Field (mathematics) | Algebraic number theory
In algebraic number theory, a quadratic field is an algebraic number field of degree two over Q, the rational numbers. Every such quadratic field is some Q(√d) where d is a (uniquely defined) square-free integer different from 0 and 1. If d > 0, the corresponding quadratic field is called a real quadratic field, and for d < 0 an imaginary quadratic field or complex quadratic field, corresponding to whether or not it is a subfield of the field of the real numbers. Quadratic fields have been studied in great depth, initially as part of the theory of binary quadratic forms. There remain some unsolved problems. The class number problem is particularly important. (Wikipedia).
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From playlist CALCULUS
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
How to analyze a quadratic function to graph
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Solving a quadratic using quadratic formula with two real 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
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
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
How do the solutions of a quadratic relate to the x intercepts of the graph
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
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
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
How to solve a quadratic 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 | ax^2+bx+c
On Class Number of Number Fields by Debopam Chakraborty
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Tobias Braun - Orthogonal Determinants
Basic concepts and notions of orthogonal representations are in- troduced. If X : G → GL(V ) is a K-representation of a nite group G it may happen that its image X(G) xes a non-degenerate quadratic form q on V . In this case X and its character χ : G → K, g 7 → trace(X(g)) are called ortho
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
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
Jacob Lurie - Tamagawa Numbers and Nonabelian Poincare Duality, I [2013]
Jacob Lurie Wednesday, August 28 3:10PM Tamagawa Numbers and Nonabelian Poincare Duality, I Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: Let q and q0 be positive definite integral quadratic forms. We say that
From playlist Number Theory
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
Markus Land - L-Theory of rings via higher categories IV
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Ana Caraiani, Modularity over CM fields
VaNTAGe Seminar, May 24, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Freitas-Le Hung-Siksek: https://arxiv.org/abs/1310.7088 Poonen-Schaefer-Stoll: https://arxiv.org/abs/math/0508174 Harris-Lan-Taylor-Thorne: https://link.springer.com/article/10.1186/s406
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
Thoughts about Andrew Ogg’s (Torsion) conjecture - Barry C. Mazur
Celebration In Honor of the Frank C. and Florence S. Ogg Professorship Topic: Thoughts about Andrew Ogg’s (Torsion) conjecture Speaker: Barry C. Mazur Affiliation: Gerhard Gade University Professor, Harvard University Date: October 13, 2022 Ogg’s celebrated conjecture can be paraphrased
From playlist Mathematics
Xevi Guitart : Endomorphism algebras of geometrically split abelian surfaces over Q
CONFERENCE Recording during the thematic meeting : "COUNT, COmputations and their Uses in Number Theory" the February 28, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematici
From playlist JEAN MORLET CHAIR
Solving 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 | x^2+bx+c