## Fundamental Theorem of Algebra

Overview page. Subjects: Mathematics.

The following important theorem in mathematics, concerned with the roots of polynomial equations:

Theorem

Every polynomial equation

*a*
_{null...}

## The Fundamental Theorem of Linear Algebra

in** Spatiotemporal Data Analysis**

December 2011; p ublished online October 2017 .

Chapter. Subjects: Social Impact of Environmental Issues (Social Science). 1119 words.

This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices,...

## Fundamental Theorem of Algebra

Overview page. Subjects: Mathematics.

The following important theorem in mathematics, concerned with the roots of polynomial equations:

Theorem

Every polynomial equation

*a*
_{null...}

## Fundamental Theorem of Algebra

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 138 words.

The following important theorem in mathematics, concerned with the roots of polynomial equations:

Theorem

Every polynomial equation

anz

## Algebra, Fundamental Theorem of

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 9 words.

## Algebra, Fundamental Theorem of

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 9 words.

## Fundamental Theorem of Algebra

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 78 words.

The following important theorem in mathematics, concerned with the roots of polynomial equations:

Every polynomial equation where the *a*
_{
i...
}null...

## From Analytic Geometry to the Fundamental Theorem of Algebra

in** Taming the Unknown**

July 2014; p ublished online October 2017 .

Chapter. Subjects: History of Mathematics. 14387 words.

This chapter follows up on the mathematical advances made during the sixteenth century, especially in the work of François Viète as he aspired to transform his algebra to realize his aim to...

## Nominal Algebra and the HSP Theorem

in** Journal of Logic and Computation**

April 2009; p ublished online October 2008 .

Journal Article. Subjects: Computing; Logic. 0 words.

Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work, it has been shown how nominal algebra can be used to specify and...

## Gauss, Karl Friedrich (1777–1855)

in** A Dictionary of Physics**

March 2019; p ublished online March 2019 .

Reference Entry. Subjects: Physics. 110 words.

who became director of Göttingen Observatory in 1806. One of the greatest mathematicians of all time, he contributed to the theory of numbers and proved the fundamental theorem of algebra....

## Abstract Crystals for Quantum Generalized Kac-Moody Algebras

in** International Mathematics Research Notices**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

In this article, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem...

## The Dehn-Nielsen-Baer Theorem

in** A Primer on Mapping Class Groups (PMS-49)**

October 2011; p ublished online October 2017 .

Chapter. Subjects: Geometry. 8920 words.

This chapter deals with the Dehn–Nielsen–Baer theorem, one of the most beautiful connections between topology and algebra in the mapping class group. It begins by defining the objects in...

## Quasi-isometries

in** Office Hours with a Geometric Group Theorist**

July 2017; p ublished online May 2018 .

Chapter. Subjects: Geometry. 11599 words.

This chapter considers the notion of quasi-isometry, also known as “coarse isometry.” A whole suite of important algebraic and geometric properties is preserved by quasi-isometries....

## Numbers and algebra

in** Algebra**

October 2015; p ublished online October 2015 .

Chapter. Subjects: Algebra. 3539 words.

‘Numbers and algebra’ introduces the number system and explains several terms used in algebra, including natural numbers, positive and negative integers, rational numbers, number...

##
Euclid's *Elements* 9. 14 and the Fundamental Theorem of Arithmetic

in** Science and Mathematics in Ancient Greek Culture**

September 2002; p ublished online February 2010 .

Chapter. Subjects: Classical History. 5745 words.

This chapter clarifies some unfamiliar concepts of Euclidean number theory and examines the bricks, constituents, and formative elements of numbers. It also considers three famous...

## Tensor Products, Characters, and Blocks of Finite-Dimensional Representations of Quantum Affine Algebras at Roots of Unity

in** International Mathematics Research Notices**

January 2011; p ublished online November 2011 .

Journal Article. Subjects: Mathematics. 14259 words.

We establish several results concerning tensor products, *q*-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the...

## Twisted Homology Cobordism Invariants of Knots in Aspherical Manifolds

in** International Mathematics Research Notices**

January 2012; p ublished online August 2011 .

Journal Article. Subjects: Mathematics. 9093 words.

We study concordance of homotopically essential, null-homologous knots in three-manifolds *M* with poly-torsion-free-abelian fundamental group. We fix a knot *J* and, using *L*
^{2}-sign...

## States on Bold Algebras: Categorical Aspects

in** Journal of Logic and Computation**

June 2011; p ublished online March 2009 .

Journal Article. Subjects: Computing; Logic. 0 words.

We study bold algebras and states on bold algebras in the context of transition from classical probability theory to fuzzy probability theory. Our aim is to point out the role of bold...

## Symmetries & Lagrangian-Hamilton-Jacobi Theory

in** Lagrangian and Hamiltonian Dynamics**

June 2018; p ublished online August 2018 .

Chapter. Subjects: Mathematical and Statistical Physics. 6949 words.

This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s...

## On the Fundamental Group of a Variety with Quotient Singularities

in** International Mathematics Research Notices**

January 2015; p ublished online December 2013 .

Journal Article. Subjects: Mathematics. 7386 words.

Let *k* be a field, and let [math] be a proper birational morphism of irreducible *k*-varieties, where [math] is smooth and *X* has at worst quotient singularities. When the characteristic of *k* i...

## Sans Symbols

in** Enlightening Symbols**

December 2016; p ublished online January 2018 .

Chapter. Subjects: History of Mathematics. 2438 words.

This chapter discusses the importance of symbols to the development of mathematics. It begins by analyzing the oldest surviving copy of Euclid's *Elements*, MS D'Orville 301, which shows how...