Fall Quarter 2017, Math 220A, Modern Algebra I
TuTh 9:30am-10:45am, LSB 1101
6724 South Hall
The following two books are required texts for this course (as well as
for Math 220B and Math 220C):
David S. Dummit, Richard M. Foote, Abstract algebra,
(Third Edition), Wiley (2004).
Serge Lang, Algebra, (Revised Third Edition), Springer (2002).
The following book may also be helpful to you:
J. J. Rotman, An introduction to the theory of groups,
For a superb account (perhaps somewhat sophisticated for a beginner),
the following is highly recommended:
J.-P. Serre, Finite Groups: An Introduction, International
Grading and Examination Policy:
There will be one take-home midterm examination. It will be handed out
in class on Thursday, November 2nd, and will be due in class on
Tuesday, November 7th. There will also be one take-home final
examination. Precise arrangements concerning the final examination
will be made later.
Homework may be assigned, and some of it may be collected from time to
time. Your work should be typed neatly (preferably in Tex) on
8 X 11 sized paper.
The final grade for the course will be determined as follows: midterm
40\%, final exam. 60\%. Homework will not count towards the final grade.
PLEASE NOTE THAT NO MAKEUP EXAMINATIONS WILL BE GIVEN
IN THIS COURSE.
The following link might take you to some problems:
The following link will take you to the Course Log:
We shall aim to cover the following topics. Additional topics will be
covered if time permits.
Groups: definitions and basic properties. Examples: permutation
groups. Subgroups. Lagrange's theorem. Cyclic groups. Quotient
groups. Isomorphism theorems.
Groups acting on sets. Sylow's theorems and applications. Composition
series. The Jordan-Holder theorem and related results. Soluble and
nilpotent groups. Finite p-groups. Finitely generated abelian