| 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""
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| Record Nr. | UNINA-9910461887903321 |
Info
The geometry of numbers [[electronic resource] /] / C.D. Olds, Anneli Lax, Giuliana P. Davidoff
