Philosophy of mathematics Books
Cambridge University Press The Works of Archimedes
Book SynopsisThis is Volume I of the first authoritative translation of Archimedes' works into English. Also provided are a scientific edition of the diagrams, a translation of the ancient commentator Eutocius and a commentary, where attention is paid to the cognitive and aesthetic nature of Archimedes' mathematical practice.Trade ReviewReview of the hardback: ' … this translation is certainly an event of great importance concerning the edition of ancient Greek mathematics. the forthcoming volumes are awaited with impatience!' Zentralblatt MATHTable of ContentsIntroduction; Translation and Commentary: On Sphere and Cylinder Book I; On Sphere and Cylinder Book II; Eutocius' Commentary to On Sphere and Cylinder Book I; Eutocius' Commentary to On Sphere and Cylinder Book II; Bibliography; Index.
£39.99
Cambridge University Press Phenomenology Logic and the Philosophy of Mathematics
Book SynopsisPhenomenology, Logic, and the Philosophy of Mathematics, first published in 2005, is about logic, mathematical knowledge and mathematical objects. It is concerned with the role of reason and intuition in the exact sciences and it analyzes many of the central positions in the philosophy of logic and philosophy of mathematics: platonism, nominalism, intuitionism, formalism, pragmatism, and others.Table of ContentsPart I. Reason, Science, and Mathematics: 1. Science as a triumph of the human spirit and science in crisis: Husserl and the Fortunes of Reason; 2. Mathematics and transcendental phenomenology; Part II. Kurt Godel, Phenomenology and the Philosophy of Mathematics: 3. Kurt Godel and phenomenology; 4. Godel's philosophical remarks on mathematics and logic; 5. Godel's path from the incompleteness theorems (1931) to Phenomenology (1961); 6. Godel and the intuition of concepts; 7. Godel and Quine on meaning and mathematics; 8. Maddy on realism in mathematics; 9. Penrose and the view that minds are not machines; Part III. Constructivism, Fulfilled Intentions, and Origins: 10. Intuitionism, meaning theory and cognition; 11. The philosophical background of Weyl's mathematical constructivism; 12. What is a proof?; 13. Phenomenology and mathematical knowledge; 14. Logicism, impredicativity, formalism; 15. The philosophy of arithmetic: Frege and Husserl.
£42.74
Cambridge University Press Thinking as Communicating
Book SynopsisThis book looks to change our thinking about thinking by looking at communication and cognition (commognition). The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.Trade Review'Sfard has provided us with one of the most impressive, unified, homogenous theories of learning …' Computer-Supported Collaborative LearningTable of ContentsIntroduction; Part I. Discourse on Thinking: 1. Puzzling about (mathematical) thinking; 2. Objectification; 3. Commognition: thinking as communicating; 4. Thinking in language; Part II. Mathematics as Discourse: 5. Mathematics as a form of communication; 6. Objects of mathematical discourse: what mathematizing is all about; 7. Routines: how we mathematize; 8. Explorations, deeds, and rituals: what we mathematize for; 9. Looking back and ahead: solving old quandaries and facing new ones.
£35.14
Cambridge University Press Archytas of Tarentum
Book SynopsisIn fourth-century Greece Archytas of Tarentum solved a famous mathematical puzzle, saved Plato from the tyrant of Syracuse and led a powerful Greek city state. This 2005 book presents an interpretation of his significance for fourth-century Greek thought and provides a full commentary on all the fragments and testimonia.Trade ReviewReview of the hardback: 'Huffman's book offers expert discussion of a variety of difficult topics … a much needed and authoritative commentary … Lucid argued, helpfully organised, and impressive in its scholarship, this book sets a high standard indeed … a rich volume of over 600 pages … there is much of real value here … a detailed and scholarly treatment of dauntingly difficulty material. Scholars owe Huffman a debt for undertaking this task, and executing it with such authority. It is a work to emulate'. Sylvia Berryman, The University of British ColumbiaReview of the hardback: 'We have here another blockbuster offering from Carl Huffman who has already put us in his debt by a definite study of Philolaus. This work will serve in turn to establish Archytas as a philosopher in his own right, and not simply a footnote to Pythagoras, as has all too often been the case hitherto.' Bryn Mawr Classical ReviewTable of ContentsPart I. Introductory Essays: 1. Life, writings and reception; 2. The philosophy of Archytas; 3. The authenticity question; Part II. Genuine Fragments: 1. Fragment 1; 2. Fragment 2; 3. Fragment 3; 4. Fragment 4; Part III: Genuine Testimonia: 1. Life and writings (A1–A6, B5–B8); 2. Moral philosophy and character; 3. Geometry: the duplication of the cube (A14 and A15); 4. Music; 5. Metaphysics; 6. Physics; 7. Miscellaneous testimonia; Appendix: Spurious writings and testimonia; Appendix: Archytas' name.
£38.52
Cambridge University Press Street Mathematics and School Mathematics Learning in Doing Social Cognitive and Computational Perspectives
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£37.04
Cambridge University Press Metaphysical Myths Mathematical Practice The Ontology and Epistemology of the Exact Sciences
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£75.00
Cambridge University Press Symmetry and its Discontents
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£71.25
Cambridge University Press Symmetry and its Discontents
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£28.99
Cambridge University Press Descartes on Forms and Mechanisms
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£54.15
Cambridge University Press An Introduction to the Philosophy of
Book SynopsisTopics covered include the realism/anti-realism debate in mathematics, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Intended as a primary text for an introductory undergraduate course in the philosophy of mathematics.Trade Review'The present book is like a warm breeze after a cold winter in the rarefied atmosphere of the philosophy of mathematics … the philosophical discussions are always clear, provocative and stimulating. One of the challenges an instructor will face by adopting this book will undoubtedly be to contain the desire of students to discuss in depth some of the issues presented and to curb their enthusiasm and desire to know more or find answers to the questions.' Mathematical ReviewsTable of Contents1. Mathematics and its philosophy; 2. The limits of mathematics; 3. Plato's heaven; 4. Fiction, metaphor, and partial truths; 5. Mathematical explanation; 6. The applicability of mathematics; 7. Who's afraid of inconsistent mathematics?; 8. A rose by any other name; 9. Epilogue: desert island theorems.
£27.99
Cambridge University Press Logic Induction and Sets London Mathematical Society Student Texts
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£38.94
Cambridge University Press Belief Revision 29 Cambridge Tracts in Theoretical Computer Science Series Number 29
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£59.22
Cambridge University Press Information Flow The Logic of Distributed Systems 44 Cambridge Tracts in Theoretical Computer Science Series Number 44
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£62.69
Cambridge University Press The Cambridge Companion to Frege
Book SynopsisGottlob Frege (18481925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.Trade Review'Central to this end were Frege's insights on quantification, the notation that expressed it, the logicist project, and the extension of mathematical notions like function and argument to natural language. The long-awaited Cambridge Companion to Frege is a compendium of Fregean scholarship that rigorously explores these and similar topics; editors Thomas Ricketts and Michael Potter have compiled a comprehensive collection of fourteen essays that individually provide focused appraisals of a number of Frege's most substantial insights.' Alexander Bozzo, University of Milwaukee'The long-awaited publication of The Cambridge Companion to Frege is a major event in Frege scholarship … Every serious reader of Frege should read it.' Notre Dame Philosophical Reviews (ndpr.nd.edu)Table of ContentsPreface; Note on translations; Chronology; 1. Introduction Michael Potter; 2. Understanding Frege's project Joan Weiner; 3. Frege's conception of logic Warren Goldfarb; 4. Dummett's Frege Peter Sullivan; 5. What is a predicate? Alex Oliver; 6. Concepts, objects, and the context principle Thomas Ricketts; 7. Sense and reference Michael Kremer; 8. On sense and reference: a critical reception William Taschek; 9. Frege and semantics Richard Heck; 10. Frege's mathematical setting Mark Wilson; 11. Frege and Hilbert Michael Hallett; 12. Frege's folly Peter Milne; 13. Frege and Russell Peter Hylton; 14. Inheriting from Frege: the work of reception, as Wittgenstein did it Cora Diamond.
£98.15
Cambridge University Press The Cambridge Companion to Frege Cambridge Companions to Philosophy
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£33.24
Cambridge University Press Between Logic and Intuition
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£83.00
Cambridge University Press Alfred Tarski Life and Logic
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£25.64
Cambridge University Press Interpreting Newton Critical Essays
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£99.75
Cambridge University Press Alfred Tarski Life and Logic
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£111.15
Cambridge University Press The Logic of Concept Expansion
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£85.50
Cambridge University Press Towards a Philosophy of Real Mathematics
Book SynopsisIn this ambitious study, David Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics, and challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines.Trade Review'Corfield's book as a whole is itself a fine specimen of a philosophical approach to mathematics that takes its questions and its resources from 'real' mathematics, showing convincingly the richness and fruitfulness of such an approach.' Philosophia Mathematica'I found this book interesting and it is certainly worth looking at if only to increase one's sense of the possibilities for the philosophy of mathematics.' Metascience'What is really special about the book under review is that it demonstrates a philosopher struggling to grapple with modern mathematics as it is actually carried out by practitioners. This is what the author means by 'real mathematics' as quoted in the book title.' Zentralblatt MATHTable of ContentsPreface; 1. Introduction: a role for history; Part I. Human and Artificial Mathematicians: 2. Communicating with automated theorem provers; 3. Automated conjecture formation; 4. The role of analogy in mathematics; Part II. Plausibility, Uncertainty and Probability: 5. Bayesianism in mathematics; 6. Uncertainty in mathematics and science; Part III. The Growth of Mathematics: 7. Lakatos's philosophy of mathematics; 8. Beyond the methodology of mathematical research programmes; 9. The importance of mathematical conceptualisation; Part IV. The Interpretation of Mathematics: 10. Higher dimensional algebra; Appendix; Bibliography; Index.
£85.50
Cambridge University Press Phenomenology Logic and the Philosophy of Mathematics
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£87.00
Cambridge University Press Thinking as Communicating
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£104.50
Cambridge University Press Mathematics and Explanation
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£17.00
Cambridge University Press Iterative Conceptions of Set
Book SynopsisThis Element will examine possibilities for articulating this solution. The author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers.
£17.00
Cambridge University Press Mathematical AntiRealism and Modal Nothingism
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£17.00
Cambridge University Press The Materiality of Numbers
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£95.00
Cambridge University Press Lakatos and the Historical Approach to Philosophy of Mathematics
Book SynopsisThis Element gives a detailed analysis of Imre Lakatos' ideas on the philosophy of mathematics. It also gives an account of how other researchers developed this approach after his death, what has been achieved so far, and what its prospects for the future might be.Table of Contents1. Introduction; 2. Lakatos' contribution to the philosophy of mathematics; 3. Lakatos' legacy in the philosophy of mathematics I (1975–1995); 4. Lakatos' legacy in the philosophy of mathematics II (1996–2023); 5. Concluding remarks; References.
£17.00
Cambridge University Press Philosophical Uses of Categoricity Arguments
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£47.49
Cambridge University Press Lakatos and the Historical Approach to Philosophy of Mathematics
Book SynopsisThis Element gives a detailed analysis of Imre Lakatos' ideas on the philosophy of mathematics. It also gives an account of how other researchers developed this approach after his death, what has been achieved so far, and what its prospects for the future might be.Table of Contents1. Introduction; 2. Lakatos' contribution to the philosophy of mathematics; 3. Lakatos' legacy in the philosophy of mathematics I (1975–1995); 4. Lakatos' legacy in the philosophy of mathematics II (1996–2023); 5. Concluding remarks; References.
£47.49
Cambridge University Press Iterative Conceptions of Set
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£47.49
Cambridge University Press Abstractionism
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£47.49
Cambridge University Press The History of Mathematical Proof in Ancient Traditions
Book SynopsisThis radical volume explores the purposes and nature of proof in a range of historical settings, overturning the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle. It opens the way to providing the first comprehensive, textually based history of proof.Trade Review'This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.' Jeremy Gray, Open University'At long last, a substantial single volume on the history of ancient mathematics makes the cutting-edge research of scholars, some of whom normally publish in other languages, accessible to the English speaking reader … this volume is a milestone - the history of ancient mathematics has its very own French revolution, and it has finally crossed the Channel.' Serafina Cuomo, British Journal for the History of Science'… a collection of meticulous, expert studies of ancient mathematical texts. The individual chapters are essential reading for historians of geometry and arithmetic, and the volume, as a whole, will no doubt become canonical in the history of mathematics. Together, Karine Chemla and her ensemble of scholars successfully make the case for revising the nineteenth-century portrait of the history of mathematical proof that prevails even today. We must question the critical editions we employ, and we must expand the history of mathematical proof to include algorithmic texts in the Greek, Mesopotamian, Indian, Chinese, and Islamic traditions.' Early Science and Medicine'The purpose of the book … is to challenge the standard narrative and design a research program to replace it with a more adequate assessment of the achievements of non-Greek mathematicians in antiquity. The pivotal question is, in what sense and by what methods were mathematical procedures justified in showing that they always produce correct results when applied?' Jochen Brüning, Common KnowledgeTable of ContentsPrologue: historiography and history of mathematical proof: a research program Karine Chemla; Part I. Views on the Historiography of Mathematical Proof: 1. The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text Bernard Vitrac; 2. Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions Ken Saito and Nathan Sidoli; 3. The texture of Archimedes' arguments: through Heiberg's veil Reviel Netz; 4. John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations Orna Harari; 5. Contextualising Playfair and Colebrooke on proof and demonstration in the Indian mathematical tradition (1780–1820) Dhruv Raina; 6. Overlooking mathematical justifications in the Sanskrit tradition: the nuanced case of G. F. Thibaut Agathe Keller; 7. The logical Greek versus the imaginative Oriental: on the historiography of 'non-Western' mathematics during the period 1820–1920 François Charette; Part II. History of Mathematical Proof in Ancient Traditions: The Other Evidence: 8. The pluralism of Greek 'mathematics' Geoffrey Lloyd; 9. Generalizing about polygonal numbers in ancient Greek mathematics Ian Mueller; 10. Reasoning and symbolism in Diophantus: preliminary observations Reviel Netz; 11. Mathematical justification as non-conceptualized practice: the Babylonian example Jens Høyrup; 12. Interpretation of reverse algorithms in several Mesopotamian texts Christine Proust; 13. Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context Karine Chemla; 14. Dispelling mathematical doubts: assessing mathematical correctness of algorithms in Bhaskara's commentary on the mathematical chapter of the Aryabhatıya Agathe Keller; 15. Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics Alexei Volkov; 16. A formal system of the Gougu method - a study on Li Rui's detailed outline of mathematical procedures for the right-angled triangle Tian Miao.
£138.70
Cambridge University Press Logicism and its Philosophical Legacy
Book SynopsisThis book will appeal to readers interested in analytic philosophy and its history. Avoiding mathematical detail and locating the relevant developments in their historical context, the book explains and extends recent advances in the philosophy of mathematics and our understanding of questions about the nature of scientific reality.Trade Review'As a philosophy major at the University of Western Ontario in 1995 I was fortunate enough to enroll in Demopoulos' history of analytic philosophy class … The essays in this volume preserve the intensity and commitment to rigorous argumentation that I first encountered in that class twenty years ago. … I look forward to Demopoulos' next contribution to these important debates.' Chris Pincock, The Journal of Bertrand Russell StudiesTable of ContentsPreface; Introduction; 1. Frege's analysis of arithmetical knowledge; 2. Carnap's thesis, on extending 'empiricism, semantics and ontology' to the realism-instrumentalism controversy; 3. Carnap's analysis of realism; 4. Bertrand Russell's The Analysis of Matter: its historical context and contemporary interest with Michael Friedman; 5. On the rational reconstruction of our theoretical knowledge; 6. Three views of theoretical knowledge; 7. Frege and the rigorization of analysis; 8. The philosophical basis of our knowledge of number; 9. The 1910 Principia's theory of functions and classes; 10. Ramsey's extensional propositional functions.
£29.44
Cambridge University Press The Cambridge Companion to Ancient Logic
Book SynopsisThis state-of-the-art overview of ancient logic for students and scholars covers the development of logic in Aristotle and the Stoics, the key concepts at the heart of the ancient logical systems and the legacy of ancient logic in the later philosophical tradition, from the Middle Ages to today.Table of ContentsPart I. The Development of Logic in Antiquity: 1. The prehistory of logic Nicholas Denyer; 2. Aristotle and Theophrastus Paolo Fait; 3. Megarians and Stoics Karlheinz Hülser; 4. Late antiquity Benjamin Morison; Part II. Key Themes: 5. Truth as a logical property and the laws of being true Walter Cavini; 6. Definition Michael Ferejohn; 7. Terms and propositions Paolo Crivelli; 8. Validity and syllogism Luca Castagnoli and Paolo fait; 9. Demonstration Alexander Bown; 10. Modalities and modal logic Marko Malink; 11. Fallacies and paradoxes Luca Castagnoli; 12. Logic in ancient rhetoric Christof Rapp; 13. Ancient logic and ancient mathematics Reviel Netz; Part III. The Legacy of Ancient Logic: 14. Ancient logic in the middle ages John Marenbon; 15. Ancient logic from the Renaissance to the birth of mathematical logic Mirella Capozzi and Leila Haaparanta; 16. Ancient logic today John Woods.
£25.64
Cambridge University Press Kants Mathematical World
Book SynopsisKant's Mathematical World aims to transform our understanding of Kant's philosophy of mathematics and his account of the mathematical character of the world. Daniel Sutherland reconstructs Kant's project of explaining both mathematical cognition and our cognition of the world in terms of our most basic cognitive capacities.Trade Review'Daniel Sutherland's Kant's Mathematical World is a remarkable scholarly achievement. The meticulously detailed analysis of Kant's theory of magnitude opens up into a comprehensive account of the mathematical character of experience, shedding new light on virtually every aspect of the first Critique and engaging with many of the liveliest current debates surrounding it. It is essential reading for scholars of Kant's theoretical philosophy.' Emily Carson, McGill University'simply outstanding … Highly recommended.' D. C. Kolb, Choice ConnectTable of ContentsPreface and acknowledgements; 1. Introduction: mathematics and the world of experience; Part I. Mathematics, Magnitudes and the Conditions of Experience: 2. Space, time and mathematics in the Critique of Pure Reason; 3. Magnitudes, mathematics, and experience in the Axioms of Intuition; 4. Extensive and intensive magnitudes and continuity; 5. Conceptual and intuitive representation: singularity, continuity, and concreteness; Interlude: the Greek mathematical tradition as background to Kant: 6. Euclid, the Euclidean mathematical tradition, and the theory of magnitudes; Part II. Kant's Theory of Magnitudes and the Role of Intuition: 7. Kant's reworking of the theory of magnitudes; 8. Kant's reformation of the metaphysics of quantity; 9. From mereology to mathematics; 10. Concluding remarks; Bibliography; Index.
£23.74
Cambridge University Press A Concise History of Mathematics for Philosophers
Presents an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. Ranges from ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous.
£17.00
Cambridge University Press Paraconsistency in Mathematics
Book SynopsisParaconsistent logic makes it possible to study inconsistent theories in a coherent way. From its modern start in the mid-20th century, paraconsistency was intended for use in mathematics, providing a rigorous framework for describing abstract objects and structures where some contradictions are allowed, without collapse into incoherence. Over the past decades, this initiative has evolved into an area of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element provides a selective introductory survey of this research program, distinguishing between `moderate'' and `radical'' approaches. The emphasis is on philosophical issues and future challenges.Table of Contents1. Invitation to Paraconsistency in Mathematics: Why and How?; 2. Set Theory; 3. Arithmetic; 4. Calculus, Topology, and Geometry; 5. Whither Paraconsistency in Mathematics?
£17.00
Cambridge University Press Elliptic and Hyperelliptic Integrals and Allied Theory
Originally published in 1938, this book focuses on the area of elliptic and hyperelliptic integrals and allied theory. The text was a posthumous publication by William Westropp Roberts (18501935), who held the position of Vice-Provost at Trinity College, Dublin from 1927 until shortly before his death.
£37.99
Hachette Books More Numbers Every Day
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£22.40
Random House USA Inc The Fractalist
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£19.95
Basic Books Significant Figures
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£22.40
DK El Libro de Las Matemticas Big Ideas
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£26.59
Farrar, Straus and Giroux A Divine Language
Book SynopsisA New York Times Book Review Editors'' ChoiceWilkinson has accomplished something more moving and original, braiding his stumbling attempts to get better at math with his deepening awareness that there's an entire universe of understanding that will, in some fundamental sense, forever lie outside his reach. Jennifer Szalai, The New York Times There is almost no writer I admire as much as I do Alec Wilkinson. His work has enduring brilliance and humanity. Susan Orlean, author of The Library Book A spirited, metaphysical exploration into math''s deepest mysteries and conundrums at the crux of middle age.Decades after struggling to understand math as a boy, Alec Wilkinson decides to embark on a journey to learn it as a middle-aged man. What begins as a personal challengeand it''s challengingsoon transforms into something greater than a belabored effort to learn math. Despite his incompetence, Wilkinson enc
£23.20
Johns Hopkins University Press Algebra in Context
Book SynopsisProvides a framework for understanding algebra and related fields. In this book, students will discover why mathematics is such a crucial part not only of civilization but also of everyday life.Trade ReviewThis book approaches the teaching of algebra to first year undergraduate students with a unique use of the art's history and development. Students that have already encountered many of these topics in a traditional format in high school or college may find this engaging framework a boon to understanding. Mathematical Association of America The book is well organized and thorough. The authors take a conglomeration of discoveries and inventions over three millennia and present them in an ordered, coherent manner. Mathematic TeacherTable of ContentsPrefaceIntroductionPart I1. Number Bases1.1. Base 61.2. Base 42. Babylonian Number System2.1. Cuneiform2.2. Mathematical Texts2.3. Number System3. Egyptian and Roman Number Systems3.1. Egyptian3.1.1. History3.1.2. Writing and Mathematics3.1.3. Number System3.2. Roman3.2.1. History3.2.2. Number System4. Chinese Number System4.1. History and Mathematics4.2. Rod Numerals5. Mayan Number System5.1. Calendar5.2. Codices5.3. Number System5.4. Native North Americans6. Indo-Arabic Number System6.1. India6.1.1. History6.1.2. Mathematics6.2. The Middle East6.2.1. History6.2.2. Mathematics6.3. Number System6.3.1. Whole Numbers6.3.2. Fractions7. ExercisesPart II8. Addition and Subtraction9. Multiplication9.1. Roman Abacus9.2. Grating or Lattice Method9.3. Ibn Labban and Chinese Counting Board9.4. Egyptian Doubling Method10. Division10.1. Egyptian10.2. Leonardo of Pisa10.3. Galley or Scratch Method11. Casting Out Nines12. Finding Square Roots12.1. Heron of Alexandria12.2. Theon of Alexandria12.3. Bakhshali Manuscript12.4. Nicolas Chuquet13. ExercisesPart III14. Sets14.1. Set Relations14.2. Finding 2n14.3. One-to-One Correspondence and Cardinality15. Rational, Irrational, and Real Numbers15.1. Commensurable and Incommensurable Magnitudes15.2. Rational Numbers15.3. Irrational Numbers15.4. I Is Uncountably Infinite15.5. card(Q), card(I), and card(R)15.6. Transfinite Numbers16. Logic17. The Higher Arithmetic17.1. Early Greek Elementary Number Theory17.1.1. Pythagoras17.1.2. Euclid17.1.3. Nicomachus and Diophantus17.2. Even and Odd Numbers17.3. Figurate Numbers17.3.1. Triangular Numbers17.3.2. Square Numbers17.3.3. Rectangular Numbers17.3.4. Other Figurate Numbers17.4. Pythagorean Triples17.5. Divisors, Common Factors, and Common Multiples17.5.1. Factors and Multiples17.5.2. Euclid's Algorithm17.5.3. Multiples17.6. Prime Numbers17.6.1. The Sieve of Eratosthenes17.6.2. The Fundamental Theorem of Arithmetic17.6.3. Perfect Numbers17.6.4. Friendly Numbers18. ExercisesPart IV19. Linear Problems19.1. Review of Linear Equations19.2. False Position19.3. Double False Position20. Quadratic Problems20.1. Solving Quadratic Equations by Completing the Square20.1.1. Babylonian201.2. Arabic201.3. Indian20.1.4. The Quadratic Formula20.2. Polynomial Equations in One Variable20.2.1. Powers20.2.2. nth Roots20.3. Continued Fractions20.3.1. Finite Simple Continued Fractions20.3.2. Infinite Simple Continued Fractions20.3.3. The Number21. Cubic Equations and Complex Numbers21.1. Complex Numbers21.2. Solving Cubic Equations and the Cubic Formula22. Polynomial EquationsRelation between Roots and CoefficientsViète and Harriot22.3. Zeros of a Polynomial22.3.1. Factoring22.3.2. Descartes's Rule of Signs22.4. The Fundamental Theorem of Algebra23. Rule of Three23.1. China23.2. India23.3. Medieval Europe23.4. The Rule of Three in False Position23.5. Direct Variation, Inverse Variation, and Modeling24. Logarithms24.1. Logarithms Today24.2. Properties of Logarithms24.3. Bases of a Logarithm24.3.1. Using a Calculator24.3.2. Comparing Logarithms24.4. Logarithm to the Base e and Applications24.4.1. Compound Interest24.4.2. Amortization24.4.3. Exponential Growth and Decay24.5. Logarithm to the Base 10 and Application to Earthquakes25. ExercisesBibliographyIndex
£84.00
Basic Books Is Math Real?: How Simple Questions Lead Us to
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£24.00
Tarquin Publications Peculiar Deaths of Famous Mathematicians
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£12.30
Wooden Books The Golden Section: Nature's Greatest Secret
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£8.50
