Elementary Number Theory -- Mathematics 580

Frank Thorne - Fall 2013

University of South Carolina


Instructor: Frank Thorne, LeConte 400G, thorne [at] math [dot] sc [dot] edu

Office Hours: Tuesdays, 10:30-11:30 and Wednesdays, 9:30-10:30 and 1:30-2:30.


Course objectives/learning outcomes:

Successful students will: In addition, students will also:

Warning. You should expect 5-8 hours of homework a week in this class, which is more than most other instructors assign; in my experience there is no other way to learn the material. Your consistent effort will certainly lead to improved understanding, and it will almost certainly lead to you earning high grades.


  • Text : Dudley, Elementary Number Theory, buy it here or at the bookstore.

    This introductory textbook is a little bit old-fashioned, but it is delightful, it is fun to read, it is geared towards beginners, and unlike some other books you don't need to remortgage your house to buy it.

  • Lectures : LeConte 121, TR, 2:50-4:05.

  • Exam schedule : In-class midterms will be on Thursday, October 3 and Thursday, November 7.

    The final exam will on Wednesday, December 11 at 12:30 p.m.

    Here are the previous midterms, with solutions.

  • Homework :

    Warning. I assign a lot of homework.

    The homework is intended to take 5-8 hours a week. That is a lot. Please count on making a consistent effort to do well in this class! Starting the night before is a bad idea.

    If homework takes you more than 10 hours on any given week, then that is more than I intended; please let me know.

    There will be at least one bonus problem on each homework, each worth one or two points, up to a maximum score of 11/10 on each week's homework. This is the only way to earn extra credit; please note that bonus problems will not be accepted late.

    Graduate credit: If you want graduate credit, you are required to do at least one bonus problem from every other homework (i.e., do one from HW1 or HW2, etc.) Bonus problems on top of that count for extra credit.

  • Grading :

    Please note. You will be graded both on correctness and on quality of exposition. Indeed, a major focus of Math 580 is the ability to communicate mathematical ideas clearly. The standard is that someone who doesn't know the answer should be able to easily follow your work. In particular, please write in complete English sentences and draw clear diagrams where appropriate. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

    Grading scale: A = 90+, B+ = 85+, B = 78+, C+ = 73+, C = 66+, D = 52+.

    Please note that my grading scale is more generous than the usual 10-point scale. However, I am a (slightly) stricter grader than most. This is intended to balance out.

      Grade component     % of grade  
      Two in-class exams     20% x 2  
      Final exam:     35%  
      Homework:     25%  

  • Contacting me : Please contact me if you have any questions about the course, about my expectations, about my lectures, about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my job to help you succeed. The best ways to get help are to come to office hours (no appointment necessary) or to e-mail me (I will almost always reply within 24 hours). If neither of these work for you then please e-mail me to set up an appointment.

    Please note: If you come to office hours, please don't be shy about interrupting me! I'm usually in the middle of something, but it can wait.

  • Make-up policy :

    If you have a legitimate conflict with any of the exams it is your responsibility to inform me at least a week before the exam. Otherwise makeup exams will be given only in case of documented emergency.

    Late homework will be accepted once per student, up to a week late; after that, no late homework please except in case of emergency.

    Academic honesty and attendance are expected of all students.

    Calculators will not be needed or allowed.

  • Schedule and homeworks :

    (Note: Daily topics are listed only for some days, and when in the future are subject to change.)

  • (R) August 22: Hanc marginis exiguitas non caperet.

  • (T) August 27: Disibility and the Euclidean algorithm (Chapter 1)

  • (R) August 29: Induction and prime factorizations (Chapter 2)

  • (T) September 3: Uniqueness of prime factorizations (Chapter 2)

  • (R) September 5: Linear Diophantine equations (Chapter 3)

  • (T) September 10: Congruences (Chapter 4)

  • Homework 1, due Tuesday, September 2.

  • Homework 2, due Thursday, September 11.

  • Homework 3, due Friday, September 26.

  • Homework 4, due Friday, October 25.

  • Homework 5, due Monday, November 11.

  • Homework 6, due Thursday, November 21.

  • Homework 7.