Interval finite element

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

Measurement, approximation and interval arithmetic (I) | Real numbers and limits Math Foundations 81

This video introduces interval arithmetic, first in the context of natural numbers, and then for integers. We start with some remarks from the previous video on the difficulties with irrational numbers, sqrt(2), pi and e. Then we give some general results about order (less than, greater

From playlist Math Foundations

Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82

We continue on with a short intro to interval arithmetic, noting the difference between the laws of arithmetic over the natural numbers and the integers. The case of rational number intervals is also briefly discussed. We end the lecture with some remarks on the vagueness of ``real number'

From playlist Math Foundations

Closed Intervals, Open Intervals, Half Open, Half Closed

00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation

From playlist Calculus

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

Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets

https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html

From playlist Fundamentals of Mathematics

Interval Notation (1 of 2: Bounded intervals)

More resources available at www.misterwootube.com

From playlist Working with Functions

Interval Notation

http://mathispower4u.wordpress.com/

From playlist Using Interval Notation

[a,b] is compact

In this video, I give a direct proof that the interval [a,b] is compact, without using the Heine-Borel Theorem. It's elementary, but not easy, my dear Watson! Heine-Borel Theorem: https://youtu.be/4jaox_jqwGM Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG

From playlist Topology

Compactness

The single, most important concept in topology and analysis: Compactness. This is explained via covers, which I'll define as well. There are tons of applications of this concept, which you can find in the playlist below Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13v

From playlist Topology

What is a Manifold? Lesson 3: Separation

He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.

From playlist What is a Manifold?

What is a Manifold? Lesson 4: Countability and Continuity

In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.

From playlist What is a Manifold?

Lecture 7: Sigma Algebras

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=OHiu2F18dFA&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

Steve Oudot (9/8/21): Signed barcodes for multi-parameter persistence via rank decompositions

In this talk I will introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode

From playlist AATRN 2021

Real Analysis | The Heine-Borel Theorem

We prove that the topological definition of compactness is equivalent to a set of real numbers being closed and bounded. Here is the last bit of the proof: https://www.youtube.com/watch?v=p9nKuqz6D9w&list=PL22w63XsKjqxqaF-Q7MSyeSG1W1_xaQoS&index=29&t=0s Please Subscribe: https://www.y

From playlist Real Analysis

Math 131 Fall 2018 092118 Cardinality

Recall definitions: injective, surjective, bijective, cardinality. Definitions: finite, countable, at most countable, uncountable, sequence. Remark: a 1-1 correspondence with the natural numbers is the same thing as a bijective sequence. Theorem: Every infinite subset of a countable set

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)

Mickaël Buchet: Every nD persistence module is the restriction of an (n+1)D indecomposable module.

Date: 6/29/2020 Title: Every nD persistence module is the hyperplane restriction of an (n+1)D indecomposable module. Abstract: In this talk, I will present a constructive process that, given a nD persistence module, builds an (n+1)D indecomposable module containing the said module as an

From playlist ATMCS/AATRN 2020

Open Covers, Finite Subcovers, and Compact Sets | Real Analysis

We introduce coverings of sets, finite subcovers, and compact sets in the context of real analysis. These concepts will be critical in our continuing discussion of the topology of the reals. The definition of a compact set, in particular, is surprisingly fundamental, and we will provide an

From playlist Real Analysis

Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018

Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

Maximum and Minimum Values (Closed interval method)

A review of techniques for finding local and absolute extremes, including an application of the closed interval method

From playlist 241Fall13Ex3