MAT 3080
  Number Theory


  Fall 2006 Course Information



Instructor De-Jun FENG
Office Room 211, Lady Shaw Building,  Tel:  2609-7965
Lectures Wednesday  2:30pm-4:15pm in  SC  LG23
Thursday 4:30pm-5:15pm in       SC  LG23
Tutorials
  Thursday  9:30am- 10:15am  SCE E106
 Thursday 12:30pm- 1:15pm   LSB G35
TA WU  Dan ,  Office:    Office hour: TBA                   Email: dwu@math.cuhk.edu.hk

 ZHANG Jia Jin       Office: AB1,  R505    Office hour:       M5-7, T5-7, W3-4.  Tel:  3163-4298
Textbook  A. Baker 
A concise introduction to the theory of numbers,  Cambridge University Press
Reference
 I. Niven, H.S. Zuckerman and H.L. Montgomery
An introduction to the theory of numbers,  John Wiley & Sons
 
D. M. Burton 
Elementary number theory, Wm. C. Brown Publishers
Grading Final exam : 50 percent
Midterm: 40 percent
Homework: 10 percent  
Exams Midterm:  Oct 18, 2:30pm -4:15 pm,  No Make Up! 
Final:  Administered by the examination section of the University.
Homework Here is the assigned homework  for the class. The homework will be collected in the box of MAT3080 (2nd follr, LSB).   Late homework  will not be accepted.
Announcement
 Here is a proof  for the result that  two  positive definite binary  forms are equivalent iff  they have the same reduced form. 

Outline:  Here is the tentative outline for the class.  Please read the indicated sections before each lecture.


  Wednesday(2:30pm-4:15pm)
    Thursday(4:30pm-5:15pm)
      Sep 6
  Fundations, division algorithm, greatest common divisor
 (1.1, 1.2, 1.3)
       Sep  7
  Euclidean algorithm (1.4)
      Sep 13
  Fundamental Theorem, properties of primes (1.5, 1.6)
      Sep 14
  Properties of primes (cont-)    (1.6)
     Sep 20
Function [x], multiplicative functions, Euler function  (2.1, 2.2, 2.3)
      Sep 21
  Mobius function  (2.4)
     Sep 27
  The function tau(n), sigma(n), average order
  (2.5, 2.6)
     Sep 28
  Average order (cont-) (2.6)
     Oct 4
  Perfect number, Riemann Zeta function (2.7, 2.8) 
     Oct 5
  Riemann Zeta function (cont- ) (2.8)
     Oct 11
  Definition of congruence, Chinese remainder theorem (3.1, 3.2)
     Oct 12
  The theorems of Fermat and Euler (3.3)
     Oct 18
   Mid-Term Exam  
     Oct 19
  Wilson's theorem  (3.4)
     Oct 25
  Lagrange's theorem (3.5) 
     Oct 26
   Primitive roots (3.6)
     Nov 1
  Primitive roots (cont-), - and indice (3.6, 3.7)
     Nov 2
  Legendre'd symbol, Euler's criterion (4.1, 4.2)
 
     Nov 8
  Euler's criterion (cont-),  Gauss's lemma  (4.2, 4.3)
     Nov 9
  Law of quadratic reciprocal (4.4)
     Nov 15
  Law of quadratic reciprocal (cont-) , Jacobi's symbol (4.4, 4.5)  		     Nov 16
 Equivalence
 
     Nov 22
  Reduction, Sum  of  two squares  (5.2, 5.3)
     Nov 23
  Sum of  two squares (cont-)  (5.3)
     Nov 29
  Sum of  four squares (5.4)
     Nov 30
  Review for final exam