ISBN: 1-58488-515-7
Publication Date: 1/27/2005
Number of Pages: 696
Provides sufficient material to design a one or two semester
course
Emphasizes concrete, particular problems
Incorporates many quick exercises throughout the text to provide
immediate reinforcement of ideas along with extensive exercise
set at the end of each chapter
Includes a new section on Galois theory
This text is for traditional undergraduate abstract algebras
courses. Taking a more natural approach than other texts, it
starts with a study of factoring in the integers, modular
arithmetic, and polynomials over the rational numbers. With this
rich fund of examples, it is then easier to consider rings, the
first abstract structure encountered. Emphasizing concrete,
particular problems, the authors incorporate numerous quick
exercises to provide immediate reinforcement of ideas and to make
the text easier to read. Each chapter ends with some warm-up
exercises plus numerous other exercises, both computational and
theoretical. A final section on Galois theory emphasizes
subfields of the complex numbers.
ISBN: 1-58488-467-3
Publication Date: 4/26/2005
Number of Pages: 480
Provides an easy-to-read, easy-to-use introduction to using the
latest version of Mathematica
Teaches by example, showing users how basic operations, like
computing an integral, can be accomplished
Focuses on errors novices will likely encounter, presenting
illustrative examples and describing how to deal with those
situations
Includes a quick-reference guide in each chapter
Although powerful and very popular in science and engineering,
Mathematica can be difficult to learn because of its large
command structure and intricate syntax. This book offers a
simple, step-by-step approach to help newcomers to Mathematica
build the skills needed to use the software in practice. Aimed at
professionals with a good mathematics background, this book
teaches by example, pointing out potential pitfalls along the way.
In an easy-to-use format not found in other books and with a
quick-reference guide in each chapter, it covers many of the
general areas of mathematics, including entering equations,
plotting, computing ordinary and partial differential equations,
and linear algebra.
Table of Contents
Introduction. Limits and Differentiation. Differential Equations.
Computing Integrals. More Integration and Computing Transforms.
Basic Linear Algebra: Matrices and Vectors. Working with Special
Functions and Special Polynomials. Basic Numerical Programming
Series: Chapman & Hall/CRC Applied Mathematics &
Nonlinear Science
ISBN: 1-58488-531-9
Publication Date: 7/26/2005
Number of Pages: 288
Includes systematic presentation of fuzzy system theories and
methodologies from the fundamentals through applications
Provides an in-depth treatment of fuzzy sets, fuzzy logic and
fuzzy control systems
Requires no previous background in fuzzy mathematics
To keep pace with and further advance the rapidly developing
field of applied control technologies, this book provides
systematic training in analytic theory and rigorous design of
fuzzy systems. Almost entirely self-contained, it establishes a
brief, yet sufficient foundation for designing and analyzing
fuzzy intelligent and control systems. It clearly explains fuzzy
sets, fuzzy logic, fuzzy inference, approximate reasoning, fuzzy
rule base, basic fuzzy PID control systems, and more. This handy
reference guide includes teaching examples as well as problem
exercises, and it can easily be used as a classroom text or
tutorial for self-study that will prepare readers for further
work in the field.
Table of Contents
Fuzzy Sets. Fuzzy Logic. Fuzzy Inference. Fuzzy Rule Base.
Intelligent Decision-Making. Fuzzy Modeling. Fuzzy Control
Systems.
Series: Discrete Mathematics and Its Applications
ISBN: 1-58488-518-1
Publication Date: 5/15/2005
Number of Pages: 512
Provides an exhaustive, state-of-the-art study of the
mathematical aspects of public key cryptography
Covers both theory and applications
Focuses on primitives based on geometric constructions, such as
elliptic and hyperelliptic curves and on methods that presume
knowledge of the group order and its factorization
Includes practical details on implementation
Contains information on standards and legal issues
Elliptic and Hyperelliptic Curve Cryptography is the first
exhaustive study of virtually all of the mathematical aspects of
public key cryptography based on the discrete log system. This
carefully constructed volume is a state-of-the-art study that
explores both theory and applications. The book covers most
aspects of elliptic curves and hyperelliptic curve cryptography
and provides a detailed study on the smart card, including
information on its main components, electronic properties, and
attacks on the embedded memory. Standards on elliptic curve
cryptography are provided along with information on some of the
legal aspects of cryptography in the European Union and the
United States.
Table of Contents
Introduction. Basic Blocks. Background on Finite Fields.
Background on p-adic Numbers. Background on Curves and Jacobians.
Background on Point Counting. Background on Complex
Multiplication. Background on Pairings. Background on Weil
Descent. Arithmetic of Elliptic Curves. Arithmetic of
Hyperelliptic Curves. Arithmetic of Special Curves. Generic
Attacks. Point Counting on Elliptic and Hyperelliptic Curves.
Implementation of Complex Multiplication. Implementation of
Pairings. Implementation of Weil Descent. Primality Testing and
Proving, Factorization. Computing Discrete Logarithms by Index
Calculus. Security of Systems Based on the DLP on EC and HEC. ID-based
Cryptography and Tripartite Key-exchange. Integer Arithmetic.
Polynomial and Power Series Arithmetic. Exponentiation. Finite
Field Arithmetic. P-adic Arithmetic. Random Number Generator.
Mathematical Countermeasures Against Side-channel Attacks.
Hardware.
Series: Discrete Mathematics and Its Applications
ISBN: 1-58488-482-7
Publication Date: 5/26/2005
Number of Pages: 256
Examines the theory of diophantine approximation and the theory
of diophantine equations with emphasis on the interactions
between these subjects
Includes many new topics related to discrete mathematics,
including factoring large integers, error-free computing, and
factoring polynomials
Provides problem sections at the end of every chapter where open
problems and conjectures are discussed
Addresses many new topics such as Apery's proof of irrationality,
polynomial Pell equation, and the abc-conjecture
Diophantine analysis is an extremely active field in number
theory because of its many open problems and conjectures.
Requiring only a basic understanding of number theory,
Diophantine Analysis is built around the detailed theory of
continued fractions and features many applications and examples.
The author includes many new topics related to discrete
mathematics, such as factoring large integers, error-free
computing, and factoring polynomials. He also provides problem
sections at the end of each chapter, where open problems are
discussed along with other new topics, such as Apery's proof of
irrationality, the polynomial Pell equation, and the abc-conjecture.
Table of Contents
Introduction: basic principles. Classical approximation theorems.
Continued fractions. The irrationality of C(3). Quadratic
irrationals. The Pell equation. Factoring with continued
fractions. Transcendental numbers. The theorem of Roth. The abc-conjecture.
P-adic numbers. The local-global principle. Hensel's lemma.