Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Right hand riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Convolutions and Polynomial Approximation
In this video, I intuitively explain and apply some deeper mathematical tools - namely convolutions and approximate identities - to prove the Weierstrass approximation theorem, which roughly states that any continuous function can be approximated by polynomials. I also make connections to
From playlist Summer of Math Exposition Youtube Videos
Midpoint riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Learn how to find the position function given the velocity and acceleration, parti
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Axioms for the Lefschetz number as a lattice valuation
"Axioms for the Lefschetz number as a lattice valuation" a research talk I gave at the conference on Nielsen Theory and Related Topics in Daejeon Korea, June 28, 2013. Chris Staecker's internet webarea: http://faculty.fairfield.edu/cstaecker/ Nielsen conference webarea: http://open.nims.r
From playlist Research & conference talks
Johnathan Bush (11/5/21): Maps of Čech and Vietoris–Rips complexes into euclidean spaces
We say a continuous injective map from a topological space to k-dimensional euclidean space is simplex-preserving if the image of each set of at most k+1 distinct points is affinely independent. We will describe how simplex-preserving maps can be useful in the study of Čech and Vietoris–Ri
From playlist Vietoris-Rips Seminar
How to use right hand riemann sum give a table
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Paul Bendich (5/12/21): Data Complexes, Obstructions, Persistent Data Merging
Title: Data Complexes, Obstructions, Persistent Data Merging Abstract: Data complexes provide a mathematical foundation for semi-automated data-alignment tools that are common in commercial database software. We develop theory that shows that database JOIN operations are subject to genuin
From playlist AATRN 2021
Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Maurice Herlihy: Distributed Computing through Combinatorial Topology
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology Models and techniques borrowed from classical combinatorial algebraic topology have yielded a variety of new lower bounds and impossibility results for distributed a
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
How to use left hand riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Computing Homology Cycles with Certified Geometry - Tamal Dey
Computing Homology Cycles with Certified Geometry Tamal Dey Ohio State University March 7, 2012
From playlist Members Seminar
Towards a Nielsen theory in digital topology
A talk given by Chris Staecker at King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on October 14 2019. This is the third in a series of 3 talks given at KMUTT. This talk presents some preliminary ideas that I hope will develop into a real Nielsen fixed point theory for
From playlist Research & conference talks
Stability, Non-approximate Groups and High Dimensional Expanders by Alex Lubotzky
Webpage for this talk: https://sites.google.com/view/distinguishedlectureseries/alex-lubotzky A live interactive session with the speaker will be hosted online on January 27, 2021, at 18:00 Indian Standard Time. Viewers can send in their questions for the speaker in advance of the live in
From playlist ICTS Colloquia
Higgs bundles, harmonic maps, and applications by Richard Wentworth
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Linear Approximations and Differentials
Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my
From playlist Partial Derivatives
Fedor Manin (3/19/22): Linear nullhomotopies of maps to spheres
I will explain some aspects of how to build (null)homotopies of maps to simply connected spaces with controlled Lipschitz constant. Most of the difficulties appear already in the case of maps between spheres, where the result is as follows: every nullhomotopic, $L$-Lipschitz map $S^m \to
From playlist Vietoris-Rips Seminar