Seydel, Rudiger U.
Tools for Computational Finance, 3rd ed.
Series: Universitext
2006, XIX, 304 p. 75 illus., Softcover
ISBN: 3-540-27923-7
About this textbook
This book is very easy to read and one can gain a quick snapshot
of computational issues arising in financial mathematics.
Researchers or students of the mathematical sciences with an
interest in finance will find this book a very helpful and gentle
guide to the world of financial engineering. SIAM review (46,
2004).
The third edition is thoroughly revised and significantly
extended. The largest addition is a new section on analytic
methods with main focus on interpolation approach and quadratic
approximation. New sections and subsections are among others
devoted to risk-neutrality, early-exercise curves,
multidimensional Black-Scholes models, the integral
representation of options and the derivation of the Black-Scholes
equation.
New figures, more exercises, more background material make this
guide to the world of financial engineering a real must-to-have
for everyone working in FE.
Written for:
Students (Master and PhD) interested in computational aspects of
mathematical finance; practitioners
Table of contents
Modelling Tools for Financial Options.- Generating Random Numbers
with Specified Distributions.- Simulation with Stochastic
Differential Equations.- Standard Methods for Standard Options.-
Finite-Element Methods.- Pricing of Exotic Options.- Appendices.
Imai, Hiroshi; Hayashi, Masahito (Eds.)
Quantum Computation and Information
From Theory to Experiment
Series: Topics in Applied Physics , Vol. 102
2006, Approx. 295 p. 49 illus., Hardcover
ISBN: 3-540-33132-8
About this book
Recently, the field of quantum computation and information has
been developing through a fusion of results from various research
fields in theoretical and practical areas. This book consists of
the reviews of selected topics charterized by great progress and
cover the field from theoretical areas to experimental ones. It
contains fundamental areas, quantum query complexity, quantum
statistical inference, quantum cloning, quantum entanglement,
additivity. It treats three types of quantum security system,
quantum public key cryptography, quantum key distribution, and
quantum steganography. A photonic system is highlighted for the
realization of quantum information processing.
Table of contents
Part I: Quantum Computation.- Quantum Identification of Boolean
Oracles.- Query Complexity of Quantum Biased Oracles.- Part II:
Quantum Information.- Quantum Statistical Inference.- Quantum
Cloning Machines.- Entanglement and Quantum Error Correction.- On
Additivity Questions.- Part III: Quantum Security.- Quantum
Computational Cryptography.- Quantum Key Distribution: Security,
Feasibility and Robustness.- Why Quantum Steganography Can Be
Stronger Than Classical Steganography.- Part IV: Realization of
Quantum Information System.- Photonic Realization of Quantum
Information Systems.
Koelink, E.; Neerven, J.v.; Pagter, B.d.; Sweers, G. (Eds.)
Partial Differential Equations and Functional Analysis
The Philippe Clement Festschrift
Series: Operator Theory: Advances and Applications , Vol. 168
2006, Approx. 300 p., Hardcover
ISBN: 3-7643-7600-7
About this book
Capturing the state of the art of the interplay between partial
differential equations, functional analysis, maximal regularity,
and probability theory, this volume was initiated at the Delft
conference on the occasion of the retirement of Philippe Clement.
It will be of interest to researchers in PDEs and functional
analysis.
Written for:
Researchers in PDE, functional analysis, numerical analysis and
probability theory
Keywords:
Ginzburg-Landau equation
harmonic analysis
interpolation
partial differential equation
reaction-diffusion equation
Table of contents
Dresselhaus, Mildred S., Dresselhaus, Gene, Jorio, Ado
Group Theory
Application to the Physics of Condensed Matter
2006, Approx. 590 p. 150 illus., Hardcover
ISBN: 3-540-32897-1
About this textbook
Every process in physics is governed by selection rules that are
the consequence of symmetry requirements. The beauty and strength
of group theory resides in the transformation of many complex
symmetry operations into a very simple linear algebra. This
concise and class-tested book has been tailored over the authorsf
30 years as instructors at MIT and Brazilfs University Federal
of Minas Gerais, based on the concept that teaching group theory
in close connection with applications helps students to learn,
understand and use it. The text and problem sets provide a
springboard for the application of the basic material presented
here to topics in semiconductor physics, and the physics of
carbon-based nanostructures.
Table of contents
1. Basic Mathematical Background.- 2. Representation Theory.- 3.
Character of a Representation.- Basis Functions.- 5. Splitting
Atomic Orbitals in a Chrystal Potential.- 6. Applications to
Selection Rules.- 7. Electronic States of Molecules.- 8.
Molecular Vibrations.- 9. Space Groups in Real Space.- 10. Space
Groups in Reciprocal Space and Representations.- 11. Applications
to Lattice Vibrations.- 12. Energy Levels in Cubic Crystals.- 13.
Energy Band Models Based on Symmetry.- 14. Spin Orbit Interaction
in Solids.- 15. Application to Energy Bands with Spin.- 16. Time
Reversal Symmetry.- 17. Permutation Groups.- 18. Symmetry
Properties of Tensors.
Eckmann, Beno
Mathematical Survey Lectures 1943-2004
2006, Approx. 250 p., Hardcover
ISBN: 3-540-33790-3
About this book
The surveys in this volume are lectures given at congresses and
workshops, at international congresses of mathematicians (plenary
or section lectures), and at special occasions like birthdays or
commemorations. They all reflect the special interests of the
respective times. Although they are in the fields of topology,
algebra and differential geometry they reveal the big changes
mathematics has undergone over the years from 1943 to 2004. New
thinking has been developed; it has created new problems, or
simply has let old problems appear in a new light.
Table of contents
Lfidee de dimension (1943).- Topology and Algebra (1943).-
Complex-analytic manifolds (1950).- Homotopie et dualite (1956).-
Groupes dfhomotopie et dualite (1958).- Homotopy and Cohomology
Theory (1962).- Simple Homotopy Type and Categories of Fractions
(1970).- Some Recent Developments in the Homology Theory of
Groups (1980).- Poincare Duality Groups of Dimension 2 are
Surface Groups (1986).- Continuous Solutions of Linear Equations
(1991).- Mathematics: Questions and Answers (1994).- Hurwitz-Radon
Matrices Revisited (1994).- Birth of Fibre Spaces, and Homotopy (1996).-
4-Manifolds, Group Invariants, and l2-Betti Numbers (1997).- The
Euler characteristic ? some Highlights in its History.- Topology,
Algebra, Analysis ? Relations and Missing Links (1999).-
Introduction to Hilbert Space Methods in Topology (2000).- Die
Zukunft der Mathematik (Hilbert 1900) (2000).- A.N. Kolmogorov (2003).-
Is Algebraic Topology a Respectable Field? (2004).- Social Choice
and Topology (2004).
Jost, Jurgen
Compact Riemann Surfaces, 3rd ed.
An Introduction to Contemporary Mathematics
Series: Universitext
2006, XVIII, 282 p. 23 illus., Softcover
ISBN: 3-540-33065-8
About this textbook
Although Riemann surfaces are a time-honoured field, this book is
novel in its broad perspective that systematically explores the
connection with other fields of mathematics. It can serve as an
introduction to contemporary mathematics as a whole as it
develops background material from algebraic topology,
differential geometry, the calculus of variations, elliptic PDE,
and algebraic geometry. It is unique among textbooks on Riemann
surfaces in including an introduction to Teichmuller theory. The
analytic approach is likewise new as it is based on the theory of
harmonic maps. For this new edition, the author has expanded and
rewritten several sections to include additional material and to
improve the presentation.
Table of contents