Date of Award

11-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Advisor

Dr. Mohamed EI Bachraoui

Second Advisor

Dr. Kanat Abdukhalikov

Third Advisor

Dr. James Griffin

Abstract

In this report we shall introduce q- Series and we shall discus some of their application to the integer partition , the sums of squares , and the binomial coefficient . We will present the basic theory of q- series including the most famous theorem and rules governing the e object such as the q-binomial theorem and the Jacobi's triple identity. We hall present the q-binomial coefficients which roughly speaking connect the binomial coefficient to q- Series , we will give the most important results on q-binomial coefficients,and we shall provide some of our new result on the divisibility of binomial coefficients. Moreover, we hall give some well-known applications of q-series to sums of two squares and to integer partition such as Ramanujan's modulo 5 congruence.

Included in

Mathematics Commons

Share

COinS