0-534-49501-X
718 pages Case Bound 7 3/8 X 9 1/4
An increasing number of computer scientists from diverse areas
are using discrete mathematical structures to explain concepts
and problems. Based on their teaching experiences, the authors
offer an accessible text that emphasizes the fundamentals of
discrete mathematics and its advanced topics. This text shows how
to express precise ideas in clear mathematical language. Students
discover the importance of discrete mathematics in describing
computer science structures and problem solving. They also learn
how mastering discrete mathematics will help them develop
important reasoning skills that will continue to be useful
throughout their careers.
Table of Contents
1. SETS, PROOF TEMPLATES, AND INDUCTION.
Basic Definitions. Exercises. Operations on Sets. Exercises. The
Principle of Inclusion-Exclusion. Exercises. Mathematical
Induction. Program Correctness. Exercises. Strong Form of
Mathematical Induction. Exercises. Chapter Review.
2. FORMAL LOGIC.
Introduction to Propositional Logic. Exercises. Truth and Logical
Truth. Exercises. Normal Forms. Exercises. Predicates and
Quantification. Exercises. Chapter Review.
3. RELATIONS.
Binary Relations. Operations on Binary Relations. Exercises.
Special Types of Relations. Exercises. Equivalence Relations.
Exercises. Ordering Relations. Exercises. Relational Databases:
An Introduction. Exercises. Chapter Review.
4. FUNCTIONS.
Basic Definitions. Exercises. Operations on Functions. Sequences
and Subsequences. Exercises. The Pigeon-Hole Principle. Exercises.
Countable and Uncountable Sets. Exercises. Chapter Review.
5. ANALYSIS OF ALGORITHMS.
Comparing Growth Rates of Functions. Exercises. Complexity of
Programs. Exercises. Uncomputability. Chapter Review.
6. GRAPH THEORY.
Introduction to Graph Theory. The Handshaking Problem. Paths and
Cycles. Graph Isomorphism. Representation of Graphs. Exercises.
Connected Graphs. The Konigsberg Bridge Problem. Exercises. Trees.
Spanning Trees. Rooted Trees. Exercises. Directed Graphs.
Applications: Scheduling a Meeting Facility. Finding a Cycle in a
Directed Graph. Priority in Scheduling. Connectivity in Directed
Graphs. Eulerian Circuits in Directed Graphs. Exercises. Chapter
Review.
7. COUNTING AND COMBINATORICS.
Traveling Salesperson. Counting Principles. Set Decomposition
Principle. Exercises. Permutations and Combinations. Constructing
the kth Permutation. Exercises. Counting with Repeated Objects.
Combinatorial Identities. Pascalfs Triangle. Exercises. Chapter
Review.
8. DISCRETE PROBABILITY.
Ideas of Chance in Computer Science. Exercises. Cross Product
Sample Spaces. Exercises. Independent Events and Conditional
Probability. Exercises. Discrete Random Variables. Exercises.
Variance, Standard Deviation, and the Law of Averages. Exercises.
Chapter Review.
9. RECURRENCE RELATIONS.
The Tower of Hanoi Problem. Solving First-Order Recurrence
Relations. Exercises. Second-Order Recurrence Relations.
Exercises. Divide-and-Conquer Paradigm. Binary Search. Merge Sort.
Multiplication of n-Bit Numbers. Divide-and-Conquer Recurrence
Relations. Exercises. Chapter Review.
IRMA Lectures in Mathematics and Theoretical Physics Vol. 7
ISBN 3-03719-012-4
May 2005, 368 pages, softcover, 17.0 cm x 24.0 cm.
Hyperbolic and kinetic equations arise in a large variety of
industrial problems. For this reason, the CEMRACS summer research
center held at CIRM in Luminy in 2003 was devoted to this topic.
During a six-week period, junior and senior researchers worked
full time on several projects proposed by industry and academia.
Most of this work was completed later on, and the results are now
reported in the present book.
The articles address modelling issues as well as the development
and comparisons of numerical methods in different situations. The
applications include multi-phase flows, plasma physics, quantum
particle dynamics, radiative transfer, sprays and aeroacoustics.
The text is aimed at researchers and engineers interested in
modelling and numerical simulation of hyperbolic and kinetic
problems arising from applications.
IRMA Lectures in Mathematics and Theoretical Physics Vol. 8
ISBN 3-03719-013-2
May 2005, 260 pages, softcover, 17.0 cm x 24.0 cm.
Since its discovery in 1997 by Maldacena, AdS/CFT correspondence
has become one of the prime subjects of interest in string
theory, as well as one of the main meeting points between
theoretical physics and mathematics. On the physical side it
provides a duality between a theory of quantum gravity and a
field theory. The mathematical counterpart is the relation
between Einstein metrics and their conformal boundaries. The
correspondence has been intensively studied, and a lot of
progress emerged from the confrontation of viewpoints between
mathematics and physics.
Written by leading experts and directed at research
mathematicians and theoretical physicists as well as graduate
students, this volume gives an overview of this important area
both in theoretical physics and in mathematics. It contains
survey articles giving a broad overview of the subject and of the
main questions, as well as more specialized articles providing
new insight both on the Riemannian side and on the Lorentzian
side of the theory.
Aimed at those who have an elementary knowledge of linear
algebra, general topology, multivariate calculus, analysis, and
algebraic topology, this book gives an introduction to some
fundamental tools of differential topology. The first part
comprising Chapters 1 to 4 is foundational. This will be useful
to general students of pure mathematics, and can be used to
design a course at the M.Sc. level in Indian universities. The
second part, consisting of Chapters 5 to 8, caters to researchers
in the areas of Topology, Geometry and Global Analysis, and
touches on advanced topics of general interest in these areas.
Finally, the third part, meant for those desirous of working in
the field of Differential Topology itself.
Some of the highlights of the book are Thom transversality, Morse
theory, Theory of handle presentation, h-cobordism theorem and
generalised Poincare conjecture, and Gromov theory of homotopy
principle of certain partial differential relations. The
intention is to acquaint the reader with some epochal discoveries
in the field of manifolds, mainly the earlier works of Stephen
Smale for which he was awarded the Fields Medal.
Contents:
Preface.
1. Basic Concepts of Manifolds
2. Approximation Theorems and Whitneyfs Embedding
3. Linear Structures on Manifolds
4. Riemannian Manifolds
5. Vector Bundles on Manifolds
6. Transversality
7. Tubular Neighbourhoods
8. Spaces of Smooth Maps
9. Morse Theory
10. Theory of Handle Presentations
11. Homotopy Classification of Regular Sections. Bibliography.
Index.
Text and Readings in Mathematics/ 34
June 2005, 454 pages, Hardcover, ISBN 81-85931-56-9
This volume contains refereed and updated version of papers
presented at the International Conference on Algebra and Number
Theory held on the occasion of the silver jubilee of the School
of Mathematics and Computer/Information Science at the University
of Hyderabad, India. There are three survey articles one the
cyclicity problem for division algebras, one on Ramanujan graphs
and supplementary zeroes of p-adic L functions of modular forms.
Three articles announce results, which are to appear elsewhere.
There are eighteen original contributions.
The theme in the section on Algebra centres on recent work on
Quadratic Forms and Division Algebras though there are also
papers on Modules of Witt vectors, the Hodge-Tate conjecture,
Calabi-Yau manifolds and Moduli stacks of vector bundles.
The section on Number Theory centres on Automorphic Forms and
Representations; however, here again there are papers on other
themes pertaining to Elliptic curves and transcendental number
theory.
This volume should be useful to young researchers especially
those interested in recent developments in Algebra and Number
Theory.
Contents:
Part I - Algebra
Fields of cohomological dimension one versus C1 -fields.
J.-L. Colliot-Thelene
Modules of Witt vectors.
Friedrich Ischebeck and Volker Kokot
On efhorizontalff invariants attached to quadratic forms.
Bruno Kahn
On the dimension and other numerical invariants of
invariants of algebras and vector products.
Larissa Cadorin, Max-Albert Knus and Markus Rost
Purity for multipliers.
Ivan Panin
Quotients of E n by a n+1 and Calabi-Yau manifolds.
Kapil Paranjpe and Dinakar Ramakrishnan
A generalized Hodge-Tate conjecture for algebraic varieties
with totally degenerate reduction over p-adic fields.
Wayne Raskind
The Cyclicity question.
David J. Saltman
Modulii stacks of vector bundles and Frobenius morphisms.
Frank Neumann and Uhlrich Stuhler
On the length of a quadratic form.
R. Parimala and V. Suresh
Division algebras over rational function fields in one variable.
L.H. Rowen, A.S. Sivatski and J.-P. Tignol
Part II - Number Theory
Distinguished non-archimedian representations.
U.K. Anandavardhanan
Zeros supplementaires de fonctions L p-adiques de
formes modulaires.
Pierre Colmez
The cyclotomic trace map and values of zeta functions.
Thomas Geisser
Ordinary forms and their local Galois representations.
Eknath Ghate
Supercuspidal representations and symmetric spaces.
Jeffrey Hakim
Overconvergent p-adic Siegel modular forms.
King Fai Lai and Chun Lai Zhao
Splitting of abelian varieties: a new local global problem.
V. Kumar Murty
Ramanujan graphs and zeta functions.
M. Ram Murty
Recovering modular forms and representations from
tensor and symmetric powers.
C.S. Rajan
On restriction of admissible representations.
Kaoru Hiraga and Hiroshi Saito
Fine Selmer groups for elliptic curves with complex
multiplication.
J. Coates and R. Sujatha
Variations on the Six Exponential Theorem.
Michel Waldschmidt
Appendix: Periods on the Kummer surface
Hironori Shiga
On the p-adic absolute CM-period symbol.
Tomokazu Kashio and Hiroyuki Yoshida
May 2005, 414 pages, Hardcover, ISBN 81-85931-57-7,
This book presents a concise treatment of stochastic calculus
and its applications. It gives a simple but rigorous treatment of
the subject including a range of advanced topics, it is useful
for practitioners who use advanced theoretical results. It covers
advanced applications, such as models in mathematical finance,
biology and engineering.
Self-contained and unified in presentation, the book contains
many solved examples and exercises. It may be used as a textbook
by advanced undergraduates and graduate students in stochastic
calculus and financial mathematics. It is also suitable for
practitioners who wish to gain an understanding or working
knowledge of the subject. For mathematicians, this book could be
a first text on stochastic calculus; it is good companion to more
advanced texts by a way of examples and exercises. For people
from other fields, it provides a way to gain a working knowledge
of stochastic calculus. It shows all readers the applications of
stochastic calculus methods and takes readers to the technical
level required in research and sophisticated modelling.
This second edition contains a new chapter on bonds, interest
rates and their options. New materials include more worked out
examples in all chapters, best estimators, more results on change
of time, change of measure, random measures, new results on
exotic options, FX options, stochastic and implied volatility,
models of the age-dependent branching process and the stochastic
Lotka-Volterra model in biology, non-linear filtering in
engineering and five new figures.
Theory:
Variation and Quadratic Variation
Basics of Probability
Brownian Motion
Ito's Formula
Stochastic Differential Equations
Diffusions
Feynman-Kac Formula
Martingales
Semimartingales
Compensators
Change of Measure
Girsanov's Theorem
Applications:
Arbitrage Pricing Theory
Options
Bonds
Interest Rates
HJM
BGM Models
Birth-Death Processes
Stochastic Lotka-Volterra Model
Non-Linear Filtering
Kalman-Bucy Filter
Random Oscillators
Readership: Academics, mathematicians, advanced undergraduates,
graduates, practitioners in finance, risk managers and electrical
engineers.
Reviews of the First Edition
E.. hard to find books on stochastic analysis which present
such a wide spectrum of results with relatively modest
prerequisites."
Mathematical Reviews
It provides a good introduction to stochastic analysis, leaving
out several of the more technical proofs. The variety of examples
and exercises suggests to use the book for self-studies.E
Zentralblatt MATH
420pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 1-86094-555-4
ISBN 1-86094-566-X(pbk)