This second edition gives a thorough introduction to the vast field
of Abstract Algebra with a focus on its rich applications. It is
among the pioneers of a new approach to conveying abstract algebra
starting with rings and fields, rather than with groups. Our
teaching experience shows that examples of groups seem rather
abstract and require a certain formal framework and mathematical
maturity that would distract a course from its main objectives. Our
philosophy is that the integers provide the most natural example of
an algebraic structure that students know from school. A student
who goes through ring theory first, will attain a solid background
in Abstract Algebra and be able to move on to more advanced topics.
The centerpiece of our book is the development of Galois Theory and
its important applications, such as the solvability by radicals and
the insolvability of the quintic, the fundamental theorem of
algebra, the construction of regular n-gons and the famous
impossibilities: squaring the circling, doubling the cube and
trisecting an angle. However, our book is not limited to the
foundations of abstract algebra but concludes with chapters on
applications in Algebraic Geometry and Algebraic Cryptography.
General
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