Interval of Convergence (silent)
Finding the interval of convergence for power series
From playlist 242 spring 2012 exam 3
The Difference Between Pointwise Convergence and Uniform Convergence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Difference Between Pointwise Convergence and Uniform Convergence
From playlist Advanced Calculus
Math 131 Spring 2022 041122 Uniform Convergence and Continuity
Exercise: the limit of uniformly convergent continuous functions is continuous. Theorem: generalization. Theorem: pointwise convergence on a compact set + extra conditions guarantees uniform convergence. Digression: supremum norm metric on bounded continuous functions. Definitions.
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Convergence: When ideas cross to produce something greater than the sum of it’s parts. We’re seeing this with fitness, travel, entertainment and the list goes on. Different ideas, different paths of research and development and different products are converging all around us. And where bet
From playlist CES 2016
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Math 101 Introduction to Analysis 113015: Compact Sets, ct'd
Compact sets, continued. Recalling various facts about compact sets. Compact implies infinite subsets have limit points (accumulation points), that is, compactness implies limit point compactness; collections of compact sets with the finite intersection property have nonempty intersectio
From playlist Course 6: Introduction to Analysis
Math 131 111416 Sequences of Functions: Pointwise and Uniform Convergence
Definition of pointwise convergence. Examples, nonexamples. Pointwise convergence does not preserve continuity, differentiability, or integrability, or commute with differentiation or integration. Uniform convergence. Cauchy criterion for uniform convergence. Weierstrass M-test to imp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Calculus: How Convergence Explains The Limit
The limit definition uses the idea of convergence twice (in two slightly different ways). Once the of convergence is grasped, the limit concept becomes easy, even trivial. This clip explains convergence and shows how it can be used to under the limit.
From playlist Summer of Math Exposition Youtube Videos
In this video, I discuss the notion of sequential compactness, which is an important concept used in topology and analogy. I also explain the similarities and differences between sequential compactness and covering compactness. Compactness: https://youtu.be/xiWizwjpt8o Bolzano-Weierstrass
From playlist Topology
Real Analysis Ep 18: Compact sets
Episode 18 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about compact sets. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.fairfield
From playlist Math 3371 (Real analysis) Fall 2020
MAST30026 Lecture 8: Compactness I
This is the first of several lectures on compactness. I recalled the proof of the Bolzano-Weierstrass theorem, defined sequential compactness in metric spaces and the characterisation of continuity of functions in terms of limits, and proved that the image of a compact set is compact. Lec
From playlist MAST30026 Metric and Hilbert spaces
16. Graph limits III: compactness and applications
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of graph limits, Prof. Zhao pro
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Metric Spaces - Lectures 19 & 20: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 10th of 11 videos. The course is about the notion of distance. You m
From playlist Oxford Mathematics Student Lectures - Metric Spaces
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Sergio Zamora (1/20/23): The lower semi-continuity of \pi_1 and nilpotent structures in persistence
When a sequence of compact geodesic spaces X_i converges to a compact geodesic space X, under minimal assumptions there are surjective morphisms $\pi_1(X_i) \to \pi_1(X)$ for i large enough. In particular, a limit of simply connected spaces is simply connected. This is clearly not true for
From playlist Vietoris-Rips Seminar
MAST30026 Lecture 13: Metrics on function spaces (Part 2)
I discussed pointwise and uniform convergence of functions, proved that the uniform limit of continuous functions is continuous, and used that to prove that Cts(X,Y) is a complete metric space with respect to the sup metric if X is compact and Y is a complete metric space. Lecture notes:
From playlist MAST30026 Metric and Hilbert spaces
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Math 131 102416 Cauchy Sequences, Completeness of Real Numbers
Subsequences: definition; sequence in a compact metric space has a convergence subsequence. Cauchy sequences: definition, diameter of a set, facts about diameter (diameter of closure is the same, intersection of nest compact sets of diameters decreasing to zero is a single point); converg
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Introduction to Absolute Convergence and Conditional Convergence
Introduction to Absolute Convergence and Conditional Convergence If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Larson Calculus 9.5 Alternating Series
Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators
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=PBMyBVPRtKA&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021