Algebraic topology

S-object

In algebraic topology, an -object (also called a symmetric sequence) is a sequence of objects such that each comes with an action of the symmetric group . The category of combinatorial species is equivalent to the category of finite -sets (roughly because the permutation category is equivalent to the category of finite sets and bijections.) (Wikipedia).

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Object Oriented Programming 1 - Classes and Objects

This is the first in a series of videos that introduce object oriented programming (OOP) using Visual Basic.NET (VB.NET). This video explains the relationship between a class and an object. It shows how the public interface of a custom class can be coded, by declaring public variables wi

From playlist Object Oriented Programming

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Introduction to Sets and Set Notation

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

From playlist Sets (Discrete Math)

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9.3.1 Sets: Definitions and Notation

9.3.1 Sets: Definitions and Notation

From playlist LAFF - Week 9

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Orbit of a set in abstract algebra

In this video we start to take a look at the orbit-stabilizer theorem. Our first stop is the orbit of a set. The orbit is created by taking an arbitrary element of a set and acting on that element by all the elements in the set of an an arbitrary group. In this video, we look at a few p

From playlist Abstract algebra

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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

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Determine if a Relation is a Function

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From playlist Intro to Functions

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The Inverse Image of a Set Under a Function: Definition and Examples

The Inverse Image of a Set Under a Function: Definition and Examples

From playlist Functions, Sets, and Relations

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What is a Group? | Abstract Algebra

Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s

From playlist Abstract Algebra

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What are Elements of Sets? | Set Theory, Cardinality, Set Elements

What are elements of sets? Recall that a set is an unordered collection of distinct objects. The elements of a set are the distinct objects that the set contains. For example, consider the set S = { 1, 2, 3 }. In this case, the numbers 1, 2, and 3 are the elements of S. While a number li

From playlist Set Theory

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Category Theory: The Beginner’s Introduction (Lesson 1 Video 5)

Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed

From playlist Category Theory: The Beginner’s Introduction

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Physics 55.4 Optics- Multiple Lenses (2 of 12) The Double Lens: General Approach

Visit http://ilectureonline.com for more math and science lectures! In this video I will first review the double lens problems in general, the lenses are not necessarily touching. Next video in this series can be seen at: https://youtu.be/GxemspUuOSU

From playlist PHYSICS 55.4 MULTIPLE LENSES

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Georg Biedermann - Higher Sheaves

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Joint work with Mathieu Anel, Eric Finster, and André Joyal Even though on the surface the theories look similar, there are basic differences between the classical theory of 1-t

From playlist Toposes online

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Physics 59 Optical Instruments (10 of 20) Magnification of a Microscope: Exact Approach

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the EXACT approach to find the magnification of a microscope given the length of microscope=20cm, focal distance object

From playlist PHYSICS 59 OPTICAL INSTRUMENTS

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Physics 55.1 Optics: Exploring Images with Thin Lenses and Mirrors (2 of 20) The Len's Equation

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the image distance, real or virtual image, magnification, and inverted or upright of an object view through a converging lens. Next video in series can be seen at: https://youtu.be/FIyc_oeYf9Y

From playlist PHYSICS 55.1 LENSES AND MIRRORS UNDERSTOOD

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Physics: Optics Ch 58.1 Refracting Surfaces (17 of 22) Refraction: Glass Rod in Water

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the locations of the images s2'=? And magnification m2=?, and s3'=?, m3=? of the corresponding objects O2, and O3 are at distance s2=4cm, and s3=20cm away from a glass rod (in water) of radius R=

From playlist PHYSICS 58.1 REFRACTING SURFACES

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Physics - Optics: Lenses (1 of 5) Lens Combinations - Two Converging Lenses

Visit http://ilectureonline.com for more math and science lectures! In this video I will show you how to find the location of the image when the object is placed 50cm in front of the 2 converging lenses.

From playlist PHYSICS - OPTICS

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Length Contraction, Time Dilation, & Relativity of Simultaneity Using Lorentz Transformation

Lorentz transformation derivation: https://youtu.be/6f_yxbtM2TI Special relativity gives us a lot of unintuitive results. We can understand why these happen using the Lorentz transformation, so we can see how coordinates in one inertial reference frame appear to an observer in a different

From playlist Special Relativity

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15 Properties of partially ordered sets

When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.

From playlist Abstract algebra

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Physics 55.1 Optics: Exploring Images with Thin Lenses and Mirrors (5 of 20) Converging Lens

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the image distances, real or virtual image, magnification, and inverted or upright of an object view through a converging lens of f=20cm and object at s=10cm, 15cm, and 18cm. Next video in serie

From playlist PHYSICS 55.1 LENSES AND MIRRORS UNDERSTOOD

Related pages

Schur functor | Highly structured ring spectrum | Symmetric group | Permutation category | Combinatorial species | Algebraic topology