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)
Resource Information
The item Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
- 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
- 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
- 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
- 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
- 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)
- 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)
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Computing-the-Continuous-Discretely-/XUQprPxS5zg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Computing-the-Continuous-Discretely-/XUQprPxS5zg/">Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra, by Matthias Beck, Sinai Robins, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>