Description: This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background material from graph theory, number theory, group theory and representation theory. The text can therefore be used as a brief introduction to these subjects as well as an illustration of how such topics are synthesised in modern mathematics.
Contents: 0. An overview; 1. Graph theory; 2. Number theory; 3. PSL2(q); 4. The graphs X^p,q; Appendix A. 4-regular graphs with large girth; Index; Bibliography.
Essential Information
First Author: Davidoff
Title: Elementary Number Theory, Group Theory and Ramanujan
Graphs
ISBN, Binding, Price: 0-521-53143-8 Paperback
ISBN, Binding, Price: 0-521-82426-5
Hardcover
Pages: 200
Approximate Publication Date: c.31/12/2002
Main Subject Category: Maths - foundations, combinatorics
Series: London Mathematical Society Student Texts, No. 55
Market (Subject)
mathematics
Level
graduate students, academic researchers
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Description: Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14 E and the natural logarithmic base, e=2.178 EStudents and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. Topics covered include the statistics of continued fractions, chaos in nonlinear systems, prime numbers, sum-free sets, isoperimetric problems, approximation theory, self-avoiding walks and the Ising model (from statistical physics), binary and digital search trees (from theoretical computer science), the Prouhet-Thue-Morse sequence, complex analysis, geometric probability and the traveling salesman problem. This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Contents: Preface; Notation; 1. Well-known constants; 2. Constants associated with number theory; 3. Constants associated with analytic inequalities; 4. Constants associated with the approximation of functions; 5. Constants associated with enumerating discrete structures; 6. Constants associated with functional iteration; 7. Constants associated with complex analysis; 8. Constants associated with geometry; Table; Index.
Essential Information
First Author: Finch
Title: Mathematical Constants
ISBN, Binding, Price: 0-521-81805-2 Hardback
Pages: 500
Approximate Publication Date: c.31/01/2003
Main Subject Category: Mathematics (general)
Series: Encyclopedia of Mathematics and its Applications, No. 94
Market (Subject)
mathematics
Level
academic researchers, graduate students
Bibliographic Details
62 line diagrams 9 tables
Series: Monographs on Statistics and Applied
Probability
ISBN: 1-58488-354-5
Publication Date: 9/20/2002
Number of Pages: 192
Forms essential reading for those interested
in repeated
measures, multi-level models, ANOVA, and
over-dispersion
Contains in-depth discussion using only the
essential technical
details, making the treatment accessible
to a wide audience, from
statisticians to applied research scientists
Incorporates signposting to enhance accessibility
and make it
valuable as both a reference a supplementary
text for coursework
Includes in each chapter a full bibliography,
exercises, and
computational and software notes
The components of variance is a notion essential
to statisticians
and quantitative research scientists working
in a variety of
fields, including the biological, genetic,
health, industrial,
and psychological sciences. Co-authored by
Sir David Cox, the pre-eminent
statistician in the field, this book provides
in-depth
discussions that set forth the principles
of the subject. It
focuses on developing the models that form
the basis for detailed
analyses as well as on the statistical techniques
themselves. The
authors include a variety of examples from
areas such as clinical
trial design, plant and animal breeding,
industrial design, and
psychometrics.
International School of Physics Enrico Fermi,
Volume 148
2002, 580 pp., hardcover
ISBN: 1-58603-270-4
This Fermi Summer School of Physics on "Experimental Quantum
Information and Computing" represents a primer on one of the
most intriguing and rapidly expanding new areas of physics. In
this part, the interest in quantum information (QI) science is
due to the discovery that a computer operating on quantum
mechanical principles can solve certain important computational
problems exponentially faster than any conceivable classical
computer. But this interest is also due to the interdisciplinary
nature of the field: the rapid growth is attributable, in part,
to the stimulating confluence of researchers and ideas from
physics, chemistry, mathematics, information theory, and computer
science. Physics plays a paramount role in QI science, as we
realize that computing is itself a physical process subject to
physical laws. The incredible growth of classical computers and
information processors in the 20th century stems from Turing's
notion that a computer is independent of the physical device
actually being used; be they relays, vacuum tubes, or
semiconductor transistors. As we strive to build useful quantum
information processors into the 21st century, we thus look for
any physical system that obeys the laws of quantum mechanics,
from single photons and atoms to quantum superconducting devices.
These Fermi lectures take us on a journey through these and other
promising current experimental candidates for QI processing,
spanning quantum optics and laser physics, atomic and molecular
physics, physical chemistry, and condensed-matter physics. While
this broad coverage of experimental physics represents a
challenge to the student, such an appreciation of these fields
will be critical in the future success of quantum technology.
Indeed, the most exciting feature of QI science is that the
technology ultimately leading to a quantum processor is likely
presently unknown.