In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws. (Wikipedia).
Quadratic App: Find Two Numbers Given Difference and Sum of Squares (Factor)
This video explains how to set up a system of equations and and then solve a quadratic equation to solve an application problem http://mathispower4u.com
From playlist Applications of Quadratic Equations
Gaussian Integral 7 Wallis Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the
From playlist Gaussian Integral
Quadratic System 2 Algebra Regents
In this video we look at the intersection between and linear and quadratic function
From playlist Quadratic Systems
Understanding the discriminant as a part of the quadratic formula
đ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Theory of numbers: Quadratic reciprocity
This lecture is part of an online undergraduate course on the theory of numbers. We state and law of quadratic reciprocity for Legendre symbols, and prove it using Gauss sums. As applications we show how to use it to calculate Legendre symbols and to test Fermat numbers to see if they are
From playlist Theory of numbers
The discriminant and finding the solutions using quadratic formula
đ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Introduction to number theory lecture 34. Gauss sums
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 define Gauss sums and use them to give another proof of the law of quadratic reciprocity
From playlist Introduction to number theory (Berkeley Math 115)
Asymptotics of number fields - Manjul Bhargava [2011]
Asymptotics of number fields Introductory Workshop: Arithmetic Statistics January 31, 2011 - February 04, 2011 January 31, 2011 (11:40 AM PST - 12:40 PM PST) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/566
From playlist Number Theory
Gaussian Integral 6 Gamma Function
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using properties of the gamma function, which
From playlist Gaussian Integral
Mod-01 Lec-14 Convergence of Gaussian Integration
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 3
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
How to solve a quadratic using the quadratic formula
đ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
CTNT 2018 - "Arithmetic Statistics" (Lecture 2) by Ălvaro Lozano-Robledo
This is lecture 2 of a mini-course on "Arithmetic Statistics", taught by Ălvaro Lozano-Robledo, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "Arithmetic Statistics" by Ălvaro Lozano-Robledo
Number Theory | Quadratic Reciprocity
We prove the quadratic reciprocity theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Quadratic Reciprocity proof -- Number Theory 23
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From playlist Number Theory v2
Proving Quadratic Reciprocity â Number Theory 23
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From playlist Number Theory
Ian Petrow (ETH ZĂŒrich) 1/4 - Kloostermania [2017]
notes for this talk: https://www.msri.org/workshops/801/schedules/21768/documents/2985/assets/27967 Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017 February 06, 2017 (04:45 PM PST - 05:45 PM PST) Speaker(s): Ian Petrow (ETH ZĂŒrich) The Kuznetsov For
From playlist Number Theory
Mod-01 Lec-13 Gauss 2-point Rule: Error
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Factor using the quadratic formula finding real irrational roots
đ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c