Series and Products in the Development of Mathematics
Cambridge University Press
Edition: 2, 3/18/2021
EAN 9781108709378, ISBN10: 1108709370
Paperback, 478 pages, 25.4 x 17.8 x 2.7 cm
Language: English
Originally published in English
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.