Paul J. Nahin
Shares the story of formula - long regarded as the gold standard for mathematical beauty - and shows why it still lies at the heart of complex number theory.
This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or...
Jurgen Neukirch; Norbert Schappacher
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich...
Joseph H. Silverman
The theory of elliptic curves is distinguished by the diversity of the methods used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation...
Rogawski, Jonathan D.; Lubotzky, Alex
The book presents the solutions to two problems: the first is the construction of expanding graphs - graphs which are of fundamental importance for communication...
This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students...
Jan Hendrik Bruinier; Gerard van der...
This book grew out of three series of lectures on "Modular Forms and their Applications". Each part treats a number of beautiful applications, and together they form a comprehensive survey...
Johannes Buchmann; Ulrich Vollmer
Deals with algorithmic problems related to binary quadratic forms. This book focuses on the algorithmic aspects of the theory. It introduces the reader to important areas of number theory such...
This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of...
This book takes the view that parallel to the pure arithmetic theory over number fields lies the algebraic-geometric theory of algebraic systems, where sections play...
Marcus, Daniel A.;
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore...
'I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.'
In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article, suggesting an answer to a problem that had long puzzled mathematicians. For the next 150 years, the world's...
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Alfred S. Posamentier; Ingmar Lehmann
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. This title demonstrates, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural...