The Decomposition of Integer Polynomials 57
Eisenstein's Irreducibility Criterion 60
Chapter 7. The Construction of Regular Polygons 63
Constructions with Straightedge and Compass 69
The Classical Construction Problems 74
Chapter 8. The Solution of Equations of the Fifth Degree 81
The Transformations of Tschirnhaus and of Bring and
Jerrard 89
Chapter 9. The Galois Group of an Equation 93
Computing the Galois Group 114
A Quick Course in Calculating with Polynomials 119
Chapter 10. Algebraic Structures and Galois Theory 125
Groups and Fields 130
The Fundamental Theorem of Galois Theory: An
Example 144
Artin's Version of the Fundamental Theorem of
Galois Theory 149
The Unsolvability of the Classical Construction
Problems 161
Epilogue 165
Index 177
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