Many complex systems--from immensely complicated ecosystems to
minute assemblages of molecules--surprise us with their simple
behavior. Consider, for instance, the snowflake, in which a great
number of water molecules arrange themselves in patterns with six-way
symmetry. How is it that molecules moving seemingly at random
become organized according to the simple, six-fold rule? How do
the comings, goings, meetings, and eatings of individual animals
add up to the simple dynamics of ecosystem populations? More
generally, how does complex and seemingly capricious
microbehavior generate stable, predictable macrobehavior?
In this book, Michael Strevens aims to explain how simplicity can
coexist with, indeed be caused by, the tangled interconnections
between a complex system's many parts. At the center of
Strevens's explanation is the notion of probability and, more
particularly, probabilistic independence. By examining the
foundations of statistical reasoning about complex systems such
as gases, ecosystems, and certain social systems, Strevens
provides an understanding of how simplicity emerges from
complexity. Along the way, he draws lessons concerning the low-level
explanation of high-level phenomena and the basis for introducing
probabilistic concepts into physical theory.
39 line illustrations
432 pages
Paperback edition
September 2006
ISBN 0-674-02259-9
ISBN: 978-0-470-05357-7
Hardcover
880 pages
March 2007
View Previous Edition of This Title
The authority on building empirical models and the fitting of
such surfaces to data?completely updated and revised
Revising and updating a volume that represents the essential
source on building empirical models, George Box and Norman
Draper?renowned authorities in this field?continue to set the
standard with the Second Edition of Response Surfaces, Mixtures,
and Ridge Analyses, providing timely new techniques, new
exercises, and expanded material.
A comprehensive introduction to building empirical models, this
book presents the general philosophy and computational details of
a number of important topics, including factorial designs at two
levels; fitting first and second-order models; adequacy of
estimation and the use of transformation; and occurrence and
elucidation of ridge systems.
Substantially rewritten, the Second Edition reflects the
emergence of ridge analysis of second-order response surfaces as
a very practical tool that can be easily applied in a variety of
circumstances. This unique, fully developed coverage of ridge
analysis?a technique for exploring quadratic response surfaces
including surfaces in the space of mixture ingredients and/or
subject to linear restrictions?includes MINITABR routines for
performing the calculations for any number of dimensions.
Many additional figures are included in the new edition, and new
exercises (many based on data from published papers) offer
insight into the methods used. The exercises and their solutions
provide a variety of supplementary examples of response surface
use, forming an extremely important component of the text.
Response Surfaces, Mixtures, and Ridge Analyses, Second Edition
presents material in a logical and understandable arrangement and
includes six new chapters covering an up-to-date presentation of
standard ridge analysis (without restrictions); design and
analysis of mixtures experiments; ridge analysis methods when
there are linear restrictions in the experimental space including
the mixtures experiments case, with or without further linear
restrictions; and canonical reduction of second-order response
surfaces in the foregoing general case.
Additional features in the new edition include:
New exercises with worked answers added throughout
An extensive revision of Chapter 5: Blocking and Fractionating 2k
Designs
Additional discussion on the projection of two-level designs into
lower dimensional spaces
This is an ideal reference for researchers as well as a primary
text for Response Surface Methodology graduate-level courses and
a supplementary text for Design of Experiments courses at the
upper-undergraduate and beginning-graduate levels.
ISBN: 978-0-470-09605-5
Hardcover
296 pages
February 2007
This text covers the essentials of point-set topology in a
relatively terse presentation, with lots of examples and
motivation along the way. Along with the standard point-set
topology topics (connected spaces, compact spaces, separation
axioms, and metric spaces), the author includes path-connectedness,
and a chapter on constructing spaces from other spaces (including
products, quotients, etc.). The text culminates in to two main
chapters, each independent of the other: 1) The Classification
Theorem for Compact, Connected Surfaces and 2) Fundamental Groups
and Covering Spaces, with Applications giving the reader the
choice of which subject best suits them.
Contents
Foreword.
Acknowledgments.
1. Introduction: Intuitive Topology.
2. Background on Sets and Functions.
3. Topological Spaces.
4. More on Open and Closed Sets and Continuous Functions.
5. New Spaces from Old.
6. Connected Spaces.
7. Compact Spaces.
8. Separation Axioms.
9. Metric Spaces.
10. The Classification of Surfaces.
11. Fundamental Groups and Covering Spaces.
References.
Index.
(Hardback)
ISBN-10: 0-19-852822-1
ISBN-13: 978-0-19-852822-7
Paperback 9780199227303
Estimated publication date: May 2007
216 pages, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 13
Description
Covers a broad spectrum of basic computational issues
Numerous GP programming examples given
End of chapter exercises reinforce the text
Remarks and solutions are provided for selected exercises in the
final chapter
This graduate text, based on years of teaching experience, is
intended for first or second year graduate students in pure
mathematics. The main goal of the text is to show how the
computer can be used as a tool for research in number theory
through numerical experimentation. The book contains many
examples of experiments in binary quadratic forms, zeta functions
of varieties over finite fields, elementary class field theory,
elliptic units, modular forms, along with exercises and selected
solutions. Sample programs are written in GP, the scripting
language for the computational package PARI, and are available
for download from the author's website.
Readership: Graduates in pure mathematics, particularly in number
theory.
Contents
Preface
1. Basic examples
2. Reciprocity
3. Positive definite binary quadratic forms
4. Sequences
5. Combinatorics
6. p-adic numbers
7. Polynomials
8. Remarks on selected exercises
References
Index