List of set identities and relations

Set Theory (Part 2): ZFC Axioms

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their

From playlist Set Theory by Mathoma

How to Identify the Elements of a Set | Set Theory

Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times

From playlist Set Theory

20 The identity element

Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera

From playlist Abstract algebra

Introduction to sets || Set theory Overview - Part 1

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty

From playlist Set Theory

Set Theory (Part 5): Functions and the Axiom of Choice

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce functions as a special sort of relation, go over some function-related terminology, and also prove two theorems involving left- and right-inverses, with the latter theorem nic

From playlist Set Theory by Mathoma

Introduction to Sets and Set Notation

This video defines a set, special sets, and set notation.

From playlist Sets (Discrete Math)

Set Theory (Part 3): Ordered Pairs and Cartesian Products

Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser

From playlist Set Theory by Mathoma

Introduction to sets || Set theory Overview - Part 2

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty

From playlist Set Theory

The S3 character table - a (somewhat) new meaning | Diffusion Symmetry 2 | N J Wildberger

With diffusion symmetry, we explore mathematical objects or physical systems by spreading or diffusing from an initial point. The algebraic objects that result are hypergroups, or fusion algebra, or one of many similar and almost equivalent systems found in combinatorics, group theory, num

From playlist Diffusion Symmetry: A bridge between mathematics and physics

GT12.1. Automorphisms of Dihedral Groups

Abstract Algebra: We compute Aut(G), Inn(G), and Out(G) when G is a dihedral group D_2n. We also show that Aut(D_2n) always contains a subgroup isomorphic to D_2n and that Aut(D_2n) may be realized as a matrix group with entries n Z/n.

From playlist Abstract Algebra

Category Theory 3.1: Examples of categories, orders, monoids

Examples of categories, orders, monoids.

From playlist Category Theory

Introduction to Set Theory

This video introduces the basic vocabulary used in set theory. http://mathispower4u.wordpress.com/

From playlist Sets

GT7. The Commutator Subgroup

EDIT: At 11:50, r^2(l-k) should be r^2l. At 14:05, index for top one should be n-2, not 2n-2. Abstract Algebra: We define the commutator subgroup for a group G and the corresponding quotient group, the abelianization of G. The main example is the dihedral group, which splits into tw

From playlist Abstract Algebra

Bettina EICK - Computational group theory, cohomology of groups and topological methods 3

The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

Live CEOing Ep 199: Database Integration in Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Database Integration in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

Representation Theory & Combinatorics of the Symmetry Group and Related Structures -Monica Vazirani

2021 Women and Mathematics - Terng Course Lecture Topic: Representation Theory & Combinatorics of the Symmetry Group and Related Structures Speaker: Monica Vazirani Affiliation: University of California, Davis Date: May 24, 2021 For more video please visit https://www.ias.edu/video

From playlist Mathematics

A Sensible Introduction to Category Theory

Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it. 27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86

From playlist Mathematics

GT17. Symmetric and Alternating Groups

EDIT: at 15:00, we have (abcde) = (abc)(cde) instead of (abc)(ade) Abstract Algebra: We review symmetric and alternating groups. We show that S_n is generated by its 2-cycles and that A_n is generated by its 3-cycles. Applying the latter with the Conjugation Formula, we show that A_5 i

From playlist Abstract Algebra

Set Theory (Part 6): Equivalence Relations and Classes

Please feel free to leave comments/questions on the video and practice problems below! In this video, I set up equivalence relations and the canonical mapping. The idea of equivalence relation will return when we construct higher-level number systems, e.g.integers, from the natural number

From playlist Set Theory by Mathoma