Hastie, T., University of Stanford, CA, USA Tibshirani, R., University of Stanford, CA, USA Friedman, J., University of Stanford, CA, USA

The Elements of Statistical Learning
Data Mining, Inference, and Prediction

2001. Approx. 550 pp. 200 figs. in color. Hardcover
0-387-95284-5

Keywords: Data Mining, Inference, Prediction

Contents: Overview of Supervised Learning.- Linear Methods for Regression.- Linear Methods for Classification.- Basic Expansions and Regularization.- Kernel Methods.- Model Assessment and Selection.- Model Inference and Averaging.- Additive Models, Trees, and Related Methods.- Boosting and Additive Trees.- Neural Networks.- Support Vector Machines and Flexible Discriminates.- Prototype Methods and Nearest Neighbors.- Unsupervised Learning.

Series: Springer Series in Statistics.

Moeschlin, O., FernUniversitat Hagen, Germany Grycko, E., FernUniversitat Hagen, Germany Poppinga, C., FernUniversitat Hagen, Germany Steinert, F., FernUniversitat Hagen, Germany

Discrete Stochastics

2001. CD-ROM. With booklet approx. 100 pp.
3-540-14913-9

This (electronic) textbook is based on courses on probability theory developed by O.Moeschlin. The aim of the present textbook is to describe the typical ways of thinking and the working methods of stochastics on an intermediate level. A problem in this context is the fact that probability theory dealing with continuous occurence spaces uses measure and integration theory to a high degree. This implies a considerable complication, which is hardly consistent, with the objective of an introduction. The way out taken here is to use a discrete occurence space. The formulations and notations are kept in such a way that they can be extended in a straightforward way to the general theory. The text is accompanied by several exercises as well as solutions. This textbook comes on a fully linked CD-ROM together with fifteen so-called experiments, i.e. screen visualizations especially of complex notions and facts. For the sake of a comfortable reading it is accompanied by a printed text.

Keywords: probability theory, discrete occurence spaces, measure theory

Contents: 1. Basics.- 2. Combinatorics.- 3. Random Experiments and Relative Frequencies.- 4. Discrete Probability Spaces.- 5. Examples for Probability Measures.- 6. Conditional Probabilities.- 7. Probability Measures on Product Spaces.- 8. Random Variables and Distributions.- 9. Stochastic Independence Convolutions.- 10. Expectations.- 11. Variance and Covariance.- 12. The Chebyshev Inequality.

System requirements: Software requirements: operation system Windows 95/98/NT, internet explorer 4 (or higher) or Netscape 4.0 (or higher); minimal hardware requirements: pentium PC, 32 MB RAM, CD-ROM drive, screen size 1024x768

Eisenbud, D., MSRI, Berkeley, CA, USA Grayson, D., University of Illinois at Urbana-Champaign, Urbana, IL, USA Stillman, M., Cornell University, Ithaca, NY, USA Sturmfels, B., University of California, Berkeley, CA, USA (Eds.)

Computations in Algebraic Geometry with Macaulay 2

2001. XVI, 329 pp. Hardcover
3-540-42230-7

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics.

Keywords: algebraic geometry, commutative algebra, symbolic algebra, Groebner bases, syzygies

Contents: Part I. Introducing Macaulay 2: 1. Ideals, Varieties and Macaulay 2 by Bernd Sturmfels.- 2. Projective Geometry and Homological Algebra by David Eisenbud.- 3. Data Types, Functions, and Programming by Daniel R. Grayson and Michael E. Stillman.- 4. Teaching the Geometry of Schemes by Gregory G. Smith and Bernd Sturmfels.- Part II. Mathematical Computations: 5. Monomial Ideals by Serkan Hosten and Gregory G. Smith.- 6. From Enumerative Geometry to Solving Systems of Polynomial Equations by Frank Sottile.- 7. Resolutions and Cohomology over Complete Intersections by Luchezar L. Avramov and Daniel R. Grayson.- 8. Algorithms for the Toric Hilbert Scheme by Stillman, Bernd Sturmfels, and Rekha Thomas.- 9. Sheaf Algorithms Using the Exterior Algebra by Wolfram Decker and David Eisenbud.- 10. Needles in a Haystack: Special Varieties via Small Fields by Frank-Olaf Schreyer and Fabio Tonoli.- 11.D-modules and Cohomology of Varieties by Uli Walther.

Series: Algorithms and Computation in Mathematics. VOL. 8

Delfs, H., University of Applied Sciences, Nurnberg, Germany
Knebl, H., University of Applied Sciences, Nurnberg, Germany

Introduction to Cryptography
Principles and Applications

2001. Approx. 300 pp. Hardcover
3-540-42278-1

Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data. This book presents the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols, such as electronic elections and digital cash. In the second part, probability theory is applied to make basic notions precise, such as the security of cryptographic schemes. More advanced topics are also addressed, such as the bit security of one-way functions and computationally perfect pseudo-random generators. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed.

Keywords: Information security, cryptography, cryptology, cryptanalysis, data encryption, security proofs, cryptographic protocols, algorithms

Contents: 1. Introduction; 2. Symmetric-Key Encryption; 3. Public-Key Cryptography; 4. Cryptographic Protocols; 5. Probabilistic Algorithms; 6. One-Way and Trapdoor Functions; 7. Bit-Security of One-Way Functions; 8. One-Way Functions and Pseudo-Randomness; 9. Provably Secure Encryptions; 10. Provably Secure Digital Signatures; A. Algebra and Number Theory; B. Probabilities and Information Theory; References; Index.

Demri, S.P., Laboratoire Specification et Verification, Cachan, France
Orlowska, E.S., National Institute of Telecommunications, Warsaw, Poland

Incomplete Information: Structure, Inference, Complexity

2001. XVIII, 401 pp. Hardcover
3-540-41904-7

This monograph presents a systematic, exhaustive and up-to-date overview of formal methods and theories for data analysis and inference inspired by the concept of rough set. The book studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information is needed in the process of analysis without external sources of information being required.
The book is intended for researchers, lecturers and graduate students who wish to get acquainted with the rough set style approach to information systems with incomplete information.

Keywords: Incomplete information, information system, rough set, deduction, complexity

Series: Monographs in Theoretical Computer Science. An EATCS Series

Molloy, M.S.O., University of Toronto, ON, Canada Reed, B.A., Universite de Paris VI, France

Graph Colouring and the Probabilistic Method

2001. Approx. 450 pp. 115 figs. Hardcover
3-540-42139-4

Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using the Lovasz Local Lemma and Concentration Inequalities developed by Talagrand.
The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings.
This gentle introduction to the probabilistic method will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probabilists.

Keywords: graphs, graph colouring, probabilistic method, algorithms

Contents: Colouring Preliminaries.- Probabilistic Preliminaries.- The First Moment Method.- The Lovasz Local Lemma.- The Chernoff Bound.- Hadwiger's Conjecture.- A First Glimpse of Total Colouring.- The Strong Chromatic Number.- Total Colouring Revisited.- Talagrand's Inequality and Colouring Sparse Graphs.- Azuma's Inequality and a Strengthening of Brooks'Theorem.- Graphs with Girth at Least Five.- Triangle-Free Graphs.- The List Colouring Conjecture.- A Structural Decomposition.- Omega,Delta, and Chi.- Near Optimal Total Colouring I: Sparse Graphs.- Near Optimal Total Colouring II: General Graphs.- Generalizations of the Local Lemma.- A Closer Look at Talagrand's Inequality.- Finding Fractional Colourings and Large Stable Sets.- Hardcore Distribution on Matchings.- The Asymptotics of Edge Colouring Multigraphs.- The Method of Conditional Expectation.- Algorithmic Aspects of the Local Lemma.

Series: Algorithms and Combinatorics. VOL. 23