MA5980: Graduate Number Theory
Text
R.A. Molin
Algebraic Number Theory
Chapman & Hall/CRC press, 1998.
Syllabus
We will try to at least cover the following sections in the above text
in the order in which they appear:
1.1,1.2,1.3,1.4,1.5,2.1,2.2,2.3,2.4,2.5,3.1,3.2,3.3,3.4,3.5,4.1,4.2,4.5
Your are responsible for the material in these sections even if it is not
presented in class.
Grading
Your grade will be based on several written homework assignments.
Assignments are alway due the next time class meets.
Start every written assignment at the top of a
new page, put your name at the beginning of each page and do not stable
different problems together. I expect the problems to be well written
in full English sentences with no gaps in detail or logic. Please
be as elegant and as concise as possible. Cite all references.
Failure to follow these instructions will result in lower marks.
Meeting times.
We are scheduled to meet on Wednesday and Friday from 1:30 to 3:00pm in
room 125 Fisher.
However some of you would prefer not to meet on Friday. So we can meet
Monday in room 125 Fisher from 1:30 to 3:00pm except when there is the
teaching seminar, when we can only meet from 2:00 to 3:00pm.
We will figure out a schedule so that we meet the
"required" 150 mins per week for 13 weeks.
First actual class.
I will be at the joint mathematics meeting in San Antonio, Texas during the
first week of classes. I will be in class Friday, January 13.
Assignments.
I will post assignments here.
- Read appendix A. Do exercises 1.x where x is 2 mod 4 and 1 < x < 19 . These are due
Wednesday, January 18. Hint work out exercises 1.5,1.9 and 1.17 or see their
solutions in the back of the text.
- Do exercises 1.x where x is 2 mod 4 and 29 < x < 35. These are due
Wednesday, January 25.
- Do exercises 1.x where x is 2 mod 4 and 29 < x < 35. These are due
Wednesday, January 25.
- Do exercises 1.x where x is 2 mod 4 and 35 < x < 67. These are due
Wednesday, February 1.
- Do exercises 1.x where x is 2 mod 4 and 80 < x < 91. These are due
Wednesday, February 22, but I'll take them as late as March 1.
- Do exercises 1.x where x is 2 mod 4 and 94 < x < 110. These are due
Wednesday, March 1.
- Do exercises 2.x where x is 2 mod 4 and 1 < x < 21. Due March 23.
Handouts
- Smith Normal Form
- Dedekind Domains
- Walecki Decomposition
- Final Exam
- Exercise 2.1 (Fix the authors typos and any other errors in the proof.
Fill in all the gaps and give a complete proof.)
- Find an isomorphic direct product of cyclic groups, when G is the
Abelian group generated by x, y, z subject to the relations:
7x+5y+2z=0, 3x+3y=0,13x+11y+2z = 0.
- Do one of the following two problems:
- Exercise 2.6
- Prove that Q(26(1/2)) is not-norm Euclidean
- Exercise 3.40
- Exhibit a Hamilton decomposition of K3(4).