The concrete tetrahedron : symbolic sums, recurrence equations, generating functions, asymptotic estimates
著者
書誌事項
The concrete tetrahedron : symbolic sums, recurrence equations, generating functions, asymptotic estimates
(Texts and monographs in symbolic computation)
Springer, c2011
- : pbk
大学図書館所蔵 全6件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 193-195
Includes index
内容説明・目次
内容説明
The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.
Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.
目次
1 Introduction
1.1 Selection Sort and Quicksort
1.2 Recurrence Equations
1.3 Symbolic Sums
1.4 Generating Functions
1.5 Asymptotic Estimates
1.6 The Concrete Tetrahedron
1.7 Problems
2 Formal Power Series
2.1 Basic Facts and Definitions
2.2 Differentiation and Division
2.3 Sequences of Power Series
2.4 The Transfer Principle
2.5 Multivariate Power Series
2.6 Truncated Power Series
2.7 Problems
3 Polynomials
3.1 Polynomials as Power Series
3.2 Polynomials as Sequences
3.3 The Tetrahedron for Polynomials
3.4 Polynomials as Solutions
3.5 Polynomials as Coefficients
3.6 Applications
3.7 Problems
4 C-Finite Sequences
4.1 Fibonacci Numbers
4.2 Recurrences with Constant Coefficients
4.3 Closure Properties
4.4 The Tetrahedron for C-finite Sequences
4.5 Systems of C-finite Recurrences
4.6 Applications
4.7 Problems
5 Hypergeometric Series
5.1 The Binomial Theorem
5.2 Basic Facts and Definitions
5.3 The Tetrahedron for Hypergeometric Sequences
5.4 Indefinite Summation
5.5 Definite Summation
5.6 Applications
5.7 Problems
6 Algebraic Functions
6.1 Catalan Numbers
6.2 Basic Facts and Definitions
6.3 Puiseux Series and the Newton Polygon
6.4 Closure Properties
6.5 The Tetrahedron for Algebraic Functions
6.6 Applications
6.7 Problems
7 Holonomic Sequences and Power Series
7.1 Harmonic Numbers
7.2 Equations with Polynomial Coefficients
7.3 Generalized Series Solutions
7.4 Closed Form Solutions
7.5 The Tetrahedron for Holonomic Functions
7.6 Applications
7.7 Problems
Appendix
A.1 Basic Notions and Notations
A.2 Basic Facts from Computer Algebra
A.3 A Collection of Formal Power Series Identities
A.4 Closure Properties at One Glance
A.5 Software
A.6 Solutions to Selected Problems
A.7 Bibliographic Remarks
「Nielsen BookData」 より