Math 343L -- APPLIED NUMBER THEORY -- Fall 2011. (Unique ID 55335)

Here is the FINAL EXAM ... and now an answer key . you can ignore half of the last problem. (At one point I was going to ask you to prove that the points of order 3 are the inflection points .

(This is a provisional outline of what we will do this semester. Everything is subject to change, and changes will be announced in class.)

Here is a homework set for you to occupy you over Thanksgiving :-).

Here is the Maple script you followed on Sept 6, to get a feel for how to work with Maple.

      Instructor: Dave Rusin ( 
      Office hrs: T, Th 11:30am-1:30pm; W 11am-1pm; and by appointment, in RLM 9.140 
      Class meets TTH  9:30am - 11:00am  in CBA 4.326

      Text: None ... yet

Course webpage:

It is unlikely that I will use Blackboard for this course (unless and until someone shows me how it can be useful!)


Basic properties of integers, including properties of prime numbers, congruences, and primitive roots. Introduction to finite fields and their vector spaces with applications to encryptions systems and coding theory.

That's the official course description. But in fact we can do whatever we like! You should alert me to topics that you think would be kewl. I have worked with cryptographers and number theorists, and used number theory in combinatorics and geometry. The sky's the limit!


Prerequisite: Mathematics 328K (Number Theory) or 343K (Abstract Algebra) with a grade of at least C. You will find the course to be very difficult if you are not comfortable with modular arithmetic, prime numbers, and linear algebra.


Homeworks: Homeworks will be assigned on a roughly weekly schedule. Collectively they will count for one-third of the semester grade. Make sure your homework is neat and orderly and is written in complete sentences where appropriate. I would like to have you work computational problems on a computer on a regular basis. Find the math department computer lab and learn how to run a program such as Maple or Magma. (We will discuss these in class as necessary.)

Exams: There will be 2 mid-term exams, approximately six weeks apart. (They will be firmly scheduled several weeks in advance.) Together they will be worth one-third of your semester grade. The final exam will be cumulative, and also worth one-third of your semester grade.

Class participation: You will not be graded on this. So it's not important, right? WRONG! Wrong, wrong, wrong!. I would like to spend some of the time every class day having students present their answers to the problems I have assigned. Trust me, if you have absolutely nothing to say during class, you're just not getting it, and you should see me pronto. It is very easy to lull yourself into believing that everything makes sense in this subject by never forcing yourself to articulate a question, to try to present a solution, or to propose an example.

Grades: Among the students in this class we will probably see every possible grade from A to F at the end of the semester. Which do you want to earn? Please write down my office location and office hours and plan to see me during the semester.

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Drop dates: Sept 9 is the last day to drop a class for a possible refund. November 1 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. Nov. 1 is also the last day a student may change registration in a class to or from the pass/fail or credit/no credit basis. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page,

Tentative Schedule

TBA Final examination: Friday, December 9, 2:00-5:00 pm