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. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation). The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating-point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is commonly preferred as an adjective to number-theoretic. (Wikipedia).
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
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
Theory of numbers:Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This is the introductory lecture, which gives an informal survey of some of the topics to be covered in the course, such as Diophantine equations, quadratic reciprocity, and binary quadratic forms.
From playlist Theory of numbers
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)
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Introduction to number theory lecture 27. Groups and number theory
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We show how many of the theorems of number theory are special cases of theorems of groups t
From playlist Introduction to number theory (Berkeley Math 115)
Introduction to number theory lecture 43 Gaussian integers
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give some applications of Gaussian integers to the binary quadratic form x^2+y^2. The t
From playlist Introduction to number theory (Berkeley Math 115)
A Short Course in Algebra and Number Theory - Elementary Number Theory
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fourth lectu
From playlist A Short Course in Algebra and Number Theory
Supersymmetric Gauge Dynamics, Part 3 - Nathan Seiberg
Supersymmetric Gauge Dynamics, Part 3 Nathan Seiberg Institute for Advanced Study July 30, 2010
From playlist PiTP 2010
85 Years of Nielsen Theory: Coincidence Points
Part 3 of a 3 part series of expository talks on Nielsen theory I gave at the conference on Nielsen Theory and Related Topics in Daejeon Korea, June 27, 2013. Part 1- Fixed Points: http://youtu.be/1Ls8mTkRtX0 Part 3- Coincidence Points: http://youtu.be/Wu2Cr3v_I44 Chris Staecker's intern
From playlist Research & conference talks
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic
Philosophy of Mathematics & Frege (Dummett 1994)
Michael Dummett gives a talk on Frege and the philosophy of mathematics. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE Another good introduction to the philosophy of mathematics: https://www.youtube.com/watch?v=XyXWnGFKTkg
From playlist Logic & Philosophy of Mathematics
The abstract chromatic number - Leonardo Nagami Coregliano
Computer Science/Discrete Mathematics Seminar I Topic: The abstract chromatic number Speaker: Leonardo Nagami Coregliano Affiliation: University of Chicago Date: March 22, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
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
Lecture 10 | String Theory and M-Theory
(November 30, 2010) Professor Leonard Susskind continues his discussion on T-Duality; explains the theory of D-Branes; models QFT and QCD; and introduces the application of electromagnetism. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of
From playlist Lecture Collection | String Theory and M-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
Supersymmetric Gauge Dynamics, Part 2 - Nathan Seiberg
Supersymmetric Gauge Dynamics, Part 2 Nathan Seiberg Institute for Advanced Study July 22, 2010
From playlist PiTP 2010
SQCD and Pairs of Pants by Shlomo Razamat
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Introduction to Number Theory, Part 1: Divisibility
The first video in a series about elementary number theory, following the book by Underwood Dudley. We define the basic concept of divisibility, and prove a fundamental lemma. Intro:(0:00) Definition of Divisibility:(6:40) Our First Theorem:(9:00)
From playlist Introduction to Number Theory