MATH 251: ABSTRACT ALGEBRA I FALL 2011 Course Info

MATH 251: ABSTRACT ALGEBRA I
FALL 2011
JOHN VOIGHT
Course Info
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Lectures: Monday, Wednesday, Friday, 11:45 a.m.–12:35 p.m.
Dates: 29 August 2011–7 December 2011
Room: Lafayette L210
Course Record Number (CRN): 90878
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Instructor: John Voight
Office: 16 Colchester Ave, Room 207C
Phone: (802) 656-2271
E-mail: [email protected]
Instructor’s Office Hours: Mondays, 2:30–4:30 p.m.; Wednesdays, 9:00–10:00
a.m.; or just make an appointment!
• Course Web Page: http://www.cems.uvm.edu/~voight/251/
• Instructor’s Web Page: http://www.cems.uvm.edu/~voight/
• Prerequisites: Math 52, 124 or permission.
• Required Text: David Dummit and Richard Foote, Abstract Algebra, Third edition,
2004.
• Grading: Homework will count for 40% of the grade. Class participation and preparedness will count for 10% of the grade. There will be two 50-minute exams that
will each count for 10% of the grade and one comprehensive final exam that will
count for 30% of the grade.
Homework
Typically, homework will be assigned each class and is due the next class. It will be
collected approximately once a week and late homework will not be accepted. The homework
assignments are posted on the course webpage.
We will go over homework in class, and after this discussion it will be collected. You may
take notes during this discussion but only if you use a red pen.
Be sure to show your work and explain how you got your answer. Correct but incomplete
answers will only receive partial credit. Part of the beauty of mathematics is in the elegance
of its proofs, and one goal of this course is for you to learn to write mathematics excellently.
Cooperation on homework is permitted (and encouraged), but if you work together, do
not take any paper away with you—in other words, you can share your thoughts (say on a
blackboard), but you have to walk away with only your understanding. In particular, write
the solution up on your own.
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Plagiarism, collusion, or other violations of the Code of Academic Integrity
(see http://www.uvm.edu/policies/student/acadintegrity.pdf)
will be referred to the The Center for Student Ethics and Standards.
Class participation and preparedness
You are expected to read the section before we cover it in class. Come with good questions!
Your participation and preparedness in class is essential for your success and will be assessed
accordingly.
You must come to my office at least once during the semester (such as during office hours).
Exams
Outside of exceptional circumstances, make-up exams will not be given. Please mark the
dates of exams (below) in your calendar.
Accommodation
Appropriate and fair accommodations will be provided for students with documented
special needs; please contact the ACCESS office (http://www.uvm.edu/~access/) directly
and early in the semester.
Students have the right to practice the religion of their choice. Each semester students
should submit in writing by the end of the second full week of classes their documented
religious holiday schedule for the semester.
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Syllabus
According to the “official” catalog description, we will cover:
Basic theory of groups, rings, fields, homomorphisms, and isomorphisms.
• Chapter 0: Basics
– 1, 29 Aug (M): Introduction
– 2, 31 Aug (W): §0.1: Basics
– 3, 2 Sep (F): §0.2: Properties of the Integers
3 Sep (M): No class, Labor Day
– 4, 7 Sep (W): §0.3: The Integers Modulo n
• Chapter 1: Introduction to Groups
– 5, 9 Sep (F): §1.1: Basic Axioms and Examples
– 6, 12 Sep (M): §1.2: Dihedral Groups
– 7, 14 Sep (W): §1.3: Symmetric Groups
– 8, 16 Sep (F): §1.4: Matrix Groups, §1.5: The Quaternion Group
– 9, 19 Sep (M): §1.6: Homomorphisms and Isomorphisms
– 10, 21 Sep (W): §1.7: Group Actions
– 11, 23 Sep (F): §2.1: Definitions and Examples
– 12, 26 Sep (M): Chapter 1 Review
• Exam 1, 28 Sep (W), covering material in §§0.1–1.6
• Chapter 2: Subgroups
– 14, 30 Sep (F): §2.2: Centralizers and Normalizers, Stabilizers, and Kernels
– 15, 3 Oct (M): §2.3: Cyclic Groups and Cyclic Subgroups
– 16, 5 Oct (W): §2.4: Subgroups Generated by Subsets
– 17, 7 Oct (F): §2.5: The Lattice of Subgroups
• Chapter 3: Quotient Groups and Homomorphisms
– 18, 10 Oct (M): §3.1: Definitions and Examples
– 19, 12 Oct (W): §3.1
– 20, 14 Oct (F): §3.2: More on Cosets and Lagrange’s Theorem
– 21, 17 Oct (M): §3.3: The Isomorphism Theorems
– 22, 19 Oct (W): §3.4: Composition Series and the Hölder Program
– 23, 21 Oct (F): §3.5: Transpositions and the Alternating Group
– 24, 24 Oct (M): §4.1: Group Actions and Permutation Representations
– 25, 26 Oct (W): §4.2: Groups Acting on Themselves
– 26, 28 Oct (F): Chapters 2–3 Review
• Exam 2, 31 Oct (M), covering material in §§2.1–3.5
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• Chapters 4 and 5: Group Actions, Direct Products, and Abelian Groups
– 28, 2 Nov (W): TBD
– 29, 4 Nov (F): §4.4: Automorphisms
– 30, 7 Nov (M): §4.5: Sylow’s Theorem
– 31: 9 Nov (W): §5.1: Direct Products
– 32, 11 Nov (F): §5.2: The Fundamental Theorem of Finitely Generated Abelian
Groups
• Chapter 7: Introduction to Rings
– 33, 14 Nov (M): §7.1: Basic Definitions and Examples
– 34, 16 Nov (W): §7.2: Polynomial Rings, Matrix Rings, and Group Rings
– 35, 18 Nov (F): §7.3: Ring Homomorphisms and Quotient Rings
21–25 Nov (M–F): No class, Thanksgiving Recess
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28 Nov (M): §7.3
30 Nov (W): §7.4: Properties of Ideals
2 Dec (F): §7.4
5 Dec (M): §7.5: Rings of Fractions
7 Dec (W): Chapter 7 Review
• Comprehensive Final Exam: Friday, December 16, 7:30 a.m.–10:15 a.m.
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