This two-volume work traces the development of series and products from 1380 to 2000 through the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the fundamental methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 deals with more recent and advanced results, such as Nevanlinna theory and deBranges' work.
Rezensionen / Stimmen
'Roy is well-known for useful scholarship. This book continues his record.' Robert E. O'Malley, University of Washington 'I often turn to Ranjan Roy for his wide-ranging works on series, both historical and contemporary. His writing is meticulous and a pleasure to read. These volumes can be used to engage undergraduates in the exploration of mathematics through its history and as a resource for anyone working in mathematics.' David M. Bressoud, Director, Conference Board of the Mathematical Sciences 'Those interested in the history of the internal evolution of mathematics from, say 1600 onwards, should approach this most readable book with a very open mind ... Of course, there exists something that may be termed `the British way of writing mathematics', and here is a beautiful example. In this sense, Roy's book is paramount with G. H. Hardy's Divergent series ... of which it can be considered a close relative.' Jose Miguel Pacheco Castelao, Mathematical Reviews/MathSciNet
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Für höhere Schule und Studium
Editions-Typ
Illustrationen
Worked examples or Exercises
Maße
Höhe: 381 mm
Breite: 272 mm
Dicke: 203 mm
Gewicht
ISBN-13
978-1-108-70943-9 (9781108709439)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Ranjan Roy is the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers and reviews on Riemann surfaces, differential equations, fluid mechanics, Kleinian groups, and the development of mathematics. He has received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He co-authored Special Functions (2001) with George Andrews and Richard Askey and co-authored chapters in the NIST Handbook of Mathematical Functions (2010); he also authored Elliptic and Modular Functions from Gauss to Dedekind to Hecke (2017) and the first edition of this book, Sources in the Development of Mathematics (2011).
Autor*in
Beloit College, Wisconsin
Volume 1: 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. The calculus of Newton and Leibniz; 8. De Analysi per Aequationes Infinitas; 9. Finite differences: interpolation and quadrature; 10. Series transformation by finite differences; 11. The Taylor series; 12. Integration of rational functions; 13. Difference equations; 14. Differential equations; 15. Series and products for elementary functions; 16. Zeta values; 17. The gamma function; 18. The asymptotic series for ln ?(x); 19. Fourier series; 20. The Euler-Maclaurin summation formula; 21. Operator calculus and algebraic analysis; 22. Trigonometric series after 1830; 23. The hypergeometric series; 24. Orthogonal polynomials; Bibliography; Index; Volume 2: 25. q-series; 26. Partitions; 27. q-Series and q-orthogonal polynomials; 28. Dirichlet L-series; 29. Primes in arithmetic progressions; 30. Distribution of primes: early results; 31. Invariant theory: Cayley and Sylvester; 32. Summability; 33. Elliptic functions: eighteenth century; 34. Elliptic functions: nineteenth century; 35. Irrational and transcendental numbers; 36. Value distribution theory; 37. Univalent functions; 38. Finite fields; Bibliography; Index.
