May 2003 | Hardback | 308 pages 1 table 16 figures | ISBN: 0-521-81722-6

In this ambitious study, David Corfield attacks the widely held
view that it is the nature of mathematical knowledge which has
shaped the way in which mathematics is treated philosophically,
and claims that contingent factors have brought us to the present
thematically limited discipline. Illustrating his discussion with
a wealth of examples, he sets out a variety of approaches to new
thinking about the philosophy of mathematics, ranging from an
exploration of whether computers producing mathematical proofs or
conjectures are doing real mathematics, to the use of analogy,
the prospects for a Bayesian confirmation theory, the notion of a
mathematical research programme, and the ways in which new
concepts are justified. His highly original book challenges both
philosophers and mathematicians to develop the broadest and
richest philosophical resources for work in their disciplines,
and points clearly to the ways in which this can be done.

Contents

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; Part
II. Mathematical Uncertainty: 5. Bayesianism in mathematics; 6.
Uncertainty in mathematics and science; Part III. The Growth of
Mathematics: 7. Lakatosfs philosophy of mathematics; 8. The
methodology of mathematical research programmes; 9. The
importance of mathematical conceptualisation; Part IV. The
Interpretation of Mathematics: 10. Higher dimensional algebra.

A Self-Help Workbook for Science and Engineering Students, 2nd Edition

June 2003 | Paperback | 600 pages 592 line diagrams 14 tables
770 exercises | ISBN: 0-521-01707-6

This friendly self-help workbook covers mathematics essential to
first-year undergraduate scientists and engineers. In the second
edition of this highly successful textbook the author has
completely revised the existing text and added a totally new
chapter on vectors. Mathematics underpins all science and
engineering degrees, and this may cause problems for students
whose understanding of the subject is weak. In this book Jenny
Olive uses her extensive experience of teaching and helping
students by giving a clear and confident presentation of the core
mathematics needed by students starting science or engineering
courses. The book contains almost 800 exercises, with detailed
solutions given in the back to allow students who get stuck to
see exactly where they have gone wrong. Topics covered include
trigonometry and hyperbolic functions, sequences and series (with
detailed coverage of binomial series), differentiation and
integration, complex numbers, and vectors.

Contents

1. Basic algebra: some reminders of how it works; 2. Graphs and
equations; 3. Relations and functions; 4. Some trigonometry and
geometry of triangles and circles; 5. Extending trigonometry to
angles of any size; 6. Sequences and series; 7. Binomial series
and proof by induction; 8. Differentiation; 9. Integration; 10.
Complex numbers; 11. Working with vectors.

Differentiation

October 2003 | Hardback | 350 pages 25 line diagrams | ISBN: 0-521-55114-5

June 2004 | Paperback | ISBN: 0-521-55912-X

Part one of the authorsf comprehensive and innovative work on
multidimensional real analysis. This book is based on extensive
teaching experience at Utrecht University and gives a thorough
account of differential analysis in multidimensional Euclidean
space. It is an ideal preparation for students who wish to go on
to more advanced study. The notation is carefully organized and
all proofs are clean, complete and rigorous. The authors have
taken care to pay proper attention to all aspects of the theory.
In many respects this book presents an original treatment of the
subject and it contains many results and exercises that cannot be
found elsewhere. The numerous exercises illustrate a variety of
applications in mathematics and physics. This combined with the
exhaustive and transparent treatment of subject matter make the
book ideal as either the text for a course, a source of problems
for a seminar or for self study.

Contents

1. Continuity; 2. Differentiation; 3. Inverse function and
implicit function theorems; 4. Manifolds; 5. Tangent spaces;
Exercises.

Series: Texts in Statistical Science Series Volume: 57

ISBN: 1-58488-325-1

Publication Date: 3/24/2003

Number of Pages: 416

Presents a practical, comprehensive guide to using a modelling
approach to analysing survival data

Provides clear, step-by-step procedures for using the methods
discussed

Includes detailed coverage of model checking diagnostics

Incorporates material on time-dependent variates, interval
censoring, and sample size determination--important topics that
few other texts address

Demonstrates the techniques using practical examples drawn from
the medical and pharmaceutical sciences

Critically acclaimed and resoundingly popular in its first
edition, Modelling Survival Data in Medical Research has been
thoroughly revised and updated to reflect the many developments
and advances--particularly in software--made in the field over
the last 10 years. Now, more than ever, it provides an
outstanding text for upper-level and graduate courses in survival
analysis, biostatistics, and time-to-event analysis.

The treatment begins with an introduction to survival analysis
and a description of four studies that lead to survival data.
Subsequent chapters then use those data sets and others to
illustrate the various analytical techniques applicable to such
data, including the Cox regression model, the Weibull
proportional hazards model, and others. This edition features a
more detailed treatment of topics such as parametric models,
accelerated failure time models, and analysis of interval-censored
data. The author also focuses the software section on the use of
SAS, summarising the methods used by the software to generate its
output and examining that output in detail.

All of the data sets used in the book are available for download
from www.crcpress.com/e_products/downloads. Profusely illustrated
with examples and written in the author's trademark, easy-to-follow
style, Modelling Survival Data in Medical Research, Second
Edition is a thorough, practical guide to survival analysis that
reflects current statistical practices.

Sergio Console Universita Di Torino, Torino, Italy

Carlos Olmos Universidad Nacional de Cordoba, Argentina

Series: Research Notes in Mathematics Series Volume: 434

ISBN: 1-58488-371-5

Publication Date: 4/25/2003

Number of Pages: 344

Provides an up-to-date and self-contained introduction to the
growing fields of submanifolds and holonomy

Presents a thorough survey of new techniques based on the
holonomy of the normal connection and their applications

Presents new proofs of recent results previously available only
in scattered in research papers

Includes open problems and exercises

Offers an extensive list of references

With special emphasis on new techniques based on the holonomy of
the normal connection, this book provides a modern, self-contained
introduction to submanifold geometry. It offers a thorough survey
of these techniques and their applications and presents a
framework for various recent results to date found only in
scattered research papers. The treatment introduces all the
basics of the subject, and along with some classical results and
hard-to-find proofs, presents new proofs of several recent
results. Appendices furnish the necessary background material,
exercises give readers practice in using the techniques, and
discussion of open problems stimulates readers' interest in the
field.