Universitext

Problems from the Discrete to the Continuous

Probability, Number Theory, Graph Theory, and Combinatorics

Authors: Pinsky, Ross

  • Treats problems from four different mathematical disciplines, under the common theme of asymptotic limits and generous use of generating function techniques
  • Presented rigorously and with enough detail to allow the advanced undergraduate student to use it for independent study
  • Excellent for a seminar course in which the students present the lectures
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Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-07965-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-07964-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.

About the authors

Ross Pinsky is a Professor in the Department of Mathematics at Technion-Israel Institute of Technology.

Table of contents (10 chapters)

  • Partitions with Restricted Summands or “the Money Changing Problem”

    Pinsky, Ross G.

    Pages 1-6

  • The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers

    Pinsky, Ross G.

    Pages 7-20

  • A One-Dimensional Probabilistic Packing Problem

    Pinsky, Ross G.

    Pages 21-34

  • The Arcsine Laws for the One-Dimensional Simple Symmetric Random Walk

    Pinsky, Ross G.

    Pages 35-48

  • The Distribution of Cycles in Random Permutations

    Pinsky, Ross G.

    Pages 49-65

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-07965-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-07964-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Problems from the Discrete to the Continuous
Book Subtitle
Probability, Number Theory, Graph Theory, and Combinatorics
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-07965-3
DOI
10.1007/978-3-319-07965-3
Softcover ISBN
978-3-319-07964-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIII, 154
Number of Illustrations and Tables
8 illustrations in colour
Topics