Abstract Algebra II

22m121, Spring 2006

Instructor: Fred Goodman




Contact Information:


MWF: 12:30-1:30 ,

214 MLH


T: 12:30P - 1:20P,

51 SH


325G Maclean Hall


goodman at math dot uiowa dot edu


Office: 319-335-0791

Paper Mail:

Fred Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242-1419 USA

Office Hours:

T, Th: 12--1 pm

Teaching Assistant:

Oscar Vega

Office hours: TBA


Oscar Vega's Website:




Click here


Frederick M. Goodman, Algebra: Abstract and Concrete, 2nd edition, Prentice Hall, 2002.

This text is required.

I. N. Herstein, Topics in Algebra, 2nd edition

This text is recommended.

Emil Artin, Galois Theory, Dover Books.

This text is recommended.

Assignment lists:

There will be 9 to 11 written assignments. Details will appear here as the assignments are made.Please see the remarks on the syllabus about the standard of explanation expected on the homework. For homework solutions, see http://www.math.uiowa.edu/~ovega/algebra/ .


Assignment 1, Due Friday, January 27

Section 6.6, Exercises 1, 5, 6, 7.

Section 6.7, Exercises 2, 3, 4.

Section 6.8, Exercises 3, 4, 5a. (note: 4 is hard, but fun).

Note: Exercises are from the online pdf version of the text, not the published textbook.

Assignment 2, Due Friday, Feb 3.

Section 3.4: 1, 2, 8, 9, 12.

Problem A: Show that two vector spaces over K are isomorphic if, and only if, they have the same dimension. (The vector spaces need not be finite dimensional.)

Problem B: Show that a subset of a vector space is a basis <=> it is maximal linearly independent <=> it is minimal spanning.

Assignment 3, Due Friday, Feb 10.

Section 3.5: 3, 4 , 5 7, 8, 10(c), 14, 15, 16.

Assignment 4, Due Friday, Feb 17.

Section M.1: 4, 5, 8, 9, 10.

Section M.2: 2, 6, 7. (from the January 6 version of chapter M)

Assignment 5, Due Friday, Feb 24.

Section M.2: 4 (from the January 6 version of chapter M)

Section M.3: 1 - 6.

Assignment 6, Due Friday, March 3.

Download pdf file with exercises for section M.4.

Unless you want to do tedious matrix reductions by hand, you will want to use a program for Smith Normal Form. Program in Mathematica. Program in Maple.

Do exercises 1, 3--9, from the pdf file.

(Exercise 3 might be hard, if you don't see the trick. Don't panic if you don't get it.)

Assignment 7, Due Friday, March 10.

Download pdf file with exercises for section M.5.

Do exercises 2-7 from the pdf file.

Assignment 8, Due Friday, March 24.

Download pdf file with exercises for section M.6.

Do exercises 4-11 from the pdf file.

Assignment 9, Due Friday, April 7.

Section 7.3: 3, 4, 5, 6, 9, 12

Section 8.1: 1-4

Assignment 10, Due Monday, April 17.

Read Section 8.3 and do the exercises (1-7). Some of these are very simple.

Section 8.5: 1, 2

Assignment 11, Due Friday, April 28.

Section 8.6: 2, 3, 5, 8, 10, 11, 13, 14, 15.


There will be one or two midterm exams, dates to be negotiated; the dates will appear here when they are known. There will be a comprehensive final exam. The text of the exams will appear here after the exams have been done by all students.

Text of first exam.

Mathematica Tutorials:

Mathematica Lesson 1: Getting started.

Mathematica Lesson 2: Mathematica as a scientific calculator.

Mathematica Lesson 3: Mathematica as a symbolic calculator.

Mathematica Lesson 4: Mathematica for calculus and graphing.

Note: sometimes students report difficulty opening Mathematica files with in Windows on university computers. This is not the fault of these files but rather something to do with the way Mathematica and Windows are set up on some of the university computers. The following procedure will work:

1. Click on the www link to the file you want to use and, when the dialogue box pops up and asks what you want to do with the file, chose save to disk. Save it to some convenient location, like the desktop, or your own floppy drive.

2. Start the Mathematica program.

3. Open the desired file from within the Mathematica program; i.e. on the main Mathematica menu bar do File -> Open . A file browser will pop up, and you can choose your file.