{"title":"M Ram Murty","description":"\u003cp\u003eDelve into the compelling works of M. Ram Murty, a celebrated author known for his contributions to number theory and mathematical exposition. Discover books that bridge complex ideas with accessible insights.\u003c\/p\u003e","products":[{"product_id":"introduction-to-p-adic-analytic-number-theory-book-mram-murty-9780821847749","title":"Introduction to P-adic Analytic Number Theory","description":"This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises, it will acquaint the non-expert with the basic ideas of the theory and encourage the novice to enter this fertile field of research.  The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.  The book treats the subject informally, making the text accessible to non-experts. It would make a nice independent text for a course geared toward advanced undergraduates and beginning graduate students.  Titles in this series are co-published with International Press, Cambridge, MA. Table of Contents: Historical introduction; Bernoulli numbers; $p$-adic numbers; Hensel's lemma; $p$-adic interpolation; $p$-adic $L$-functions; $p$-adic integration; Leopoldt's formula for $L_p(1,\\chi)$; Newton polygons; An introduction to Iwasawa theory; Bibliography; Index.  Review from Mathematical Reviews: The exposition of the book is clear and self-contained. It contains numerous exercises and is well-suited for use as a text for an advanced undergraduate or beginning graduate course on $p$-adic numbers and their applications...the author should be congratulated on a concise and readable account of $p$-adic methods, as they apply to the classical theory of cyclotomic fields...heartily recommended as the basis for an introductory course in this area. 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These problems gave focus for the exponential development of mathematical thought over the following century. The tenth problem asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved in a series of papers written by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. They showed that no such algorithm exists.  This book is an exposition of this remarkable achievement. Often, the solution to a famous problem involves formidable background. Surprisingly, the solution of Hilbert's tenth problem does not. What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Godel's incompleteness theorems.  Copious exercises are included at the end of each chapter to guide the student gently on this ascent. For the advanced student, the final chapter highlights recent developments and suggests future directions. The book is suitable for undergraduates and graduate students. It is essentially self-contained.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50628709646609,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50628710596881,"sku":"GOR012704422","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":53729443447057,"sku":"CIN1470443996G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470443996.jpg?v=1751210411"},{"product_id":"indian-philosophy-book-m-ram-murty-9781554810352","title":"Indian Philosophy","description":"\u003cp\u003eThis book introduces the vast topic of Indian philosophy. 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Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book. One of the most attractive features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point the latest discoveries as are presented in the final chapters can be fully appreciated.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062426435857,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062429712657,"sku":"NIN9783764358013","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52148280262929,"sku":"NLS9783764358013","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3764358017.jpg?v=1750807414"},{"product_id":"mathematical-legacy-of-srinivasa-ramanujan-book-m-ram-murty-9788132207696","title":"The Mathematical Legacy of Srinivasa Ramanujan","description":"Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. 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These essays, based on the lectures given by the authors focus on a subset of Ramanujan's significant papers and show how these papers shaped the course of modern mathematics.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062882468113,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062885581073,"sku":"NIN9788132207696","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52658711396625,"sku":"NLS9788132207696","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/8132207696.jpg?v=1750808012"},{"product_id":"introduction-to-the-circle-method-book-m-ram-murty-9781470472030","title":"An Introduction to the Circle Method","description":"The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. 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The book is a collection of about 500 problems in algebraic number theory, systematically arranged to reveal ideas and concepts in the evolution of the subject.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52408065294609,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52408065851665,"sku":"NLS9780387221823","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387221823.jpg?v=1758773920"},{"product_id":"mathematical-legacy-of-srinivasa-ramanujan-book-m-ram-murty-9788132217435","title":"The Mathematical Legacy of Srinivasa Ramanujan","description":"Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. 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