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.
    1. 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.
    2. Do exercises 1.x where x is 2 mod 4 and 29 < x < 35. These are due Wednesday, January 25.
    3. Do exercises 1.x where x is 2 mod 4 and 29 < x < 35. These are due Wednesday, January 25.
    4. Do exercises 1.x where x is 2 mod 4 and 35 < x < 67. These are due Wednesday, February 1.
    5. 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.
    6. Do exercises 1.x where x is 2 mod 4 and 94 < x < 110. These are due Wednesday, March 1.
    7. Do exercises 2.x where x is 2 mod 4 and 1 < x < 21. Due March 23.
  • Handouts
    1. Smith Normal Form
    2. Dedekind Domains
    3. Walecki Decomposition
    1. Final Exam
      1. Exercise 2.1 (Fix the authors typos and any other errors in the proof. Fill in all the gaps and give a complete proof.)
      2. 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.
      3. Do one of the following two problems:
        1. Exercise 2.6
        2. Prove that Q(26(1/2)) is not-norm Euclidean
      4. Exercise 3.40
      5. Exhibit a Hamilton decomposition of K3(4).