Titlebook: ;

DOTE

The Integers,o, three, …”, “eins, zwei, drei, …”, “y?, èr, san,…”, or their equivalent, in whatever may be our mother tongue. By childhood we have assimilated, without too much conscious effort, the elementary properties of the addition, subtraction, multiplication and division of the natural numbers; in this te

licence

Introduction to Rings,dean Algorithm for finding the greatest common divisor of two given integers. ‘Polynomials’ share many properties in common with the integers, having a division algorithm and a corresponding Euclidean Algorithm. As our treatment of polynomials proceeds, initially somewhat informally, it will become

Canopy

Introduction to Groups,to consider two binary operations. Since simplicity usually has some advantages we shall in this chapter consider only one binary operation. We begin therefore with the notion of a ‘semigroup’ from which we shall be led to consider a ‘group’, one of the most fundamental structures in modern mathemat

神圣將軍

Topics in Group Theory,results of cardinal importance in the theory of finite groups. In the first of these, we establish the structure of Abelian groups and, in the second, we establish the existence of the so-called ‘Sylow p-subgroups’ of a finite group.

吸引力

aptitude

osteoclasts

Rings,We first formulated the abstract concept of a ring from our considerations of the integers and of polynomials. It is our aim to carry forward and to develop the concept of a ring, for which the integers will continue to serve as a useful exemplar.

深淵

Maximum Drift Velocity in Semiconductors, and mappings may lead to a better understanding of the underlying mathematical processes. We shall outline those aspects of sets and mappings which are relevant to present purposes and, for the delectation of the reader, conclude with a few logical paradoxes in regard to sets.

Tidious

nonsensical