Field (mathematics)

Stufe (algebra)

In field theory, a branch of mathematics, the Stufe (/ʃtuːfə/; German: level) s(F) of a field F is the least number of squares that sum to −1. If −1 cannot be written as a sum of squares, s(F) = . In this case, F is a formally real field. Albrecht Pfister proved that the Stufe, if finite, is always a power of 2, and that conversely every power of 2 occurs. (Wikipedia).

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Group Definition (expanded) - Abstract Algebra

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin

From playlist Abstract Algebra

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Giorgi Ottaviani: Effective aspects of the geometry of tensors - Lecture 1

HYBRID EVENT Recorded during the meeting "French Computer Algebra Days​" the February 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiov

From playlist Algebraic and Complex Geometry

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Algebra for Beginners | Basics of Algebra

#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten

From playlist Linear Algebra

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Abstract Algebra: The definition of a Ring

Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th

From playlist Abstract Algebra

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24C3: Meine Finger gehören mir (de)

Speakers: Constanze Kurz, starbug Die nächste Stufe der biometrischen Vollerfassung Zum 1. November 2007 ging der biometrische Reisepass in die nächste Ausbaustufe. Seitdem müssen reisewillige Bürger neben dem frontalen Gesichtsbild auch noch ihre Fingerabdrücke abgeben. Wir wollen

From playlist 24C3: Full steam ahead

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Gianluca Orlando: Frustration in a spin model: chirality transitions via a variational analysis

CONFERENCE Recorded during the meeting " ​ Beyond Elasticity: Advances and Research Challenges " the May 17, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician

From playlist Analysis and its Applications

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The dissipation properties of transport noise - Franco Flandoli

Analysis Seminar Topic: The dissipation properties of transport noise Speaker: Franco Flandoli Affiliation: Scuola Normale Superiore di Pisa Date: March 15, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Ring Definition (expanded) - Abstract Algebra

A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin

From playlist Abstract Algebra

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9H The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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What is Abstract Algebra? (Modern Algebra)

Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t

From playlist Abstract Algebra

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9F The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

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The Lie-algebra of Quaternion algebras and their Lie-subalgebras

In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st

From playlist Algebra

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Algebra - Ch. 4: Exponents & Scientific Notation (1 of 35) What is an Exponent?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an exponent. A number or symbol placed above another number or symbol that indicates the power the number or symbol at the bottom is raised. The number at the bottom is called the base

From playlist ALGEBRA CH 4 EXPONENTS AND SCIENTIFIC NOTATION

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FIT2.3.3. Algebraic Extensions

Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.

From playlist Abstract Algebra

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Kristin Courtney: "The abstract approach to classifying C*-algebras"

Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" Kristin Courtney - Westfälische Wilhelms-Universität Münster Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu

From playlist Actions of Tensor Categories on C*-algebras 2021

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Rahim Moosa 11/14/14

Title: Differential Varieties with Only Algebraic Images

From playlist Fall 2014

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Homeschool Algebra 2 - What Every Homeschool Parent Needs to Know

TabletClass Math Homeschool: https://tabletclass.com/ How to homeschool Algebra 2 successfully. Need help with homeschooling Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus? Check out TabletClass Math for all your homeschooling needs: https://tabletclass.com/ .

From playlist Homeschool Math

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Units in a Ring (Abstract Algebra)

The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar

From playlist Abstract Algebra

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Homeschool Geometry Before Algebra 2

TabletClass Math: https://tabletclass.com/ This video explains why you should homeschool geometry before algebra 2.

From playlist Homeschool Math

Related pages

Quadratically closed field | Algebraic number field | Disjoint sets | Witt group | Pfister form | Subgroup | Field theory (mathematics) | Characteristic (algebra) | Finite field | Mathematics | Field (mathematics) | Local field | Natural number | Pythagoras number | Cyclic group | Formally real field | Index of a subgroup