208 pages | 234x156mm
978-0-19-958783-4 | Hardback | July 2010 (estimated)
978-0-19-958784-1 | Paperback | July 2010 (estimated)
Offers a complete introduction to logic in exceptionally clear and concise form
Attractively priced - easily affordable by students
Has been extensively road-tested before publication, as the text for the logic course at Oxford
More precise and reliable than any other introduction to logic
Ideal basis for the study of philosophy -- offers a real understanding of how and why logic works
Supporting website contains exercises, examples, and sample examination papers
The Logic Manual is a clear and concise introduction to logic for beginning philosophy students. It offers a complete introductory course, guiding the reader carefully through the topics in logic that are most important for the study of philosophy. It covers propositional and predicate logic with and without identity. It includes an account of the semantics of these languages including definitions of truth and satisfaction. Natural deduction is used as a proof system. Volker Halbach introduces the essential concepts through examples and informal explanations as well as through abstract definitions.
The Logic Manual provides the best entry to the general abstract way of thinking about language, logic, and semantics which is characteristic of contemporary philosophy. Exercises, examples, and sample examination papers are provided on an accompanying website.
Readership: Undergraduate students of logic, especially on philosophy courses but also mathematics and linguistics.
1: Sets, Relations, and Arguments
2: Syntax and Semantics of Propositional Logic
3: Formalisation in Propositional Logic
4: The Syntax of Predicate Logic
5: The Semantics of Predicate Logic
6: Natural Deduction
7: Formalisation in Predicate Logic
8: Identity and Definite Descriptions
Natural Deduction Rules
600 pages | 150 line, 30 halftone b/w illustrations | 246x171mm
978-0-19-850625-6 | Hardback | June 2010 (estimated)
Covers a wide range of problems (rods, plates, shells) and applications
Accessible to readers without background in mechanics, minimal mathematical pre-requisites
Detailed, fully explicit solutions to practical problems
Rigorous mathematical arguments supported by an intuitive presentation
Can serve as an introduction to elasticity and nonlinear science
We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced nonlinear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.
Readership: Students and researchers in mechanical engineering, physics, computer graphics, bio-mechanics, and applied mathematics.
1: Introduction
2: Three-dimensional elasticity
I: RODS
3: Equations for elastic rods
4: Mechanics of the human hair
5: Rippled leaves, uncoiled springs
II: PLATES
6: The equations for elastic plates
7: End effects in plate buckling
8: Finite amplitude buckling of a strip
9: Crumpled paper
10: Fractal buckling near edges
III: SHELLS
11: Geometric rigidity of surfaces
12: Shells of revolution
13: The elastic torus
14: Spherical shell pushed by a wall
Appendix A: Calculus of variations: a worked example
Appendix B: Boundary and interior layers
Appendix C: The geometry of helices
Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity
224 pages | 20 b/w line and hlftone illustrations | 216x138mm
978-0-19-958814-5 | Paperback | August 2010 (estimated)
Accessible to a broad range of people with an interest in science
Written in a non-technical language
Extensively illustrated
Discusses the science-society interface
Takes a different perspective to other books on cosmology
Cosmology has undergone a revolution in recent years. The exciting interplay between astronomy and fundamental physics has led to dramatic revelations, including the existence of the dark matter and the dark energy that appear to dominate our cosmos. But these discoveries only reveal themselves through small effects in noisy experimental data. Dealing with such observations requires the careful application of probability and statistics.
But it is not only in the arcane world of fundamental physics that probability theory plays such an important role. It has an impact in many aspects of our everyday life, from the law courts to the lottery.
Why then do so few people understand probability? And why do so few people understand why it is so important for science? Why do so many people think that science is about absolute certainty when, at its core, it is actually dominated by uncertainty?
This book attempts to explain the basics of probability theory, and illustrate their application across the entire spectrum of science.
Readership: Graduates, researchers and professionals accross physics, astrophysics, statistics and cosmology. General readers interested in science or probability.
1: Probable Nature
2: The Logic of Uncertainty
3: Lies, Damned Lies, and Astronomy
4: Bayesians Versus Frequentists
5: Randomness
6: From Engines and Entropy
7: Quantum Roulette
8: Believing the Big Bang
9: Cosmos and Its Discontents
10: Life, the Universe and Everything
11: Summing Up
Oxford Graduate Texts
336 pages | 20 b/w line illustrations | 240x168mm
978-0-19-856675-5 | Paperback | August 2010 (estimated)
Comprehemsive introduction to an essential tool in theoretical physics
Pedagogical presentation by experienced teacher and author
Class-tested
The main goal of this work is to familiarize the reader with a tool, the path integral, that offers an alternative point of view on quantum mechanics, but more important, under a generalized form, has become the key to a deeper understanding of quantum field theory and its applications, which extend from particle physics to phase transitions or properties of quantum gases.
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis.
Path integrals are powerful tools for the study of quantum mechanics, because they emphasize very explicitly the correspondence between classical and quantum mechanics.
Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding and simple calculations of physical quantities in the semi-classical limit. We will illustrate this observation with scattering processes, spectral properties or barrier penetration.
The formulation of quantum mechanics based on path integrals, if it seems mathematically more complicated than the usual formulation based on partial differential equations, is well adapted to systems with many degrees of freedom, where a formalism of Schrodinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.
Readership: Primary: Graduate students and lecturers in theoretical physics, in particular in particle and statistical physics. Secondary: mathematicians.
1: Gaussian integrals
2: Path integral in quantum mechanics
3: Partition function and spectrum
4: Classical and quantum statistical physics
5: Path integrals and quantization
6: Path integral and holomorphic formalism
7: Path integrals: fermions
8: Barrier penetration: semi-classical approximation
9: Quantum evolution and scattering matrix
10: Path integrals in phase space
Quantum mechanics: minimal background
A1: Hilbert space and operators
A2: Quantum evolution, symmetries and density matrix
A3: Position and momentum. Scrodinger equation
184 pages | 92 line and 23 halftone illustrations | 216x138mm
978-0-19-959002-5 | Paperback | October 2010 (estimated)
A
Accessible and entertaining style
Insightful overview to appeal to lay-readers and maths-lovers alike
Includes entertaining illustrations, photos and drawings (some by famous cartoonists)
Develops readers' knowledge at a gentle and digestible pace
David Acheson's extraordinary little book makes mathematics accessible to everyone. From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers. Every short chapter is carefully crafted to ensure that no one will get lost on the journey. Packed with puzzles and illustrated by world famous cartoonists, this is one of the most readable and imaginative books on mathematics ever written.
Readership: This book is designed to make mathematics accessible, interesting and entertaining to the non-expert: it will appeal to interested lay readers, school teachers, parents, and mathematics, physics, engineering, and computer science students from ages fifteen to fifty.
1: 1089 and All That
2: "In Love with Geometrie"
3: But ... that's Absurd ...
4: The Trouble with Algebra
5: The Heavens in Motion
6: All Change!
7: On Being as Small as Possible
8: "Are We Nearly There?"
9: A Brief History of pi
10: Good Vibrations
11: Great Mistakes
12: What is the Secret of All Life?
13: e=2.718 ...
14: Chaos and Catastrophe
15: Not Quite the Indian Rope Trick
16: Real or Imaginary?
144 pages | 15 black and white halftones | 174x111mm
978-0-19-958405-5 | Paperback | February 2011 (estimated)
A short introduction to the number world, looking at different types of numbers and how they behave
Reveals the astonishing richness and variety of numbers, including primes, imaginary and complex numbers, to infinity and beyond
Explains how numbers interact and influence modern applications and practices, for example in the encryption of confidential data
Written by an experienced mathematician with a history of writing in a non-technical way
Numbers are integral to our everyday lives and feature in everything we do. In this Very Short Introduction Peter M. Higgins, the renowned mathematics writer, unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number.
Higgins paints a picture of the number world, considering how the modern number system matured over centuries. Explaining the various number types and showing how they behave, he introduces key concepts such as integers, fractions, real numbers, and imaginary numbers. By approaching the topic in a non-technical way and emphasising the basic principles and interactions of numbers with mathematics and science, Higgins also demonstrates the practical interactions and modern applications, such as encryption of confidential data on the internet.
Readership: Readers interested in maths and those with a fascination for numbers, in particular students and teachers of mathematics.
1: How not to think about numbers: the trouble with bases
2: The unending series of primes
3: Perfect and not so perfect numbers
4: Cryptography: the secret life of the primes
5: Numbers that count
6: A peek below the waterline of the number iceberg
7: To infinity and beyond
8: Numbers but not as we know them
Further Reading
Index