All reading references refer to Dummit and Foote's Abstract Algebra, 3rd edition, except when explicitly marked otherwise.
For more of a progression through the book and videos at the undergraduate level, please visit Taylor's excellent list of videos on abstract algebra
An excellent graduate course on group theory, taught by Richard Borcherds
An excellent graduate course on Galois theory, also taught by Richard Borcherds
Syllabus for Algebra qualifying exam
Jump to: Week 2 · Week 3 · Week 4 · Week 5 · Week 6 · Week 7 · Week 9 · Week 10 · Week 11 · Week 12 · Week 13
Week 1
Reading On using LaTeX:
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Videos On using LaTeX:
On the dihedral group:
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Week 2
Reading Dummit and Foote reading:
Further reading for qual problems:
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Videos On subgroups:
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Week 3
Reading Dummit and Foote reading:
Further reading for qual problems:
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Videos On group homomorphisms:
On the isomorphism theorems:
On solvable groups:
On direct products:
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Week 4
Reading Dummit and Foote reading:
Further reading for qual problems:
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Videos On group actions:
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Week 5
Reading Dummit and Foote reading:
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Videos On the Sylow theorems:
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Week 6
Reading Dummit and Foote reading:
Further reading for qual problems:
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Videos On direct products:
On semidirect products:
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Week 7
Reading Dummit and Foote reading:
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Videos On p-groups:
On nilpotent groups:
On groups of medium order:
On free groups:
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Week 9
Reading Dummit and Foote reading:
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Videos From Borcherd's course on Galois theory:
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Week 10
Reading Dummit and Foote reading:
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Videos From Borcherd's course on Galois theory:
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Week 11
Reading Dummit and Foote reading:
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Videos From Borcherd's course on Galois theory:
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Week 12
Reading Topic:
Dummit and Foote reading:
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Videos From Borcherd's course on Galois theory:
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Week 13
Reading Topic:
Dummit and Foote reading:
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Videos From Borcherd's course on Galois theory:
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