MATH 406 -- Introduction to Number Theory

Section 0101 -- Fall, 2011

Instructor: Thomas Haines
Office: 4403 Mathematics Bldg
Phone: (301) 405-5103

MATH 406 is an introduction to number theory, covering the basic theoretical groundwork related mainly to factorization and congruences. Applications include data encryption schemes such as RSA.

Here is the syllabus for the course, including exam dates, and grading policy. It also includes a list of supplemental texts we will use during the course.

READ THIS: The honor pledge; academic integrity; what constitutes cheating

Class Times: MWF: 11:00-11:50 am.
Room: MTH 0103.
Homework: Homework will be assigned once a week. CHECK THIS SPACE WEEKLY for assignments! The assignments below are tentative until one week-before the due date. This means that I reserve the right to modify any problem set below until one week before it is due. You are encouraged to work with your classmates on the homework, but remember that your personal understanding will be tested on exams. As a general rule, only some of the problems you turn in will be marked by the grader.

ANNOUNCEMENTS:

08/26/11: Here is an old Exam 1 I gave a few years ago.

11/09/11: Here is an old Exam 2 I gave a few years ago. Solutions .

11/28/11: Solutions to Exam 2.

12/12/11: Sample final exam .

HOMEWORK 1 (Due 09/07/11): 1.1 #4,5, (you don't have to use the well-ordering property; you can do it as in lecture for the square root of 2), 11, 27 Challenge problem: #19; 1.3 #2.

HOMEWORK 2 (Due 09/14/11): 1.1 #32-34 (show #33 as stated is false by giving a counterexample; then give the correct statement and prove it!); 1.2 #23,24 (in #24 "Exercise 21" should be "Exercise 23"); 1.3 #5,8,24,30; 1.4 #7,8.

HOMEWORK 3 (Due 09/21/11): 1.5 #5,17,19,38,42; 3.1 #6-9, 13.

HOMEWORK 4 (Due 09/28/11): 3.1 #29; 3.3 #11-13, 16, 24; 3.4 #4; 3.5 #5,7, 10.

HOMEWORK 5 (Due 10/05/11): 3.5 #11-13,32,45,49; 3.6 #4; 3.7 #1(c,e), 16.

HOMEWORK 6 (Due 10/12/11): 4.1 #3,8,27,32-36; 4.2 #2(c-e), 8. (NOTE: Exam 1 will cover material up to and including 4.2.)

HOMEWORK 7 (Due 10/19/11): 4.2 #10,15; 4.3 #4(c-d), 12, 13; 5.1 #2(c),4(b),22.

HOMEWORK 8 (Due 10/26/11): 6.1 #3,4,11,17,22; 6.3 #3-5,10,; 7.1 #2,4.

HOMEWORK 9 (Due 11/02/11): 7.1 #6, 34; 7.2 #10,11,35; 7.3 #4; 7.4 #17,18,20, 23, 24.

HOMEWORK 10 (Due 11/09/11): 8.1 #5,6,16 ; 8.3 #1,4; 8.4 #2,5,12,15.

HOMEWORK 11 (Due 11/16/11): 9.1 #5,7,11,14-17 ; 9.2 #9-11. (NOTE: Exam 2 will cover material from Exam 1 up to and including this homework.)

HOMEWORK 12 (Due 11/23/11): 9.3 #2,8,10,13,14; 9.4 #2,7.

HOMEWORK 13 (Due 11/30/11): 9.4 #8-10; 11.1 #1,5,7,12,28(a),47.

HOMEWORK 14 (Due 12/07/11): 11.1 #44,48; 11.2 #1(c-e),3-6; 11.3 #1(f),2,3.

HOMEWORK 15 (Due MONDAY 12/12/11): 13.1 #1-5; 13.3 #2(g,h), 3(d).

EXTRA PROBLEMS : 11.1 #???; 11.2 #??; 13.1 #??; 13.3 #??.