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Chapter 2: Matrices
Chapter 2: Matrices

Effective descent morphisms for Banach modules
Effective descent morphisms for Banach modules

Diophantine Equations CMT: 2011-2012
Diophantine Equations CMT: 2011-2012

Algebra 2 - Adventist Education
Algebra 2 - Adventist Education

Morita equivalence for regular algebras
Morita equivalence for regular algebras

A finite equational base for CCS with left merge and communication merge
A finite equational base for CCS with left merge and communication merge

... that proves that they should not be equated. (We refer to the survey [Aceto et al. 2005b] for a discussion of proof techniques and for an overview of results and open problems in the area. We remark in passing that one of our main results in this paper, viz. Corollary 4.10, solves the open problem m ...
CCSS Numbers and Operations Fractions 3-5
CCSS Numbers and Operations Fractions 3-5

MAP to Khan Academy:
MAP to Khan Academy:

strongly complete logics for coalgebras
strongly complete logics for coalgebras

The symplectic Verlinde algebras and string K e
The symplectic Verlinde algebras and string K e

... so (10) has positive valuation if and only if ζ2m i valuation if and only if  = p for some i. Indeed, sufficiency follows from the fact that ((x + i i−1 1)p − 1)/((x + 1)p − 1) is an Eisenstein polynomial with root ζpi − 1. To see necessity, if ζ − 1 has positive valuation, so does ζ p − 1, so it suffi ...
Lie algebra cohomology and Macdonald`s conjectures
Lie algebra cohomology and Macdonald`s conjectures

Algebraic and Transcendental Numbers
Algebraic and Transcendental Numbers

6.4/6.6 Worksheet #1 Name: Geometry Hour: _____ Definition: A
6.4/6.6 Worksheet #1 Name: Geometry Hour: _____ Definition: A

STRONGLY ZERO-PRODUCT PRESERVING MAPS ON
STRONGLY ZERO-PRODUCT PRESERVING MAPS ON

STRONGLY ZERO-PRODUCT PRESERVING MAPS ON NORMED
STRONGLY ZERO-PRODUCT PRESERVING MAPS ON NORMED

Constructing elliptic curves over finite fields with prescribed torsion
Constructing elliptic curves over finite fields with prescribed torsion

CHAPTER X THE SPECTRAL THEOREM OF GELFAND
CHAPTER X THE SPECTRAL THEOREM OF GELFAND

20. Cyclotomic III - Math-UMN
20. Cyclotomic III - Math-UMN

THE CONGRUENT NUMBER PROBLEM 1. Introduction
THE CONGRUENT NUMBER PROBLEM 1. Introduction

... Example 3.4. Since Fermat showed 1 and 2 are not congruent numbers, there is no arithmetic progression of 3 rational squares with common difference 1 or 2 (or, more generally, common difference a nonzero square or twice a nonzero square). We now can explain the origin of the peculiar name “congruent ...
3-3 Solving Inequalities by Multiplying or Dividing
3-3 Solving Inequalities by Multiplying or Dividing

a.6 linear inequalities in one variable
a.6 linear inequalities in one variable

Conf
Conf

trig identities
trig identities

dissertationes mathematicae universitatis tartuensis 53
dissertationes mathematicae universitatis tartuensis 53

On the representation of operators in bases of compactly supported
On the representation of operators in bases of compactly supported

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History of algebra

As a branch of mathematics, algebra emerged at the end of 16th century in Europe, with the work of François Viète. Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.This article describes the history of the theory of equations, called here ""algebra"", from the origins to the emergence of algebra as a separate area of mathematics.
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