Math 406 - Introduction to Number Theory

Instructor: Kathryn (Kate) Truman
Office: Math Building 4410
Email: rendke (at math dot umd dot edu)

Course Info: Summer Session II 2005
July 11 - Aug 19
M - F, 11:00 - 12:20
Room 0303 (Math Bldg)

Office Hours: M-F, 12:30-1:00pm and by appointment.

Book: Elementary Number Theory and Its Applications, 5/e ,Kenneth H. Rosen, 2005, Addison-Wesley, ISBN 0-321-23707-2

Grader: Luquan Yu - Office MTH 2121

Tutor: Kevin Wilson - M-F 12:30-2:30, MTH 0403

Course Description:

Math 406 is an introduction to number theory. Number Theory is one of the most beautiful and elegant areas of mathematics. It also happens to be useful. Through this course I hope to give an idea of both the elegance and the usefulness of number theory as well as introduce you to basic proof techniques. You will be expected to read, understand and do proofs in this course. If you are not yet comfortable with proofs you will be by the end of the semester. To really learn mathematics you need to do mathematics, so you will be expected to work on problem sets. You should also read the material from the text before each class. For a description of the material to be covered see the math departments course syllabus here. The syllabus I handed out in class (in PDF format) is here.

Chapters and sections to be covered (tentative):

Exam 1:
Chapter 1 - all             3.5 days
Chapter 3 - Sections 1-5             3 days
Chapter 4 - Sections 1-3 , 6             3 days
Chapter 5 - Sections 1-3 , 5             1-2 days
Exam 2:
Chapter 6 - all             3 days
Chapter 7 - Sections 1-2             2 days
Chapter 8 - parts             1 day
Chapter 9 - Sections 1-3             2-3 days
Final (Cumulative):
Chapter 11 - Sections 1-3             3 days
Chapter 13 - Sections 1-2             1-2 days
Chapter 14 - Sections 1-2             1-2 days

Grading:

Two 1 hour Exams (100 pts each)           200 pts
Homework 75 pts
Quizzes 125 pts
Final (Cumulative) 150 pts
Total 550 pts

Exam Dates: July 26th, August 9th
Final Date: August 19th

Quiz Dates (tentative): July 15th, July 21st, August 1st, August 5th, August 12th or 15th, and August 17th.

Exam/Quiz Makeup Policy: Exam/Quiz makeups will only be given for University Excused Absences. Any student with a valid reason to be excused from an exam must contact me prior to the exam, either by email or by phone (leave a message at 301.405.5047), and present documentation at the next class session attended. If you need to be excused for a religious observance, you should let me know as soon as possible, but in any case no later than the end of the schedule adjustment period.

You can find old exams given in this course at testbank.

You can find the take home quiz (due Thursday August 18th) and the review for the final exam here

Homework Assignments:

All assignments are tentative until given in class - you are responsible for checking this page or asking me for updates if you miss class.

Assigned Problems Due date Solutions (evens) Other suggested problems
Assignment 1:
1.1 - 4, 28 (to simplify, you may assume the sets are disjoint)
1.2 - 2(a,b), 4(b), 18
1.3 - 4, 24
1.4 - 4, 24
1.5 - 6, 28,36		 7/14/05 solutions 1.1 - 2, 7, 11, 21, 34
1.2 - 8, 15, 19
1.3 - 1, 7, 13, 30
1.4 - 13, 17, 39
1.5 - 5, 8, 13, 33
Assignment 2:
3.1 - 8, 20
3.2 - 12, 20(a)
3.3 - 4, 8, 14		 7/18/05 solutions 3.1 - 3, 6, 13, 15(b)
3.2 - 3, 10(c,d)
3.3 - 3, 23, 31, 30(b-assume a)
Assignment 3:
3.4 - 2(a,b), 4(a,b)
3.5 - 10, 36, 40 (use Lemma 3.5, not Lemma 3.4)
4.1 - 4, 8, 22		 7/20/05 solutions 3.4 - 5(b), 7(b)
3.5 - 2, 11, 19, 20
4.1 - 2(c,f), 3(c), 5, 7(a,d), 15(a), 19, 25
Assignment 4:
4.2 - 6, 18
4.3 - 2, 8, 16(a)
4.6 - 2(a,d)
5.1 - 2(b), 4(b), 22
5.3 - Set up a round robin for 6 teams
5.5 - 6(a)		 7/25/05 solutions 4.2 - 1(b,d), 10, 15
4.3 - 4(c), 12, 15
5.1 - 1(b), 3(b), 12
5.3 - 1(c,d)
5.5 - 5(a)
Assignment 5:
6.1 - 6, 16, 22, 28
6.2 - 2, 12, 16(b,d)
6.3 - 2, 8		 7/29/05
Due by 5pm		 solutions 6.1 - 11, 26, 33, 34
6.2 - 9, 18(a)
6.3 - 1(b), 11(a), 13
Assignment 6:
7.1 - 2(b,d), 6, 12, 16
7.2 - 2(a), 6(b), 8
9.1 - 2(b,c), 4(b,e), 10, 14		 8/3/05 solutions 7.1 - 3, 5, 11, 18, 25
7.2 - 1(a,e), 5(a), 9
9.1 - 7, 15, 19
Assignment 7:
9.2 - 6, 8, 10
9.3 - 2, 4(a), 6(a)
3.6 - 4(a,c)
8.1 - 6, 12
8.2 - 16
8.4 - 6, 16		 8/8/05 solutions 9.2 - 9, 16
9.3 - 11
3.6 - 15
8.1 - 3
8.2 - 1, 13, 17
8.4 - 11
Assignment 8:
11.1 - 8, 10, 14, 20
11.2 - 2, 4, 6
11.3 - 2		 8/12/05 solutions 11.1 - 3, 7, 12, 27
11.2 - 1, 5
11.3 - 1, 3
Assignment 9:
13.1 - 2, 12
13.2 - 4
DO CH13 and CH14 on seperate sheets to hand in
14.1 - 2(b), 4(b), 8		 8/16/05 solutions 13.1 - 3, 6
13.2 - 3
14.1 - 1(a), 6, 11, 27
14.2 - 2, 11, 17(a,b)

Late Homework policy: No late homework will be accepted, since I will be posting solutions the day that homework is due. University Excused Absences will be dealt with on a case-by-case basis.

Exams Given: