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
Arithmetic statistics over number fields and function fields - Alexei Entin
Alexei Entin Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
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
Calculus 5.2c - Infinitesimals - Archimedes
Infinitesimals, what they are, and their early use by Archimedes. The Archimedes Palimpsest.
From playlist Calculus Chapter 5 (selected videos)
Math 131 Lecture #04 091216 Complex Numbers, Countable and Uncountable Sets
Recall the complex numbers: the plane with addition and multiplication. Geometric interpretation of operations. Same thing as a+bi. Complex conjugate. Absolute value (modulus) of a complex numbers; properties (esp., triangle inequality). Cauchy-Schwarz inequality. Recall Euclidean sp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Complex surfaces 4: Ruled surfaces
This talk gives an informal survey of ruled surfaces and their role in the Enriques classification. We give a few examples of ruled surfaces, summarize the basic invariants of surfaces, and sketch how one classifies the surfaces of Kodaira dimension minus infinity.
From playlist Algebraic geometry: extra topics
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
This talk is the first of two talks that give a proof of the Riemann Roch theorem, in the spacial case of nonsingular complex plane curves. We divide the Riemann-Roch theorem into 3 pieces: Riemann's theorem, a topological theorem identifying the three definitions of the genus, and Roch'
From playlist Algebraic geometry: extra topics
Ramanujan Conjecture and the Density Hypothesis - Shai Evra
Joint IAS/Princeton University Number Theory Seminar Topic: Ramanujan Conjecture and the Density Hypothesis Speaker: Shai Evra Affiliation: Princeton University Date: November 19, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Robert Kucharczyk: The geometry and arithmetic of triangular modular curves
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: In this talk I will take a closer look at triangle groups acting on the upper half plane. Except for finitely many special cases, which are hig
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"
Low degree points on curves. - Vogt - Workshop 2 - CEB T2 2019
Isabel Vogt (MIT) / 27.06.2019 Low degree points on curves. In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris–S
From playlist 2019 - T2 - Reinventing rational points
Towards Strong Minimality and the Fuchsian Triangle Groups - J. Nagloo - Workshop 3 - CEB T1 2018
Joel Nagloo (City University of New York) / 29.03.2018 Towards Strong Minimality and the Fuchsian Triangle Groups From the work of Freitag and Scanlon, we have that the ODEs satisfied by the Hauptmoduls of arithmetic subgroups of SL2(Z) are strongly minimal and geometrically trivial. A c
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Elliptic Curves - Lecture 1 - Introduction to diophantine equations
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Tomoyoshi Ibukiyama: Survey on quaternion hermitian lattices and its application to supersingular...
CIRM HYBRID EVENT The theme of the survey is how arithmetic theory of quatenion hermitian lattices can be applied to the theory of supersingular abelian varieties. Here the following geometric objects will be explained by arithmetics. Principal polarizations of superspecial abelian varieti
From playlist Number Theory
Rational and Irrational Numbers - N2
A review of the difference between rational and irrational numbers and decimals - including square rootes and fraction approximations of pi.
From playlist Arithmetic and Pre-Algebra: Number Sense and Properties
