Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorization
From playlist Abstract Algebra
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
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
Landau-Ginzburg - Seminar 2 - Introduction
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this second seminar Dan Murfet explains how to compose permutations from a geometric perspective. The webpage for this seminar is https://metauni.org/lg/. Yo
From playlist Landau-Ginzburg seminar
15 - Algorithmic aspects of the Galois theory in recent times
Orateur(s) : M. Singer Public : Tous Date : vendredi 28 octobre Lieu : Institut Henri Poincaré
From playlist Colloque Evariste Galois
Ex: Definite Integral Involving a Basic Rational Function
This video provides an example of how to evaluate a definite integral involving a basic rational function. We find the area under the function on the closed interval. Site: http://mathispower4u.com
From playlist Definite Integrals and The Fundamental Theorem of Calculus
Some remarks on Landau--Siegel zeros - Alexandru Zaharescu
Joint IAS/Princeton University Number Theory Seminar Some remarks on Landau--Siegel zeros Alexandru Zaharescu University of Illinois at Urbana–Champaign Date: March 11, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
What is the max and min of a horizontal line on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Prime Numbers and their Mysterious Distribution (Prime Number Theorem)
Primes are the building blocks of math. But just how mysterious are they? Our study of prime numbers dates back to the ancient Greeks who first recognized that certain numbers can't be turned into rectangles, or that they can't be factored into any way. Over the years prime numbers have
From playlist Prime Numbers
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
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
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
AN ELEMENTARY PROOF OF BERTRAND'S POSTULATE! Special #SoMe1
I love when a deep result in mathematics is provable only with elementary techniques, like basic knowledge of combinatorics and arithmetic. In this video I will present the queen of this proofs, namely the Erdős' proof of the Bertrand's postulate, which states that it is always possible to
From playlist Summer of Math Exposition Youtube Videos
Landau-Ginzburg - Seminar 13 - Systems of t derivatives
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Rohan Hitchcock takes the work on division in the previous seminar and uses it to define a "system of t-derivatives" for a quasi-regular sequence
From playlist Metauni
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
Landau-Ginzburg - Seminar 6 - Matrix factorisations and geometry
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Rohan Hitchcock defines matrix factorisations and gives some examples, and explains how to extract an algebraic set from a matrix factorisation.
From playlist Metauni
Mod-01 Lec-29 Ginsburg - Landau Theory, Flux Quantization
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
Can p-adic integrals be computed? - William Duke
Automorphic Forms William Duke Thomas Hales April 6, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-automorphicforms Confere
From playlist Mathematics
2. Lec 1 (continued); The Landau-Ginzburg Approach Part 1
MIT 8.334 Statistical Mechanics II: Statistical Physics of Fields, Spring 2014 View the complete course: http://ocw.mit.edu/8-334S14 Instructor: Mehran Kardar In this lecture, Prof. Kardar continues his discussion of the principles of collective behavior from particles to fields, and intr
From playlist MIT 8.334 Statistical Mechanics II, Spring 2014
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics