Algebra Pdf

This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry.

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.

Geometric algebra (GA), also known as Clifford algebra, is a powerful unifying framework for geometric computations that extends the classical techniques of linear algebra and vector calculus in a structural manner. Its benefits include cleaner computer-program solutions for known geometric computation tasks, and the ability to address increasingly more involved applications.