Math 402 - Modern Algebra, II
This course is a continuation of the Math 401 course as taught in Section 1
in the Fall of
2011.
The
notes/text
for the course will be updated as the course goes along. The course
will start with Chapter 6. The previous 5 chapters were covered in the
previous semester in Math 401. It is not critical that all of that material
be known prior to starting Math 402, but the basic ideas will be assumed.
Missing details can be looked up easily, but will tend not to interfere
with the material in Math 402.
Do not assume that the material in any of the notes is stable unless listed
as stable here. Minor typos may be corrected even after a chapter is
labeled as stable. Chapters beyond what is labeled as stable are either
"under construction" or date from an earlier version of this course and need
to be changed. If you read ahead it will give an idea of what is to come,
but details may differ by the time we get there.
Status of the text
- At this time (1/29/2012), the chapters through Chapter 6 are stable.
-
At this time (2/2/2012), Chapter 7 through the end of Section 7.3.5 is
stable as far as text. There may be exercises added. Sections after 7.3.5
will definitely change.
-
At this time (2/6/2012), Chapter 7 should be stable.
-
At this time (2/16/2012), Chapter 8 should be stable..
-
At this time (2/27/2012), Chapter 9 should be stable. Some changes were
made to Section 9.3 on 3/3/2012
Test 1: Tuesday, 3/13/2012, 11:40 AM - 1:05 PM. Material covered will be
limited to the arguments that go into the following:
- Proposition 6.1.1.
- Lemma 7.2.2.
- Lemma 7.3.1.
- Proposition 7.3.2.
- Theorem 7.3.3.
- Lemma 7.3.4.
- Lemma 8.2.1.
- Lemma 8.2.3.
-
At this time (3/3/2012), Chapter 10 should be stable.
-
At this time (3/15/2012), Chapter 11 should be stable.
-
(3/25/2012), added half page (Section 11.9) to end of Chapter 11.
-
At this time (3/27/2012), Chapter 12 should be stable.
Final: Wednesday, 5/16/2012, 8:30 AM - 10:30 AM, SL-206.
Material covered will be
limited to the the following:
- Section 10.3, definitions.
- Proposition 10.4.1, statement and proof. (Proof preceeds statement.)
- Lemma 10.5.1, Statement only and fact in the sentence following the
statement.
- Section 10.6.1, definition of characteristic.
- Section 11.2.1, definitions.
- Lemma 11.3.5, statement and proof.
- Theorem 11.4.1, statement only.
- Lemma 11.4.2, statement and proof.
- Theorem 11.5.2, statement and proof
- Theorem 12.3.1, statement and proof and needed definitions.
- Section 13.2, all arguments.
- Corollary 13.3.5, statement only.
- Section 13.4, definitions.
- Proposition 13.4.1, statement only.
- Proposition 13.4.2, statement only.
- Proposition 13.5.1, statement and proof.
- Theorem 13.6.4, statement only.
- Section 13.6.3, know how to do examples like the one in the first two
paragraphs.
- Section 14.3 (subsection on normal extensions), definition of a normal
extension.
Tests will be announced in class and here.
Attendance in class will be particularly important in this course and
regular attendance will be insisted upon.