Bøger af M. Ram Murty

This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

Presents material suitable for a two semester graduate course in analysis. Based on courses given by the author since 2007, it is targeted towards graduate students preparing for a research career in mathematics.

Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900. It asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. This book is an exposition of their achievement.

This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker's theorem, Schanuel's conjecture, and Schneider's theorem.

Provides an introduction to Indian philosophy. Beginning with a study of the major Upanishads, it surveys the philosophical ideas contained in the Bhagavadgita. After a short excursion into Buddhism, it summarises the salient ideas of the six systems of Indian philosophy: Nyaya, Vaisesika, Samkhya, Yoga, Purva Mimamsa, and Vedanta.

This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.

Focusing on a subset of Ramanujan's significant papers, this book gives an informal account of major developments that emanated from his work in the 20th and 21st centuries. The essays presented here show how Ramanujan shaped the course of modern mathematics.

This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods.

The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved