‎algebraic Groups And Number Theory

Authors: Adhikari, Mahima Ranjan
Discusses the basic concepts of algebraic topology with numerous related illustrations and applications
Approaches the topic nearly “from scratch” and accompanies students through its natural development
Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic
Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes
Reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to pursue further study

Authors: Adhikari, Mahima Ranjan
Discusses the basic concepts of algebraic topology with numerous related illustrations and applications
Approaches the topic nearly “from scratch” and accompanies students through its natural development
Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic
Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes
Reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to pursue further study

The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring.

The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.