Lal R. Algebra 1. Groups, Rings, Fields and Arithmetic 2017 torrent

Textbook in PDF format

Algebra has played a central and decisive role in all branches of mathematics and, in turn, in all branches of science and engineering. It is not possible for a lecturer to cover, physically in a classroom, the amount of algebra which a graduate student (irrespective of the branch of science, engineering, or mathematics in which he prefers to specialize) needs to master. In addition, there are a variety of students in a class. Some of them grasp the material very fast and do not need much of assistance. At the same time, there are serious students who can do equally well by putting a little more effort. They need some more illustrations and also more exercises to develop their skill and confidence in the subject by solving problems on their own. Again, it is not possible for a lecturer to do sufficiently many illustrations and exercises in the classroom for the purpose. This is one of the considerations which prompted me to write a series of three volumes on the subject starting from the undergraduate level to the advance postgraduate level. Each volume is sufficiently rich with illustrations and examples together with numerous exercises. These volumes also cater for the need of the talented students with difficult, challenging, and motivating exercises which were responsible for the further developments in mathematics. Occasionally, the exercises demonstrating the applications in different disciplines are also included. The books may also act as a guide to teachers giving the courses. The researchers working in the field may also find it useful.
Language of Mathematics 1 (Logic)
Language of Mathematics 2 (Set Theory)
Number System
Group Theory
Fundamental Theorems
Permutation Groups and Classical Groups
Elementary Theory of Rings and Fields
Number Theory 2
Structure Theory of Groups
Structure Theory Continued
Arithmetic in Rings