Lecture on Galois Theory by Emil Artin
Book Contents :-
PART-I LINEAR ALGEBRA
A. Fields
B. Vector Spaces 1
C. Homogeneous Linear Equations
D. Dependence and Independence of Vectors
E. Non-homogeneous Linear Equations
F.* Determinants
PART-II FIELD THEORY
A. Extension Fields
B. Polynomials
C. Algebraic Elements
D. Splitting Fields
E. Unique Decomposition of Polynomials into Irreducible Factors
F. Group Characters
G.* Applications and Examples to Theorem
H. Normal Extensions
I. Finite Fields
J. Roots of Unity
K. Noether Equations
L. Rummer's Fields
M. Simple Extensions
N. Existence of a Normal Basis
O. Theorem on Natural Irrationalities
PART-III APPLICATIONS
By A. N. Milgram
A. Solvable Groups
B. Permutation Groups
C. Solution of Equations by Radicals
D. The General Equation of Degree n
E. Solvable Equations of Prime Degree
F. Ruler and Compass Construction
About this book :-
"Galois Theory: Lectures Delivered at the University of Notre Dame" by "Emil Artin" is a foundational mathematics book that presents galois theory in a clear, lecture-based style. The text comes from Artin’s university lectures and is valued for its natural flow and strong intuition. Instead of heavy abstraction, the book develops ideas gradually, making it approachable for readers with a solid background in algebra.
The book explains how "field extensions" and "polynomials" are connected through "group theory", leading to the central concept of "galois groups". Artin’s method emphasizes understanding structure and symmetry, helping readers grasp the deeper meaning behind algebraic results. Linear algebra ideas are smoothly integrated to support the theory and maintain clarity.
A key strength of the book is its treatment of "applications", especially the solvability of equations by radicals and the role of symmetry in algebra. Although concise, the book is rigorous and intellectually rewarding. It is well suited for advanced undergraduate and graduate students and remains a classic reference for learning modern algebra.
Book Detail :-
Title:
Lecture on Galois Theory by Emil Artin
Publisher:
University of Notre Dame Press
Year:
1971
Pages:
96
Type:
PDF
Language:
English
ISBN-10 #:
1258244330
ISBN-13 #:
978-1258244330
License:
External Educational Resource
Amazon:
Amazon
About Author :-
The author
Emil Artin
was a leading 20th-century Austro-German mathematician best known for shaping modern "algebra". He made foundational contributions to "galois theory", "number theory", and "class field theory", introducing ideas that are still central to advanced mathematics today. His work emphasized structure, abstraction, and deep theoretical insight. Artin was also a gifted teacher whose lectures were admired for their "clarity" and "conceptual depth". His courses at the University of Notre Dame inspired the famous lecture notes that became "Galois Theory". Through both research and teaching, Artin helped define how higher algebra is studied and understood in the modern era.
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