Number Theory (1701-503)
SUMMER 2000

INSTRUCTOR: Dr. Abdul Hassen
 

Course Number: 1701-503
LEVEL:    Gradute Course

TEXT: An Introduction to the Theory of Numbers (5th Ed.) by I. Niven, H. Zuckerman, H. Montgomery, John Wiley

CONTENT:     In this course we will study the following topics.

1.    Divisibility and Prime Numbers

        Basic Properties
        Primes

2.    The Theory of Congruences

    Basic Properties
    Residue Systems
    Higher Order Congruence
    Quadratic Residues
    Quadratic Reciprocity.

3.    Some Diophantine Equation

           The Equations ax + by =c.
            Pythagorean triples
            Fermat's Last Theorem

4.    Simple Continued Fractions,

            Basic Properties
            Approximation of Irrationals by Rationals
            Pell's Equations

        5.    Primes and Multiplicative Number Theory

            The Prime Number Theorem
            Dirichlet Series

        6.    Algebriac Numbers

                Basic Concepts
                Algebraic Integers

Relevant Web Sites:

Some of the famous Number Theorists:

Pythagoras  Euclid,  Erdös, Euler,  Fermat, Gauss, Goldbach, Hilbert, Lagrange,  Ramanujan,

Female mathematicians Biographies of Women Mathematicians

The MacTutor History of Mathematics archive

 Eric's Treasure Troves of Sciences,

Favorite Mathematical Constants,

Things of interest to Number Theorists

What is New in Mathematics

Mathematics Organizations

The American Mathematical Society

The Mathematical Association of America

 Some of my colleagues whose  web pages are (mathematically) informative:

Thomas Osler,  Eric Milou, Hieu Nguyen (Rowan University) Paul Pasles(Villanova University, PA)  Doron Zeilberger (Temple University)

 
For your comments: Hassen@rowan.edu

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This page was last updated on 2/11/2000