Math 8510, Fall 2018

Groups, Part 1: An introduction to groups. (33 pages, Beamer slides. Updated Sept 3, 2018)
Groups, Part 2: Group actions. (29 pages, Beamer slides. Updated Sept 10, 2018)
Groups, Part 3: The Sylow Theorems. (33 pages, Beamer slides. Updated Sept 21, 2018)
Groups, Part 4: Universal properties, commutators, and solvable groups. (12 pages, handwritten. Updated Sept 21, 2018)
Groups, Part 5: Products, coproducts, and categories. (13 pages, handwritten. Updated Oct 10, 2018)
Groups, Part 6: Nilpotent groups and finite abelian groups. (9 pages, handwritten. Updated Oct 12, 2018)
Groups, Part 7: Free groups, free objects, and group presentations. (15 pages, handwritten. Updated Oct 26, 2018)

Rings, Part 1: Rings and ideals. (27 pages, Beamer slides. Updated Nov 16, 2018)
Rings, Part 2: Fraction fields and localizations. (4 pages, handwritten. Updated Nov 12, 2018)
Rings, Part 3: Polynomial rings. (15 pages, Beamer slides. Updated Nov 16, 2018)
Rings, Part 4: Hilbert's basis theorem. (5 pages, handwritten. Updated Nov 28, 2018)
Rings, Part 5: The Chinese Remainder Theorem. (5 pages, handwritten. Updated Dec 4, 2018)
Rings, Part 6: Divisibility and factorization. (23 pages, Beamer slides. Updated Dec 4, 2018)

HW 1: pdf | tex. Topics: Groups, subgroups, and homomorphisms. Due Mon, Aug 29.
HW 2: pdf | tex. Topics: Group actions. Due Wed, Sept 12.
HW 3: pdf | tex. Topics: Sylow theory. Due Wed, Sept 19.
HW 4: pdf | tex. Topics: Commutators and solvable groups. Due Wed, Sept 26.
HW 5: pdf | tex. Topics: Products, and coproducts. Due Wed, Oct 3.
HW 6: pdf | tex. Topics: Categories and universal properties. Due Wed, Oct 10.
HW 7: pdf | tex. Topics: Nilpotent groups, semidirect products. Due Wed, Oct 17.
HW 8: pdf | tex. Topics: Free groups and free objects. Due Fri, Oct 26.
HW 9: pdf | tex. Topics: Group presentations. Due Fri, Nov 2.
HW 10: pdf | tex. Topics: Rings and ideals. Due Monday, Nov 12.
HW 11: pdf | tex. Topics: Fraction fields and localizations. Due Tues, Nov 20.
HW 12: pdf | tex. Topics: Polynomial rings. Due Fri, Nov 30.
HW 13: pdf | tex. Topics: Chinese remainder theorem. Due Fri, Dec 7.
HW 14: pdf | tex. Topics: Divisibility and factorization. Not assigned.