### Mevcut:*

Materyal Türü | Demirbaş Numarası | Yer Numarası | Raf Konumu | Mevcut Konumu | Materyal Istek |
---|---|---|---|---|---|

E-Kitap | 1816097-1001 | QA164 -167.2 | SPRINGER E-Kitap Koleksiyonu | Arıyor... | Arıyor... |

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### Özet

### Özet

This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

### İncelemeler 1

### İnceleme Seç

All mathematics majors study the topics they will need to know, should they want to go to graduate school. But most will not, and many 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 (San Francisco State Univ.) and Robins (Temple Univ.) have written the perfect text for such a course. This material reinforces and extends ideas from calculus (partial fractions), advanced calculus (Green's theorem), numerical analysis (Euler-Maclauren summation), analysis (Fourier transform, but in the finite setting), complex analysis (elliptic functions), combinatorics (generating functions), and even recreational mathematics (magic squares). Students will also likely meet for the first time some basic topics (Dedekind sums). But no hodgepodge; the book develops a consistent theme--the relation between the (continuous) volume of a polytope (a notion that generalizes polygon and polyhedron) and its discrete volume, namely, the number of integer points that lie inside it. With these familiar tools, the authors lead students to a host of results that will seem simultaneously concrete and magical and almost certainly unfamiliar. Summing Up: Highly recommended. General readers; lower-division undergraduates through faculty. D. V. Feldman University of New Hampshire