Texts & Monographs in Symbolic Computation

An Invitation to Analytic Combinatorics

From One to Several Variables

Authors: Melczer, Stephen

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  • Interactive computer algebra worksheets allow deeper understanding of the material
  • Many fully worked detailed examples help to illustrate advanced theoretical methods
  • Unique blend of theory, computation, and applications 
  • Appeals to students and researchers in multiple areas of mathematics, computer science, and physics
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  • ISBN 978-3-030-67080-1
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Hardcover $149.99
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About this book

This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains.

After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions.

Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.


About the authors

Stephen Melczer is an Assistant Professor in the Department of Combinatorics and Optimization at the University of Waterloo. Prior to joining Waterloo, he was a CRM-ISM postdoctoral fellow at the Université du Québec à Montréal, a postdoctoral fellow at the University of Pennsylvania, and a visiting scholar at the University of Illinois Urbana-Champaign. His research adapts methods from algebraic and differential geometry, analysis, and topology to create effective tools for combinatorics, mathematics, and computer science. He received doctorates from the École normale supérieure de Lyon and the University of Waterloo in 2017, and is a recipient of a Governor General Silver Academic Medal.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-67080-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-67079-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
An Invitation to Analytic Combinatorics
Book Subtitle
From One to Several Variables
Authors
Series Title
Texts & Monographs in Symbolic Computation
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-67080-1
DOI
10.1007/978-3-030-67080-1
Hardcover ISBN
978-3-030-67079-5
Series ISSN
0943-853X
Edition Number
1
Number of Pages
XVIII, 418
Number of Illustrations
9 b/w illustrations, 36 illustrations in colour
Topics