Theorems in algebraic number theory
In mathematics, in the field of algebraic number theory, a Bauerian extension is a field extension of an algebraic number field which is characterized by the prime ideals with inertial degree one in the extension. For a finite degree extension L/K of an algebraic number field K we define P(L/K) to be the set of primes p of K which have a factor P with inertial degree one (that is, the residue field of P has the same order as the residue field of p). Bauer's theorem states that if M/K is a finite degree Galois extension, then P(M/K) ⊇ P(L/K) if and only if M ⊆ L. In particular, finite degree Galois extensions N of K are characterised by set of prime ideals which split completely in N. An extension F/K is Bauerian if it obeys Bauer's theorem: that is, for every finite extension L of K, we have P(F/K) ⊇ P(L/K) if and only if L contains a subfield K-isomorphic to F. All field extensions of degree at most 4 over Q are Bauerian.An example of a non-Bauerian extension is the Galois extension of Q by the roots of 2x5 − 32x + 1, which has Galois group S5. (Wikipedia).
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erkläre ich kurz das Riemann-Integral mit Ober- und Untersumme. Die Definition ist übliche, die im 1. Semester eingeführt w
From playlist Analysis
How to apply u substitution to radicals
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
Learn how to use u substitution to integrate a polynomial
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
How to apply u substitution to a rational function
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
Learn how to find the antiderivative of a polynomial
👉 Learn how to find the antiderivative (integral) of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integr
From playlist The Integral
Das Integral 1/(x^4+2x^2cosh(2a)+1)
Englische Version: https://youtu.be/i2oLozX7-S4 Erstes Integral: https://www.youtube.com/watch?v=lKhNviR-BF0 Heute werden wir ein Integral besprechen, welches dem ersten Integral auf meinem Kanal sehr ähnlich ist. Hierzu benutzen wir unter Anderem Partialbruchzerlegung und Faktorisierung.
From playlist Integrale
How to find the antiderivative of a quadratic polynomial
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
When do fractional differential equations have solutions that extend?
When do fractional differential solutions have solutions that extend? New research to appear in Journal of Classical Analysis! http://files.ele-math.com/articles/jca-05-11.pdf doi:10.7153/jca-05-11 This note discusses the question: When do nonlinear fractional differential equations of a
From playlist Mathematical analysis and applications
Alessandro Desantis - Extensions Are Dead, Long Live Extensions! | SolidusConf 2019
Alessandro Desantis takes us through the future of extensions on Solidus. "Extensions Are Dead, Long Live Extensions!" What is the true place of extensions in the Solidus ecosystem and what does their future look like? In this talk, I will walk you through the challenges Solidus extension
From playlist SolidusConf 2019
Terraforming Jupyter: Changing JupyterLab to suit your needs
Terraforming Jupyter: Changing JupyterLab to suit your needs Stephanie Stattel (Bloomberg LP), Paul Ivanov (Bloomberg LP) As the next-generation user interface for Project Jupyter, JupyterLab is at its core an extensible environment. JupyterLab extensions can be created to modify themes,
From playlist JupyterCon in New York 2018
Evolving Chrome Extensions with Manifest V3 - Simeon Vincent - JSConf US 2019
Browser extensions are a defining feature of the web experience, but they're far from perfect. The Chrome team is planning to make a number of changes to improve privacy, security, and performance. In this session we’ll dive into some of the biggest issues with the current platform, where
From playlist JSConf US 2019
Galois theory: Infinite Galois extensions
This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We
From playlist Galois theory
Iwasawa invariants for elliptic curves in a family by Sujatha Ramdorai
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)
OHM 2013: The quest for the client-side elixir against zombie browsers
For more information visit: http://bit.ly/OHM13_web To download the video visit: http://bit.ly/OHM13_down Playlist OHM 2013: http://bit.ly/OHM13_pl Speaker: Zoltan Balazs Hacking client side protection systems (sandboxes, internet security suites, financial endpoint protection systems) w
From playlist OHM 2013
OWASP AppSec EU 2013: I'm in ur browser, pwning your stuff
For more information and to download the video visit: http://bit.ly/appseceu13 Playlist OWASP AppSec EU 2013: http://bit.ly/plappseceu13 Speaker: Krzysztof Kotowicz Browser extensions can let you easily make notes, entertain you with a game, or take an annotated screenshot of the website
From playlist OWASP AppSec EU 2013
Galois theory: Separable extensions
This lecture is part of an online graduate course on Galois theory. We define separable algebraic extensions, and give some examples of separable and non-separable extensions. At the end we briefly discuss purely inseparable extensions.
From playlist Galois theory
CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 1
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 - Infinite Galois Theory (by Keith Conrad)
Learn how to find the general solution to an antiderivative of cosine
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral