Lectures related to Relations, Sequences, Summation: Summary of Week 5

Relations, Sequences and Summations

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

Sets and Operations: Introduction to Mathematics

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

Relations, Sequences, Summation: Quiz

Covers cardinality of sets, poset, equivalence relations, and geometric progressions through a quiz on Kahoot.

Relations in Computer Science

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

Relations and Sequences

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

Cardinality of Sets: Countable and Uncountable

Explores cardinality, countable sets, and examples of countable and uncountable sets.

Cardinality of Sets: Countable and Uncountable

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Sets, Functions and Relations: Constructing Sets

Covers power sets, tuples, Cartesian product, truth sets, and set cardinality with illustrative examples.

Sets, Functions and Relations: Constructing Sets

Explains constructing sets and determining set cardinality.

Cartesian Product and Equivalence Classes

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

Sets and Functions

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

Relations, Sequences and Summations

Covers topics on relations, sequences, and summations, including lattices, recurrence relations, and sigma notation.

Linear Algebra: Bijections and Cardinality

Explores bijections in linear algebra and the concept of cardinality between sets.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Linear Algebra: Sets and Operations

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

Relations: Sets, Functions and Composition

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

Cardinality and Group Theory

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

Introduction to Category Theory: Examples

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

Relations, Sequences, Summation: Cantor Diagonalization

Covers countable and uncountable sets, sequences, summation, and Cantor's Diagonalization proof.

Relations: Sets, Functions and Composition

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