Series: Universitext,
2005, Approx. 200 p., Softcover
ISBN: 3-540-25305-X
About this textbook
Proposing a wide range of mathematical models that are currently
used in life sciences may be regarded as a challenge, and that is
precisely the challenge that this book takes up. Of course this
panoramic study does not claim to offer a detailed and exhaustive
view of the many interactions between mathematical models and
life sciences. This textbook provides a general overview of
realistic mathematical models in life sciences, considering both
deterministic and stochastic models and covering dynamical
systems, game theory, stochastic processes and statistical
methods. Each mathematical model is explained and illustrated
individually with an appropriate biological example. Finally
three appendices on ordinary differential equations, evolution
equations, and probability are added to make it possible to read
this book independently of other literature.
Table of contents
General Introduction.- Continuous-time Dynamical Systems.-
Discrete-time Dynamical Systems.- Game Theory and Evolution.-
Markov Chains and Diffusions.- Random Arborescent Models.-
Statistics.- Appendices.
The Kenneth O. May Lectures
Series: CMS Books in Mathematics,
2005, Approx. 365 p., Hardcover
ISBN: 0-387-25284-3
About this book
This book brings together for the first time the Kenneth May
Lectures that were given at the annual meetings of the Canadian
Society for History and Philosophy of Mathematics. All
contributions are of high scholarly value, yet accessible to an
audience with a wide range of interests. They provide a historian’s
perspective on mathematical developments and deal with a variety
of topics covering Greek applied mathematics, the mathematics and
science of Leonhard Euler, mathematical modeling and phenomena in
ancient astronomy, Turing and the origins of artificial
intelligence to name only a few.
Table of contents
* Preface * * Introduction: The Birth and Growth of a Community
by Amy Shell-Gellasch * History or Heritage? An Important
Distinction in Mathematics and for Mathematics Education, by Ivor
Grattan-Guinness * Ptolemy’s Mathematical Models and their
Meaning, by Alexander Jones * Mathematics, Instruments and
Navigation, 1600-1800, by Jim Bennett * Was Newton’s Calculus a
Dead End? The Continental Influence of Maclaurin’s Treatise of
Fluxions, byJudith V. Grabiner * The Mathematics and Science of
Leonhard Euler (1707-1783), by R¨udiger Thiele * Mathematics in
Canada before 1945: A Preliminary Survey by Thomas Archibald and
Louis Charbonneau * The Emergence of the American Mathematical
Research Community, by Karen Hunger Parshall * 19th Century Logic
Between Philosophy and Mathematics, by Volker Peckhaus * The
Battle for Cantorian Set Theory, by Joseph W. Dauben * Hilbert
and his Twenty-Four Problems, by R¨udiger Thiele * Turing and
the Origins of AI, by Stuart Shanker * Mathematics and Gender:
Some Cross-Cultural Observations, by Ann Hibner Koblitz
Series: Undergraduate Texts in Mathematics,
2005, Approx. 240 p., Hardcover
ISBN: 0-387-25530-3
About this textbook
This new textbook demonstrates that geometry can be developed in
four fundamentally different ways, and that all should be used if
the subject is to be shown in all its splendor. Euclid-style
construction and axiomatics seem the best way to start, but
linear algebra smooths the later stages by replacing some
tortuous arguments by simple calculations. And how can one avoid
projective geometry? It not only explains why objects look the
way they do; it also explains why geometry is entangled with
algebra. Finally, one needs to know that there is not one
geometry, but many, and transformation groups are the best way to
distinguish between them. In this book, two chapters are devoted
to each approach, the first being concrete and introductory,
while the second is more abstract.
Geometry, of all subjects, should be about taking different
viewpoints, and geometry is unique among mathematical disciplines
in its ability to look different from different angles. Some
students prefer to visualize, while others prefer to reason or to
calculate. Geometry has something for everyone, and students will
find themselves building on their strengths at times, and working
to overcome weaknesses at other times. This book will be suitable
for a second course in geometry and contains more than 100
figures, and a large selection of exercises in each chapter.
Table of contents
* Preface * Straightedge and compass * Euclid's approach to
geometry * Coordinates * Vectors and Euclidean spaces *
Perspective * Projective planes * Transformations * Non-Euclidean
geometry * References * Index
ISBN: 0849337380
Publication Date: 5/27/2005
Number of Pages: 376
Offers the first detailed, systematic treatment of Jones's set
function T, homogeneous contiua, and n-fold hyperspaces available
in book form
Discusses results previously addressed only in research papers
and others presented here for the first time
Presents theorems not found in print anywhere else
Includes many illustrations that help clarify the definitions and
proofs
Breaks new ground with important unsolved problems and unique
problems for research
Specialized as it might be, Continuum Theory is one of the most
intriguing areas in mathematics. However, despite being popular
journal fare, few books have thoroughly explored this aspect of
topology. In Topics on Continua, Sergio Macias, one of the
field's leading scholars, presents four of his favorite continuum
topics: inverse limits, Jones' set function T, homogenous
continua, and n-fold hyperspaces. With over a decade of teaching
experience, Macias is able to put forth an exceptionally cogent
discussion that gives beginning mathematicians a strong grounding
in Continuum Theory, then proceeds to present the most complete
set of theorems and proofs ever contained in a single topology
volume.
Table of Contents
Preliminaries, including an introduction to Product Topology.
Inverse Limits and Related Topics. Jones Set Function T. A
Theorem of E.G. Effros. Decomposition Theorems. n-Fold
Hyperspaces. Questions.
Series: Pure and Applied Mathematics Volume: 272
ISBN: 0849337437
Publication Date: 6/28/2005
Number of Pages: 510
Comprises chapters written by the leading specialists in their
fields
Includes specific content of special relevance to a large cross-section
of scientists including meteorologists, engineers, and physicists
Fully loaded with examples of practical application
Strengthens the linkage between mathematics and emerging areas of
science and technology such as superconductors as well as with
data analysis of environmental studies and chaos
It is the responsibility of knowledgeable mathematicians to align
the use of mathematics with the physical world, as mathematics
cannot prosper in isolation. Comprising the works of experts, who
presented at a symposium on Mathematics for Real World Problems
held in Sydney, Australia in 2003, each of the sections in this
book closes the gap between theoretical mathematics and applied
sciences. Aimed at those who are interested in acquiring
knowledge of contemporary applied analysis to solve concrete
problems, the book is divided into four parts: Mathematics for
Technology; Wavelet Methods for Real World Problems; Classical
and Fractal Methods for Physical Problems; and Trends in
Variational Methods.
Table of Contents
Mathematics for Technology: Industrial Mathematics. Mathematical
Models and Algorithms for Type II Superconductors. Wavelet
Methods for Real-World Problems. Wavelet frames and
Multiresolution Analysis. Comparison of Wavelet Procedures.
Trends in Wavelet Applications. Wavelet Methods for Indian
Rainfall Data. Wavelet Analysis of Tropospheric and Lower
Stratospheric Gravity Waves. Advanced Data Processes of Some
meteorological Parameters. Classical and Fractal Methods for
Physical Problems: Gradient Catastrophe in Heat Propagation with
Second Sound. Acoustic Waves in a Perturbed Layered Ocean. Non-Linear
Planar Oscillation of a Satellite Leading to Chaos under the
Influence of Third-Body Torque. Chaos Using MATLAB in the Motion
of a satellite under the Influence of Magnetic Torque.
Mathematical Tools for Signal Analysis. Trends in Variational
Methods: Elliptic Inverse Problems. Quantum Kinetic Equations for
Dense Systems. Convergence and the Optimal Choice of the Relation
Parameter for a Class of Iterative Methods. On a Special Class of
Sweeping Process. Applications of Variational Methods.