with illustrative examples.

Relations: Definitions and Properties

Explains binary relations, reflexive, symmetric, antisymmetric, and transitive relations on a set.

Relations: Sets, Functions and Composition

Covers binary relations, functions, set operations, composition, and n-ary relations.

Binary Relations and Cartesian Products

Explores binary relations, Cartesian products, and applications between sets, emphasizing their properties and significance.

Relations: Sets, Functions and Composition

Covers binary relations, functions, composition, and n-ary relations with examples.

Logical Expressions and Equivalence Relations

Covers logical expressions, sets, elements, and equivalence relations.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Equivalence Relations: Classes, Partitions

Covers equivalence relations, classes, and partitions of a set.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Functions and Integers

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Equivalence Relations: Relations, Sequences and Summations

Explores equivalence relations, functions, subsets, and De Morgan's laws.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Sets, Functions and Relations: Summary of Week 4

Covers sets, functions, and relations, including functions' properties and binary relations.

Relational Algebra and SQL: Foundations of Database Management

Introduces the relational model and relational algebra, focusing on SQL and its operations for effective database management.

Cartesian Product and Equivalence Classes

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Differential Equations: Mathematical Complements

Covers the definition of differential equations and their relation to functions and derivatives.