MATH3110 (Number Theory)

MATH3110, Spring 2004

Instructor: Dr R.M. Green

Venue: MWF 9, DUAN G2B21

Office: MATH 313

Email: rmg [AT] euclid.colorado.edu

Office Hours: M 2, W 3, F 10, or by appointment

Text

A friendly introduction to Number Theory by Joseph H. Silverman (second edition)

Outline of syllabus

We plan to cover the first 20 chapters of the text, and selected chapters beyond the 20th.

Grading

Your grade will be computed from:

• Homework: 1/6 of final grade;
• Two Midterms: 1/4 of final grade each;
• Final Exam: 1/3 of final grade.

The three examination scores may be individually curved to produce an appropriate profile.

Tests

The two midterms will be held during class on Wednesday, February 11, and Wednesday, March 17, 2004. The final exam is on Tuesday May 4 from 4.30pm to 7pm in the usual classroom. Bring your CU student ID to all of your tests.

Homework

Homework is due at the beginning of class. Some, but not all of the problems will be graded. Show all your working.

Students With Disabilities

If you qualify for accommodation because of disability, please submit a letter from Disability Services (DS) to your instructor early in the semester so that your needs may be addressed. DS determines accommodations based on documented disabilities (303-492-8671, Willard 322, www.colorado.edu/sacs/disabilityservices).

Missed Exams

If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify your instructor at least two weeks in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented illness), that midterm exam score will be replaced by your other midterm exam grade. If you miss both exams for acceptable reasons, your course grade will be based entirely on your final exam score. If you miss the final exam and have not rescheduled it in advance, you will get an F or an incomplete in the course, depending on the circumstances.

Religious Obligations

If you have a religious obligation that conflicts with one of the exams, please let your instructor know at least two weeks in advance. For the University's policy on religious obligations see www.colorado.edu/policies/index.html.

Student Classroom and Course-Related Behavior

See the University's policy at www.colorado.edu/policies/index.html.

Honor Code

For information on the University's honor code see www.colorado.edu/academics/honorcode/. All work on exams must be your own without help from other students. You are encouraged to work together in solving homework problems; however, the write-up of the homework problems should be your own.

Deadlines

To add a course:

Wed 21 Jan: deadline to add a course without the instructor's signature.

Fri 30 Jan: deadline to add a course without petitioning your dean.

To drop a course

Wed 28 Jan: deadline to drop a course without the instructor's signature.

Wed 25 Feb: deadline to drop a course without petitioning your dean.

To arrange a change in your final exam schedule

Fri 20 Feb: deadline for students who have three or more final exams the same day to make arrangements to change their final exam schedule.

Homework assignments

Assignment 1 (assigned Mon 12 Jan, due Mon 26 Jan)

page 12: 1.2, 1.3, 1.4 (a)

page 18: 2.1 (a), 2.2, 2.3 (a), 2.6

Graded: 1.3 (3), 1.4 (a) (2), 2.2 (2), 2.6 (3)

Assignment 2 (assigned Wed 21 Jan, due Mon 2 Feb)

page 21: 3.1 (a, b), 3.2

page 26: 4.2 (a, b, c, d)

page 32: 5.1, 5.4 (a, b), 5.5 (a)

Graded: 3.1 (a, b) (3 points), 5.1 (4 points), 5.4 (a, b) (3 points)

Assignment 3 (assigned Mon 26 Jan, due Mon 9 Feb)

page 41: 6.1 (a), 6.2 (a, b)

page 49: 7.1, 7.4 (a, b), 7.5

page 56: 8.1 (b), 8.2, 8.3, 8.4 (a, c)

Graded: 6.2 (b) (3 points), 7.4 (a, b) (4 points), 8.1 (b) (3 points)

Assignment 4 (assigned Mon 2 Feb, due Mon 16 Feb)

page 63: 9.1 (a), 9.2 (a), 9.3 (a), 9.4

Graded: 9.1 (a) (3 points), 9.3 (a) (2 points), 9.4 (5 points)

Assignment 5 (assigned Mon 9 Feb, due Mon 23 Feb)

page 67: 10.1, 10.2

page 73: 11.1, 11.2 (a), 11.3, 11.5 (a, b), 11.9

Graded: 11.3 (3 points), 11.5 (a, b) (2 points each), 11.9 (3 points)

Assignment 6 (assigned Mon 16 Feb, due Mon 1 Mar)

page 80: 12.2 (a)

page 86: 13.2, 13.3, 13.4 (c, d)

page 91: 14.2, 14.3 (a, b)

Graded: 12.2 (a) (4 points), 13.3 (3 points), 14.3 (a, b) (3 points)

Assignment 7 (assigned Mon 23 Feb, due Mon 8 Mar)

page 99: 15.2, 15.3 (a, b), 15.7 (a, c)

Graded: 15.3 (a, b) (3 points), 15.7 (a) (2 points), 15.7 (c) (5 points)

Assignment 8 (assigned Mon 1 Mar, due Mon 15 Mar)

page 107: 16.1, 16.3, 16.5

page 112: 17.1, 17.2, 17.5 (a, b)

Graded: 16.3 (a) (3 points), 17.1 (4 points), 17.5 (a, b) (3 points)

Assignment 9 (assigned Mon 8 Mar, due Wed 31 Mar)

page 117: 18.1

page 123: 19.1 (a, b), 19.2, 19.3

Graded: 19.2, 19.3 (5 points each, plus 2 bonus points for 18.1)

Assignment 10 (assigned Mon 15 Mar, due Mon 5 Apr)

page 132: 20.4, 20.6, 20.7 (a), 20.8

Graded: 20.4 (3 points), 20.6 (4 points), 20.8 (3 points)

Assignment 11 (assigned Mon 29 Mar, due Mon 12 Apr)

page 139: 21.1, 21.2, 21.3, 21.4 (a)

Graded: 21.2 (4 points), 21.3 (3 points), 21.4 (a) (3 points)

Assignment 12 (assigned Mon 5 Apr, due Mon 19 Apr)

page 149: 22.1, 22.3

Additional problems for Assignment 12 (assigned Mon 12 Apr, due Mon 19 Apr)

page 160: 23.1 (a, b), 23.3, 23.4, 23.6

Graded: 22.3 (c, d) (4 points), 23.1 (a, b) (2 points), 23.4 (4 points)

Assignment 13 (assigned Mon 19 Apr, due Mon 26 Apr)

page 169: 24.1, 24.3, 24.4, 24.6

Graded: 24.1 (4 points), 24.3 (3 points), 24.6 (3 points)

Final scores

A

1082 and above (highest score was 1194)

(8 students)

A-

1058-1073

(2 students)

B

965-1028

(7 students)

B-

953-955

(3 students)

C

840-892

(3 students)

C-

834

(1 student)

D+

830

(1 student)

D

747-794

(2 students)

F

683 and below (lowest score was 184)

(4 students)