Jon Barwise, John Etchemendy

Turing's World 3.0 for Windows

the Center for the Study of Language and Information Publication Lecture Notes series

Description
Turingfs World is a self-contained introduction to Turing machines, one of the fundamental notions of logic and computer science. The text and accompanying diskette allow the user to design, debug, and run
sophisticated Turing machines in a graphical environment.

Turingfs World introduces users to the key concepts in computability theory through a sequence of over 100 exercises and projects. Within minutes, users learn to build simple Turing machines using a convenient package
of graphical functions. Exercises then progress through a significant portion of elementary computability theory, covering such topics as the Halting problem, the Busy Beaver function, recursive functions and undecidability. Version 3.0 is an extensive revision and enhancement of earlier releases of the program, allowing the construction of one-way and two-way finite state machines (finite automata), as well as non-deterministic Turing and finite-state machines. Special exercises allow users to expore these alternative
machines.

Chapter Contents
1. About Turing machines; 2. Running Turingfs machines; 3. Building Turingfs machines; 4. Editing a state diagram; 5. Using submachines; 6. Other features of Turingfs world; 7. Other kinds of machines; 8. Additional exercises and projects; Appendix: Windows terminology; Index

Binding: Paperback

ISBN: 1881526887

A. W. van der Vaart

Asymptotic Statistics

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit
experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a
novel way. Suitable as a text for a graduate or Masterfs level statistics course, this book will also give researchers in statistics, probability, and their applications an overview of the latest research in asymptotic statistics.

Chapter Contents
1. Introduction; 2. Stochastic convergence; 3. The Delta method; 4. Moment estimators; 5. M- and Z-estimators; 6. Contiguity; 7. Local asymptotic normality; 8. Efficiency of estimators; 9. Limits of experiments; 10. Bayes procedures; 11. Projections; 12. U-statistics; 13. Rank, sign, and permutation statistics; 14. Relative efficiency of tests; 15. Efficiency of tests; 16. Likelihood ratio tests; 17. Chi-square tests; 18. Stochastic convergence in metric spaces; 19. Empirical processes; 20. The functional Delta method; 21. Quantiles and order statistics; 22. L-statistics; 23. The bootstrap; 24. Nonparametric density estimation; 25. Semiparametric models.

Binding: Paperback
Also available as Hardback

ISBN: 0521784506

Oskar Bolza

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Lectures on the Calculus of Variations: Third Edition

Description

Based on lectures delivered at the AMS meeting in 1901, this book describes the progress in calculus of variations made in the last 30 years of the
nineteenth century. Among other topics, the author describes the landmark results of Weierstrass on sufficient conditions for the extremum of a
functional in terms of the second variation. Also discussed are Kneser's sufficient conditions, Weierstrass's theory of the isoperimetric problem, and
Hilbert's theorem on the existence of an extremum of an integral. Although the original book was written nearly 100 years ago, it remains very
useful in learning about classical calculus of variations.

Contents

The first variation of the integral $\int_{x_0}^{x_1}F(x,y,y')dx$
The second variation of the integral $\int_{x_0}^{x_1}F(x,y,y')dx$
Sufficient conditions for an extremum of the integral $\int_{x_0}^{x_1}F(x,y,y')dx$
Weierstrass's theory of the problem in parameter representation
Kneser's theory
Weierstrass's theory of the isoperimetric problems
Hilbert's existence theorem
Index

Details:

Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS Chelsea Publishing
Publication Year: 1973
ISBN: 0-8218-2144-X
Paging: 269 pp.
Binding: Hardcover