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1.

図書
図書
1. Selected papers on discrete mathematics (: cloth ; : paper)
Donald E. Knuth
出版情報: Stanford, Calif. : CSLI Publications, c2003  xvi, 812 p. ; 23 cm
シリーズ名: CSLI lecture notes ; no. 106
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目次情報: 続きを見る
Combinatorial Analysis and Computers / 1：
Two Notes on Notation / 2：
Bracket Notation for the 'Coefficient of' Operator / 3：
Johann Faulhaber and Sums of Powers / 4：
Notes on Thomas Harriot / 5：
A Permanent Inequality / 6：
Overlapping Pfaffians / 7：
The Sandwich Theorem / 8：
Combinatorial Matrices / 9：
Aztec Diamonds, Checkerboard Graphs, and Spanning Trees / 10：
Partitioned Tensor Products and Their Spectra / 11：
Oriented Subtrees of an Arc Digraph / 12：
Another Enumeration of Trees / 13：
Abel Identities and Inverse Relations / 14：
Convolution Polynomials / 15：
Polynomials Involving the Floor Function / 16：
Construction of a Random Sequence / 17：
An Imaginary Number System / 18：
Tables of Finite Fields
Finite Semifields and Projective Planes / 20：
A Class of Projective Planes / 21：
Notes on Central Groupoids / 22：
Huffman's Algorithm via Algebra / 23：
Wheels Within Wheels / 24：
Complements and Transitive Closures / 25：
Random Matroids / 26：
The Asymptotic Number of Geometries / 27：
Permutations with Nonnegative Partial Sums / 28：
Efficient Balanced Codes / 29：
The Knowlton - Graham Partition Problem / 30：
Permutations, Matrices, and Generalized Young Tableaux / 31：
Enumeration of Plane Partitions / 32：
A Note on Solid Partitions / 33：
Identities from Partition Involutions / 34：
Subspaces, Subsets, and Partitions / 35：
The Power of a Prime That Divides a Generalized Coefficient / 36：
An Almost Linear Recurrence / 37：
Recurrence Relations Based on Minimization / 38：
A Recurrence Related to Trees / 39：
The First Cycles in an Evolving Graph / 40：
The Birth of the Giant Component / 41：
Index
Combinatorial Analysis and Computers / 1：
Two Notes on Notation / 2：
Bracket Notation for the 'Coefficient of' Operator / 3：
2.

図書
図書
2. Topology and category theory in computer science
edited by G.M. Reed, A.W. Roscoe, and R.F. Wachter
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, c1991  390 p. ; 24 cm
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Topology, computer science and the mathematics of convergence / A.W. Roscoe
The soundness and completeness of axioms for CSP processes / Stepen Blamey
Classifying unbounded nondeterminism in CSP / Geoff Barrett ; Michael Goldsmith
Algebraic posets, algebraic cpo's and models of concurrency / Michael W. Mislove
Concurrency semantics based on metric domain equations / J.W. de Bakker ; J.J.M.M. Rutten
On topological characterization of behavioral properties / Marta Z. Kwiatkowska
Order and strongly sober compactifications / J.D. Lawson
Totally bounded spaces and compact ordered spaces as domains of computation / Michael B. Smyth
A characterization of effective topological spaces II / Dieter Spreen
The importance of cardinality, separability, and compactness in computer science with an example from numerical signal analysis / Klaus E. Grue
Digital topology: a comparison of the graph-based and topological approaches / T.Y. Kong
Tiling the plane with one tile / D. Girault-Beauquier ; M. Nivat
An algebraic axiomatization of linear logic models / Narcisco Marti-Oliet ; Jose Meseguer
Types as theories / Joseph A. Goguen
Topology, computer science and the mathematics of convergence / A.W. Roscoe
The soundness and completeness of axioms for CSP processes / Stepen Blamey
Classifying unbounded nondeterminism in CSP / Geoff Barrett ; Michael Goldsmith
3.

図書
図書
3. Geometric computing science : first steps
Robert Hermann
出版情報: Brookline, MA : Math Sci Press, c1991  xiii, 400 p. ; 24 cm
シリーズ名: Interdisciplinary mathematics ; v. 25
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4.

図書
図書
4. Discrete mathematics : elementary and beyond (: hard ; : pbk)
L. Lovász, J. Pelikán, K. Vesztergombi
出版情報: New York : Springer, c2003  ix, 290 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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5.

図書
図書
5. Sets and numbers, graphs and algebra, logic and machines, linear geometry
Guerino Mazzola, Gérard Milmeister, Jody Weissmann
出版情報: Berlin : Springer, c2004  xii, 357 p. ; 24 cm
シリーズ名: Universitext ; . Comprehensive mathematics for computer scientists ; 1
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目次情報: 続きを見る
Sets, Numbers, and Graphs / I：
Fundamentals-Concepts and Logic / 1：
Propositional Logic / 1.1：
Architecture of Concepts / 1.2：
Axiomatic Set Theory / 2：
The Axioms / 2.1：
Basic Concepts and Results / 2.2：
Boolean Set Algebra / 3：
The Boolean Algebra of Subsets / 3.1：
Functions and Relations / 4：
Graphs and Functions / 4.1：
Relations / 4.2：
Ordinal and Natural Numbers / 5：
Ordinal Numbers / 5.1：
Natural Numbers / 5.2：
Recursion Theorem and Universal Properties / 6：
Recursion Theorem / 6.1：
Universal Properties / 6.2：
Universal Properties in Relational Database Theory / 6.3：
Natural Arithmetic / 7：
Natural Operations / 7.1：
Euclid and the Normal Forms / 7.2：
Infinities / 8：
The Diagonalization Procedure / 8.1：
The Classical Number Domains ${\op Z}, {\op Q}, {\op R}$ and ${\op C}$ / 9：
Integers ${\op Z}[$ / 9.1：
Rationals ${\op Q}$ / 9.2：
Real Numbers ${\op R}$ / 9.3：
Complex Numbers ${\op C}$ / 9.4：
Categories of Graphs / 10：
Directed and Undirected Graphs / 10.1：
Morphisms of Digraphs and Graphs / 10.2：
Cycles / 10.3：
Construction of Graphs / 11：
Some Special Graphs / 12：
n-ary Trees / 12.1：
Moore Graphs / 12.2：
Planarity / 13：
Euler's Formula for Polyhedra / 13.1：
Kuratowski's Planarity Theorem / 13.2：
First Advanced Topic / 14：
Floating Point Arithmetic / 14.1：
Example for an Addition / 14.2：
Algebra, Formal Logic, and Linear Geometry / II：
Monoids, Groups, Rings, and Fields / 15：
Monoids / 15.1：
Groups / 15.2：
Rings / 15.3：
Fields / 15.4：
Primes / 16：
Prime Factorization / 16.1：
Roots of Polynomials and Interpolation / 16.2：
Formal Propositional Logic / 17：
Syntactics: The Language of Formal Propositional Logic / 17.1：
Semantics: Logical Algebras / 17.2：
Signification: Valuations / 17.3：
Axiomatics / 17.4：
Formal Predicate Logic / 18：
Syntactics: First-order Language / 18.1：
Semantics: S-Structures / 18.2：
Signification: Models / 18.3：
Languages, Grammars, and Automata / 19：
Languages / 19.1：
Grammars / 19.2：
Automata and Acceptors / 19.3：
Categories of Matrixes / 20：
What Matrixes Are / 20.1：
Standard Operations on Matrixes / 20.2：
Square Matrixes and their Determinant / 20.3：
Modules and Vector Spaces / 21：
Linear Dependence, Bases, and Dimension / 22：
Bases in Vector Spaces / 22.1：
Equations / 22.2：
Affine Homomorphisms / 22.3：
Algorithms in Linear Algebra / 23：
Gauss Elimination / 23.1：
The LUP Decomposition / 23.2：
Linear Geometry / 24：
Euclidean Vector Spaces / 24.1：
Trigonometric Functions from Two-Dimensional Rotations / 24.2：
Gram's Determinant and the Schwarz Inequality / 24.3：
Eigenvalues, the Vector Product, and Quaternions / 25：
Eigenvalues and Rotations / 25.1：
The Vector Product / 25.2：
Quaternions / 25.3：
Second Advanced Topic / 26：
Galois Fields / 26.1：
The Reed-Solomon (RS) Error Correction Code / 26.2：
The Rivest-Shamir-Adelman (RSA) Encryption Algorithm / 26.3：
Further Reading / A：
Index
Sets, Numbers, and Graphs / I：
Fundamentals-Concepts and Logic / 1：
Propositional Logic / 1.1：
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