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The Resource Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource)

Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource)

Creator
Author
Contributor
Summary
This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart's theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler-Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: zYou owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.y — MAA Reviews zThe book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.y — Zentralblatt MATH zThis beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.y — Mathematical Reviews zMany departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.y — CHOICE
Language
eng
Work
Publication
Extent
XX, 285 p. 54 illus., 1 illus. in color.
Contents
  • The Coin-Exchange Problem of Frobenius
  • A Gallery of Discrete Volumes
  • Counting Lattice Points in Polytopes: The Ehrhart Theory
  • Reciprocity
  • Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms
  • Magic Squares
  • Finite Fourier Analysis
  • Dedekind Sums
  • Zonotopes
  • h-Polynomials and h*-Polynomials
  • The Decomposition of a Polytope Into Its Cones
  • Euler-Maclaurin Summation in Rd
  • Solid Angles
  • A Discrete Version of Green's Theorem Using Elliptic Functions
Isbn
9781493929696
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-2969-6
Instance
Label
Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra
Title
Computing the Continuous Discretely
Title remainder
Integer-Point Enumeration in Polyhedra
Statement of responsibility
by Matthias Beck, Sinai Robins
Creator
Contributor
Author
Subject
Language
eng
Summary
This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart's theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler-Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: zYou owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.y — MAA Reviews zThe book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.y — Zentralblatt MATH zThis beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.y — Mathematical Reviews zMany departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.y — CHOICE
Member of
http://library.link/vocab/creatorName
Beck, Matthias
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Robins, Sinai.
  • SpringerLink (Online service)
Series statement
Undergraduate Texts in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Computer mathematics
  • Convex geometry
  • Discrete geometry
  • Number theory
  • Combinatorics
Label
Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-2969-6
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
The Coin-Exchange Problem of Frobenius -- A Gallery of Discrete Volumes -- Counting Lattice Points in Polytopes: The Ehrhart Theory -- Reciprocity -- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms -- Magic Squares -- Finite Fourier Analysis -- Dedekind Sums -- Zonotopes -- h-Polynomials and h*-Polynomials -- The Decomposition of a Polytope Into Its Cones -- Euler-Maclaurin Summation in Rd -- Solid Angles -- A Discrete Version of Green's Theorem Using Elliptic Functions
Control code
978-1-4939-2969-6
Dimensions
unknown
Extent
XX, 285 p. 54 illus., 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493929696
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-2969-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)932167022
Label
Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-2969-6
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
The Coin-Exchange Problem of Frobenius -- A Gallery of Discrete Volumes -- Counting Lattice Points in Polytopes: The Ehrhart Theory -- Reciprocity -- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms -- Magic Squares -- Finite Fourier Analysis -- Dedekind Sums -- Zonotopes -- h-Polynomials and h*-Polynomials -- The Decomposition of a Polytope Into Its Cones -- Euler-Maclaurin Summation in Rd -- Solid Angles -- A Discrete Version of Green's Theorem Using Elliptic Functions
Control code
978-1-4939-2969-6
Dimensions
unknown
Extent
XX, 285 p. 54 illus., 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493929696
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-2969-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)932167022

Subject

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