Mathematical foundations Books
Springer Fachmedien Wiesbaden Die Gödel'schen Unvollständigkeitssätze: Eine geführte Reise durch Kurt Gödels historischen Beweis
Book SynopsisIm Jahr 1931 erschien im Monatsheft für Mathematik und Physik ein Artikel mit dem geheimnisvoll klingenden Titel Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In dieser Arbeit hat Kurt Gödel zwei Unvollständigkeitssätze bewiesen, die unseren Blick auf die Mathematik von Grund auf verändert haben. Gödels Sätze manifestieren, dass zwischen dem Begriff der Wahrheit und dem Begriff der Beweisbarkeit eine Kluft besteht, die wir nicht überwinden können. Die Mathematik fügt sich in kein formales Korsett.Seit ihrer Entdeckung sind die Unvollständigkeitssätze in aller Munde und eine Flut an Büchern widmet sich ihrem fulminanten Inhalt. Doch kaum ein Werk behandelt die Gödel‘sche Arbeit in ihrer ursprünglichen Form − und dies hat triftige Gründe: Seine komplexen, in akribischer Präzision beschriebenen Argumentationsketten, die vielen Definitionen und Sätze und die heute weitgehend überholte Notation machen Gödels historisches Meisterwerk zu einer schwer zu lesenden Arbeit.In diesem Buch wird Gödels Beweis aus dem Jahr 1931 detailliert aufgearbeitet. Alle Einzelschritte werden erläutert und anhand zahlreicher Beispiele verständlich erklärt. Doch dieses Buch ist mehr als eine kommentierte Fassung der historischen Arbeit. Die Beweise der Unvollständigkeitssätze in vollem Umfang zu verstehen, bedingt, die Geschichte zu verstehen, und so versetzen zahlreiche Exkurse den Leser in die Zeit zu Beginn des zwanzigsten Jahrhunderts zurück. Es ist die Zeit, in der die Mathematik die größte Krise ihrer Geschichte durchlebte, die Typentheorie und die axiomatische Mengenlehre Gestalt annahmen und sich Hilberts formalistische Logik und Brouwers intuitionistische Mathematik mit offenem Visier gegenüber standen.Die 2. Auflage ist vollständig durchgesehen.Stimme zur ersten Auflage: „...eine didaktisch sehr gut gemachte Darstellung.“ Prof. Dr. Matthias Homeister, FH BrandenburgTable of ContentsEinleitung.- Die formalen Grundlagen der Mathematik.- Beweisskizze.- Das System P.- Primitiv-rekursive Funktionen.- Die Grenzen der Mathematik.- Epilog.
£36.09
Birkhauser Verlag AG Algorithmische Methoden: Zahlen, Vektoren,
Book SynopsisDas Lehrbuch diskutiert gängige Fragen der Analysis und linearen Algebra und verwendet für die rechnergestützten Antworten die Software Matlab und Mathematica. Es stellt mathematische Standard-Algorithmen im Detail vor und zeigt deren Umsetzung in die Programme. Zusätzlich erläutert es, wie deren Funktionen Probleme lösen. Die Inhalte sind nach Datentypen (Polynome, reelle Funktionen, Matrizen) gegliedert. Im Vordergrund: die Objekte am Rechner, Grundoperationen an diesen Objekten und typische Fragen. Mit Algorithmen in Pseudocode. Plus zum Download: Programme für Mathematica und Matlab, alle Beispiele, Grafiken, interaktive Elemente.Trade ReviewFrom the reviews:“Algorithmic methods are useful tools for solving technical, scientific, or industrial problems. … This book for students in the first or second year presents the basic knowledge necessary for applying the methods to different problems. … The presentation is given in mathematical rigorous style and no further reading … to be required to read the text or design a course. … underlying course was designed for students of technical mathematics, but is as well suited for computer science students in the area of scientific computing.” (Thomas Rauber, Zentralblatt MATH, Vol. 1181, 2010)Table of ContentsEinleitung.- I. Grundbegriffe und Grundfragen einer algorithmischen Mathematik:1. Probleme, Lösungen und Algorithmen.- 2 Einführende Beispiele zur algorithmischen Lösung am Computer.- 3. Kondition eines Problems.- 4. Eigenschaften von Algorithmen.- II. Zahlbereiche: 5. Natürliche und ganze Zahlen.- 6. Kongruenzklassen modulo m.- 7. Rationale Zahlen.- 8. Reelle Zahlen.- III. Vektoren: 9. Mathematische Grundlagen.- 10. Vektoren am Computer.- 11. Euklidsches Skalarprodukt in Rm.- 12. Orthonormalisierung in Rm.- IV. Univariate Polynome: 13. Mathematische Grundlagen.- 14. Polynome am Computer.- 15. Polynomdivision und größter gemeinsamer Teiler.- 16. Polynomauswertung in R.- 17. Polynominterpolation in R.
£17.09
Springer Verlag, Singapore Advances in Mathematical Logic: Dedicated to the
Book SynopsisGaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science. Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines. This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18–20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti. Table of ContentsS. Fuchino and A. Ottenbreit Ottenbreit Maschio Rodrigues, Reflection principles, generic large cardinals, and the Continuum Problem.- D. Ikegami and N. Trang, On supercompactness of ω1.- S. Iwata, Interpolation properties for Sacchetti’s logics.- T. Kurahashi, Rosser provability and the second incompleteness theorem.- H. Kurokawa, On Takeuti’s early view of the concept of set.- Yo Matsubara and T. Usuba, On Countable Stationary Towers.- M. Ozawa, Reforming Takeuti’s Quantum Set Theory to Satisfy De Morgan’s Laws.- T. Usuba, Choiceless Lowenheim-Skolem property and uniform definability of grounds.- M. Yasugi, Y. Tsujii, T. Mori, Irrational-based computability of functions.- M. Yasugi, “Gaisi Takeuti’s finitist standpoint” and its mathematical embodiment.- Y. Yoshinobu, Properness under closed forcing.
£103.99
Taylor & Francis Ltd An Introduction to Mathematical Proofs
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£87.39
Taylor & Francis Ltd Algorithmic and Computational Robotics New Directions 2000 WAFR
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Taylor & Francis Ltd Unmatched
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£99.75
Taylor & Francis Ltd Separation of Variables and Exact Solutions to Nonlinear PDEs
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£128.25
Taylor & Francis Ltd Discrete Problems in Nature Inspired Algorithms
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Taylor & Francis Ltd Data Structure Practice
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Taylor & Francis Ltd Multiscale Theory of Composites and Random Media
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Taylor & Francis Ltd Divided Spheres
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£99.75
Taylor & Francis Ltd Games Gambling and Probability
Book SynopsisThe goal for this textbook is to complement the inquiry-based learning movement. According to the author, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Topics are presented mathematically as questions about the games themselves are posed.Table of Contents1. Mathematics and Probability. 1.1. Introduction. 1.2. About Mathematics. 1.3. Probability. 1.4. Candy (Yum)! 1.5. Exercises. 2. Roulette and Craps: Expected Value. 2.1. Roulette. 2.2. Summations. 2.3. Craps. 2.4. Exercises. 3. Counting: Poker Hands. 3.1. Cards and Counting. 3.2. Seven Card Pokers. 3.3. Texas Hold'Em. 3.4. Exercises. 4. More Dice: Counting and Combinations, and Statistics. 4.1. Liar's Dice. 4.2. Arkham Horror. 4.3. Yahtzee. 4.4. Exercises. 5. Game Theory: Poker Bluffing and Other Games. 5.1. Bluffing. 5.2. Game Theory Basics. 5.3. Non-Zero Sum Games. 5.4. Three-Player Game Theory. 5.5. Exercises. 6. Probability/Stochastic Matrices: Board Game Movement. 6.1. Board Game Movement. 6.2. Pay Day (The Board Game). 6.3. Monopoly. 6.4. Spread, Revisited. 6.5. Exercises. 7. Sports Mathematics: Probability Meets Athletics. 7.1. Sports Betting. 7.2. Game Theory and Sports. 7.3. Probability Matrices and Sports. 7.4. Winning a Tennis Tournament. 7.5. Repeated Play: Best of Seven. 7.6. Exercises 8. Blackjack: Previous Methods Revisited. 8.1. Blackjack. 8.2. Blackjack Variants. 8.3. Exercises. 9. A Mix of Other Games. 9.1. The Lottery. 9.2. Bingo. 9.3. Uno. 9.4. Baccarat. 9.5. Farkle. 9.6. Scrabble. 9.7. Backgammon. 9.8. Memory. 9.9. Zombie Dice. 9.10. Exercises. 10. Betting Systems: Can You Beat the System? 10.1. Betting Systems. 10.2. Gambler's Ruin. 10.3. Exercises. 11. Potpourri: Assorted Adventures in Probability. 11.1. True Randomness? 11.2. Three Dice "Craps". 11.3. Counting "Fibonacci" Coins "Circularly". 11.4. Compositions and Probabilities. 11.5. Sicherman Dice. 11.6. Traveling Salesmen. 11.7. Random Walks and Generating Functions. 11.8. More Probability! Appendices. Index.
£80.74
Taylor & Francis Frege Dedekind and Peano on the Foundations of Arithmetic Routledge Revivals
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£128.25
Taylor & Francis Frege Dedekind and Peano on the Foundations of Arithmetic Routledge Revivals
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Taylor & Francis Ltd The Geometry of Vector Fields Routledge Revivals
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Taylor & Francis Ltd The Geometry of Vector Fields Routledge Revivals
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£33.99
Taylor & Francis Ltd Approximation with QuasiSplines
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£137.75
Taylor & Francis Ltd Mathematical Conundrums
Book SynopsisWant to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included. Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge. But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisite Variety of algebraic, route-drawing, and geometrical conundrums Hints section for the lateral puzzles Warm-up excercises to sharpen the wits Full solutions to every problem Barry R. Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Readerâs Digest, The Sunday Telegraph, and Prospect magazine. His book Challenging Logic Puzzles Mensa has sold over 100,000 copies. As well as a PhD in Shakespeare Studies, Barry has a masterâs degree and academic publications in quantum physics. He is now working on a revised theory of the hydrogen atom. Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist! For more information please visit http://barryispuzzled.com.Table of Contents1. Introduction. 2. Mind sharpeners. 3. Geometry. 4. Arithmetic. 5. Algebra. 6. Programmable Puzzles. 7. Logic. 8. Visual-lateral
£23.99
Taylor & Francis Ltd Electronic String Art
Book SynopsisString art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting rules are used to create beautiful images that can both adorn walls and excite young minds. The downside of this highly tactile activity is that it is quite time-consuming and rigid. By contrast, electronic string art offers much more flexibility to set up or change nail locations and counting rules, and the images created from those changes change instantaneously.Electronic String Art: Rhythmic Mathematics invites readers to use the author's digital resources available on the ESA website to play with the parameters inherent in string art models while offering concise, accessible explanations of the underlying mathematical principles regarding how the images were created and how they change. Readers will have the opportunity to creaTable of ContentsPart I. Preliminary Issues. 1. Introduction and Overview. 2. How Polygons are Drawn. 3. String Art Basics. 4. Issues involving Commonality. 5. Cycles. 6. Alternative ways to Obtain an Image. 7. Levels of Subdivision Points. 8. Shape-Shifting Polygons. 9. An Overarching Question. 10. Functionally Modified String Art files. 11. A sampling of Image Archetypes. 12. n = P images. 13. 60-Second Images. 14. Challenge Questions for Part II. 15. Centered-Point Flowers. 16. Double Jump Models. 17. Four Color Clock Arithmetic. 18. Larger Jump Set Models. 19. Busting out of our Polygonal Constraint. 20. Challenge Questions for Part III. 21. Basic Properties of Numbers. 22. Angles in Polygons and Stars. 23. Modular Arithmetic. 24. Modular Multiplicative Inverses, MMI. 25. A Guide to the Web Model. 26. Suggestions for Mathematics Teachers.
£37.99
Cambridge University Press Proof Theory
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£35.14
Cambridge University Press Handbook of Categorical Algebra Categories and Structures v 2 Encyclopedia of Mathematics and its Applications 51 Volume 2 Categories and and its Applications Series Number 51
Book SynopsisThe Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second introduces important classes of categories that have played a fundamental role in the subject's development and applications.Table of ContentsPreface; Introduction to the handbook; 1. Abelian categories; 2. Regular categories; 3. Algebraic theories; 4. Monads; 5. Accessible categories; 6. Enriched category theory; 7. Topological categories; 8. Fibred categories; Bibliography; Index.
£76.94
Cambridge University Press Domains and Lambda Calculi 46 Cambridge Tracts in Theoretical Computer Science Series Number 46
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£52.60
Cambridge University Press Consequences of Martins Axiom 84 Cambridge Tracts in Mathematics Series Number 84
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Cambridge University Press Mathematical Logic with Special Reference to the Natural Numbers
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£55.91
Cambridge University Press Elementary Matrices
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£39.89
Cambridge University Press Theory of Matroids 26 Encyclopedia of Mathematics and its Applications Series Number 26
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£59.22
Cambridge University Press Introduction to Categories Homological Algebra and Sheaf Cohomology
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£39.89
Cambridge University Press Approximation Theory and Optimization
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Cambridge University Press Nonnegative Matrices and Applications 64 Encyclopedia of Mathematics and its Applications Series Number 64
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£63.37
Cambridge University Press Semimodular Lattices Theory and Applications 73 Encyclopedia of Mathematics and its Applications Series Number 73
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Cambridge University Press Algebraic Theories A Categorical Introduction to General Algebra 184 Cambridge Tracts in Mathematics Series Number 184
Book SynopsisFirst up-to-date treatment of the categorical view of sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry, and mathematical physics. A stimulating read for graduate students and researchers in category theory, general algebra, theoretical computer science and algebraic topology.Trade Review'The book is very well written and made as self-contained as it is reasonable for the intended audience of graduate students and researchers.' Zentralblatt MATHTable of ContentsForeword F. W. Lawvere; Introduction; Preliminaries; Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories; 2. Sifted and filtered colimits; 3. Reflexive coequalizers; 4. Algebraic categories as free completions; 5. Properties of algebras; 6. A characterization of algebraic categories; 7. From filtered to sifted; 8. Canonical theories; 9. Algebraic functors; 10. Birkhoff's variety theorem; Part II. Concrete Algebraic Categories: 11. One-sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of Σ-algebras; 14. S-sorted algebraic categories; Part III. Selected Topics: 15. Morita equivalence; 16. Free exact categories; 17. Exact completion and reflexive-coequalizer completion; 18. Finitary localizations of algebraic categories; A. Monads; B. Abelian categories; C. More about dualities for one-sorted algebraic categories; Summary; Bibliography; Index.
£105.45
Cambridge University Press A Students Guide to Data and Error Analysis
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£66.50
Cambridge University Press Recent Trends in Combinatorics
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£35.14
Cambridge University Press A Students Guide to Data and Error Analysis
Book SynopsisAll students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.Trade Review"Overall, this would be a nice text or reference to accompany a short course in statistics for undergraduate science or engineering..also useful for researchers desiring a primer or review...Recommended." - CHOICETable of ContentsPart I. Data and Error Analysis: 1. Introduction; 2. The presentation of physical quantities with their inaccuracies; 3. Errors: classification and propagation; 4. Probability distributions; 5. Processing of experimental data; 6. Graphical handling of data with errors; 7. Fitting functions to data; 8. Back to Bayes: knowledge as a probability distribution; Answers to exercises; Part II. Appendices: A1. Combining uncertainties; A2. Systematic deviations due to random errors; A3. Characteristic function; A4. From binomial to normal distributions; A5. Central limit theorem; A6. Estimation of the varience; A7. Standard deviation of the mean; A8. Weight factors when variances are not equal; A9. Least squares fitting; Part III. Python Codes; Part IV. Scientific Data: Chi-squared distribution; F-distribution; Normal distribution; Physical constants; Probability distributions; Student's t-distribution; Units.
£25.64
Cambridge University Press Model Theory Algebra and Geometry 39 Mathematical Sciences Research Institute Publications Series Number 39
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Cambridge University Press The Logic of Quantum Mechanics Volume 15 Encyclopedia of Mathematics and its Applications Series Number 15
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£55.09
Cambridge University Press Random Matrix Models and their Applications 40 Mathematical Sciences Research Institute Publications Series Number 40
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£45.59
Cambridge University Press Brouwers Cambridge Lectures on Intuitionism
Book SynopsisOriginally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics in intuitionism such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.Table of ContentsFrontispiece L. E. J. Brouwer; Editorial preface; 1. Historical introduction and fundamental notions; 2. General properties of species, spread directions, spreads and spaces; 3. Order; 4. Precision analysis of the continuum; 5. The bunch theorem; Appendix; Notes; References; Index.
£37.37
Cambridge University Press New Perspectives in Algebraic Combinatorics 38 Mathematical Sciences Research Institute Publications Series Number 38
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Cambridge University Press Combinatorial Games TicTacToe Theory 114 Encyclopedia of Mathematics and its Applications Series Number 114
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Cambridge University Press Combinatorics
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Cambridge University Press LMS 23 Parallelisms London Mathematical Society Lecture Note Series Series Number 23
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Cambridge University Press LMS 38 Surveys in Combinatorics 79 London Mathematical Society Lecture Note Series Series Number 38
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Cambridge University Press Surveys in Combinatorics Invited Papers for the Ninth British Combinatorial Conference 1983 82 London Mathematical Society Lecture Note Series Series Number 82
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Cambridge University Press LMS 87 Surveys in Set Theory London Mathematical Society Lecture Note Series Series Number 87
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Cambridge University Press LMS 47 Coding the Universe London Mathematical Society Lecture Note Series Series Number 47
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Cambridge University Press Finite Geometries and Designs Proceedings of the Second Isle of Thorns Conference 1980 49 London Mathematical Society Lecture Note Series Series Number 49
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Cambridge University Press Combinatorics Proceedings of the Eighth British Combinatorial Conference University College Swansea 1981
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