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Finding the Roots of Algebraic Equations

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0011
Subject:
Mathematics, History of Mathematics

This chapter highlights some of the struggles to solve fifth-degree polynomials as well as the development of the idea of a group and its application to answering the question of solvability of ... More


Understanding Polynomial Equations in n Unknowns

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0012
Subject:
Mathematics, History of Mathematics

This chapter examines the search for simultaneous solutions which eventually led to the creation of whole new algebraic constructs over the course of the eighteenth and nineteenth centuries. The ... More


Visions, Dreams, and Mathematics

Barry Mazur

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0006
Subject:
Mathematics, History of Mathematics

This chapter considers the role of visions and dreams in mathematics by focusing on Leopold Kronecker's desire—or dream—to find solutions to a large and interesting collection of polynomial ... More


Matrix equations

Leiba Rodman

in Topics in Quaternion Linear Algebra

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161853
eISBN:
9781400852741
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161853.003.0014
Subject:
Mathematics, Algebra

This chapter presents applications to polynomial matrix equations, algebraic Riccati equations, and linear quadratic regulators. Without attempting to develop in-depth exposition of the topics, this ... More


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