MATH 4043 NUMBER THEORY    FALL 2006

 

 

 

Instructor:    Dr. B. Landman

Section:        01

Class Times: T, R 12:30-1:45

Office:                     310 Boyd

Office Hours: T,R 11:30-12:30, 1:45-2:15, or by appointment

E-mail: landman@westga.edu

Phone:          678-839-6489

Textbook:     Elementary Number Theory, Sixth Edition, by David M. Burton

Prerequisite: Successful Completion of MATH 2853 (Linear Algebra) and MATH 3003 (Transition to Higher Mathematics)

 

Topics: We will study divisibility properties of the integers, primes and their distribution, congruences including the Chinese remainder theorem, Fermat’s theorem, Wilson’s theorem, special number theoretic functions, the Euler-phi function, the quadratic reciprocity theorem, perfect numbers, and the Fibonacci sequence

 

 

Grading: Grades will be based on two in-class tests, a comprehensive in-class final exam, homework, and team problems.

 

Tests: The dates for the tests and final exam are as follows:

 

                 Test 1 Tuesday, September 26

Test 2 Tuesday, November 14

Final Exam Thursday, December 7, 11A.M.- 1P.M.

 

Homework: There will be regularly assigned homework (typically once per week) that will be collected and graded. Discussion among students about the homework is permitted, and encouraged. However, each individual must write up his or her own solutions, which should demonstrate that individual’s understanding of the work. In other words, your written work must clearly be your own; NO ONE IS TO SHOW A SOLUTION TO ANOTHER STUDENT BEFORE THE ASSIGNMENT IS DUE. A violation of this will result in a grade of 0 for that entire assignment, even if only one problem is copied (whether a student was the “copier” or “was copied from” will not matter: a grade of 0 will be given for the homework grade).

 

 

 

 

Team Problems: Some problems will be assigned as “team problems,” where a group of 2-3 students will be given a particular problem. These problems will be assigned on (most) Thursdays, the teams will begin working on the problems during the latter part of Thursday’s class, and will present their solutions to the class at the next class meeting on Tuesday. Grades for each assignment will be either a 0 or a 10 per problem, depending on whether the team is able to present their solution in class (partial solutions are acceptable, as long as meaningful effort was contributed by the team members). For each problem, all members of a given team will receive the same grade (unless some member(s) did not participate). The make-up of the teams will change from week to week.

Grading Procedure: The final grade for the course will be determined as follows:

 

Two tests:      30%

Final exam 25%

Homework 25%

Team Problems 20%

 

 

Grading Scale: A: 89 or higher

B: at least 78, but less than 89

C: at least 67, but less than 78

D: at least 56, but less than 67

F: less than 56

 

Make-up Test Policy: There will be no make-up tests given under any circumstances. If one test is missed, the final exam score will be used in its place. If both are missed, the final exam score will replace one of the tests, and the other test score will be 0.

 

Homework Policy: Homework will not be accepted later than the date it is due. Your lowest homework score will be dropped. If a homework assignment is late, then it will represent the “dropped” assignment. Don’t be late with your homework! (I will accept homework up to 5P.M. on the date it is due).

 

Academic Honesty: Homework solutions that are not your own work (even one statement!) will result in a grade of 0 for that homework assignment. If this occurs on a second homework assignment, the student will receive a grade of F for the course. Any act of academic dishonesty on one of the tests or the final exam will result in an F for the course.

 

 

 

 

Classroom rules: It is important that every student and the instructor be able to learn and work in an atmosphere conducive to learning. Interruptions, excessive noise, or other potentially distracting behavior should not take place during the scheduled class time. The following are not allowed during class time (12:30-1:45): cell phones ringing, beeping, etc. (all cell phones must be off!); eating or drinking; classroom conversation not relevant to class discussion; sleeping; excessive tardiness; leaving class early without prior notice to the instructor; any other disruptive behavior. Violations of these rules will be handled as follows: (a) 1st violation: warning (b) 2nd or 3rd violation: 5 pts off of final exam score for each violation; (c) more than 3 violations: student will be removed from class and receive a W (or WF if after the deadline for withdrawal without penalty).

 

Other:         

It is strongly recommended that you allow at least six hours each week, outside of class, for homework and study (more would be better!).

 

Important Dates: see test and final exam dates above

                                  August 16, Wednesday: Last day to add or drop a class

                                  October 6, Friday: Last day to withdraw with grade of W

                                 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ASSIGNMENTS (CORRECT VERSION)

 

Section         Exercises

 

1.1                 1a-h, 2-10,12

1.2                 1-6,8-12,13a-g

1.3                 1-7,10,12

1.4                 1,3-8,11

1.5                 2,3a,b,d,e,f,6,12

1.6                 1,2a,b,3,5a-g,7a-f,8

1.7                 1a,b,3,12c,d,e

2.1                 1-19 (read solution to 18 in back of book)

2.2                 1-7,8a,c,e,g,i,k,o,9b,c,d,14,15,17

2.3                 1a-h,2a-h,3,4,9,10,12,17,20

2.4                 1,2,5a,c,6a,b,c,8a-f,k,l,9a,b,15a,b,c,f

2.6*    1-4,6,10,11,14

3.1*               1,2,4,5,6a-e,8,9,10,20a-e

3.2*               1,4a,c

4.1*               1-5

4.2*               1,3

4.3*               1a-h,2

 

* - as time permits