Algebra in Ancient and Modern Times

This book, which is intended for undergraduate students having no background in calculus, attempts to trace the growth of algebra from its origins in ancient times to its present state as a major part of mathematics and a powerful tool in theoretical physics. Especially interesting is the treatment of Indian mathematics in the period between the sixth and twelfth centuries, and the work of the Italian mathematicians during the fifteenth and sixteenth centuries that led to the solution of the cubic and biquadratic equations and signalled the birth of modern algebra. After this the book goes on to introduce complex numbers and treat some of the themes from modern algebra, such as quaternions, Clifford algebras, and some of their applications, including the Dirac equation of the quantum spinning electron. This book can be used as a text for a non-traditional course in algebra for students. It contains a large number of exercises many of which go deeper into some of the topics discussed in the text. These exercises may be used to develop independent projects for the more ambitious students.