My Wish Lists Login / Join

Algebraic Equations

By: EDGAR DEHN

Write A Review

Paperback | 1 August 2017

At a Glance

Paperback
208 Pages

Dimensions(cm)
20.9 x 14.2 x 2.54

Paperback

RRP $34.99

$32.75

or 4 interest-free payments of $8.19 with

Ships in 5 to 7 business days

This text focuses on the basics of algebraic theory, giving detailed explanations of integral functions, permutations, and groups, and Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.

Meticulous and complete, this presentation of Galois' theory of algebraic equations is geared toward upper-level undergraduate and graduate students. The theories of both Lagrange and Galois are developed in logical rather than historical form and given a thorough exposition. For this reason, Algebraic Equations is an excellent supplementary text, offering students a concrete introduction to the abstract principles of Galois theory. Of further value are the many numerical examples throughout the book, which appear with complete solutions.

A third of the text focuses on the basic ideas of algebraic theory, giving detailed explanations of integral functions, permutations, and group in addition to a very clear exposition of the symmetric group and its functions. A study of the theory of Lagrange follows. After a discussion of various groups (including isomorphic, transitive, and Abelian groups), a detailed study of Galois theory covers the properties of the Galoisian function, the general equation, reductions of the group, natural irrationality, and other features. The book concludes with the application of Galoisian theory to the solution of such special equations as Abelian, cyclic, metacyclic, and quintic equations.

About the Author

Edgar Dehn was an Instructor in Mathematics at Columbia University.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Algebra Science Science in General History of Mathematics

List of Theorems	p. viii
List of Adopted Conventions	p. ix
Integral Function
Interpolation	p. 1
Division	p. 3
Reduction	p. 6
Primitive function	p. 7
Linear factors	p. 8
Equations and Permutations
Discovery of Lagrange	p. 11
Solution of cubic	p. 13
Connection with permutations	p. 15
Algebra of Permutations
Notation	p. 17
Degree	p. 18
Combination	p. 19
Order	p. 21
Association	p. 23
Inverse	p. 24
Identity	p. 26
Group and Subgroup
Group	p. 27
Subgroup	p. 29
Conjugate subgroups	p. 32
Rule of transforms	p. 34
Normal subgroup	p. 36
Symmetric Group and Its Functions
Generator	p. 38
Symmetric sum	p. 40
Computation of symmetric sum	p. 41
Another computation	p. 44
Resultant	p. 46
Resultant as determinant	p. 47
Discriminant	p. 50
Composition of Symmetric Group
Composition-series	p. 53
Alternating function	p. 54
Alternating group	p. 56
Composition of S and A	p. 59
Subgroups of S and A	p. 61
Group on functions	p. 64
Theory of Lagrange
Resolvent equation	p. 66
Lagrange's Theorem	p. 67
Lagrange's Theorem, Continued	p. 70
Plan of Lagrange	p. 74
Lagrange's solvent	p. 75
Special case of solvents	p. 78
Limits of Lagrange's plan	p. 80
General Equations
Quadratic equation	p. 82
Cubic equation	p. 83
Cubic equation, Continued	p. 85
Cubic equation, Continued	p. 87
Cubic equation, Continued	p. 88
Biquadratic equation	p. 90
Biquadratic equation, Continued	p. 93
Biquadratic equation, Continued	p. 95
More About Groups
Isomorphic groups	p. 99
Transitive group	p. 101
Imprimitive group	p. 104
Quotient-group	p. 107
Subgroups of quotient-group	p. 110
Maximum normal subgroup	p. 111
Constancy of composition-factors	p. 113
Abelian group	p. 115
Theorem of Cauchy	p. 118
Metacyclic group	p. 120
Note on abstract group	p. 126
Domain
Algebraic domain	p. 129
Algebraic domain, Continued	p. 131
Conjugate domains	p. 133
Conjugate domains, Continued	p. 135
Normal domain	p. 136
Theory of Galois
Special equation	p. 139
Galoisian function	p. 140
Galoisian resolvent	p. 143
Galoisian group	p. 145
Properties of Galoisian group	p. 146
Plan of Galois	p. 149
General equation	p. 153
Duality of plans	p. 155
Irreducible equation	p. 156
Applications	p. 158
Imprimitive equation	p. 161
Reduction of group	p. 163
Natural irrationality	p. 169
Special Equations
Abelian equation	p. 171
Cyclic equation	p. 172
Roots of unity	p. 175
Congruence	p. 176
Fermat's Theorem	p. 179
Cyclotomic equation	p. 182
Discriminant of cyclotomic equation	p. 184
Applications	p. 185
Metacyclic equation	p. 190
Quintic equation	p. 195
Index	p. 201
Table of Contents provided by Ingram. All Rights Reserved.

Algebraic Equations

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Mathematics

Numeracy in Early Childhood

Shared Contexts For Teaching And Learning

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

Humble Pi

A Comedy of Maths Errors

A Little History of Mathematics

Little Histories

The Golden Ratio

Divine Beauty of Mathematics

Primary Mathematics

4th Edition - Integrating Theory with Practice

Statistics and Data Handling for Biologists

A Student's Guide

Statistics and Data Handling for Biologists

A Student's Guide

The Score

How to Stop Playing Someone Else's Game

Stochastic Control in Energy, Environmental and Resource Management Applications

Emerging Methodologies and Applications in Modelling, Identification and Control

Dynamics of Marine Structures

Mathematics of Uncertainty Applied to Global Issues

Sustainability, Mistreatment of Women, Nuclear Power, Smart Cities, Digitalization

Data Science and Social Research III

Epistemology, Methods, Technology, Applications, and Relation to Artificial Intelligence

Antifragile

Things That Gain from Disorder

Recent Advances in Information Systems

Proceedings of the ICRAIS, Pointe aux Piments, Mauritius, 10-12 September 2025

Calculus

9th edition - Early Transcendentals, Metric

Second Grade Math with Confidence Bundle

Math with Confidence

Infinite Game

From the bestselling author of Start With Why

Modal Semirings and Applications

Trends in Logic

Discrete Mathematics with Applications, Metric Edition

5th edition

Oxford Maths for Australian Schools Year 6 Practice and Mastery Book

3rd Edition

Oxford Maths for Australian Schools Year 4 Value Pack

3rd Edition

Fooled By Randomness

The Hidden Role of Chance in Life and in the Markets

The Black Swan

The Impact of the Highly Improbable

This product is categorised by