2003 Approx. 350 p. Softcover
1-85233-713-3
David Harland describes the historical development
of particle
physics, and explains, in a non-mathematical
way, how particle
physics has influenced the structure of the
Universe from the
very beginning of time. He demonstrates the
close links between
discoveries in particle physics and in cosmology
up to the
present. He describes how our understanding
of the Universe has
developed from the discovery that the Universe
is expanding, to
the idea that all matter originated in a
hot, Big Bang, then
explains the many subtle improvements to
the basic theory that
have been necessary to understand how the
very smallest particles
and earliest structures (the 'microscale')
in the Universe
evolved to produce the Universe as it is
now (the 'macroscale').
The author also describes how scientists
are attempting to
develop a 'Theory of Everything' that would
explain how an
instant after the Big Bang a single primordial
force was
transformed into the four forces of nature
that we observe today,
which hitherto were believed to be 'fundamental'.
Keywords: cosmology, galaxy, black holes
Contents: Expanding Universe.- Within the
Atom.- The Big Bang.-
Do we live in a black hole?
Series: Springer Praxis Books.
2003 Approx. 255 p. 93 illus. With CD-ROM.
Softcover
0-387-95523-2
Intended as a companion for textbooks in
mathematical methods for
science and engineering, this book presents
a large number of
numerical topics and exercises together with
discussions of
methods for solving such problems using Mathematica(R).
The
accompanying CD contains Mathematica Notebooks
for illustrating
most of the topics in the text and for solving
problems in
mathematical physics. Although it is primarily
designed for use
with the author's "Mathematical Methods:
For Students of
Physics and Related Fields," the discussions
in the book
sufficiently self-contained that the book
can be used as a
supplement to any of the standard textbooks
in mathematical
methods for undergraduate students of physical
sciences or
engineering.
Contents: Mathematica in a Nutshell.- Vectors
and Matrices in
Mathematica.- Integration.- Infinite Series
and Finite Sums.-
Numerical Solutions of ODE's: Theory.- Numerical
Solutions of
ODE's: Examples Using Mathematica.
Series: Undergraduate Texts in Contemporary
Physics.
3rd ed. 2003 Approx. 850 p. 162 illus. Hardcover
0-387-00230-8
This is a fully revised edition of the best-selling
Introduction
to Maple. The book presents the modern computer
algebra system
Maple, teaching the reader not only what
can be done by Maple,
but also how and why it can be done. The
book also provides the
necessary background for those who want the
most of Maple or want
to extend its built-in knowledge. Emphasis
is on understanding
the Maple system more than on factual knowledge
of built-in
possibilities. To this end, the book contains
both elementary and
more sophisticated examples as well as many
exercises. The
typical reader should have a background in
mathematics at the
intermediate level. Andre Heck began developing
and teaching
Maple courses at the University of Nijmegen
in 1987. In 1989 he
was appointed managing director of the CAN
Expertise Center in
Amsterdam. CAN, Computer Algebra in the Netherlands,
stimulates
and coordinates the use of computer algebra
in education and
research. In 1996 the CAN Expertise Center
was integrated into
the Faculty of Science at the University
of Amsterdam, into what
became the AMSTEL Institute. The institute
program focuses on the
innovation of computer activities in mathematics
and science
education on all levels of education. The
author is actively
involved in the research and development
aimed at the integrated
computer learning environment Coach for mathematics
and science
education at secondary school level.
Contents: Introduction to Computer Algebra.-
The First Steps:
Calculus on Numbers.- Variables and Names.-
Getting Around with
Maple.- Polynomials and Rational Functions.-
Internal Data
Representation and Substitution.- Manipulation
of Polynomials and
Rational Expressions.- Functions.- Differentiation.-
Integration
and Summation.- Series, Approximation, and
Limits.- Composite
Data Types.- The Assume Facility.- Simplification.-
Graphics.-
Solving Equations.- Differential Equations.-
The Linear-Algebra
Package.- Linear Algebra: Applications.-
The Groebner Basis.-
References.- Index.
2003 XII, 300 p. Hardcover
0-387-00425-4
This textbook on applied probability is intended
for graduate
students in applied mathematics, biostatistics,
computational
biology, computer science, physics, and statistics.
It
presupposes knowledge of multivariate calculus,
linear algebra,
ordinary differential equations, and elementary
probability
theory. Given these prerequisites, Applied
Probability presents a
unique blend of theory and applications,
with special emphasis on
mathematical modeling, computational techniques,
and examples
from the biological sciences. Chapter 1 reviews
elementary
probability and provides a brief survey of
relevant results from
measure theory. Chapter 2 is an extended
essay on calculating
expectations. Chapter 3 deals with probabilistic
applications of
convexity, inequalities, and optimization
theory. Chapters 4 and
5 touch on combinatorics and combinatorial
optimization. Chapters
6 through 11 present core material on stochastic
processes. If
supplemented with appropriate sections from
Chapters 1 and 2,
there is sufficient material here for a traditional
semester-long
course in stochastic processes covering the
basics of Poisson
processes, Markov chains, branching processes,
martingales, and
diffusion processes. Finally, Chapters 12
and 13 develop the Chen-Stein
method of Poisson approximation and connections
between
probability and number theory. Kenneth Lange
is Professor of
Biomathematics and Human Genetics and Chair
of the Department of
Human Genetics at the UCLA School of Medicine.
He has held
appointments at the University of New Hampshire,
MIT, Harvard,
and the University of Michigan. While at
the University of
Michigan, he was the Pharmacia & Upjohn
Foundation Professor
of Biostatistics.
Contents: Basic Notions of Probability Theory.-
Calculation of
Expectations.- Convexity, Optimization, and
Inequalities.-
Combinatorics.- Combinatorial Optimization.-
Poisson Processes.-
Discrete-Time Markov Chains.- Continuous-Time
Markov Chains.-
Branching Processes.- Martingales.- Diffusion
Processes.- Poisson
Approximation.- Number Theory.
Series: Springer Texts in Statistics.
2003 Approx. 200 p. Softcover
3-540-00362-2
This book is the first textbook treatment
of a significant part
of such results. It focuses on so-called
equivariant methods,
based on the Borsuk-Ulam theorem and its
generalizations. The
topological tools are intentionally kept
on a very elementary
level (for example, homology theory and homotopy
groups are
completely avoided). No prior knowledge of
algebraic topology is
assumed, only a background in undergraduate
mathematics, and the
required topological notions and results
are gradually explained.
Keywords: Combinatorics, applications of
algebraic topology,
discrete geometry
Contents:
Preliminaries.- 1 Simplicial Complexes: 1.1
Topological spaces; 1.2
Homotopy equivalence and homotopy; 1.3 Geometric
simplicial
complexes; 1.4 Triangulations; 1.5 Abstract
simplicial complexes;
1.6 Dimension of geometric realizations;
1.7 Simplicial complexes
and posets.- 2 The Borsuk-Ulam Theorem: 2.1
The Borsuk-Ulam
theorem in various guises; 2.2 A geometric
proof; 2.3 A discrete
version: Tucker's lemma; 2.4 Another proof
of Tucker's lemma.- 3
Direct Applications of Borsuk--Ulam: 3.1
The ham sandwich
theorem; 3.2 On multicolored partitions and
necklaces; 3.3
Kneser's conjecture; 3.4 More general Kneser
graphs: Dolnikov's
theorem; 3.5 Gale's lemma and Schrijver's
theorem.- 4 A
Topological Interlude: 4.1 Quotient spaces;
4.2 Joins (and
products); 4.3 k-connectedness; 4.4 Recipes
for showing k-connectedness;
4.5 Cell complexes.- 5 Z_2-Maps and Nonembeddability:
5.1
Nonembeddability theorems: An introduction;
5.2 Z_2-spaces and Z_2-maps;
5.3 The Z_2-index; 5.4 Deleted products good
...; 5.5 ... deleted
joins better; 5.6 Bier spheres and the Van
Kampen-Flores theorem;
5.7 Sarkaria's inequality; 5.8 Nonembeddability
and Kneser
colorings; 5.9 A general lower bound for
the chromatic number.- 6
Multiple Points of Coincidence: 6.1 G-spaces;
6.2 E_nG spaces and
the G-index; 6.3 Deleted joins and deleted
products; 6.4 Necklace
for many thieves; 6.5 The topological Tverberg
theorem; 6.6 Many
Tverberg partitions; 6.7 Z_p-index, Kneser
colorings, and p-fold
points; 6.8 The colored Tverberg theorem.-
A Quick Summary.-
Hints to Selected Exercises.- Bibliography.-
Index.
Series: Universitext.