What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Instruments for length and area: dots, lines, and little wheels
A talk given at the Mathematics Colloquium of Fairfield University, October 27, 2022. Intended for university undergraduates, but should be mostly understandable to anybody. Should be mostly understandable by anyone, I mention some calculus from time to time. #longimeter #planimeter #dot
From playlist Research & conference talks
Functional Analysis - Part 24 - Uniform Boundedness Principle / Banach–Steinhaus Theorem
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Watch the whole series: https://bright.jp-g.de/functional-analysis/ Functional analysis series: https://www.youtube.com/playlist?list=PLBh2i93oe2qsGKDOsuVVw-OCA
From playlist Functional analysis
Jacobian chain rule and inverse function theorem
A lecture that discusses: the general chain rule for the Jacobian derivative; and the inverse function theorem. The concepts are illustrated via examples and are seen in university mathematics.
From playlist Several Variable Calculus / Vector Calculus
A dot planimeter, invented by Steinhaus and Abell (independently) in the 1920s and 1930s. This is episode 54 of my video series about old calculating devices. See the references and download & print your own dot planimeter: http://cstaecker.fairfield.edu/~cstaecker/machines/dotplanimeter
From playlist Calculating Devices Review / HowTos
Andrew Putman - The Steinberg representation is irreducible
The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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
Katie's #MegaFavNumbers - the MEGISTON, and Steinhaus-Moser notation
This video is part of the MegaFavNumbers project. Maths YouTubers have come together to make videos about their favourite numbers bigger than one million, which we are calling #MegafavNumbers. We want *you*, the viewers, to join in! Make your own video about your favourite mega-number. Yo
From playlist MegaFavNumbers
Steinhaus Longimeter Review / HowTo
The Steinhaus Longimeter, invented in the 1930s by Hugo Steinhaus. This is episode 29 of my video series about calculating devices. Download PDF of the longimeters I use here: http://cstaecker.fairfield.edu/~cstaecker/machines/longimeter.html End song inspired by "Hotter Than a Molotov
From playlist Calculating Devices Review / HowTos
Bala Krishnamoorthy (9/16/20): Steinhaus filtration and stable paths in the Mapper
Title: Steinhaus Filtration and Stable Paths in the Mapper Abstract: Two central concepts of topological data analysis are persistence and the Mapper construction. Persistence employs a sequence of objects built on data called a filtration. A Mapper produces insightful summaries of data,
From playlist AATRN 2020
Hajime Ishihara: The constructive Hahn Banach theorem, revisited
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The Hahn-Banach theorem, named after the mathematicians Hans Hahn and Stefan Banach who proved it independently in the late 1920s, is a central tool in functional analys
From playlist Workshop: "Constructive Mathematics"
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Functional Analysis Lecture 24 2014 04 24 Applications of the Baire Category Theorem
Recall result: a complete metric space is not meager. Application: the points of discontinuity of a limit of continuous functions is meager. Lemma: existence of a smaller ball on which the limit function is epsilon-approximated by one of the continuous functions. Application: nowhere
From playlist Course 9: Basic Functional and Harmonic Analysis
Here's How Massive Icebreaker Ships Plow Through Frozen Seas
Impossible Engineering | Thursdays at 9/8c These specialized ships help create paths by pushing into ice pockets. Full Episodes Streaming FREE on Science Channel GO: https://www.sciencechannelgo.com/impossible-engineering/ More of the Impossible! http://www.sciencechannel.com/tv-shows/imp
From playlist Impossible Engineering
The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously
Ham sandwiches are delicious, but they’re also pretty useful when it comes to understanding the universe. Is Anything Truly Random? - https://youtu.be/tClZGWlRLoE Read More: The Ham Sandwich Theorem Is a Delicious and Puzzling Mathematical Principle https://curiosity.com/topics/the-ham
From playlist Elements | Seeker
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
A central limit theorem for Gaussian polynomials...... pt2 - Anindya De
Anindya De Institute for Advanced Study; Member, School of Mathematics May 13, 2014 A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions In this talk, we will continue, the proof of the Central Limit theorem from my las
From playlist Mathematics