Group Theory

IntroBooks Team

Beschreibung

By many expert mathematicians, group theory is often 
addressed as a central part of mathematics. It finds its origins 
in geometry, since geometry describes groups in a detailed 
manner. The theory of polynomial equations also describes the 
procedure and principals of associating a finite group with any 
polynomial equation. This association is done in such a way 
that makes the group to encode information that can be used 
to solve the equations. This equation theory was developed by 
Galois. Finite group theory faced a number of changes in near 
past times as a result of classification of finite simple groups. 
The most important theorem when practicing group theory is 
theorem by Jordan holder. This theorem shows how any finite 
group is a combination of multiple finite simple groups. 
Group theory is a term that is mainly used fields related to 
mathematics such as algebraic calculations. In abstract algebra, 
groups are referred as algebraic structures. Other terms of 
algebraic theories, such as rings, fields and vector spaces are 
also seen as group. Of course with some additional operations 
and axioms, mathematicians accept them as a group. The 
methods and procedures of group theory effect many parts 
and concepts of mathematics as well as algebra on a large 
scale. Linear algebraic groups and lie groups are two main 
branches or say categories of group theory that have advanced 
enough to be considered as a subject in their own 
perspectives. 
Not only mathematics, group theory also finds its roots in 
various physical systems, especially in crystals and hydrogen 
atom. They might be modeled by symmetry groups. Thus it 
can be said that group theory possess close relations with 
representation theory. Principals and ideas of group theory are 
practically applied in the fields of physic, material science and 
chemistry of course. Group theory is also considered as a 
central key in the studies and practices of cryptography. In 
2000s, more than 10000 pages were published in the time 
span of 1960 to 1980. These publications were a collaborative 
effort in order to culminating the result as a complete 
classification of infinite simple groups. For the practitioners and 
learners of mathematics or even physics the theory of groups 
has a great importance. Not all aspects of this theory are used 
in mathematics or physics. But there are some ideas and 
principals that help a lot as you advance to higher level 
mathematics, it is very same with the physics. Full application of 
this wide theory is not possible on a single subject anyhow. 
However it is partially applied in both cases, and still leaves a 
great influence.

Verfügbar seit: 09.11.2019.

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