Algebraic number theory

Number theory Full Course [A to Z]

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio

From playlist Number Theory

Algebraic number theory and rings I | Math History | NJ Wildberger

In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include

From playlist MathHistory: A course in the History of Mathematics

Algebraic number theory and rings II | Math History | NJ Wildberger

In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include

From playlist MathHistory: A course in the History of Mathematics

Intro to Number Theory and The Divisibility Relation

This video introduces the divisibility relation and provided several examples. mathispower4u.com

From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

FIT2.3.1. Algebraic Numbers

Field Theory: We consider the property of algebraic in terms of finite degree, and we define algebraic numbers as those complex numbers that are algebraic over the rationals. Then we give an overview of algebraic numbers with examples.

From playlist Abstract Algebra

Theory of numbers: Multiplicative functions

This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.

From playlist Theory of numbers

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

Math Major Guide | Warning: Nonstandard advice.

A guide for how to navigate the math major and how to learn the main subjects. Recommendations for courses and books. Comment below to tell me what you think. And check out my channel for conversation videos with guests on math and other topics: https://www.youtube.com/channel/UCYLOc-m8Wu

From playlist Math

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

SHM - 16/01/15 - Constructivismes en mathématiques - Frédéric Brechenmacher

Frédéric Brechenmacher (LinX, École polytechnique), « Effectivité et généralité dans la construction des grandeurs algébriques de Kronecker »

From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques

Modular theory and QFT (Lecture 1) by Nima Lashkari

Infosys-ICTS String Theory Lectures Modular theory and QFT Speaker: Nima Lashkari (Purdue University) Date: 03 February 2020 to 05 February 2020 Venue: Emmy Noether ICTS-TIFR, Bengaluru Lecture 1: Monday, 3 February 2020 at 11:30 am Lecture 2: Tuesday, 4 February 2020 at 11:30 am Le

From playlist Infosys-ICTS String Theory Lectures

Nigel Higson: Real reductive groups, K-theory and the Oka principle

The lecture was held within the framework of Follow-up Workshop TP Rigidity. 29.4.2015

From playlist HIM Lectures 2015

Balt van REES - 2/2 Chiral algebras

From playlist Summer School 2018: Supersymmetric Localization and Exact Results

An Introduction to Class-S and Tinkertoys (Lecture 2 )by Jacques Distler

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

Recent developments in non-commutative Iwasawa theory I - David Burns

David Burns March 25, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Modular theory and QFT (Lecture 2) by Nima Lashkari

Infosys-ICTS String Theory Lectures Modular theory and QFT Speaker: Nima Lashkari (Purdue University) Date: 03 February 2020 to 05 February 2020 Venue: Emmy Noether ICTS-TIFR, Bengaluru Lecture 1: Monday, 3 February 2020 at 11:30 am Lecture 2: Tuesday, 4 February 2020 at 11:30 am Le

From playlist Infosys-ICTS String Theory Lectures

Set Theory (Part 14a): Constructing the Complex Numbers

Please leave your thoughts and questions below! In this video, we will extend the real numbers to the complex numbers and investigate the algebraic structure of the complex numbers after defining addition and multiplication of these new objects. We will also begin to see how complex numbe

From playlist Set Theory by Mathoma

"New Paradigms in Invariant Theory" - Roger Howe, Yale University [2011]

HKUST Institute for Advanced Study Distinguished Lecture New Paradigms in Invariant Theory Speaker: Prof Roger Howe, Yale University Date: 13/6/2011 Video taken from: http://video.ust.hk/Watch.aspx?Video=6A41D5F6B1A790DC

From playlist Mathematics