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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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