Why Study the Mathematical Theory of Groups?
The title of this page recalls a familiar series of instructional books on computer topics that require no previous knowledge of the subject, giving explanations that would be considered too elementary for the notice of the specialist. Of course, they are not for “dummies” but for those intelligent enough to want to learn, and who can learn relying on their own resources. The purpose of this page is to explain the wonderful algebraic properties of matrix representations of finite groups, which are not only delightful, but also useful in many connections. This theory extends naturally to infinite and continuous groups, so it may be considered fundamental and general. One reason to study groups is the mathematical beauty of the subject, but an equally valid reason is for its practical application, especially in quantum mechanics and related subjects. The source of this application is that groups express symmetry. In the macroscopic world, we observe coarse bodies and represent them by id
