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).
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
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
9.3.1 Sets: Definitions and Notation
9.3.1 Sets: Definitions and Notation
From playlist LAFF - Week 9
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
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
Determine if a Relation is a Function
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From playlist Intro to Functions
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
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
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
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
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
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
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
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
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
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
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
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
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