Notes and Problems for Mat 592

For Section twenty-two of the text:

For Section twenty-three of the text:

Problems 1, 3, 7, 9, 13, 17, 22, 26, 35, 36.
As discussed, there is no class Tuesday, Jan 27. You should read sections 22 and 23 carefully. There are a few important ideas in those sections (such as multi-variable polynomial rings and Eisenstein's criterion), that have not been discussed in class.
Class will meet Jan 29. Sebastian Pauli will be there to discuss the problems in sections 22,23.
Quiz II (Take-home: Due 02/05.)
Note - the quiz says due 02/04 - that's a misprint.
Solution to Quiz I

For Section twenty-six of the text:

For Section twenty-seven of the text:

For Section twenty-nine of the text:

For Section thirty of the text:

For Section thirty-one of the text:

For Section thirty-three of the text:

For Section thirty-six of the text:

For Section thirty-seven of the text:

For Section thirty-eight of the text:

Problems 2, 4, 10, 11, 13, 14.
In class, we discuss using integral matrices and the Smith normal form to compute quotients of free abelian groups. This material is not in the text, but can be found in many versions on the internet and in algebra texts.
Here are some brief notes. For more information, you might start with the Wikipedia version. More detail and proofs about elementary matrices can be found in some online notes by Ralph Howard.
Quiz VII (Take-home: Due 4/2.)
Quiz VIII (Take-home: Due 4/9.)

For Section thirty-nine of the text:

For Section forty of the text:

For Section forty-five of the text:

For Section forty-six of the text:

For Section forty-seven of the text:

Problems 1, 3, 5, 9, 13, 16.
For the impatient, here's a partial version of the exam. The complete version will be posted tomorrow.(May 1)
Exam.