Topology | Simplicial sets | Algebraic topology
In mathematics, a Δ-set S, often called a semi-simplicial set, is a combinatorial object that is useful in the construction and triangulation of topological spaces, and also in the computation of related algebraic invariants of such spaces. A Δ-set is somewhat more general than a simplicial complex, yet not quite as general as a simplicial set. As an example, suppose we want to triangulate the 1-dimensional circle . To do so with a simplicial complex, we need at least three vertices, and edges connecting them. But delta-sets allow for a simpler triangulation: thinking of as the interval [0,1] with the two endpoints identified, we can define a triangulation with a single vertex 0, and a single edge looping between 0 and 0. (Wikipedia).
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks.
From playlist Handmade geometric toys
Reviews the intuitive notion of a continuous-time impulse or Dirac delta function and the sifting property. http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files.
From playlist Background Material
Ex: Limit Definition - Find Delta Values, Given Epsilon For a Limit
This video explains how to determine which delta values satisfy a given epsilon of a limit. http://mathispower4u.com
From playlist Limits
Ex 1: Limit Definition - Determine Delta for an Arbitrary Epsilon (Linear)
This video explains how to determine an expression of delta for an arbitrary epsilon that can be used to prove a limit exists. http://mathispower4u.com
From playlist Limits
Limits 1b - Delta-Epsilon Formulation
Calculus: We present the delta-epsilon definition of a limit, explain the various parts pictorially, and show how to choose delta when presented with a given epsilon. We show that delta = .1 works for f(x) = x^2 at x_0 =2 when epsilon = 1/2.
From playlist Calculus Pt 1: Limits and Derivatives
Ex 2: Limit Definition - Determine Delta for an Arbitrary Epsilon (Quadratic)
This video explains how to determine an expression of delta for an arbitrary epsilon that can be used to prove a limit exists. http://mathispower4u.com
From playlist Limits
Introduction to the Dirac Delta Function
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to the Dirac Delta Function
From playlist Differential Equations
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Calculus I - 1.2.3 The Epsilon-Delta Limit Definition
In this video we formalize the definition of a limit and explore strategies for determining the value of delta for a given or variable value of epsilon. Video Chapters: Intro 0:00 Informal to Formal Limit Definition 0:08 Finding Delta for Given Epsilon 3:50 Finding Delta in Terms of Epsil
From playlist Calculus I - Complete Course Under Construction
Arithmetic progressions and spectral structure - Thomas Bloom
Computer Science/Discrete Mathematics Seminar II Topic: Arithmetic progressions and spectral structure Speaker: Thomas Bloom Affiliation: University of Cambridge Date: October 13, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Math 131 Fall 2018 101018 Continuity and Compactness
Definition: bounded function. Continuous image of compact set is compact. Continuous image in Euclidean space of compact set is bounded. Extreme Value Theorem. Continuous bijection on compact set has continuous inverse. Definition of uniform continuity. Continuous on compact set impl
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Introduction to additive combinatorics lecture 10.1 --- the structure and properties of Bohr sets.
An important informal idea in additive combinatorics is that of a "structured" set. One example of a class of sets that are rich in additive structure is the class of Bohr sets, which play the role in general finite Abelian groups that subspaces play in the special case of groups of the fo
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
In this analysis-packed video, I present the concept of covering compactness. This concept is best understood via some counterexamples. Then, in the second part of the video, I give a nice application of that concept by showing that a continuous function from a compact set to the real numb
From playlist Real Analysis
Lecture 13: Limits of Functions
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We begin to discuss limits of functions, in
From playlist MIT 18.100A Real Analysis, Fall 2020
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 101 Fall 2017 112717 Open Sets and Continuity
Definitions: open set, closed set; examples. Statement of DeMorgan's Laws. Definition: pre-image. Example. Theorem: f is continuous iff the preimage of any open set is open. Motivation for compact sets.
From playlist Course 6: Introduction to Analysis (Fall 2017)
Proof for Unions and Intersections of Open Sets | Real Analysis
We prove the union of a collection of open sets is open, and the intersection of a finite collection of open sets is open. To do this, we use basic set operation properties and the definition of open sets. #RealAnalysis Intro to Open Sets: https://youtu.be/pnWgj8jjs3w Real Analysis playl
From playlist Real Analysis
Joseph Bonin: Delta-matroids as subsystems of sequences of Higgs lifts
Abstract: Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which symmetric differences replace set differences. One way to get a delta-matroid is to t
From playlist Combinatorics
Delta Functions and Gauss' Law
An introduction to Dirac Delta Functions, and their use in describing charge distributions and in Gauss' Law.
From playlist Phys 331 Uploads
Hausdorff Dimension Analogues of the Elekes - Ronyai Theorem and Related Problems - Orit Raz
Computer Science/Discrete Mathematics Seminar II Topic: Hausdorff Dimension Analogues of the Elekes - Ronyai Theorem and Related Problems Speaker: Orit Raz Affiliation: Hebrew University; Visitor, School of Mathematics Date: April 04, 2023 If f is a real polynomial and A and B are finit
From playlist Mathematics