This book is a condensed version of my Mathematics and Its History, which has reached a
third edition and is now too encyclopedic/overweight to be covered in a single course. Since …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

Since 1973, Galois theory has been educating undergraduate students on Galois groups
and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular …

This comprehensive book covers both long-standing results in the theory of polynomials and
recent developments which have until now only been available in the research literature …

The book gives a detailed account of the development of the theory of algebraic equations,
from its origins in ancient times to its completion by Galois in the nineteenth century. The …

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This
course on field theory is the first semester of the year-long graduate algebra course here at …

This article gives a brief sketch of the evolution of group theory. It derives from a firm
conviction that the history of mathematics can be a useful and important integrating …

В книге изложены основные результаты исследований по теории многочленов, как
классические, так и современные. Большое внимание уделено 17-й проблеме …

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, whose
masters were Abel, Gauss, Jacobi, and Legendre. This book presents an introductory …

The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes
called) are provided, together with many examples and applications. Galois connections …