1. Models
Timothy Gowers
in Mathematics: A Very Short Introduction
‘Models’ introduces the concept and purposes of mathematical models. From working out the best trajectory for throwing a stone, rolling a pair of dice, and predicting population growth and ...
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Applied Mathematics: A Very Short Introduction
Alain Goriely
Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. Applied Mathematics: A Very Short Introduction ...
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3. How are mathematical ideas disseminated?
Jacqueline Stedall
in The History of Mathematics: A Very Short Introduction
‘How are mathematical ideas disseminated?’ considers how mathematical ideas are passed from one person to another, from one culture to another, or from one generation to another. Reading ...
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Introduction: the Greek way
J. L. Heilbron
in The History of Physics: A Very Short Introduction
The Introduction explains that Greek physics—physica—with its eye to ethics, its indifference to mathematics and experiment, and its independence of states and courts, is noticeably ...
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16. Evidence and Theory
Jonathan Barnes
in Aristotle: A Very Short Introduction
‘Evidence and Theory’ argues that Aristotle’s account of the world is wholly exploded, mostly because sixteenth- and seventeenth-century scientists applied quantitative methods in studying ...
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7. Logic
Jonathan Barnes
in Aristotle: A Very Short Introduction
‘Logic’ explores Aristotle’s syllogistic. In the Prior Analytics Aristotle uses ‘proposition’ for simple sentences and ‘term’ for their salient parts. Thus a proposition affirms or denies ...
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3. Proofs
Timothy Gowers
in Mathematics: A Very Short Introduction
‘Proofs’ is concerned with the concept of a proof, that is, an argument that puts a statement beyond all possible doubt. One of the most famous proofs in mathematics shows that the square ...
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5. Science and philosophy
Jerry Brotton
in The Renaissance: A Very Short Introduction
The word ‘ambivalence’ best captures the mood of the transformations in popular and applied sciences of the 15th and 16th centuries. We want to know more, but can we know too much? ‘Science ...
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1. Life and work
A. C. Grayling
in Russell: A Very Short Introduction
‘Life and work’ outlines the contributions of Bertrand Russell to the technical fields of logic and philosophy as well as describing his private life — his marriages, agnosticism, pacifism, ...
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10. Centaurs and other animals
Rob Iliffe
in Newton: A Very Short Introduction
‘Centaurs and other animals’ examines the final decade of Newton's life. Newton continued his relentless pursuit of religious truth: massive drafts on early church history survive, many ...
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6. Getting inside mathematics
Jacqueline Stedall
in The History of Mathematics: A Very Short Introduction
Who invented algebra? Who invented calculus? ‘Getting inside mathematics’ looks at the possible answers to these questions alongside the introduction of mathematical notation and the ...
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4. Eratosthenes and the system of the world
Peter Thonemann
in The Hellenistic Age: A Very Short Introduction
Few aspects of the Hellenistic world have captivated the modern imagination so much as the Museum and Library of Ptolemaic Alexandria, a dedicated institution of learning and research, ...
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6. Pythagoras and other mysteries
Catherine Osborne
in Presocratic Philosophy: A Very Short Introduction
‘Pythagoras and other mysteries’ explains how Pythagoras and his followers acquired a reputation for mathematical and geometrical investigations. They conducted their mathematics in a ...
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2. Logic and philosophy
A. C. Grayling
in Russell: A Very Short Introduction
‘Logic and philosophy’ shows that Russell's first truly original philosophical endeavour was to show that mathematics rests on logic. The project failed, but a number of important ...
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8. Some frequently asked questions
Timothy Gowers
in Mathematics: A Very Short Introduction
Is it true that mathematicians are past it by the time they are 30? Why are there so few women mathematicians? Do mathematics and music go together? Why do so many people positively dislike ...
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2. Playing philosophically
Rob Iliffe
in Newton: A Very Short Introduction
‘Playing philosophically’ considers Newton's early life, describing how his immersion in worlds of practical ingenuity not only offered portents of his great future, but led directly to it. ...
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8. In the city
Rob Iliffe
in Newton: A Very Short Introduction
‘In the city’ describes how the years after the completion of the Principia witnessed some of the most intense intellectual activity of Newton's life. He researched furiously into the vexed ...
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1. A national man
Rob Iliffe
in Newton: A Very Short Introduction
‘A national man’ reviews the various biographies of Newton which appeared after his death on 20 March 1727. John Conduitt supervised the collection of virtually all the significant ...
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1. Mathematics: myth and history
Jacqueline Stedall
in The History of Mathematics: A Very Short Introduction
‘Mathematics: myth and history’ considers some well-known names in the field of mathematics: Pythagoras, Euclid, Diophantus, Pierre de Fermat, Leonhard Euler, and Andrew Wiles, the man you ...
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2. What is mathematics and who is a mathematician?
Jacqueline Stedall
in The History of Mathematics: A Very Short Introduction
‘What is mathematics and who is a mathematician?’ questions the meaning and use of the terms based on the Greek mathemata, which simply meant ‘what has been learned’. The history of ...
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