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Call number: | SPRINGER-2013-9781461436317:ONLINE Show nearby items on shelf |
Title: | A Logical Introduction to Proof [electronic resource] |
Author(s): |
Daniel W Cunningham |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or bridge course between calculus and advanced mathematics courses. Theauthors approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may alsobe beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument foranalyzing the structure of mathematical assertions and is a tool for composing mathematical proof s. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted tothe logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs eac h presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theoremsconcerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamenta l theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts thatappear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finall y, Chapter 9 presents proof strategies that explicitly show students how todeal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful s ummary of strategies for dealing with proofs |
Note: | Springer eBooks |
Contents: | Preface |
The Greek Alphabet | |
1. Propositional Logic | |
2. Predicate Logic | |
3. Proof Strategies and Diagrams | |
4. Mathematical Induction | |
5. Set Theory | |
6. Functions | |
7. Relations | |
8. Core Concepts in Abstract Algebra | |
9. Core Concepts in Real Analysis | |
A Summary of Strategies | |
References | |
List of Symbols. Index | |
ISBN: | 9781461436317 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2012-9781461442653:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Structures and Proofs [electronic resource] |
Author(s): |
Larry J Gerstein |
Date: | 2012 |
Edition: | 2nd ed. 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a bridge course can help ensure a smooth transition.Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuitionand rigorand the flexible thinkingrequired to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graphtheory, several new sections on number theory (including primitive roots, with an appli cation to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Froma review of the first edition: ...Gerstein wantsvery gentlyto teach his students to think. He wants to show t hem how to wrestle with a problem (one that is more sophisticated than plug and chug), how to build a solution,and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I th ink students will find appealing. ...I am confident that a student who works throughGerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. Gersteins book states quite plainly that the text is desi gned for use in a transitions course. Nothing benefits atextbook author more than having his goals clearly in mind, and Gersteins book achieves its goals. I would be happy to use it in a transitions course. Steven Krantz, American Mathematical Monthly |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface to the First Edition | |
1. Logic | |
2. Sets | |
3. Functions | |
4. Finite and Infinite Sets | |
5. Combinatorics | |
6. Number Theory | |
7. Complex Numbers | |
Hints and Partial Solutions to Selected Odd | |
Numbered Exercises | |
Index | |
ISBN: | 9781461442653 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics , Logic, Symbolic and mathematical , Number theory |
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Call number: | SPRINGER-2008-9783540772705:ONLINE Show nearby items on shelf |
Title: | Field Arithmetic [electronic resource] |
Author(s): |
Michael D Fried Moshe Jarden |
Date: | 2008 |
Edition: | Third Edition |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students caneffectively learn gener alizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only completetreatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed)fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Thosethat are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a newgeneration: Is the solvable closure of the rationals PAC and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First itremoves many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third e dition reports on five open problems (out of thirtyfour open problems of the second edition) thathave been partially or fully solved since that edition appeared in 2005 |
Note: | Springer eBooks |
Contents: | Infinite Galois Theory and Profinite Groups |
Valuations and Linear Disjointness | |
Algebraic Function Fields of One Variable | |
The Riemann Hypothesis for Function Fields | |
Plane Curves | |
The Chebotarev Density Theorem | |
Ultraproducts | |
Decision Procedures | |
Algebraically Closed Fields | |
Elements of Algebraic Geometry | |
Pseudo Algebraically Closed Fields | |
Hilbertian Fields | |
The Classical Hilbertian Fields | |
Nonstandard Structures | |
Nonstandard Approach to Hilberts Irreducibility Theorem | |
Galois Groups over Hilbertian Fields | |
Free Profinite Groups | |
The Haar Measure | |
Ef | |
ISBN: | 9783540772705 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v11 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Field theory (Physics) , Geometry , Logic, Symbolic and mathematical , Number theory |
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Call number: | SPRINGER-2007-9780817645410:ONLINE Show nearby items on shelf |
Title: | Number Theory [electronic resource] : An Introduction via the Distribution of Primes |
Author(s): |
Benjamin Fine Gerhard Rosenberger |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of thewhole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Key Topics and Features: * Solidintroduction to analytic number theory, including full pro ofs of Dirichlets Theorem and the Prime Number Theorem * Solid treatment of algebraic number theory, including a complete presentation of primes, prime factorizations inalgebraic number fields, and unique factorization of ideals * First treatment in book form of the AKS algorithm that shows that primality testing is of polynomial time * Many interesting side topics, such as primality testing andcryptography, Fermat and Mersenne numbers, and Carmichael numbers The books user-friendly style, historical cont ext, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) makeit ideal for self study as well as classroom use. Intended for upper level undergraduates and beginning graduate students, the only pre requisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. Allnecessary concepts from abstract algebra and complex analysis are introduced in the book |
Note: | Springer eBooks |
Contents: | Preface |
Introduction and Historical Remarks | |
Basic Number Theory | |
The Infinitude of Primes | |
The Density of Primes | |
Primality Testing: An Overview | |
Primes and Algebraic Number Theory | |
Exercises | |
Bibliography and Cited References | |
Index | |
ISBN: | 9780817645410 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Data structures (Computer science) , Matrix theory , Global analysis (Mathematics) , Logic, Symbolic and mathematical , Number theory |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2005-9783540269496:ONLINE Show nearby items on shelf |
Title: | Field Arithmetic [electronic resource] |
Author(s): |
Michael D Fried Moshe Jarden |
Date: | 2005 |
Edition: | Second Edition |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students caneffectively learn gener alizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only completetreatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed)fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Thosethat are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a newgeneration: Is the solvable closure of the rationals PAC and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? |
Note: | Springer eBooks |
Contents: | Infinite Galois Theory and Profinite Groups |
Valuations and Linear Disjointness | |
Algebraic Function Fields of One Variable | |
The Riemann Hypothesis for Function Fields | |
Plane Curves | |
The Chebotarev Density Theorem | |
Ultraproducts | |
Decision Procedures | |
Algebraically Closed Fields | |
Elements of Algebraic Geometry | |
Pseudo Algebraically Closed Fields | |
Hilbertian Fields | |
The Classical Hilbertian Fields | |
Nonstandard Structures | |
Nonstandard Approach to Hilberts Irreducibility Theorem | |
Galois Groups over Hilbertian Fields | |
Free Profinite Groups | |
The Haar Measure | |
Ef | |
ISBN: | 9783540269496 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | A Series of Modern Surveys in Mathematics : v11 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Field theory (Physics) , Geometry , Logic, Symbolic and mathematical , Number theory |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2004-9781402018985:ONLINE Show nearby items on shelf |
Title: | Galois Connections and Applications |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (502 p.) |
Note: | 10.1007/978-1-4020-1898-5 |
Contents: | Adjunctions and Galois Connections: Origins, History and Development -- Categorical Galois Theory: Revision and Some Recent Developments -- The Polarity between Approximation and Distribution -- Galois Connections and Complete |
Sublattices -- Galois Connections for Operations and Relations -- Galois Connections and Polynomial Completeness -- Q-Independence and Weak Automorphisms -- A Survey of Clones Closed Under Conjugation -- Galois Connections for Partial | |
Algebras -- Complexity of Terms and the Galois Connection Id-Mod -- Iterated Galois Connections in Arithmetic and Linguistics -- Deductive Systems and Galois Connections -- A Galois Correspondence for Digital Topology -- Galois | |
Connections in Category Theory, Topology and Logic -- Dyadic Mathematics — Abstractions from Logical Thought | |
ISBN: | 9781402018985 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 565 |
Keywords: | Mathematics , Programming languages (Electronic computers) , Data structures (Computer science) , Artificial intelligence , Algebra , Mathematics , Algebra , Mathematics, general , Programming Languages, Compilers, Interpreters , Artificial Intelligence (incl. Robotics) , Data Structures |
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Call number: | SPRINGER-2003-9783642558269:ONLINE Show nearby items on shelf |
Title: | Computer Algebra Handbook Foundations · Applications · Systems |
Author(s): | |
Date: | 2003 |
Size: | 1 online resource (637 p.) |
Note: | 10.1007/978-3-642-55826-9 |
Contents: | 1 Development, Characterization, Prospects -- 1.1 Historical Remarks -- 1.2 General Characterization -- 1.3 Impact on Education -- 1.4 Impact on Research -- 1.5 Computer Algebra — Today and Tomorrow -- 2 Topics of Computer Algebra -- |
2.1 Exact Arithmetic -- 2.2 Algorithms for Polynomials and Power Series -- 2.3 Linear Algebra -- 2.4 Constructive Methods of Number Theory -- 2.5 Algorithms of Commutative Algebra and Algebraic Geometry -- 2.6 Algorithmic Aspects of | |
the Theory of Algebras -- 2.7 Computational Group Theory -- 2.8 Algorithms of Representation Theory -- 2.9 Algebraic Methods for Constructing Discrete Structures -- 2.10 Summation and Integration -- 2.11 Symbohc Methods for | |
DiflFerential Equations -- 2.12 Symbolic/Numeric Methods -- 2.13 Algebraic Complexity Theory -- 2.14 Coding Theory and Cryptography -- 2.15 Algorithmic Methods inUniversal Algebra and Logic -- 2.16 Knowledge Representation and Abstract | |
Data Types -- 2.17 On the Design of Computer Algebra Systems -- 2.18 Parahel Computer Algebra Systems -- 2.19 Interfaces and Standardization -- 2.20 Hardware Implementation of Computer Algebra Algorithms -- 3 Applications of Computer | |
Algebra -- 3.1 Physics -- 3.2 Mathematics -- 3.3 Computer Science -- 3.4 Engineering -- 3.5 Chemistry -- 3.6 Computer Algebra in Education -- 4 Computer Algebra Systems -- 4.1 General Purpose Systems -- 4.2 Special Purpose Systems -- | |
4.3 Packages -- 5 Meetings and Publications -- 5.1 Conferences and Proceedings -- 5.2 Books on Computer Algebra -- Cited References -- Index for Authors’ Contributions | |
ISBN: | 9783642558269 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Computer science , Algebra , Algorithms , Computer software , Mathematics , Mathematical Software , Algebra , Algorithms , Symbolic and Algebraic Manipulation |
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Call number: | SPRINGER-2003-9781461200536:ONLINE Show nearby items on shelf |
Title: | Ordered Sets An Introduction |
Author(s): |
Bernd S. W Schröder |
Date: | 2003 |
Size: | 1 online resource (391 p.) |
Note: | 10.1007/978-1-4612-0053-6 |
Contents: | 1 The Basics -- 1.1 Definition and Examples -- 1.2 The Diagram -- 1.3 Order-Preserving Mappings/Isomorphism -- 1.4 Fixed Points -- 1.5 Ordered Subsets/The Reconstruction Problem -- Exercises -- Remarks and Open Problems -- 2 Chains, |
Antichains and Fences -- 2.1 Chains and Zorn’s Lemma -- 2.2 Well-ordered Sets -- 2.3 A Remark on Duality -- 2.4 The Rank of an Element -- 2.5 Antichains and Dilworth’s Chain Decomposition Theorem -- 2.6 Dedekind Numbers -- 2.7 Fences | |
and Crowns -- 2.8 Connectivity -- Exercises -- Remarks and Open Problems -- 3 Upper and Lower Bounds -- 3.1 Extremal Elements -- 3.2 Covers -- 3.3 Lowest Upper and Greatest Lower Bounds -- 3.4 Chain-Completeness and the Abian-Brown | |
Theorem -- Exercises -- Remarks and Open Problems -- 4 Retractions -- 4.1 Definition and Examples -- 4.2 Fixed Point Theorems -- 4.3 Dismantlability -- 4.4 The Fixed Point Property for Ordered Sets of Width 2 or Height 1 -- 4.5 Li and | |
Milner’s Structure Theorem -- 4.6 Isotone Relations -- Exercises -- Remarks and Open Problems -- 5 Lattices -- 5.1 Definition and Examples -- 5.2 Fixed Point Results/The Tarski-Davis Theorem -- 5.3 Embeddings/The Dedekind-MacNeille | |
Completion -- 5.4 Irreducible Points in Lattices -- 5.5 Finite Ordered Sets vs. Distributive Lattices -- 5.6 More on Distributive Lattices -- Exercises -- Remarks and Open Problems -- 6 Truncated Lattices -- 6.1 Definition and Examples | |
-- 6.2 Recognizability and More -- 6.3 The Fixed Clique Property -- 6.4 Triangulations of Sn -- 6.5 Cutsets -- 6.6 Truncated Noncomplemented Lattices -- Exercises -- Remarks and Open Problems -- 7 The Dimension of Ordered Sets -- 7.1 | |
(Linear) Extensions of Orders -- 7.2 Balancing Pairs -- 7.3 Defining the Dimension -- 7.4 Bounds on the Dimension -- 7.5 Ordered Sets of Dimension 2 -- Exercises -- Remarks and Open Problems -- 8 Interval Orders -- 8.1 Definition and | |
Examples -- 8.2 The Fixed Point Property for Interval Orders -- 8.3 Dedekind’s Problem for Interval Orders and Reconstruction -- 8.4 Interval Dimension -- Exercises -- Remarks and Open Problems -- 9 Lexicographic Sums -- 9.1 Definition | |
and Examples -- 9.2 The Canonical Decomposition -- 9.3 Comparability Invariance -- 9.4 Lexicographic Sums and Reconstruction -- 9.5 An Almost Lexicographic Construction -- Exercises -- Remarks and Open Problems -- 10 Sets PQ = Hom(Q, | |
P) and Products -- 10.1 Sets PQ = Hom(Q, P) -- 10.2 Finite Products -- 10.3 Infinite Products -- 10.4 Hashimoto’s Theorem and Automorphisms of Products -- 10.5 Arithmetic of Ordered Sets -- Exercises -- Remarks and Open Problems -- 11 | |
Enumeration -- 11.1 Graded Ordered Sets -- 11.2 The Number of Graded Ordered Sets -- 11.3 The Asymptotic Number of Graded Ordered Sets -- 11.4 The Number of Nonisomorphic Ordered Sets -- 11.5 The Number of Automorphisms -- Exercises -- | |
Remarks and Open Problems -- 12 Algorithmic Aspects -- 12.1 Algorithms -- 12.2 Polynomial Efficiency -- 12.3 NP problems -- 12.4 NP-completeness -- 12.5 So It’s NP-complete -- 12.6 A Polynomial Algorithm for the Fixed Point Property in | |
Graded Ordered Sets of Bounded Width -- Exercises -- Remarks and Open Problems -- A A Primer on Algebraic Topology -- A.l Chain Complexes -- A.2 The Lefschetz Number -- A.3 (Integer) Homology -- A.4 A Homological Reduction Theorem -- | |
Remarks and Open Problems -- B Order vs. Analysis -- B.2 Fixed Point Theorems -- B.3 An Application -- Remarks and Open Problems -- References | |
ISBN: | 9781461200536 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Ordered algebraic structures , Mathematical logic , Algebraic topology , Combinatorics , Mathematics , Mathematical Logic and Foundations , Order, Lattices, Ordered Algebraic Structures , Combinatorics , Algebraic Topology |
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Call number: | SPRINGER-2002-9783709105252:ONLINE Show nearby items on shelf |
Title: | Advanced Arithmetic for the Digital Computer Design of Arithmetic Units |
Author(s): |
Ulrich W Kulisch |
Date: | 2002 |
Size: | 1 online resource (1 p.) |
Note: | 10.1007/978-3-7091-0525-2 |
Contents: | 1. Fast and Accurate Vector Operations -- 1.1 Introduction -- 1.2 Implementation Principles -- 1.3 High-Performance Scalar Product Units (SPU) -- 1.4 Comments on the Scalar Product Units -- 1.5.1 Scalar Product Units for |
Top-Performance Computers -- 1.6 Hardware Accumulation Window -- 1.7 Theoretical Foundation of Advanced Computer Arithmetic -- Bibliography and Related Literature -- 2. Rounding Near Zero -- 2.1 The one dimensional case -- 2.2 Rounding | |
in product spaces -- Bibliography and Related Literature -- 3. Interval Arithmetic Revisited -- 3.1 Introduction and Historical Remarks -- 3.2 Interval Arithmetic, a Powerful Calculus to Deal with Inequalities -- 3.3 Interval | |
Arithmetic as Executable Set Operations -- 3.4 Enclosing the Range of Function Values -- 3.5 The Interval Newton Method -- 3.6 Extended Interval Arithmetic -- 3.7 The Extended Interval Newton Method -- 3.8 Differentiation Arithmetic, | |
Enclosures of Derivatives -- 3.9 Interval Arithmetic on the Computer -- 3.10 Hardware Support for Interval Arithmetic | |
ISBN: | 9783709105252 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Arithmetic and logic units, Computer , Microprocessors , Architecture, Computer , Algorithms , Computer mathematics , Numerical analysis , Mathematics , Computational Science and Engineering , Arithmetic and Logic Structures , Processor Architectures , Computer System Implementation , Algorithms , Numerical Analysis |
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Call number: | SPRINGER-2001-9783709162804:ONLINE Show nearby items on shelf |
Title: | Symbolic Algebraic Methods and Verification Methods |
Author(s): | |
Date: | 2001 |
Size: | 1 online resource (266 p.) |
Note: | 10.1007/978-3-7091-6280-4 |
Contents: | Topological Concepts for Hierarchies of Variables, Types and Controls -- Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem -- Symbolic-Numeric Algorithms for Polynomials: Some Recent Results -- |
Symbolic-Numeric QD-Algorithms with Applications in Function Theory and Linear Algebra -- On the Isoefficiency of the Parallel Descartes Method -- Matrix Methods for Solving Algebraic Systems -- A Feasibility Result for Interval | |
Gaussian Elimination Relying on Graph Structure -- Solution of Systems of Polynomial Equations by Using Bernstein Expansion -- Symbolic-Algebraic Computations in Modeling Language for Mathematical Programming -- Translation of Taylor | |
Series into LFT Expansions -- Quasi Convex-Concave Extensions -- Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic -- Derivative-Based Sub division in Multi-dimensional Verified Gaussian Quadrature -- | |
On the Shape of the Fixed Points of [f]([x]) = [A][x] + [b] -- Exact Computation with leda_real - Theory and Geometrie Applications -- Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations -- Geometric Series | |
Bounds for the Local Errors of Taylor Methods for Linear n-th-Order ODEs -- Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems -- Fast Verification Algorithms in MATLAB -- The Linear Complementarity | |
Problem with Interval Data -- Some Numerical Methods for Nonlinear Least Squares Problems -- A New Insight of the Shortley-Weller Approximation for Diriehlet Problems -- How Orthogonality is Lost in Krylov Methods | |
ISBN: | 9783709162804 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Arithmetic and logic units, Computer , Computers , Computer science , Algebra , Algorithms , Numerical analysis , Mathematics , Numerical Analysis , Algebra , Theory of Computation , Algorithms , Symbolic and Algebraic Manipulation , Arithmetic and Logic Structures |
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Call number: | SPRINGER-2000-9783642572807:ONLINE Show nearby items on shelf |
Title: | Classification and Information Processing at the Turn of the Millennium Proceedings of the 23rd Annual Conference of the Gesellschaft für Klassifikation e.V., University of Bielefeld, March 10–12, 1999 |
Author(s): | |
Date: | 2000 |
Size: | 1 online resource (492 p.) |
Note: | 10.1007/978-3-642-57280-7 |
Contents: | 1: Data Analysis and Classification -- New Developments in Latent Variable Models -- Regression-Type Models for Kohonen’s Self-Organizing Networks -- Relational Data Analysis, Discrimination and Classification -- Data Types and |
Information: Beyond the Current Practice of Data Analysis -- Two-Mode Three-Way Asymmetric Multidimensional Scaling with Constraints on Asymmetry -- Regularized Discriminant Analysis with Optimally Scaled Data -- Recurrence Properties | |
in Two-Mode Hierarchical Clustering -- On Pyramidal Classification in the Delimitation of Climatic Regions in Catalonia -- On the Modal Understanding of Triadic Contexts -- Clustering and Scaling: Grouping Variables in Burt Matrices -- | |
Standardisation of Data Set under Different Measurement Scales -- Neural Networks for Two-Group Classification Problems with Monotonicity Hints -- A Bridge from the Nearest Neighbour to the Fixed Bandwidth in Nonparametric Functional | |
Estimation -- Clustering Techniques for the Detection of Business Cycles -- Simulated Annealing Optimization for Two-mode Partitioning -- 2: Computer Science, Computational Statistics, and Data Mining -- Competitiveness of Evolutionary | |
Algorithms -- Intelligent Data Analysis via Linguistic Data Summaries: A Fuzzy Logic Approach -- Algorithm Selection Support for Classification -- Society of Knowledge — Interdisciplinary Perspectives of Information Processing in | |
Virtual Networks -- What is Computational Statistics? -- A Development Framework for Nature Analogic Heuristics -- Systematizing and Evaluating Data Mining Methods -- On Textures: A Sketch of a Texture-Based Image Segmentation Approach | |
-- Automatic Texture Classification by Visual Properties -- Java Servlets versus CGI — Implications for Remote Data Analysis -- Generating Automatically Local Feature Groups of Complex and Deformed Objects -- Decision Tree Construction | |
by Association Rules -- Learning Complex Similarity Measures -- Graphical Programming in Statistics: The XGPL Prototype -- 3: Management Science, Marketing, and Finance -- Measuring Brand Loyalty on the Individual Level: a Comparative | |
Study -- Facility Location Planning with Qualitative Location Factors -- Testing the Multinomial Logit Model -- Time Optimal Portfolio Selection: Mean-variance-efficient Sets for Arithmetic and Geometric Brownian Price Processes -- | |
Analyzing Multigroup Data with Structural Equation Models -- Validity of Customized and Adaptive Hybrid Conjoint Analysis -- Analysis of the Assessments of One’s Values Among Different Cohorts in Age and Sex by Multidimensional Scaling | |
-- Impacts of Hedging with Futures on Optimal Production Levels -- How to Integrate Stock Price Jumps into Portfolio Selection -- A Multivariate GARCH-M Model for Exchange Rates in the US, Germany and Japan -- A Model for Constructing | |
Quadratic Objective Functions and its Applications to Price Adjustments -- 4: Biology, Genome Analysis, and Medicine -- Phylogeny Inference by Minimum Conflict -- Detecting Change-Points in Aircraft Noise Effects -- A Generalized | |
Estimating Equations Approach to Quantifying the Influence of Meteorological Conditions on Hand Dermatitis -- Discrimination in Paired Data Situations -- Classification of Multidimensional Visual Field Data for Glaucoma Diagnosis -- | |
Quality of Life of Cancer Patients: A Multi-set Analysis -- A New Approach on Nonparametric Repeated Measures Analysis of Variance -- 5: Text Analysis and Information Retrieval -- GERHARD (German Harvest Automated Retrieval and | |
Directory) -- Automatic Labelling of References for Internet Information Systems -- Architecture and Retrieval Methods of a Search Assistant for Scientific Libraries -- Computer Aided Evaluations of Linguistic Atlases: Prom Automatic | |
Classification to Dialectometry -- Structured Phrases for Indexing and Retrieval of Research Topics -- Author and Subject Index | |
ISBN: | 9783642572807 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Computer science , Information technology , Business , Data structures (Computer science) , Probabilities , Statistics , Econometrics , Computer Science , Data Structures, Cryptology and Information Theory , Econometrics , IT in Business , Statistics for Business/Economics/Mathematical Finance/Insurance , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2000-9781441986221:ONLINE Show nearby items on shelf |
Title: | A Course in Model Theory An Introduction to Contemporary Mathematical Logic |
Author(s): |
Bruno Poizat |
Date: | 2000 |
Size: | 1 online resource (443 p.) |
Note: | 10.1007/978-1-4419-8622-1 |
Contents: | 1 Elementary Classes of Relations -- The Language Associated with a Relation -- 3 Extensions of the Language: Structures -- 4 Compactness -- 5 The Back-and-Forth Method in ?-Saturated Models -- 6 Examples Illustrating the |
Back-and-Forth Method -- 7 Arithmetic -- 8 Ordinals and Cardinals -- 9 Saturated Models -- 10 Prime Models -- 11 Heirs -- 12 Special Sons, Morley Sequences -- 13 The Fundamental Order -- 14 Stability and Saturated Models -- 15 Forking | |
-- 16 Strong Types -- 17 Notions of Rank -- 18 Stability and Prime Models -- 19 Stability, Indiscernible Sequences and Weights -- 20 Dimension in Models of a Totally Transcendental Theory -- Index of Notation | |
ISBN: | 9781441986221 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical logic , Mathematics , Mathematical Logic and Foundations |
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Call number: | SPRINGER-1998-9783642854736:ONLINE Show nearby items on shelf |
Title: | A Course on Borel Sets |
Author(s): |
S. M Srivastava |
Date: | 1998 |
Note: | 10.1007/978-3-642-85473-6 |
Contents: | 1 Cardinal and Ordinal Numbers -- 1.1 Countable Sets -- 1.2 Order of Infinity -- 1.3 The Axiom of Choice -- 1.4 More on Equinumerosity -- 1.5 Arithmetic of Cardinal Numbers -- 1.6 Well-Ordered Sets -- 1.7 Transfinite Induction -- 1.8 |
Ordinal Numbers -- 1.9 Alephs -- 1.10 Trees -- 1.11 Induction on Trees -- 1.12 The Souslin Operation -- 1.13 Idempotence of the Souslin Operation -- 2 Topological Preliminaries -- 2.1 Metric Spaces -- 2.2 Polish Spaces -- 2.3 Compact | |
Metric Spaces -- 2.4 More Examples -- 2.5 The Baire Category Theorem -- 2.6 Transfer Theorems -- 3 Standard Borel Spaces -- 3.1 Measurable Sets and Functions -- 3.2 Borel-Generated Topologies -- 3.3 The Borel Isomorphism Theorem -- 3.4 | |
Measures -- 3.5 Category -- 3.6 Borel Pointclasses -- 4 Analytic and Coanalytic Sets -- 4.1 Projective Sets -- 4.2 ?11 and ?11 Complete Sets -- 4.3 Regularity Properties -- 4.4 The First Separation Theorem -- 4.5 One-to-One Borel | |
Functions -- 4.6 The Generalized First Separation Theorem -- 4.7 Borel Sets with Compact Sections -- 4.8 Polish Groups -- 4.9 Reduction Theorems -- 4.10 Choquet Capacitability Theorem -- 4.11 The Second Separation Theorem -- 4.12 | |
Countable-to-One Borel Functions -- 5 Selection and Uniformization Theorems -- 5.1 Preliminaries -- 5.2 Kuratowski and Ryll-Nardzewski’s Theorem -- 5.3 Dubins — Savage Selection Theorems -- 5.4 Partitions into Closed Sets -- 5.5 Von | |
Neumann’s Theorem -- 5.6 A Selection Theorem for Group Actions -- 5.7 Borel Sets with Small Sections -- 5.8 Borel Sets with Large Sections -- 5.9 Partitions into G? Sets -- 5.10 Reflection Phenomenon -- 5.11 Complementation in Borel | |
Structures -- 5.12 Borel Sets with ?-Compact Sections -- 5.13 Topological Vaught Conjecture -- 5.14 Uniformizing Coanalytic Sets -- References | |
ISBN: | 9783642854736 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 180 |
Keywords: | Mathematics , Mathematical logic , Topology , Mathematics , Mathematical Logic and Foundations , Topology |
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Call number: | SPRINGER-1993-9789401582322:ONLINE Show nearby items on shelf |
Title: | Algorithms: Main Ideas and Applications |
Author(s): |
Vladimir Uspensky |
Date: | 1993 |
Size: | 1 online resource (270 p.) |
Note: | 10.1007/978-94-015-8232-2 |
Contents: | Notation and Terminology -- 1.0 Preliminary notions of the theory of algorithms: constructive objects and aggregates local properties and local actions -- 1.1 The general notion of an algorithm as an independent (separate) concept -- |
1.2 Representative computational models -- 1.3 The general notion of a calculus as an independent (separate) concept -- 1.4 Representative generating models -- 1.5 Interrelations between algorithms and calculuses -- 1.6 Time and Space | |
as complexities of computation and generation -- 1.7 Computable functions and generable sets decidable sets enumerable sets -- 1.8 The concept of a ?-recursive function -- 1.9 Possibility of an arithmetical and even Diophantine | |
representation of any enumerable set of natural numbers -- 1.10 Construction of an undecidable generable set -- 1.11 Post’s reducibility problem -- 1.12 The concept of a relative algorithm, or an oracle algorithm -- 1.13 The concept of | |
a computable operation -- 1.14 The concept of a program programs as objects of computation and generation -- 1.15 The concept of a numbering and the theory of numberings -- 1.16 First steps in the invariant, or machine-independent, | |
theory of complexity of computations -- 1.17 The theory of complexity and entropy of constructive objects -- 1.18 Convenient computational models -- 2.1 Investigations of mass problems -- 2.2 Applications to the foundations of | |
mathematics: constructive semantics -- 2.3 Applications to mathematical logic: formalized languages of logic and arithmetic -- 2.4 Computable analysis -- 2.5 Numbered structures -- 2.6 Applications to probability theory: definitions of | |
a random sequence -- 2.7 Applications to information theory: the algorithmic approach to the concept of quantity of information -- 2.8 Complexity bounds for particular problems -- 2.9 Influence of the theory of algorithms on | |
algorithmic practice -- Appendix. Probabilistic Algorithms (How the Use of Randomness Makes Computations Shorter) -- A.1 Preliminary remarks -- A.2 Main results -- A.3 Formal definitions -- References -- Author Index | |
ISBN: | 9789401582322 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 251 |
Keywords: | Mathematics , Logic , Computers , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Theory of Computation , Logic |
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Call number: | SPRINGER-1993-9789401120807:ONLINE Show nearby items on shelf |
Title: | Finite and Infinite Combinatorics in Sets and Logic |
Author(s): | |
Date: | 1993 |
Size: | 1 online resource (453 p.) |
Note: | 10.1007/978-94-011-2080-7 |
Contents: | Extensions of the Erd?s—Rado Theorem -- Zero Sum Trees: A Survey of Results and Open Problems -- On Superatomic Boolean Algebras -- Representing Rings Using Continuous Function -- Homogeneous Directed Graphs -- Ordinal Partition |
Behavior of Finite Powers of Cardinals -- Some Subdirect Products of Finite Nilpotent Groups -- Three Remarks on End-Faithfulness -- True Embedding Partition Relations -- Lattices Related to Separation in Graphs -- Ramsey Numbers for | |
Sets of Five Vertex Graphs With Fixed Number of Edges -- Finite Structures With Few Types -- Recognition Problem in Reconstruction for Decomposable Relations -- The Average Size of Nonsingular Sets in a Graph -- Some Canonical | |
Partition Ordinals -- The Group of Automorphisms of a Relational Saturated Structure -- On Canonical Ramsey Numbers for Coloring Three-Element Sets -- Large Subgroups of Infinite Symmetric Groups -- Homogeneous Partially Ordered Sets | |
-- Cardinal Representations -- A Vertex-to-Vertex Pursuit Game Played With Disjoint Sets of Edges -- Graphs and Posets With no Infinite Independent Set -- Problems About Planar Orders -- Superstable and Unstable Theories of Order -- | |
Advances in Cardinal Arithmetic -- Conjectures of Rado and Chang and Cardinal Arithmetic -- Random Structures and Zero-One Laws -- Isotone Maps: Enumeration and Structure -- Problem Sessions | |
ISBN: | 9789401120807 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO ASI Series, Series C: Mathematical and Physical Sciences: 411 |
Keywords: | Mathematics , Computer science , Mathematical logic , Discrete mathematics , Combinatorics , Mathematics , Discrete Mathematics , Mathematics, general , Combinatorics , Discrete Mathematics in Computer Science , Mathematical Logic and Foundations |
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Call number: | SPRINGER-1992-9783540470212:ONLINE Show nearby items on shelf |
Title: | Primality Testing and Abelian Varieties Over Finite Fields |
Author(s): |
Leonard M Adleman |
Date: | 1992 |
Size: | 1 online resource (144 p.) |
Note: | 10.1007/BFb0090185 |
Contents: | Acknowledgement -- Overview of the algorithm and the proof of the main theorem -- Reduction of main theorem to three propositions -- Proof of proposition 1 -- Proof of proposition 2 -- Proof of proposition 3 |
ISBN: | 9783540470212 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1512 |
Keywords: | Mathematics , Arithmetic and logic units, Computer , Computers , Number theory , Combinatorics , Mathematics , Number Theory , Theory of Computation , Combinatorics , Arithmetic and Logic Structures |
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Call number: | SPRINGER-1992-9781461228226:ONLINE Show nearby items on shelf |
Title: | Logic from Computer Science Proceedings of a Workshop held November 13–17, 1989 |
Author(s): | |
Date: | 1992 |
Size: | 1 online resource (608 p.) |
Note: | 10.1007/978-1-4612-2822-6 |
Contents: | Preface -- The Imperative Future: Past Successes Future Actions -- A Logical Operational Semantics of Full Prolog: Part III. Built-in Predicates for Files, Terms, Arithmetic and Input-Output -- Computability and Complexity of Higher |
Type Functions -- Constructively Equivalent Propositions and Isomorphisms of Objects, or Terms as Natural Transfomrations -- Logics for Termination and Correctness of Functional Programs -- Transparent Grammars -- Designing Unification | |
Procedures Using Transformations: A survey -- NormaL Forms and Cut-Free Proofs as Natural Transformations -- Computer Implementation and Applications of Kleene’s S-M-N and Recursion Theorems -- 0–1 Laws for Fragments of Second-Order | |
Logic: an Overview -- No Counter-Example Interpretation and Interactive Computation -- Semantic Characterizations of Number Theories -- Constructive Kripke Semantics and Realizability -- Splitting and Density for the Recursive Sets of | |
a Fixed Time Complexity -- Reals and Forcing with an Elementary Topos -- Completeness Theorems for Logics of Feature Structures -- Concurrent Programs as Strategies in Games -- Finite and Infinite Dialogues -- Some Relations Between | |
Subsystems of Arithmetic and Complexity of Computations -- Logics for Negation as Failure -- Normal Varieties of Combinators -- Complexity of Proofs in Classical Propositional Logic | |
ISBN: | 9781461228226 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematical Sciences Research Institute Publications: 21 |
Keywords: | Mathematics , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Mathematical Logic and Formal Languages |
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Call number: | SPRINGER-1990-9781461306092:ONLINE Show nearby items on shelf |
Title: | Mathematical Logic |
Author(s): | |
Date: | 1990 |
Size: | 1 online resource (420 p.) |
Note: | 10.1007/978-1-4613-0609-2 |
Contents: | Heyting Session (Invited Papers) -- On the Early History of Intuitionistic Logic -- Heyting and Intuitionistic Geometry -- Summer School (Invited Lectures) -- Provability Logics for Relative Interpretability -- Constructive |
Mathematics and Computer-Assisted Reasoning Systems -- Markov’s Constructive Mathematical Analysis: the Expextations and Results -- Normalization Theorems for the Intuitionistic Systems with Choice Principles -- Formalizing the Notion | |
of Total Information -- Structural Rules and a Logical Hierarchy -- Semantics of Non-classical First Order Predicate Logics -- On the Computational Power of the Logic Programs -- Some Relations among Systems for Bounded Arithmetic -- A | |
Survey of Intuitionistic Descriptive Set Theory -- Interpretability Logic -- Hierarchies of Provably Computable Functions -- Conference (Contributed Papers) -- Sequent Calculus for Intuitionistic Linear Propositional Logic -- Order | |
Isomorphisms — a Constructive Measure-Theoretic View -- 1-Generic Enumeration Degrees Below Oe’ -- Remarks on Denjoy Sets -- Normal Modal Logic in Which the Heyting Proposotional Calculus Can be Embedded -- Lattices Adequate for | |
Intutionistic Predicate Logic -- A Note on Boolean Modal Logic -- Completeness and Incompleteness in the Bimodal Base L(R,?R) -- A Temporal Logic for Event Structures -- Completeness of Propositional Dynamic Logic with Infinite | |
Repeating -- An Equivalence between Polinomial Constructivity of Markov’s Principle and Equality P=NP -- Effective Enumerations of Abstract Structures -- Modal Characterization of the Classes of Finite and Infinite Quasi-Ordered Sets | |
-- Least Fixed Points in Preassociative Combinatory Algebras -- Participants, Contributors and Programme Committee Members | |
ISBN: | 9781461306092 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Logic , Algebra , Field theory (Physics) , Functional analysis , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Functional Analysis , Logic , Field Theory and Polynomials |
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Call number: | SPRINGER-1987-9783540480495:ONLINE Show nearby items on shelf |
Title: | Classification Theory Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic held in Chicago, Dec. 15–19, 1985 |
Author(s): | |
Date: | 1987 |
Size: | 1 online resource (508 p.) |
Note: | 10.1007/BFb0082228 |
Contents: | Classification theory: 1985 -- Concrete representations of lattices and the fundamental order -- The classification of small weakly minimal sets I -- Orthogonality of types in separably closed fields -- Countable or ?1-like models of |
Presburger's arithmetic -- An exposition of OTOP -- Exercises on Local Weight -- Locally modular regular types -- Choosing elements in a saturated model -- Degrees of models with prescribed Scott set -- Shrinking, stretching, and codes | |
for homogeneous structures -- Freedom via forcing: Uniform construction of relatively free or generic structures -- Simple superstable theories -- Universal classes -- Classification of non elementary classes II abstract elementary | |
classes -- On almost categorical theories | |
ISBN: | 9783540480495 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 1292 |
Keywords: | Mathematics , Mathematical logic , Mathematics , Mathematical Logic and Foundations |
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Call number: | SPRINGER-1986-9783662072165:ONLINE Show nearby items on shelf |
Title: | Field Arithmetic |
Author(s): |
Michael D Fried |
Date: | 1986 |
Size: | 1 online resource (460 p.) |
Note: | 10.1007/978-3-662-07216-5 |
Contents: | 1. Infinite Galois Theory and Profinite Groups -- 2. Algebraic Function Fields of One Variable -- 3. The Riemann Hypothesis for Function Fields -- 4. Plane Curves -- 5. The ?ebotarev Density Theorem -- 6. Ultraproducts -- 7. Decision |
Procedures -- 8. Algebraically Closed Fields -- 9. Elements of Algebraic Geometry -- 10. Pseudo Algebraically Closed Fields -- 11. Hilbertian Fields -- 12. The Classical Hilbertian Fields -- 13. Nonstandard Structures -- 14. | |
Nonstandard Approach to Hilbert’s Irreducibility Theorem -- 15. Profinite Groups and Hilbertian Fields -- 16. The Haar Measure -- 17. Effective Field Theory and Algebraic Geometry -- 18. The Elementary Theory of e-free PAC Fields -- | |
19. Examples and Applications -- 20. Projective Groups and Frattini Covers -- 21. Perfect PAC Fields of Bounded Corank -- 22. Undecidability -- 23. Frobenius Fields -- 24. On ?-free PAC Fields -- 25. Galois Stratification -- 26. Galois | |
Stratification over Finite Fields -- Open Problems -- References | |
ISBN: | 9783662072165 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics: 11 |
Keywords: | Mathematics , Algebraic geometry , Algebra , Field theory (Physics) , Mathematical logic , Mathematics , Field Theory and Polynomials , Mathematical Logic and Foundations , Algebraic Geometry |
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Call number: | SPRINGER-1981-9783642678295:ONLINE Show nearby items on shelf |
Title: | Applications of Number Theory to Numerical Analysis |
Author(s): |
Hua Loo Keng |
Date: | 1981 |
Size: | 1 online resource (244 p.) |
Note: | 10.1007/978-3-642-67829-5 |
Contents: | 1. Algebraic Number Fields and Rational Approximation -- §1.1. The units of algebraic number fields -- §1.2. The simultaneous Biophantine approximation of an integral basis -- §1.3. The real eyelotomie field -- §1.4. The units of a |
eyelotomie field -- §1.5. Continuation -- §1.6. The Drriehlet field -- §1.7. The cubic field -- Notes -- 2. Recurrence Relations and Rational Approximation -- §2.1. The recurrence formula for the elementary symmetric fonction -- §2.2. | |
The generalization of Sn -- §2.3. PV numbers -- § 2.4. The roots of the equation F(x) = 0 -- §2.5. The roots of the equation G(x) = 0 -- §2.6. The roots of the equation E(x) = 0 -- §2.7. The irreducibility of a polynomial -- §2.8. The | |
rational approximations of ?, ?, ? -- Notes -- 3. Uniform Distribution -- §3.1. Uniform distribution -- §3.2. Vinogradov’s lemma -- §3.3. The exponential sum and the discrepancy -- §3.4. The number of solutions to the congruence -- | |
§3.5. The solutions of the congruence and the discrepancy -- §3.6. The partial summation formula -- §3.7. The comparison of discrepancies -- §3.8. Eational approximation and the solutions of the congruence -- §3.9. The rational | |
approximation and the discrepancy -- §3.10. The lower estimate of discrepancy -- Notes -- 4. Estimation of Discrepancy -- §4.1. The set of equi-distribution -- §4.2. The Halton theorem -- §4.3. The p set -- §4.4. The gp set -- §4.5. | |
The eonstruetion of good points -- §4.6. The ?s set -- §4.7. The ? set -- §4.8. The ease s = 2 -- §4.9. The glp set -- Notes -- 5. Uniform Distribution and Numerical Integration -- §5.1. The function of bounded variation -- §5.2. | |
Uniform distribution and numerical integration -- §5.3. The lower estimation for the error term of quadrature formula -- §5.4. The quadrature formulas -- Notes -- 6. Periodic Functions -- §6.1. The classes of functions -- §6.2. Several | |
lemmas -- §6.3. The relations between Hs?(C), Qs?(C) and Es?(C) -- §6.4. Periodic functions -- § 6.5. Continuation -- Notes -- 7. Numerical Integration of Periodic Functions -- §7.1. The set of equi-distribution and numerical | |
integration -- §7.2. The p set and numerical integration -- §7.3. The gp set and numerical integration -- §7.4. The lower estimation of the error term for the quadrature formula -- §7.5. The solutions of congruences and numerical | |
integration -- §7.6. The glp set and numerical integration -- §7.7. The Sarygin theorem -- §7.8. The mean error of the quadrature formula -- §7.9. Continuation -- Notes -- 8. Numerical Error for Quadrature Formula -- §8.1. The | |
numerical error -- §8.2. The comparison of good points -- §8.3. The computation of the ? set -- §8.4. The computation of the ?s set -- §8.5. Examples of other F s sets -- §8.6. The computation of a glp set -- §8.7. Several remarks -- | |
§8.8. Tables -- § 8.9. Some examples -- Notes -- 9. Interpolation -- §9.1. Introduction -- §9.2. The set of equi-distribution and interpolation -- §9.3. Several lemmas -- §9.4. The approximate formula of the function of E?s(C) -- §9.5. | |
The approximate formula of the function of Q?s(C) -- §9.6. The Bernoulli polynomial and the approximate polynomial -- §9.7. The ? results -- Notes -- 10. Approximate Solution of Integral Equations and Differential Equations -- §10.1. | |
Several lemmas -- § 10.2. The approximate solution of the Fredholm integral equation of second type -- § 10.3. The approximate solution of the Volterra integral equation of second type -- §10.4. The eigenvalue and eigenfunction of the | |
Fredholm equation -- § 10.5. The Cauehy problem of the partial differential equation of the parabolic type -- § 10.6. The Diriehlet problem of the partial differential equation of the elliptic type -- § 10.7. Several remarks -- Notes | |
-- Appendix Tables | |
ISBN: | 9783642678295 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Arithmetic and logic units, Computer , Numerical analysis , Number theory , Mathematics , Number Theory , Numerical Analysis , Arithmetic and Logic Structures |
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Call number: | SPRINGER-1979-9781461394419:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Logic Set Theory Computable Functions Model Theory |
Author(s): |
Jerome Malitz |
Date: | 1979 |
Size: | 1 online resource (198 p.) |
Note: | 10.1007/978-1-4613-9441-9 |
Contents: | I: An Introduction to Set Theory -- 1.1 Introduction -- 1.2 Sets -- 1.3 Relations and Functions -- 1.4 Pairings -- 1.5 The Power Set -- 1.6 The Cantor-Bernstein Theorem -- 1.7 Algebraic and Transcendental Numbers -- 1.8 Orderings -- |
1.9 The Axiom of Choice -- 1.10 Transfinite Numbers -- 1.11 Paradise Lost, Paradox Found (Axioms for Set Theory) -- 1.12 Declarations of Independence -- II: An Introduction to Computability Theory -- 2.1 Introduction -- 2.2 Turing | |
Machines -- 2.3 Etemonstrating Computability without an Explicit Description of a Turing Machine -- 2.4 Machines for Composition, Recursion, and the “Least Operator” -- 2.5 Of Men and Machines -- 2.6 Non-computable Functions -- 2.7 | |
Universal Machines -- 2.8 Machine Enumerabihty -- 2.9 An Alternate Definition of Computable Function -- 2.10 An Idealized Language -- 2.11 Definabihty in Arithmetic -- 2.12 The Decision Problem for Arithmetic -- 2.13 Axiomatizing | |
Arithmetic -- 2.14 Some Directions in Current Research -- III: An Introduction to Model Theory -- 3.1 Introduction -- 3.2 The First Order Predicate Calculus -- 3.3 Structures -- 3.4 Satisfaction and Truth -- 3.5 Normal Forms -- 3.6 The | |
Compactness Theorem -- 3.7 Proof of the Compactness Theorem -- 3.8 The Lowenheim-Skolem Theorem -- 3.9 The Prefix Problem -- 3.10 Interpolation and Definabihty -- 3.11 Herbrand’s Theorem -- 3.12 Axiomatizing the Validities of L -- 3.13 | |
Some Recent Trends in Model Theory | |
ISBN: | 9781461394419 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical logic , Mathematics , Mathematical Logic and Foundations |
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Call number: | SPRINGER-1972-9783540371625:ONLINE Show nearby items on shelf |
Title: | Conference in Mathematical Logic — London ’70 |
Author(s): | |
Date: | 1972 |
Size: | 1 online resource (358 p.) |
Note: | 10.1007/BFb0059533 |
Contents: | Inductive definitions and analogues of large cardinals -- Compact injectives and Non-Standard Analysis -- Non-axiomatizability results in infinitary languages for higher-order structures -- ? 1 1 models and ? 1 1 -categoricity -- Infinitary propert ies, local functors, and systems of ordinal functions -- Logics containing S4 without the finite model property -- An ?-calculus system for first-order S4 -- Craig's interpolation theorem for modal logics -- A note on models and submodels of arithmetic -- An application of ultra-products to prime rings with polynomial identities -- Embedding nondistributive lattices in the recursively enumerable degrees -- Direct powers with distinguished diagonal -- Solution of problems of choquet and puritz -- Some B. R ussell's sprouts (1903 – 1908) -- On models of arithmetic -- -definability in set theory -- Initial segments and implications for the structure of degrees -- Abstracts of contributed papers |
ISBN: | 9783540371625 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 255 |
Keywords: | Mathematics , Mathematics , Mathematics, general |
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Call number: | SPRINGER-1971-9781468499155:ONLINE Show nearby items on shelf |
Title: | Introduction to Axiomatic Set Theory |
Author(s): |
Gaisi Takeuti |
Date: | 1971 |
Size: | 1 online resource (251 p.) |
Note: | 10.1007/978-1-4684-9915-5 |
Contents: | 1 Introduction -- 2 Language and Logic -- 3 Equality -- 4 Classes -- 5 The Elementary Properties of Classes -- 6 Functions and Relations -- 7 Ordinal Numbers -- 8 Ordinal Arithmetic -- 9 Relational Closure and the Rank Function -- 10 Cardinal Numbe rs -- 11 The Axiom of Choice, the Generalized Continuum Hypothesis and Cardinal Arithmetic -- 12 Models -- 13 Absoluteness -- 14 The Fundamental Operations -- 15 The Gödel Model -- 16 The Arithmetization of Model Theory -- 17 Cohen’s Method -- 18 Forci ng -- 19 Languages, Structures, and Models -- Problem List -- Index of Symbols |
ISBN: | 9781468499155 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 1 |
Keywords: | Mathematics , Mathematics , Mathematics, general |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-1965-9783662257623:ONLINE Show nearby items on shelf |
Title: | Functional Analysis |
Author(s): |
Kôsaku Yosida |
Date: | 1965 |
Size: | 1 online resource (458 p.) |
Note: | 10.1007/978-3-662-25762-3 |
Contents: | 0. Preliminaries -- I. Semi-norms -- II. Applications of the Baire-Hausdorff Theorem -- III. The Orthogonal Projection and F. Riesz’ Representation Theorem -- IV. The Hahn-Banach Theorems -- V. Strong Convergence and Weak Convergence -- VI. Fouri er Transform and Differential Equations -- VII. Dual Operators -- VIII. Resolvent and Spectrum -- IX. Analytical Theory of Semi-groups -- X. Compact Operators -- XI. Normed Rings and Spectral Representation -- XII. Other Representation Theorems in Linear Spaces -- XIII. Ergodic Theory and Diffusion Theory -- XIV. The Integration of the Equation of Evolution |
ISBN: | 9783662257623 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete: 123 |
Keywords: | Mathematics , Arithmetic and logic units, Computer , Topology , Mathematics , Topology , Arithmetic and Logic Structures |
Availability: | Click here to see Library holdings or inquire at
Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please. |
More info: | Amazon.com |
More info: | Barnes and Noble |
Full Text: | Click here |
Location: | ONLINE |
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