Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers
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
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
An Amazing Connection Between the Riemann Hypothesis and Topology
https://gregoriousmaths.com/2021/08/19/a-couple-of-other-connections-between-number-theory-and-topology/ 0:00 Introduction and plan 2:32 The Riemann hypothesis 7:22 Introducing the complex we will study 19:41 Studying the asymptotic behaviour of \beta_k(\Delta_n) 22:54 Some number theoret
From playlist Summer of Math Exposition Youtube Videos
Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
Calculus - Application of Differentiation (10 of 60) Fermat's Theorem Explained
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Fermat's Theorem.
From playlist CALCULUS 1 CH x APPLICATIONS OF DIFFERENTIATION
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)
A Prime Surprise (Mertens Conjecture) - Numberphile
Dr Holly Krieger discusses Merterns' Conjecture. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Holly (playlist): http://bit.ly/HollyKrieger Dr Holly Krieger is the C
From playlist Women in Mathematics - Numberphile
Risk Management Lesson 8A: Industrial Models for Credit Risk
In this first part of Lesson 8, we deal with two important credit risk models developed by the industry. Topics: - Moody's KMV - CreditMetrics (J.P. Morgan & Co.)
From playlist Risk Management
Fin Math L5-2: A simple exchange rate model
In this second part of Lesson 5, we consider a simple exchange rate model, which allows us to see the Cameron-Martin theorem in action. The model also introduces a particular version of the exponential martingale that will be essential for us later. I ask you to spend some time reasoning a
From playlist Financial Mathematics
Counting GL2(ℤ)GL2(Z) orbits on binary quartic forms and applications - Arul Shankar
Arul Shankar Princeton University; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Math 131 Spring 2022 042722 Properties of Analytic Functions, continued
Recall: analytic functions are infinitely (term-by-term) differentiable. Relation of coefficients and values of derivatives. Remark: analytic functions completely determined by values on an arbitrarily small interval. Analytic functions: convergence at an endpoint implies continuity the
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Fin Math L5-3: Towards Black-Scholes-Merton
Welcome to the last part of Lesson 5. In this video we cover some last relevant topics to finally deal with the Black-Scholes-Merton theorem, which will be the starting point of all our pricing exercises. Here you can download the new chapter of the lecture notes: https://www.dropbox.com/s
From playlist Financial Mathematics
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 4
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)
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
The Selberg sieve (Lecture 1) by Stephan Baier
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020