UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN MATHEMATICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester VI - Application Oriented Subject II - Elementary Number Theory

An Introduction top the Theory of Nmbers(V^th Edition) by Ivan Niven,Herbert S.Zuckarman and Hugh L.Montgometry John Wiley & Sons, lnc.2001 Price $ 6.95

Chapter (1) Divisibility
Chapter (2) 2.1 Congruences
2.2 Solution of Congruences
2.3 Chinese Remaining Theorem
2.8 From page 97 to page 104
(cor 2.42, Th 2.43 and cor 2.44 are omitted)
2.10 Number Theory from an Algebric view point
2.11 Groups rings and fields

Chapter (3) 3.1 Quadratic Residues
3.2 Quadratic reciprocity
3.3 The Jacobi Symbol

Chapter (4) 4.1 Greatest Integer Function
4.2 Arithmetic Function
4.3 The Mobius Inversion formule
4.5 Combinational Number Theory
(4.4 is omitted)

Chapter (5) 5.1 The equation ax+by=c
5.2 Simulataneous Linear Equations
5.3 Pythagorean Triplesv 5.4 Assorted Examples
(only simple problem should be asked)

Books for Reference:

1. Elementary Theory of Numbers, cy. Hsiung, Allied Publishers, 1995.

2. Elmentary Number Theory, Allyn and Bacon lnc.,Boston, 1980.

3. Introduction to Analytic Number Theory, Tom. M.Apostal, Narosa Publishing House, New Delhi, 1989.