Arithmetic functions | Lattice points | Unsolved problems in mathematics
In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function. The various studies of the behaviour of the divisor function are sometimes called divisor problems. (Wikipedia).
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
906,150,257 and the Pólya conjecture (MegaFavNumbers)
#MegaFavNumbers "Most numbers have an odd number of prime factors!" ...or do they...? Ben chats about the large counterexample to Polya's conjecture, for Matt Parker and James Grime's MegaFavNumbers project. Ben is @SparksMaths on twitter and at http://www.bensparks.co.uk on the web
From playlist MegaFavNumbers
Why does the distributive property Where does it come from
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
What are the Inverse Trigonometric functions and what do they mean?
👉 Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-
From playlist Evaluate Inverse Trigonometric Functions
How to Simplify an Expression Using Distributive Property - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Half-Isolated Zeros and Zero-Density Estimates - Kyle Pratt
50 Years of Number Theory and Random Matrix Theory Conference Topic: Half-Isolated Zeros and Zero-Density Estimates Speaker: Kyle Pratt Affiliation: University of Oxford Date: June 23, 2022 We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros
From playlist Mathematics
How do we multiply polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Find the value of the trigonometric expression using inverse
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Thomas Stoll: On generalised Rudin-Shapiro sequences
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 26, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Elliptic Curves - Lecture 6b - Divisors and differentials
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
Schemes 35: Divisors on a Riemann surface
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we discuss the divisors on Riemann surfaces of genus 0 or 1, and show how the classical theory of elliptic functions determines the divisor cla
From playlist Algebraic geometry II: Schemes
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 6 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Schemes 36: Weil and Cartier divisors
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define Weil and Cartier divisors and divisor classes, and give some simple examples of the groups of divisor classes.
From playlist Algebraic geometry II: Schemes
Elliptic Curves - Lecture 7 - Riemann-Roch, Hurwitz, and Weierstrass 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
Elliptic Curves - Lecture 9b - The (Picard) group law
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
Weil conjectures 2: Functional equation
This is the second lecture about the Weil conjectures. We show that the Riemann-Roch theorem implies the rationality and functional equation of the zeta function of a curve over a finite field.
From playlist Algebraic geometry: extra topics
Introduction to the Distributive Property
This video explains the distributive property and provides examples on how to use the distributive property. http://mathispower4u.yolasite.com/
From playlist The Distributive Property and Simplifying Algebraic Expressions