Prove that there is a prime number between n and n!
A simple number theory proof problem regarding prime number distribution: Prove that there is a prime number between n and n! Please Like, Share and Subscribe!
From playlist Elementary Number Theory
Discover how to calculate the limit of n!/n^n as n approaches infinity. This is Chapter 4 Problem 12 from the MATH1231/1241 Calculus notes. Presented by Dr John Steele from the UNSW School of Mathematics and Statistics.
From playlist Mathematics 1B (Calculus)
An Infinite Product Conjecture - Monday Math Nugget #2
Today we're answering a question posed in the comment section of the previous MMN... The conjecture is: since any quotient of finite products of integers cannot be an integer if all factors in the numerator are odd and at least one in the denominator is even, then a quotient of infinite
From playlist Monday Math Nuggets
Induction Inequality Proofs (2 of 4: Considering one side of the inequality)
More resources available at www.misterwootube.com
From playlist Further Proof by Mathematical Induction
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
Finding the sum or an arithmetic series using summation notation
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is
From playlist Series
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
How to determine the infinite sum of a geometric series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Using mathematical induction to prove a formula
👉 Learn how to apply induction to prove the sum formula for every term. Proof by induction is a mathematical proof technique. It is usually used to prove that a formula written in terms of n holds true for all natural numbers: 1, 2, 3, . . . To prove by induction, we first show that the f
From playlist Sequences
Dependent random choice - Jacob Fox
Marston Morse Lectures Topic: Dependent random choice Speaker: Jacob Fox, Stanford University Date: October 26, 2016 For more videos, visit http://video.ias.edu
From playlist Mathematics
Members’ Colloquium Topic: Thresholds Speaker: Jinyoung Park Affiliation: Stanford University Date: May 16, 2022 Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for
From playlist Mathematics
Eric Riedl: A Grassmannian technique and the Kobayashi Conjecture
Abstract: An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces X in â„™n: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie
From playlist Algebraic and Complex Geometry
A problem in Elementary Geometry - Michael Atiyah [2011]
Name: Michael Atiyah Event: SCGP Weekly Talk Title: A problem in Elementary Euclidean Geometry Date: 2011-10-25 @1:00 PM Location: 103 Abstract: Over a decade ago I stumbled across a new and apparently very elementary problem in Euclidean Geometry involving n distinct points in 3-space. E
From playlist Mathematics
The Generalized Ramanujan Conjectures and Applications - Lecture 1 by Peter Sarnak
Lecture 1: The Generalized Ramanujan Conjectures Abstract: One of the central problems in the modern theory of automorphic forms is the Generalized Ramanujan Conjecture.We review the development and formulation of these conjectures as well as recent progress. While the general Conjecture
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
János Pintz: Polignac numbers and the consecutive gaps between primes
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
Stanley-Wilf limits are typically exponential - Jacob Fox
Jacob Fox Massachusetts Institute of Technology October 7, 2013 For a permutation p, let Sn(p) be the number of permutations on n letters avoiding p. Stanley and Wilf conjectured that, for each permutation p, Sn(p)1/n tends to a finite limit L(p). Marcus and Tardos proved the Stanley-Wilf
From playlist Mathematics
Gromov–Witten Invariants and the Virasoro Conjecture (Remote Talk) by Ezra Getzler
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
The Structure of Selmer Groups of Elliptic Curves by Chan-Ho Kim
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Zagier's conjecture on zeta(F,4) - Alexander Goncharov
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Zagier's conjecture on zeta(F,4) Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics Date: November 10, 2017 For more videos, please visit http://video.ias.
From playlist Mathematics
Learn how to use mathematical induction to prove a formula
👉 Learn how to apply induction to prove the sum formula for every term. Proof by induction is a mathematical proof technique. It is usually used to prove that a formula written in terms of n holds true for all natural numbers: 1, 2, 3, . . . To prove by induction, we first show that the f
From playlist Sequences