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The geometry of numbers [[electronic resource] /] / C.D. Olds, Anneli Lax, Giuliana P. Davidoff
| The geometry of numbers [[electronic resource] /] / C.D. Olds, Anneli Lax, Giuliana P. Davidoff |
| Autore | Olds C. D (Carl Douglas), <1912-1979.> |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, c2000 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina | 512/.75 |
| Altri autori (Persone) |
LaxAnneli
DavidoffGiuliana P |
| Collana | The Anneli Lax new mathematical library |
| Soggetto topico |
Geometry of numbers
Number theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-88385-955-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover ""; ""Title Page""; ""Contents""; ""Preface""; ""Part I Lattice Points and Number Theory""; ""1 Lattice Points and Straight Lines""; ""1.1 The Fundamental Lattice""; ""1.2 Lines in Lattice Systems""; ""1.3 Lines with Rational Slope""; ""1.4 Lines with Irrational Slope""; ""1.5 Broadest Paths without Lattice Points""; ""1.6 Rectangles on Paths without Lattice Points""; ""Problem Set for Chapter 1""; ""References""; ""2 Counting Lattice Points""; ""2.1 The Greatest Integer Function, [x ]""; ""Problem Set for Section 2.1""; ""2.2 Positive Integral Solutions of ax + by = n""
""Problem Set for Section 2.2""""2.3 Lattice Points inside a Triangle""; ""Problem Set for Section 2.3""; ""References""; ""3 Lattice Points and the Area of Polygons""; ""3.1 Points and Polygons""; ""3.2 Pick's Theorem""; ""Problem Set for Section 3.2""; ""3.3 A Lattice Point Covering Theorem for Rectangles""; ""Problem Set for Section 3.3""; ""References""; ""4 Lattice Points in Circles""; ""4.1 How Many Lattice Points Are There?""; ""4.2 Sums of Two Squares""; ""4.3 Numbers Representable as a Sum of Two Squares""; ""Problem Set for Section 4.3"" ""4.4 Representations of Prime Numbers as Sums of TwoSquares""""4.5 A Formula for R(n)""; ""Problem Set for Section 4.5""; ""References""; ""Part II An Introduction to the Geometry of Numbers""; ""5 Minkowski's Fundamental Theorem""; ""5.1 Minkowski's Geometric Approach""; ""Problem Set for Section 5.1""; ""5.2 Minkowski M-Sets""; ""Problem Set for Section 5.2""; ""5.3 Minkowski's Fundamental Theorem""; ""Problem Set for Section 5.3""; ""5.4 (Optional) Minkowski's Theorem in n Dimensions""; ""References""; ""6 Applications of Minkowski's Theorems""; ""6.1 Approximating Real Numbers"" ""6.2 Minkowski's First Theorem""""Problem Set for Section 6.2""; ""6.3 Minkowski's Second Theorem""; ""Problem for Section 6.3""; ""6.4 Approximating Irrational Numbers""; ""6.5 Minkowski's Third Theorem""; ""6.6 Simultaneous Diophantine Approximations""; ""Reading Assignment for Chapter 6""; ""References""; ""7 Linear Transformations and Integral Lattices""; ""7.1 Linear Transformations""; ""Problem Set for Section 7.1""; ""7.2 The General Lattice""; ""7.3 Properties of the Fundamental Lattice""; ""Problem Set for Section 7.3""; ""7.4 Visible Points"" ""8 Geometric Interpretations of Quadratic Forms""""8.1 Quadratic Representation""; ""8.2 An Upper Bound for the Minimum Positive Value""; ""8.3 An Improved Upper Bound""; ""8.4 (Optional) Bounds for the Minima of Quadratic Formsin More Than Two Variables""; ""8.5 Approximating by Rational Numbers""; ""8.6 Sums of Four Squares""; ""References""; ""9 A New Principle in the Geometry of Numbers""; ""9.1 Blichfeldt's Theorem""; ""9.2 Proof of Blichfeldt's Theorem""; ""9.3 A Generalization of Blichfeldt's Theorem""; ""9.4 A Return to Minkowski's Theorem"" ""9.5 Applications of Blichfeldt's Theorem"" |
| Record Nr. | UNINA-9910461887903321 |
Olds C. D (Carl Douglas), <1912-1979.>
|
||
| Washington, DC, : Mathematical Association of America, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The geometry of numbers / / C.D. Olds, Anneli Lax, Giuliana P. Davidoff
| The geometry of numbers / / C.D. Olds, Anneli Lax, Giuliana P. Davidoff |
| Autore | Olds C. D (Carl Douglas), <1912-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, c2000 |
| Descrizione fisica | 1 online resource (xvi, 174 pages) : digital, PDF file(s) |
| Disciplina | 512/.75 |
| Altri autori (Persone) |
LaxAnneli
DavidoffGiuliana P |
| Collana | The Anneli Lax new mathematical library |
| Soggetto topico |
Geometry of numbers
Number theory |
| ISBN | 0-88385-955-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Lattice Points and Number Theory -- An Introduction to the Geometry of Numbers -- Gaussian Integers, by Peter D. Lax -- The Closest Packing of Convex Bodies -- Brief Biographies -- Solutions and Hints. |
| Record Nr. | UNINA-9910826528903321 |
|
Olds C. D (Carl Douglas), <1912->
|
||
| Washington, DC, : Mathematical Association of America, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||