Algebraic Structures and Applications

摘要

This chapter presents important and useful algebraic structures, that of a group. Group theory and group theoretical methods have played a vital role in certain crucial areas in these developments. Group theory is a vast subject with wide applications both within mathematics and in the real-world problems. The chapter discusses polynomial rings over the field of all real numbers and the field of all complex numbers. The study of these rings leads to the understanding of algebraic and projective geometry which has a wide range of applications in such diverse areas as robotics and computer vision. Every rigid motion is the composite of a translation and an orthogonal transformation which may be a rotation or a reflection in the above sense. Geometrical applications help in understanding the physical phenomena.