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