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FIELD THEORY (M1, Adamson)

Lecture Topic : (Pure Math) FIELD THEORY (M1, Adamson)

Prerequisites : Abstract Algebra (Sen, M1);

Recommended Text(s) :

“Introduction to Field Theory”, 2nd Edn., Iain T. Adamson, Dover, 2007.

Approx price new on Amazon.com (hard copy) : $7

Approx price second hand on Amazon.com (hard copy) : $4

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) : Field Theory, Adamson

Lectures and Links :

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Lecture 1  (link)

Ch.1   Definition and Examples

Ch.2   Maps & Relations on Sets

Ch.3   Elementary Consequences of the Definitions

Ch.4   Subgroups

Ch.5   Cosets and Lagrange’s Theorem

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Lecture 2  (link)

Ch.7   NormalSubgroups and Quotient Groups

Ch.8   The Homomorphism Theorem

Ch.9   Permutations

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Lecture 3  (link)

Ch.10   The Orbit-Stabilizer Theorem

Ch.11   The Sylow Theorems

Ch.12   Applications of Sylow Theory

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Lecture 4  (link)

Ch.13   Direct Products

Ch.14   Classification of Finite Abelian Groups

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Lecture 5   (link)

Ch.15   The Jordan-Holder Theorem

Ch.16   Composition Factors and Chief Factors

Ch.17   Solvable Groups

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Lecture 6   (link)

Ch.18   Examples of Solvable Groups

Ch.19   Semidirect Products and Wreath Products

Ch.20   Extensions

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Lecture 7   (link)

Ch.21   Central and Cyclic Extensions

Ch.22   Groups with at most 31 Elements

Ch.23   The Projective Special Linear Groups

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Lecture 8   (link)

Ch.24   The Mathieu Groups

Ch.25   The Classification of Finite Simple Groups

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Lecture 9  (link)

Appendix A   Prerequisites from Number Theory and Linear Algebra

Appendix B   Groups of Order < 32

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Links to Other Lecturers on this Topic :

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