First Course in Theory of Equations by Leonard Dickson
First Course in Theory of Equations - Table of Contents
- 1. Complex Numbers and Geometry
- 2. Theorems on Roots of Equations
- 3. Constructions with Ruler and Compasses
- 4. Cubic and Quartic Equations (Cardan & Ferrari)
- 5. The Graph of an Equation
- 6. Isolation of Real Roots (Sturm's Theorem)
- 7. Solution of Numerical Equations
- 8. Determinants and Linear Systems
- 9. Symmetric Functions and Elementary Sums
- 10. Elimination, Resultants, and Discriminants
- A. Fundamental Theorem of Algebra Proof
What You Will Learn in First Course in Theory of Equations
First Course in the Theory of Equations by Leonard Eugene Dickson is an authoritative, classic mathematical text that provides a rigorous, highly structured foundation in polynomial equations, root evaluation techniques, and early modern algebraic methods. Published by John Wiley & Sons, this foundational volume guides readers through complex number arithmetic, fundamental theorems on polynomial roots, classical ruler and compass geometric constructions, Cardan and Ferrari solution formulas for cubic and quartic polynomials, graphical analysis, Sturm and Budan real root isolation methods, numerical root approximation algorithms (Horner and Newton-Raphson), linear systems via determinants, elementary symmetric functions, and elimination theory using resultants and discriminants with exceptional clarity and logical precision.
Designed for undergraduate mathematics majors, secondary educators, history of mathematics researchers, and self-study algebra enthusiasts, this classic work bridges elementary numerical algebra directly with abstract polynomial ring concepts. Dickson details step-by-step algebraic derivations, constructibility proofs, symmetric polynomial representations, and explicit resultant matrix constructions. Whether you are studying classical Galois theory prerequisites, exploring geometric constructibility limits, or reviewing historical numerical approximation algorithms, this book offers an indispensable roadmap.
Recognized globally as a masterpiece of classical exposition, it stands as one of the best introductory references for mastering polynomial theory and root approximation methods. By connecting geometric compass constructions directly to polynomial field extensions and symmetric functions, it serves as an essential tool for learning classical polynomial algebra with confidence.
Book Details & Specifications
Title:
First Course in Theory of Equations by Leonard Dickson
Publisher:
John Wiley & Sons, Inc
Year:
1922
Pages:
207
Type:
PDF
Language:
English
ISBN-10 #:
1172078408
ISBN-13 #:
978-1172078400
License:
Public Domain Work
Amazon:
Amazon
About the Author: Leonard Eugene Dickson
The author Leonard Eugene Dickson
(1874–1954) was a preeminent American mathematician and Professor of Mathematics at the University of Chicago, widely celebrated as one of the most prolific and influential algebraists in history. He was the first recipient of a doctorate in mathematics at the University of Chicago and served as president of the American Mathematical Society (AMS).
Through First Course in the Theory of Equations, Dickson delivers a masterfully structured, clear presentation of classical polynomial analysis. His rigorous proof pathways, historic context, and accessible numerical algorithms make this volume a classic reference for polynomial equations and symmetric functions valued by mathematicians worldwide.
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