numbertheory115a

MATH 115A. INTRODUCTION TO NUMBER THEORY.

Instructor: Azer Akhmedov

         Office: South Hall 6702
         Office Hours: Wednesday 3-6pm.
         E-mail: akhmedov AT math.ucsb.edu

        TEXTBOOK: "An Introduction to the theory of numbers" by Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery.


        GRADING: SCHEME 1. Homework: 20%, MIDTERMS: 20% + 20% = 40%,    FINAL: 40%
SCHEME 2. Homework: 20%, MIDTERMS: 15% + 15% = 30%,    FINAL: 50%

                               I will choose the better of the two grades.

        HOMEWORK: Homeworks are due every Friday in class. You will find them on this page starting Tuesday, Jan. 08.
                                    As an exception, the first homwork is due on Monday, January 14th.
                                    There will be a total of 10 homeworks. I'll drop the lowest score and substitute it with the highest.

        MIDTERMS:   Midterm 1. Time: February 6th. 1-00-1:50pm. Place: In classroom.
                                   Midterm 2. Time: March 3rd. 1-00-1:50pm. Place: In classroom.
                                 Books and calculators are not allowed. You may use one 3x5 notecard. Please bring ID and one big bluebook.

                                   REVIEW SESSION is on SUNDAY, 4:30-5:30pm at South Hall, Room 6635.
                                   PRACTICE PROBLEMS

        FINAL:            Time/Place: THURSDAY, March 20th, 4-7pm. IN CLASSROOM.
                                 Books and calculators are not allowed. You may use one 3x5 notecard. Please bring ID and one big bluebook.
                                  REVIEW SESSION is on WEDNESDAY, 4:30-5:30pm at South Hall, Room 6635.
  PRACTICE PROBLEMS




          Tentative Course Scedule:

Date	Topic	Homework	Notes
01/07	Prime Numbers. Euclid's Theorem.
01/09	Divisibility.
01/11	Euclidean Algorithm.
01/14	The Binomial Theorem.	Section 1.2. # 1, 5, 6, 13, 14, 15, 21, 24, 31.
01/16	Congruences.
01/18	Fermat's Little Theorem.	Section 1.3. # 5, 9, 11, 13, 18, 21, 27.
01/21	MARTIN LUTHER KING Jr. DAY
01/23	Wilson's Theorem.
01/25	Review. Euler's Function.	Section 2.1. # 1, 2, 6, 10, 11, 12, 14, 19.
01/28	Solutions of Congruences Chinese Remainder Theorem
01/30	Sum of Two Squares.
02/01	Groups. Definition, Examples.	Sect.2.2. # 3, 4, 5. Sect.2.3. # 3, 10, 15, 18, 29.
02/04	Isomorphism of Groups.
02/06	MIDTERM 1.
02/08	Quadratic Residues.	Sect.2.4. # 2, 3. Sect.2.10. # 1, 2, 3, 4, 5, 7
02/11	Quadratic Reciprocity.
02/13	Jacobi Symbol.
02/15	Jacobi Symbol.	Sec.3.1. # 1, 3, 7, 10. Sec.3.2. # 6, 7, 8, 9, 10, 11.
02/18	PRESIDENTS DAYS
02/20	Binary Quadratic Forms.
02/22	Reduction of Quadratic Forms.
02/25	Sums of Two Squares Revisited.	Sec.3.3 # 1, 2, 4, 6, 7.
02/27	Positive Definite Quadratic Forms
02/29	Review of the Chapter.
03/03	MIDTERM 2.	Sec.3.4. #1, 2, 6, 7, 8, 9, 10.
03/05	Greatest Integer Function.
03/07	Arithmetic Functions.
03/10	Sum of Divisors. Perfect Numbers.
03/12	Mobius Inversion Formula.	Sec. 4.1. # 1, 3, 6, 16, 30. Sec. 4.2. # 1, 2, 3, 9, 14.
03/14