Analytic number theory

Transcendental number theory

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways. (Wikipedia).

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Transcendental numbers powered by Cantor's infinities

In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track

From playlist Recent videos

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5 Transcendental Functions

In this chapter I look at the limits of transcendental functions. It includes an explanation of the squeeze or sandwich theorem.

From playlist Life Science Math: Limits in calculus

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"Transcendental Number Theory: Recent Results and Open Problem​s" by Prof. Michel Waldschmidt​

This lecture will be devoted to a survey of transcendental number theory, including some history, the state of the art and some of the main conjectures.

From playlist Number Theory Research Unit at CAMS - AUB

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Galois theory: Field extensions

This lecture is part of an online course on Galois theory. We review some basic results about field extensions and algebraic numbers. We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use thi

From playlist Galois theory

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Transcendental Functions 9 Proof of the First Derivative of e to the x.mov

Proof of the first derivative of the function e to the power x.

From playlist Transcendental Functions

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Galois theory: Transcendental extensions

This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.

From playlist Galois theory

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FIT2.3.2. Cardinality and Transcendentals

Field Theory: We show that the set of algebraic numbers is countable and that any extension of a countable field F by a transcendental is countable. We then give an overview of known results on transcendental numbers.

From playlist Abstract Algebra

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Transcendental Functions 1 Introduction.mov

Transcendental Functions in Calculus.

From playlist Transcendental Functions

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Adventures in Perturbation Theory by Jake Bourjaily

PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online

From playlist Recent Developments in S-matrix Theory (Online)

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Daniel Huybrechts: Algebraic and arithmetic aspects of twistor spaces

I will recall the well-known notion of twistor spaces for K3 surfaces (and Hyperkähler manifolds) and discuss some natural questions relating to the algebraic and arithmetic geometry of their fibres. Recording during the meeting "The Geometry of Algebraic Varieties" the October 02, 2019 a

From playlist Algebraic and Complex Geometry

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Transcendental Numbers

Transcendental Numbers In this video, I define the concepts of algebraic and transcendental numbers, which have to do with roots of polynomials. In particular, I show that the number ((2^1/2 - 3)/5)^1/3, even though complicated-looking, is algebraic. Enjoy! Check out my Real Numbers Play

From playlist Real Numbers

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Sebastian Eterović, UC Berkeley

April 12, Sebastian Eterović, UC Berkeley Existential Closedness and Differential Algebra

From playlist Spring 2022 Online Kolchin seminar in Differential Algebra

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Transcendental number | Axel Thue | Class number problem | Gelfond–Schneider theorem | Set theory | Countable set | Diophantine approximation | Fundamental theorem of algebra | Zero of a function | Coefficient | Clearing denominators | Schanuel's conjecture | Almost all | Transcendence degree | Constant problem | Liouville number | Joseph Liouville | Algebraic number | Uncountable set | Polynomial | Model theory | Siegel's lemma | David Hilbert | Gelfond's constant | Auxiliary function | Rational number | Roth's theorem | Squaring the circle | Apéry's constant | Degree of a polynomial | Serge Lang | Euler's identity | Lindemann–Weierstrass theorem | Natural number | Function (mathematics) | Closed-form expression | Field (mathematics) | Integer | Real number | Algebraic function | Multiplicity (mathematics) | Kurt Mahler | Baker's theorem | Number theory | Algebraic independence | Bijection | Ferdinand von Lindemann | Gelfond–Schneider constant | Diophantine equation | Complex number | Karl Weierstrass | Charles Hermite | Irrational number | Alexander Gelfond | Klaus Roth | Cardinality | Cantor's diagonal argument | Carl Ludwig Siegel | Alan Baker (mathematician) | Champernowne constant