In this video we introduce Fermat's little theorem and give a proof using congruences. The content of this video corresponds to Section 7.2 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Theory of numbers: Fermat's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se
From playlist Theory of numbers
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues
Fermat's Little Theorem ← Number Theory
Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven usin
From playlist Number Theory
New isoperimetric inequalities for convex bodies - Amir Yehudayoff
Computer Science/Discrete Mathematics Seminar I Topic: New isoperimetric inequalities for convex bodies Speaker: Amir Yehudayoff Affiliation: Technion - Israel Institute of Technology Date: November 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
Siddharth Vishwanath (8/3/20): Statistical invariance of Betti numbers in the thermodynamic regime
Title: Statistical invariance of Betti numbers in the thermodynamic regime Abstract: Suppose we are given a family of probability distributions indexed by a parameter set, and a point-cloud observed i.i.d. at random from a distribution belonging to this family. The asymptotic behaviour of
From playlist ATMCS/AATRN 2020
Proving Law of Cosines - Trigonometry
This video goes through a proof of the Law of Cosines. The Cartesian x-y plane is utilized to prove the Law of Cosines. To understand this proof, the viewer should be familiar with the definition of the trigonometric functions, the Pythagorean Theorem, and the Pythagorean Identity. Stude
From playlist Trigonometry (old videos)
Ziyang Gao - Number of Points on Curves: a Conjecture of Mazur
With Philipp Habegger we recently proved a height inequality, using which one can bound the number of rational points on 1-parameter families of curves in terms of the genus, the degree of the number field and the Mordell-Weil rank (but no dependence on the Faltings height). This gives an
From playlist Journée Gretchen & Barry Mazur
Guido Montúfar : Fisher information metric of the conditional probability politopes
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Grigorios Paouris - Empirical Isoperimetric Inequalities outside convexity - IPAM at UCLA
Recorded 07 February 2022. Grigorios Paouris of Texas A&M University - College Station presents Empirical Isoperimetric Inequalities outside convexity at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Several classical isoperimetric inequalities for convex s
From playlist Workshop: Calculus of Variations in Probability and Geometry
“Érika Roldán (3/11/20): Evolution of the homology and related properties of the Eden growth model”
Title: Evolution of the homology and related geometric properties of the Eden Growth Model Abstract: The Eden growth model (EGM) is a discrete stochastic model of cell or bacterial growth: in the d-dimensional cubical lattice, start with one cell at the origin; then at each time step, add
From playlist AATRN 2020
Yasu Hiraoka: Limit theorem for persistence diagrams and related topics
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
Accounting Lecture 10 - Petty Cash
From the free study guides and course manuals at www.my-accounting-tutor.com. Accounting for petty cash funds, cash over and short, and internal controls.
From playlist Accounting Lectures