Series: Monographs in Computer Science,
2004, XX, 388 p. 63 illus., Hardcover
ISBN: 0-387-40115-6
Due: December 31, 2004
About this book
The book is a focused survey on probabilistic program semantics,
conceived to tell a coherent story with a uniform notation. It is
grouped into three themes: Part I is for 'users' of the
techniques who will be developing actual programs; Part II gives
mathematical foundations intended for those studying exactly how
it was done and how to build semantic structures/models in their
own work; and Part III describes a very 'hot' research direction,
temporal logic and model checking.
Topics and features:
- introduces readers to very up-to-date research in the
mathematics of rigorous development of randomized (probabilistic)
algorithms
- illustrates by example the typical steps necessary in computer
science to build a mathematical model of any programming paradigm
- presents results of a large and integrated body of research in
the area of 'quantitative' program logics
An advanced research survey monograph, integrating three major
topic areas: random/probabilistic algorithms, assertion-based
program reasoning, and refinement programming models. Essential
foundation topic for modern sequential programming methodology.
Table of contents
Introduction to pGCL.- Invariants and variants for probabilistic
loops.- Case studies in termination .- Probabilistic data
refinement.- Theory for the demonic model.- Geometry of
probabilistic programs.- Proven rules for probabilistic loops.-
Transformer hierarchy.- Quantitative temporal logic qTL.-
Quantitative algebra of qTL.- Quantitative modal u-calculus of
qMu, and games.- Appendixes.- Index.
Series: Texts in Theoretical Computer Science. An EATCS
Series,
2005, Approx. 400 p., Hardcover
ISBN: 3-540-23342-3
Due: January 2005
About this textbook
This book presents a "practical theory" of reactive
systems, with formal foundations in Temporal Logic of Actions.
The theory supports incremental development of operational,
object-oriented models in steps that preserve already established
properties. Models are given in an action-oriented language, and
their modularity relates to aspects in aspect-oriented
programming. The emphasis is on theoretical understanding of
reactive behaviors, and on using "horizontal"
modularity to manage their complexity.
Special chapters are devoted to the applicability of the theory
to distributed and real-time systems. Incremental specification
is illustrated in the book by a number of examples of varying
size and complexity.
Written for:
Graduates, researchers
Keywords:
Aspect-oriented Specification
Incremental Modeling
Reactive Systems
Temporal Logic of Actions
Series: Graduate Texts in Mathematics, Vol. 228
2005, XV, 436 p. 29 illus., Hardcover
ISBN: 0-387-23229-X
Due: January 2005
About this textbook
This book introduces the theory of modular forms with an eye
toward the Modularity Theorem:
All rational elliptic curves arise from modular forms.
The topics covered include
* elliptic curves as complex tori and as algebraic curves,
* modular curves as Riemann surfaces and as algebraic curves,
* Hecke operators and Atkin--Lehner theory,
* Hecke eigenforms and their arithmetic properties,
* the Jacobians of modular curves and the Abelian varieties
associated to Hecke eigenforms,
* elliptic and modular curves modulo~$p$ and the Eichler?Shimura
Relation,
* the Galois representations associated to elliptic curves and to
Hecke eigenforms.
As it presents these ideas, the book states the Modularity
Theorem in various forms, relating them to each other and
touching on their applications to number theory.
A First Course in Modular Forms is written for beginning graduate
students and advanced undergraduates. It does not require
background in algebraic number theory or algebraic geometry, and
it contains exercises throughout.
Table of contents
Preface * Modular Forms, Elliptic Curves, and Modular Curves *
Modular Curves as Riemann Surfaces * Dimension Formulas *
Eisenstein Series * Hecke Operators * Jacobian and Abelian
Varieties * Modular Curves as Algebraic Curves * The Eichler-Shimura
Relation and L-Functions * Galois Representations * Hints and
Answers to the Exercises * Bibliography * List of Symbols * Index
* References
ISBN: 3-527-40534-8
Hardcover
740 pages
April 2005
Description
All there is to know about functional analysis, integral
equations and calculus of variations in a single volume.
This advanced textbook is divided into two parts: The first on
integral equations and the second on the calculus of variations.
It begins with a short introduction to functional analysis,
including a short review of complex analysis, before continuing a
systematic discussion of different types of equations, such as
Volterra integral equations, singular integral equations of
Cauchy type, integral equations of the Fredholm type, with a
special emphasis on Wiener-Hopf integral equations and Wiener-Hopf
sum equations.
After a few remarks on the historical development, the second
part starts with an introduction to the calculus of variations
and the relationship between integral equations and applications
of the calculus of variations. It further covers applications of
the calculus of variations developed in the second half of the 20th
century in the fields of quantum mechanics, quantum statistical
mechanics and quantum field theory.
Throughout the book, the author presents over 150 problems and
exercises ? many from such branches of physics as quantum
mechanics, quantum statistical mechanics, and quantum field
theory ? together with outlines of the solutions in each case.
Detailed solutions are given, supplementing the materials
discussed in the main text, allowing problems to be solved making
direct use of the method illustrated. The original references are
given for difficult problems. The result is complete coverage of
the mathematical tools and techniques used by physicists and
applied mathematicians
Intended for senior undergraduates and first-year graduates in
science and engineering, this is equally useful as a reference
and self-study guide.
Table of contents
1. Function Spaces, Linear Operators and Green Functions
2. Integral Equations and Greens Functions
3. Integral Equations of Volterra type
4. Integral Equations of the Fredholm type
5. Hilbert-Schmidt Theory of Symmetric Kernel
6. Singular Integral Equations of Cauchy type
7. Wiener-Hopf Method and Wiener-Hopf Integral Equation
8. Non-linear Integral Equations
9. Calculus of Variations: Fundamentals
10. Calculus of Variations: Applications
This textbook provides a calculus-based introduction to
economics. Students blessed with a working knowledge of the
calculus will find that this text facilitates their study of the
basic analytical framework of economics. The textbook examines a
wide range of micro and macro topics, including prices and
markets, equity versus efficiency, Rawls versus Bentham,
accounting and the theory of the firm, optimal lot size and just
in time, monopoly and competition, exchange rates and the balance
of payments, inflation and unemployment, fiscal and monetary
policy, IS-LM analysis, aggregate demand and supply, speculation
and rational expectations, growth and development, exhaustible
resources and over-fishing. While the content is similar to that
of conventional introductory economics textbook, the assumption
that the reader knows and enjoys the calculus distinguishes this
book from the traditional text.
Contents:
Production Possibilities
Supply and Demand: Where do Prices come from?
Maximizing Satisfaction
The Business Enterprise: Theory of the Firm
Market Structure
Distribution: Who Gets What?
Monitoring Economic Performance
GDP Accounting and the Multiplier
Money, Prices and Output
Dynamics, Expectations and Inflation
Growth and Development
Readership: Undergraduates with a working knowledge of calculus;
graduate business school students with strong quantitative
skills; as a supplemental read for calculus-aware students
enrolled in a traditional micro or macro economics course; anyone
with a quantitative bent who enjoys reading about economics and
business developments in the popular press but wants to take a
deeper and more structured look at how economists analyze the way
the system works. This text does not presume prior course work in
economics.
"For two years I have used drafts of Lovell's text at the
Navel Academy. I have found it to be ideally suited for a one-semester
introductory course for mathematically-inclined students. This
text has several advantages over the conventional text in terms
of content and organization. The treatment of welfare economics
and the dynamics of growth Eto name but two examples Efar
exceeds the standard."
Matthew Baker
Department of Economics
United States Naval Academy
"Mike Lovell has written the book we would all like to write
for the students we would all like to teach. Organizing his
introductory text around the calculus and optimization, Lovell
achieves a streamlined presentation of essential concepts. This
economy leaves room for numerous, carefully crafted applications.
Lovell moves easily from classics, such as Edgeworth and
Hotelling, to recent innovations, such as rational expectations.
In the process he shows the introductory student the elegance and
power of the handful of concepts that underpins much of our
discipline. It will be a treat to teach from this text."
C M Jones
Department of Economics
Bowdoin College, USA
632pp Pub. date: Aug 2004
ISBN 981-238-825-7
ISBN 981-238-857-5(pbk)