Chapter 01•Analysis & Tactics
The Symmetry of Roots: An Introduction to Galois Theory
Chapter 02•Analysis & Tactics
Splitting Fields & Field Automorphisms
Chapter 03•Analysis & Tactics
Worked Example: The Splitting Field of $x^4 - 2$
Chapter 04•Analysis & Tactics
The Abel-Ruffini Theorem: The Quintic Barrier
Practice Quiz•Interactive Assessment
ISI M.Math / CMI PhD Entrance StyleExam-Style Practice Problem
Let f(x) = x⁴ − 2 ∈ ℚ[x]. Which of the following are TRUE about its splitting field E over ℚ?
A
The splitting field is ℚ(⁴√2).
B
[E : ℚ] = 8.
C
Gal(E/ℚ) ≅ D₄ (dihedral group of order 8).
D
f(x) is solvable by radicals.
Peer Interaction
Academic Doubts & Colloquium
24 Active Discussions
RS
Ritwik Sen, TIFR CAM2 days ago • Research Scholar
Excellent exposition! The interactive proof canvas in section 2 made the oscillation argument crystal clear. Looking forward to the follow-up article on measure theory applications.