Paperback (ISBN-10: 052144862X | ISBN-13: 9780521448628)
Hardback (ISBN-10: 0521443903 | ISBN-13: 9780521443906)
Published August 2005 | 181 pages | 228 x 152 mm
This book presents a functional approach to the construction, use
and approximation of Greenfs functions and their associated
ordered exponentials. After a brief historical introduction, the
author discusses new solutions to problems involving particle
production in crossed laser fields and non-constant electric
fields. Applications to problems in potential theory and quantum
field theory are covered, along with approximations for the
treatment of color fluctuations in high-energy QCD scattering,
and a model for summing classes of eikonal graphs in high-energy
scattering problems. The book also presents a variant of the
Fradkin representation which suggests a new non-perturbative
approximation scheme, and provides a qualitative measure of the
error involved in each such approximation. Covering the basics as
well as more advanced applications, this book is suitable for
graduate students and researchers in a wide range of fields,
including quantum field theory, fluid dynamics and applied
mathematics.
? Describes Greenfs functions, the basis for the modern
description of interactions, and their applications
? Contains new solutions to problems involving particle
production in crossed laser fields and non-constant electric
fields
? A valuable reference text for graduate students and researchers
working on causal interactions
Contents
Preface; 1. Introduction; 2. Elementary functional methods; 3.
Schwinger-Fradkin methods; 4. Lasers and crossed lasers; 5.
Special variants of the Fradkin representation; 6. Quantum chaos
and vectorial interactions; 7. Infrared approximations; 8. Models
of high-energy, non-Abelian scattering; 9. Unitary ordered
exponentials.
Hardback (ISBN-10: 0521837820 | ISBN-13: 9780521837828)
Published August 2005 | 368 pages | 228 x 152 mm
Offering a collection of fifteen essays that deal with issues at
the intersection of phenomenology, logic, and the philosophy of
mathematics, this book is divided into three parts. Part I,
Reason, Science, and Mathematics contains a general essay on
Husserlfs conception of science and logic, an essay of
mathematics and transcendental phenomenology, and an essay oN
phenomenology and modern pure geometry. Part II is focused on
Kurt Godelfs interest in phenomenology. It explores Godelfs
ideas and also some work of Quine, Penelope Maddy and Roger
Penrose. Part III deals with elementary, constructive areas of
mathematics. These are areas of mathematics that are closer to
their origins in simple cognitive activities and in everyday
experience. This part of the book contains essays on
intuitionism, Hermann Weyl, the notion of constructive proof,
Poincare and Frege.
? Discusses Kurt Godelfs interest in phenomenology
? Presents new views about the role of intentionality in
mathematics and logic
? Up-to-date analyses of phenomenology and the exact sciences
Contents
Part 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.
Godelfs philosophical remarks on mathematics and logic; 5.
Godelfs 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 Weylfs mathematical constructivism;
12. What is a proof?; 13. Phenomenology and mathematical
knowledge; 14. Logicism, impredicativity, formalism; 15. The
philosophy of arithmetic: Frege and Husserl.
Paperback (ISBN-10: 052154985X | ISBN-13: 9780521549851)
Hardback (ISBN-10: 0521840511 | ISBN-13: 9780521840514)
available from January 2006
This new edition has been fully revised to build on the enormous
success of its popular predecessor. It now includes new features
introduced by readersf requests including a new chapter on
propensity score, more detail on clustered data and Poisson
regression and a new section on analysis of variance. As before
it describes how to perform and interpret multivariable analysis,
using plain language rather than complex derivations and
mathematical formulae. It is the perfect introduction for all
clinical researchers. It focuses on the nuts and bolts of
performing research and prepares the reader to perform and
interpret multivariable models. Numerous tables, graphs and tips
help to simplify and explain the process of performing
multivariable analysis. The text is illustrated with many up-to-date
examples from the medical literature on how to use multivariable
analysis in clinical practice and in research.
? Provides a nonmathematical introduction
? Nuts and bolts practical approach for clinical relevance
? Provides answers to basic questions
Contents
Preface;1. Introduction; 2. Common uses of multivariable models;
3. Outcome variables in multivariable analysis; 4.Types of
independent variables in multivariable analysis; 5. Assumptions
of multiple linear regression, logistic regression, and
proportional hazards analysis; 6. Relationship of independent
variables to one another; 7. Setting up a multivariable analysis;
8. Performing the analysis; 9. Interpreting the analysis; 10.
Checking the assumptions of the analysis; 11. Propensity scores;12.
Correlated observations; 13. Validation of models; 14. Special
topics; 15. Publishing your study; 16. Summary: steps for
constructing a multivariable model.
Paperback (ISBN-10: 0521543169 | ISBN-13: 9780521543163)
Hardback (ISBN-10: 052183550X | ISBN-13: 9780521835503)
available from November 2005
Textbook
Lecturers can request inspection copies of this title.
Courses: All biology or life sciences degree courses require
students to study statistics in some form. Students will have to
take compulsory short introductory statistics courses. This book
is ideal for these courses.
Levels: FIRST YEAR UNDERGRADUATE AND UP
Statistics Explained is a reader-friendly introduction to
experimental design and statistics for undergraduate students in
the life sciences, particularly those who do not have a strong
mathematical background. Hypothesis testing and experimental
design are discussed first. Statistical tests are then explained
using pictorial examples and a minimum of formulae. This class-tested
approach, along with a well-structured set of diagnostic tables
will give students the confidence to choose an appropriate test
with which to analyse their own data sets. Presented in a lively
and straight-forward manner, Statistics Explained will give
readers the depth and background necessary to proceed to more
advanced texts and applications. It will therefore be essential
reading for all bioscience undergraduates, and will serve as a
useful refresher course for more advanced students.
? Written specifically for life science undergraduates,
particularly those without a strong mathematical background
? Extremely clear explanations, using minimal equations and
avoiding jargon
? Written by an experienced teacher, and all material has been
extensively classroom-tested
Contents
Preface; 1. Introduction; 2. eDoing Sciencef - hypotheses,
experiments and disproof; 3. Collecting and displaying data; 4.
Introductory concepts of experimental design; 5. Probability
helps you make a decision about your results; 6. Working from
samples - data, populations and statistics; 7. Normal
distributions - test for comparing the means of one or two
samples; 8. Type 1 and Type 2 error, power and sample size; 9.
Single factor analysis of variance; 10. Multiple comparisons
after ANOVA; 11. Two factor analysis of variance; 12. Important
assumptions of analysis of variance: transformations and a test
for equality of variances; 13. Two factor analysis of variance
without replication, and nested analysis of variance; 14.
Relationships between variables: linear correlation and linear
regression; 15. Simple linear regression; 16. Non-parametric
statistics; 17. Non-parametric tests for nominal scale data; 18.
Non-parametric tests for ratio, interval or ordinal scale data;
19. Choosing a test; 20. Doing science responsibly and ethically.
Series: Cambridge Tracts in Mathematics (No. 82)
Paperback (ISBN-10: 0521023947 | ISBN-13: 9780521023948)
There was also a Hardback of this title but it is no longer
available
available from November 2005
The theory of polycyclic groups is a branch of infinite group
theory which has a rather different flavour from the rest of that
subject. This book is a comprehensive account of the present
state of this theory. As well as providing a connected and self-contained
account of the group-theoretical background, it explains in
detail how deep methods of number theory and algebraic group
theory have been used to achieve some very recent and rather
spectacular advances in the subject. Up to now, most of this
material has only been available in scattered research journals,
and some of it is new. This book is the only unified account of
these developments, and will be of interest to mathematicians
doing research in algebra, and to postgraduate students studying
that subject.
Contents
Preface; Notation; 1. The elements, 2. Malfcevfs theorems; 3.
Extensions; 4. Arithmetical methods; 5. Faithful representations;
6. On unipotent groups; 7. Semi-simple splitting; 8. Soluble Z-linear
groups; 9. A finiteness theorem; 10. Polycyclic groups with
isomorphic finite quotients; 11. Examples; Appendix; References;
Index.