David Corfield

Towards a Philosophy of Real Mathematics

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.


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. Lakatosfs 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.

Jenny Olive

Maths: A Student's Survival Guide
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.


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.

J. J. Duistermaat, J. A. C. Kolk

Multidimensional Real Analysis, I

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 authorsf 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.

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

David Collett University of Reading, UK

Modelling Survival Data in Medical Research, Second Edition

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.

Jurgen Berndt University of Hull, England, UK
Sergio Console Universita Di Torino, Torino, Italy
Carlos Olmos Universidad Nacional de Cordoba, Argentina

Submanifolds and Holonomy

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.