Dealing chiefly with functions of a single real variable, this text is geared toward advanced undergraduates and graduate students. It features the topics usually discussed in a rigorous first course in analysis: limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. No previous knowledge of calculus is assumed.A distinguished educator and researcher, author Robert A. Rankin wrote many influential papers on number theory and the theory of functions. This text is the product of countless lectures over a two-decade period to students at the Universities of Cambridge, Birmingham, and Glasgow. The author's experience as an instructor prompted his inclusion of numerous examples at the end of nearly every section. In addition to testing understanding of preceding theories and providing practice in carrying out techniques, the examples encourage imaginative thinking. Those marked with an asterisk feature hints for solution.

International Series of Monographs in Pure and Applied Mathematics: An Introduction to Mathematical Analysis

Science & Math

Rankin, Robert A.

Mathematics

Pergamon Press

Dealing chiefly with functions of a single real variable, this text is geared toward advanced undergraduates and graduate students. It features the topics usually discussed in a rigorous first course in analysis: limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. No previous knowledge of calculus is assumed. A distinguished educator and researcher, author Robert A. Rankin wrote many influential papers on number theory and the theory of functions. This text is the product of countless lectures over a two-decade period to students at the Universities of Cambridge, Birmingham, and Glasgow. The author's experience as an instructor prompted his inclusion of numerous examples at the end of nearly every section. In addition to testing understanding of preceding theories and providing practice in carrying out techniques, the examples encourage imaginative thinking. Those marked with an asterisk feature hints for solution.

An Introduction to Mathematical Analysis

Dover Publications

This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.

Modular Forms and Functions

Cambridge University Press

This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate studen

The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. 
Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996.

Ramanujan: Letters and Commentary (History of Mathematics)

Berndt, Bruce C.

Amer Mathematical Society

The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources.Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical results in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. "Ramanjuan: Letters and Commentary" was selected for the "Choice" list of Outstanding Academic Books for 1996.

Ramanujan Aiyangar, Srinivasa

See the best price to sell, buy, or rent books by Rankin, Robert A.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Rankin, Robert A.

See the best price to sell, buy, or rent books by Rankin, Robert A.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

International Series of Monographs in Pure and Applied Mathematics: An Introduction to Mathematical Analysis

An Introduction to Mathematical Analysis

Modular Forms and Functions

Modular Forms and Functions

Ramanujan: Letters and Commentary (History of Mathematics)

Ramanujan: Letters and Commentary (History of Mathematics)