Course Code: MATH-403

Number Theory

Credit Hours: 3

Prerequisites: Linear Algebra

Objectives of course:

The focus of the course is on study of the fundamental properties of integers and

develops ability to prove basic theorems. The specific objectives include study of

division algorithm, prime numbers and their distributions, Diophantine equations and

the theory of congruences.

Course Contents:

Divisibility, Euclid’s theorem, Congruences, Elementary properties, Residue classes

and Euler’s function. Linear congruence and congruence of higher degree,

Congruences with prime moduli, The theorems of Fermat, Euler and Wilson., Primitive

roots and indices, Integers belonging to a given exponent, composite moduli Indices,

Quadratic Residues, Composite moduli, Legendre symbol, Law of quadratic

reciprocity, the Jacobi symbol, Number-Theoretic Functions, Mobius function, the

function [x], Diophantine Equations, Equations and Fermat’s conjecture for n = 2, n = 4.

Recommended Books:

1.Rosen K.H.,2000. Elementary Number theory and its Applications. 4

th ed.

USA:Addison-Wesley.

2. Apostal T.M., 2010. Introduction to Analytic Number Theory. 3rd ed. NY: Springer.

3. Griffin H., 1954. Elementary Theory of Numbers. 1st ed. NY Mc Graw Hill.

4. William J. Leveque, Topics in Number Theory, Volumes I and II.

5. D.M. Burton, Elementary Number Theory, McGraw-Hill, 2007.

6. S.B. Malik , Basic Number Theory, Vikas Publishing

**RESEARCH PROJECT**

*N/A*

**ASSESSMENT CRITERIA**

Mid exam: 30

Sessional: 20

Project: --

Assignments: 10

Presentation: 10

Final exam: 50

Total: 100

**RULES AND REGULATIONS**

*75% attendance is compulsory to appear in Final Term exam.*