Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.
The discovery of a 138-page manuscript in Srinivasa Ramanujan's handwriting, found by George Andrews at Trinity College in 1976, is likened to a monumental cultural find, akin to Beethoven's lost symphony. This "lost notebook" of Ramanujan contains groundbreaking mathematical insights, shedding light on the genius of one of history's most influential mathematicians. The manuscript has since sparked significant interest and research in the mathematical community, revealing new dimensions of Ramanujan's work and its implications.
The book delves into the legacy of mathematician Ramanujan, focusing on the journey of his notebooks from his death in 1920 to their eventual publication. G. H. Hardy's advocacy led to the 1957 release of a photostat edition, but it lacked editing. In 1977, Berndt took on the significant task of editing these notebooks, uncovering unproven theorems and unique results that challenge existing mathematical literature, highlighting Ramanujan's extraordinary contributions to the field.
Focusing on the profound mathematical findings of Srinivasa Ramanujan, this final volume delves into advanced results, particularly emphasizing continued fractions, a topic of great interest to Ramanujan. With a depth of exploration likely surpassing earlier volumes, it aims to inspire further research among mathematicians captivated by Ramanujan's extraordinary contributions. The work serves as a culmination of insights from his "Notebooks," first published in 1957, and seeks to encourage ongoing investigation into his remarkable ideas.
The narrative explores the extraordinary life of Srinivasa Ramanujan, highlighting his remarkable contributions to mathematics despite facing numerous challenges. It delves into his self-taught genius, his profound insights into number theory, and his collaboration with prominent mathematicians like G.H. Hardy. The book also examines themes of cultural identity, the struggle for recognition, and the impact of his work on modern mathematics, painting a vivid picture of a man whose legacy continues to influence the field today.
Set during 1903-1914, this volume delves into the mathematical discoveries of Ramanujan, who worked in isolation and documented his findings without proofs. Following his death, efforts to edit his notebooks began, culminating in this fourth volume that focuses on proving results from the second and third notebooks, as well as some from the first. With over half of the findings being new and unique, the book includes complete proofs and references for known results, showcasing the groundbreaking nature of Ramanujan's work.
Focused on the mathematical discoveries of Ramanujan from 1903 to 1914, this volume continues the effort to edit his notebooks, which contain a mix of known and original results. Despite the incomplete editing by G.N. Watson and B.M. Wilson after Ramanujan's death, this work aims to provide clarity and accessibility to his findings. It follows a previous photostat edition published in 1957, contributing to the ongoing exploration of Ramanujan's significant yet unproven contributions to mathematics.