Lectures: MW 10:00am-11:15am in CHB C223
Instructor: Daniel Corey, daniel.corey[at]unlv.edu
Office Hours: Monday & Wednesday: TBD (my office is CDC-09 912)
Textbook: Abstract Algebra 3rd ed. by Dummit and Foote. Chapters 1-5, 7
Midterm Exam: Oct. 23 (during class)
Final Exam: Dec 9 10:10am-12:10pm (Monday). Location CHB C223.
The underlined part refers to the section in the text, and the numbers refer to the exercises at the end of the respective section.
Assignment 1 1.3 2, 6 (do all elements, not just those of order 4), 9a, 10 (ignore the last sentence), 12, 16; 1.4 10 (replace the phrase "subgroup of GL_2(R)" with "matrix group"), 11ab (let F=R); Due Wednesday Sept 4.
Assignment 2 0.3: 12, 13, 14; 1.1: 8, 13, 22, 31; 2.1: 1, 6, 15; Due Sept 11
Assignment 3 1.2 4; 1.5 1; 1.6 4, 17, 23; 2.3 4, 12, 19 2.4 14, 19; Due Sept 20
Assignment 4 3.1: 9, 14abc, 22, 32 (only the first sentence), 33, 36, 41; 3.2: 4, 8, 14, 16; Due Sept 27
Assignment 5 3.3 3, 4, 7, 9; 1.7 15, 17; 2.2 12; Due Oct 4
Assignment 6 4.1 1, 6; 4.2 2, 7; 4.3 2, 6, 11, 27; Due Oct 11
Assignment 7 4.4 1, 3, 13, 14, 15; 4.5 1, 6, 8, 15, 45; Due Oct 18
Assignment 8 3.4 1 5.1 5; 5.4 3, 4 5.5 8 (Only the first sentence), 9 (first 2 sentences). Due Nov 1
Assignment 9 5.2: 4, 9; 7.1 11, 13, 14, 26, 27; 7.2 1, 3, 5, 10; Due Nov 8
Assignment 10 7.1 5, 25 7.3 2, 6, 7, 13, 32, 33; Due Nov 22
Assignment 11 7.3 10, 19, 22, 29, 7.4 14a-d, 15; Optional
Below is the plan for the semester. I will try my best to stick to this schedule, but it may be modified as necessary. Take this as a rough outline for the semester; if a topic is not explicitly mentioned here, this does not mean it is or is not covered.
Dates: Aug. 26-28
Topics: Overview of group theory. Matrix and permutation groups. Alternating group.
Dates: Sept. 2-4
Topics: Abstract groups. Subgroups.
Notes: No class on Sept. 2 ( Labor day)
Dates: Sept. 9-11
Topics: Subgroups generated by a set. Dihedral and Quaternion groups. Group homomorphisms and isomorphisms. Cyclic groups.
Dates: Sept. 16-18
Topics: cosets and Lagrange's theorem, Quotients of abelian groups. Normal Subgroups.
Dates: Sept 23-25
Topics: Quotient by a normal subgroup. Isomorphism theorems. Group actions.
Dates: Sept 30-Oct. 2
Topics: Orbits, Stabilizers, Orbit-Stabilizer formula. Cayley's theorem. class equation.
Dates: Oct. 7-9
Topics: Automorphisms. Sylow theorems. Cauchy's theorem. Applications to classification of small groups.
Dates: Oct 14-16
Topics: Proof of the Sylow theorems. Simple groups. A_n is simple. Semidirect products.
Dates: Oct. 21-23
Topics: Subgroups of Z^n, Smith normal form.
Dates: Oct. 28-30
Topics: Classification of finitely generated abelian groups. Direct and semidirect products. Rings.
Dates: Nov. 4-6
Topics: Rings, examples, zero divisors, units
Dates: Nov. 11-13
Topics: Subrings, ring homomorphisms
Note: No class Nov. 11 (Veterans day)
Dates: Nov. 18-20
Topics: Ideals, quotients
Dates: Nov. 25-27
Topics: Chinese remainder theorem. prime and maximal ideals.
Dates: Dec 2-4