TABLE OF CONTENTS

(The sections marked with an asterisk have been herein added to the content of the first edition)

Page

LINEAR ALGEBRA                         1

A . Fields                   1

Vector Spaces                      1

Homogeneous Linear Equations               2

Dependence and Independence of Vectors                    4

Non-homogeneous Linear Equations                   9

*           Determinants                        11

FIELD THEORY       ,                      21

Extension Fields                  21

Polynomials              22

Algebraic Elements                         25

Splitting Fields                      30

Unique Decomposition of Polynomials

into Irreducible Factors                    33

Group Characters                 34

G* Applications and Examples to Theorem 13               38

Normal Extensions              41

Finite Fields              49

J. Roots of Unity       • •. ■ ■           56

K. Noether Equations                      57

L Kummer's Fields               59

M. Simple Extensions                      64

N. Existence of a Normal Basis      ,                      66

Q, Theorem on Natural Irrationalities                    67

APPLICATIONS

By A. N. Mil gram                                        69

Solvable Groups                  69

Permutation Groups                         70

Solution of Equations by Radicals                        72

The General Equation of Degree n.                      74

Solvable Equations of Prime Degree                   76

Ruler and Compass Construction             801