Series and Products in the Development of Mathematics: Volume 2

Second of two volumes tracing the development of series and products. Second edition adds extensive material from original works.

Ranjan Roy (Author)

9781108709378, Cambridge University Press

Paperback / softback, published 18 March 2021

476 pages
25.3 x 17.6 x 2.6 cm, 0.89 kg

'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

This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining 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 methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.

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.

Subject Areas: Popular science [PDZ], History of mathematics [PBX]