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GALOIS THEORY (M1, Rotman)

Lecture Topic : (Pure Math) GALOIS THEORY (M1, Rotman)

Prerequisites : Galois Theory (Sen, M1); Group Theory(Sen, M1);

Recommended Text(s) :

“Galois Theory”, 2nd Edn., Joseph Rotman, Springer, 1998.

Approx price new on Amazon.com : $45

Approx price second hand on Amazon.com : $40

Availability free on eMule.com : Yes

eMule search key word(s) : Rotman, Galois Theory

Lectures and Links :

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Lecture 1  (link)

Ch.1   Symmetry

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Lecture 2  (link)

Ch.2   Rings

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Lecture 3  (link)

Ch.3   Domains and Fields

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Lecture 4 (link)

Ch.4   Homomorphisms and Ideals

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Lecture 5  (link)

Ch.5   Quotient Rings

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Lecture 6  (link)

Ch.6   Polynomial Rings over Fields

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Lecture 7  (link)

Ch.7   Prime Ideals and Maximal Ideals

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Lecture 8  (link)

Ch.8   Irreducible Polynomials

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Lecture 9  (link)

Ch.9   Classical FOrmulas

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Lecture 10  (link)

Ch.10   Splitting Fields

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Lecture 11  (link)

Ch.11   The Galois Group

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Lecture 12  (link)

Ch.12   Roots of Unity

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Lecture 13  (link)

Ch.13   Solvability by Radicals

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Lecture 14  (link)

Ch.14  Independenceof Characters

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Lecture 15  (link)

Ch.15   Galois Extensions

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Lecture 16  (link)

Ch.16   The Fundamental Theorem of Galois Theory

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Lecture 17  (link)

Ch.17   Applications

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Lecture 18  (link)

Ch.18   Galois’s Great Theorem

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Lecture 19  (link)

Ch.19   Discriminants

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Lecture 20  (link)

Ch.20   Galois Groups of Quadratics, Cubics, and Quartics

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Lecture 21  (link)

Ch.21   Epilogue

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Lecture 22  (link)

Appendix A : Group Theory Dictionary

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Lecture 23  (link)

Appendix B : Group Theory Used in the Text

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Lecture 24  (link)

Appendix C : Ruler-Compass Constructions

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Lecture 25  (link)

Appendix D : Old-Fashioned Galois Theory

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