MATH 115B. INTRODUCTION TO NUMBER THEORY.

                       

  Instructor: Azer Akhmedov

  OFFICE:          South Hall, Room 6702.
  Office Hours:    Wednesday, 3-6pm.


 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 Monday in class. You will find them on this page.
                                    There will be a total of 10 homeworks. I'll drop the lowest score and substitute it with the highest.

        MIDTERMS:   Midterm 1. Time: May 5th. 1-00-1:50pm.   Place: In classroom.  PRACTICE PROBLEMS
                                   Midterm 2. Time: June 02nd. 1-00-1:50pm.  Place: In classroom.
                                   Books and calculators are not allowed. You may use one 3x5 notecard. Please bring ID and one bluebook.
                                  

       FINAL EXAM: Time: Wednesday, June 11th, 4-7pm.   Place: In classroom.
                                   Final Exam covers all the material taught during the quarter.



       I intend to cover the following topics:

      Chapter 5.  Diophantine Equations.

          Liner Eqautions.
          Simultaneous Linear Equations.
          Pythagorean Triples.
          Other examples of Diophantine Eqautions.


      Chapter 6. Farey Fractions and Irrational Numbers.

          Rational Approximations.
          Irrational Numbers.
          Geometry of Numbers.


      Chapter 7.  Simple Continued Fractions.

         The Euclidean Algorithm.
         Uniqueness.
         Infinite Continued Fractions.
         Irrational Numbers and Best Possible Approximations.
         Periodic Continued Fractions.
         Pell's Equation.


   Chapter 8. Primes and Multiplictive Number Theory.

         Elementary Prime Number estimates.
         Dirichlet Series.
         Estimates in Arithmetic Functions.
         Primes in Arthmetic Progressions.


    HWK #1. Due Monday April 7th. 
     Section 5.4.  # 1, 2, 7, 10.
     Section 5.1.  # 2, 5, 8, 9.

    HWK #2. Due Friday, April 11th.
      Section 5.3.  # 1, 2, 6, 7, 8, 9, 10.
      Section 5.4.  # 10, 12.

   HWK #3. Due Friday, April 18th.
      Section 6.3.  # 1, 2, 3, 6, 10.
      Section 6.4.  # 1, 2, 4, 12.

   HWK #4. Due Monday, April 28th.
      Section 7.1.  # 1, 3, 4, 5.
      Section 7.2.  # 1.
      Section 7.3.  # 1, 3, 4.

  HWK #5. Due Monday, May 05th.
    
    Section 7.4. # 1, 2, 3.
    Section 7.6. # 1, 2, 3.
    Section 7.7. # 2, 3.

 HWK #6.  Due Monday, May 12th.

  Section 7.8. # 3, 5, 6, 7, 8, 9, 10, 11.


HWK # 7.  Due Monday, May 19th.

   Section  8.1.  # 4, 5, 6, 8, 11, 12, 13.  


HWK #8. Due Friday, June 06th.

    HWK 8