Lecture on Galois Theory by Emil Artin and A. N. Milgram
Lecture on Galois Theory - Table of Contents
PART I: LINEAR ALGEBRA
- A. Fields
- B. Vector Spaces
- 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 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. Kummer'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
What You Will Learn in Lecture on Galois Theory
Galois Theory by Emil Artin (with additions by A. N. Milgram) is a famous mathematical masterwork that delivers a modern, field-theoretic approach to one of abstract algebra's most elegant subjects. This fundamental volume guides readers through vector spaces, field extensions, splitting fields, character groups, and normal extensions without losing sight of logical clarity and precision.
Designed for undergraduate and graduate mathematics students, this foundational text reformulates classical polynomial solvability using modern linear algebra and field extensions. Artin presents elegant, minimalist proofs for core theorems, while Milgram provides concrete applications to solvable groups, permutation groups, and ruler and compass constructions. Whether you are studying Galois theory for the first time or seeking a definitive reference, this book offers an essential roadmap.
Recognized worldwide as a classic of 20th-century mathematical exposition, it remains one of the best Galois theory books for self-study. By balancing axiomatic field theory with historical application problems, it serves as an indispensable resource for mastering modern Galois theory with confidence.
Book Details & Specifications
Title:
Lecture on Galois Theory by Emil Artin and A. N. Milgram
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 the Author: Emil Artin
The author Emil Artin
was one of the preeminent algebraists of the 20th century, renowned for his foundational contributions to algebraic number theory, field theory, and non-commutative algebra. A professor at Hamburg, Indiana, and Princeton Universities, he made breakthrough discoveries including Artin reciprocity and Artin L-functions, shaping the trajectory of modern abstract algebra.
Derived from his landmark lecture series at the University of Notre Dame and augmented by Arthur N. Milgram, Galois Theory remains a gold standard in mathematical pedagogy. Artin's clean, modern style replaced messy computational techniques with field-theoretic elegance, creating a classic reference for Galois theory that continues to inspire generations of mathematicians.
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