Lectures related to Relations in Computer Science

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

Introduces binary relations, functions, and various types of relations in sets.

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

Logical Expressions and Equivalence Relations

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

Mathematical Analysis: Functions and Composition

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

Analysis IV: Convolution and Hilbert Structure

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Relations: Reflexive, Symmetric, Antisymmetric, Transitive

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

Real Functions: Definitions and Properties

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

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Discrete Mathematics: Logic, Structures, Algorithms

Covers the basics of discrete mathematics, focusing on logic, structures, and algorithms for computer systems.

Equivalence Relations: Relations, Sequences and Summations

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

Relations: Definitions and Properties

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

Functions and Integers

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Relations and Sequences

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

Linear Algebra: Applications and Definitions

Covers the definition of applications, image of elements, and direct and reciprocal images.

Lebesgue Integration: Simple Functions

Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.

Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.