MATH 573 Section 001: Abstract Algebra I
Fall 2011
3 Credit Hours
Primary Instructor: Dr. Gregory Knese
Syllabus subject to change.
The biggest prerequisite is mathematical maturity which I would define as the ability to read and do proofs. It would be beneficial to have seen undergraduate group, ring, and field theory, as well as linear algebra.
The class is TTh 11am-12:15pm in Gordon Palmer 207. The final exam is Dec 16, 8-10:30am.
This is a first graduate course on Group Theory. We shall cover the basics of groups and move on to the isomorphism theorems, group actions (G-sets), the Sylow theorems, Normal series, and finite direct products.
Course catalog description: Fundamental aspects of group theory are covered. Topics include Sylow theorems, semi-direct products, free groups, composition series, nilpotent and solvable groups, and infinite groups.
Specifically, we will cover:
Chapter 1: permutations, cycles, factorization into disjoint cycles, even and odd permutations, semigroups, groups, homomorphisms.
Chapter 2: subgroups, lagrange's theorem, cyclic groups, normal subgroups, quotient groups, noether isomorphism theorems, correspondence theorem, direct products
Chapter 7: automorphism groups, semidirect products
Chapter 3: conjugates, symmetric groups, some representation theorems, G-sets
Chapter 4: p-Groups, Sylow theorems, groups of small order
Chapter 5: Some Galois theory, Jordan-Holder theorem, Solvable groups, central series and nilpotent groups, p-groups
Chapter 6: the basis theorem, fundamental theorem of finite abelian groups
Time permitting we will dive into some of the topics: canonical forms, free abelian groups, finitely generated abelian groups
There will be one midterm exam and a final. Both exams are cumulative. The midterm is on Oct 11 in class at the regular time. The final exam is Dec 16 (8am-10:30am).
There will be weekly written homework assignments. These should be written up nicely, just as you might write up an English essay. (It is not necessary to type, but I would encourage you to do so with the typesetting program LaTeX )
You may consult with other students or myself on how to do a problem only after you have given a genuine effort to solve the problem. After you have solved your homework problems, your solutions must be written completely independently.
Grading breakdown:
Final: 30%
Midterm: 20%
Homework: 50%
Letter grades will be determined using a the scale: A+ = [97,100], A = [93.5, 97), A- = [90, 93.5), and so on for B,C,D, and F = [0,60)
Your midterm exam score will be replaced by your final exam score if it is to your benefit. For this reason, there will be no make-up for missing the midterm: if you miss the midterm it will be replaced by your final exam. No one should miss the final.
10% of your homework scores will be dropped and therefore late homework will not be accepted.
You are expected to be prepared for and participate in every class. Being prepared essentially means doing any assigned reading and recommended problems ahead of time. This is essential for doing well in this class. Coming to class "cold" is not recommended.
I will take attendance but it will not be a formal part of your grade.
Rotman's "An Introduction to the Theory of Groups" Fourth edition.
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