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Analytic Number Theory for Beginners
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this seco...
An Introduction to q-analysis
Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
Pi - Unleashed
Never in the 4000 year history of research into Pi have results been so prolific as at present. In their book Jörg Arndt and Christoph Haenel describe the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focussed on new methods of computation whose speed outstrips that of predecessor methods by orders of magnitude. The book comes with a CD-ROM containing not only the source code of all programme described, but also related texts and even complete libraries.
Srinivasa Ramanujan
This book offers a unique account on the life and works of Srinivasa Ramanujan—often hailed as the greatest “natural” mathematical genius. Sharing valuable insights into the many stages of Ramanujan’s life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan’s collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan’s life, work and indelible contributions to mathematics.
SRINIVASA RAMANUJAN
Srinivasa Ramanujan (1887–1920) was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Largely self-taught, Ramanujan's early work was marked by groundbreaking theorems that he discovered intuitively, without formal proofs. His work, though largely unknown outside of India, was eventually recognized by British mathematician G.H. Hardy, who invited him to Cambridge University. There, Ramanujan collaborated with Hardy, producing influential results in areas such as partition theory and the properties of prime numbers. Despite struggling with health issues and the challenges of adapting to life in England, Ramanujan's genius shone brightly. He produced a wealth of original work, including the famous Ramanujan primes and his highly accurate approximations for pi. Ramanujan's legacy continues to influence mathematics today, with numerous formulas and concepts bearing his name, and he remains an iconic figure in the history of mathematics.
Number Theory in the Spirit of Ramanujan
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded ...
Reviews in Number Theory, 1984-96
These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984. With the publication of these review volumes, readers now have available reviews in number theory covering more than half a century.
