In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables where a, b, c are the coefficients. When the coefficients can be arbitrary complex numbers, most results are not specific to the case of two variables, so they are described in quadratic form. A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory. Since the late nineteenth century, binary quadratic forms have given up their preeminence in algebraic number theory to quadratic and more general number fields, but advances specific to binary quadratic forms still occur on occasion. Pierre Fermat stated that if p is an odd prime then the equation has a solution iff , and he made similar statement about the equations , , and . and so on are quadratic forms, and the theory of quadratic forms gives a unified way of looking at and proving these theorems. Another instance of quadratic forms is Pell's equation . Binary quadratic forms are closely related to ideals in quadratic fields, this allows the class number of a quadratic field to be calculated by counting the number of reduced binary quadratic forms of a given discriminant. The classical theta function of 2 variables is , if is a positive definite quadratic form then is a theta function. (Wikipedia).
Understanding the discriminant as a part of the quadratic formula
👉 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 38. Binary quadratic forms
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 start the discussion of binary quadratic forms, define the discriminant, and give a cond
From playlist Introduction to number theory (Berkeley Math 115)
The discriminant and finding the solutions using quadratic formula
👉 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
Vector form of multivariable quadratic approximation
This is the more general form of a quadratic approximation for a scalar-valued multivariable function. It is analogous to a quadratic Taylor polynomial in the single-variable world.
From playlist Multivariable calculus
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
Solve a quadratic equation using the quadratic formula when their are imaginary solutions
👉 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
CTNT 2018 - "Arithmetic Statistics" (Lecture 2) by Álvaro Lozano-Robledo
This is lecture 2 of a mini-course on "Arithmetic Statistics", taught by Álvaro 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 Álvaro Lozano-Robledo
Learn to find the solutions of a quadratic by applying the quadratic formula
👉 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
Counting GL2(ℤ)GL2(Z) orbits on binary quartic forms and applications - Arul Shankar
Arul Shankar Princeton University; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
CTNT 2018 - "Arithmetic Statistics" (Lecture 3) by Álvaro Lozano-Robledo
This is lecture 3 of a mini-course on "Arithmetic Statistics", taught by Álvaro 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 Álvaro Lozano-Robledo
How to use the quadratic formula to solve a quadratic equation
👉 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
Using the quadratic formula to solve an equation
👉 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
Geometry-of-Numbers Techniques in Arithmetic Statistics (Lecture 3) by Arul Shankar
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Alex Kontorovich: Local-Global in Thin Orbits and Applications
The lecture was held within the framework of the Hausdorff Trimester Program: Harmonic Analysis and Partial Differential Equations and the Workshop: Analytic Number Theory of the Hausdorff Center for Mathematics 17.07.2014 This video was created and edited with kind support from eCampus
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
CTNT 2018 - "Computational Number Theory" (Lecture 4) by Harris Daniels
This is lecture 4 of a mini-course on "Computational Number Theory", taught by Harris Daniels, 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 - "Computational Number Theory" by Harris Daniels
Find the complex roots of an equation using the quadratic formula
👉 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 | Equation
CTNT 2020 - Elliptic curves and the local-global principle for quadratic forms - Asher Auel
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Twisted integral orbit parametrizations - Aaron Pollack
Short talks by postdoctoral members Topic: Twisted integral orbit parametrization Speaker: Aaron Pollack Affiliation: Member, School of Mathematics Date: October 4, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Solving using the quadratic formula with complex solutions
👉 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