Peter G. Hinman

Fundamentals of Mathematical Logic

Summary

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Godel’s Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory.

Based on the author’s more than 35 years of teaching experience, the book develops students’ intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Details

ISBN: 1-56881-262-0
Year: 2005
Format: Hardcover
Pages: 896

Reviews

“I expect this book to become the standard graduate logic text for the new century, based on the enthusiastic reception from students in our course last year.”

Doug Cenzer

Recommendations

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Barrett O'Neill
University of California, Los Angeles, California, U.S.A.

Elementary Differential Geometry, Revised 2nd Edition

Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces.

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

Contents

Preface
Introduction
Chapter 1: Calculus on Euclidean Space:
Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds.
Chapter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution.
Chapter 6: Geometry of Surfaces in R3:
The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces.
Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet.
Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.
Appendix
Bibliography
Answers to Odd-Numbered Exercises
Subject Index

Rudolf Freund / William Wilson / Ping Sa

Regression Analysis , Second Edition

Complete discussion of analysis of data including
estimation, diagnostics, and remedial actions

Examples and exercises contain real data and
graphical illustration for ease of interpretation

Outputs from SAS 7, SPSS 7, Excel, and Minitab are
used for illustration, but any major statistical
software package will work equally well

Data sets are furnished on data diskette and on web page

Reviews

"...is well-written , well-organized, and succeeds in making regression analysis understandable, without being overly technical." Donice McCune, Stephen F. Austin University

"I would say that this book is excellent from both a pedagogical perspective and a learning perspective (by the student). The instructor will enjoy discussing various concepts and then illustrating the concepts through the thorough examples. 6. This textbook will help give the students additional mathematical maturity for handling other statistics courses, especially applied courses like Analysis of Variance." Steven Garren, James Madison University

Description

The book provides complete coverage of the Aclassical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.

Contents

1. The Analysis of Means: A Review of Basics and an
Introduction to Linear Models
2. Simple Linear Regression:Linear Regression with
One Independent Variable
3. Multiple Regression
4. Problems with Observations
5. Multicollinearity
6. Problems with the Model
7. Curve Fitting
8. Introduction to Nonlinear Models
9. Indicator Variables
10. Categorical Response Variables
11. Generalized Linear Models
Appendix A: Statistical Tables
Appendix B: A Brief Introduction to Matrices
Appendix C: Estimation Procedures
References

Readership: Because of the universal appeal of statistics and statistical methodology, most graduate programs include as part of their curriculum one or two course in statistical methods. In addition, undergraduate students majoring in mathematics or statistics are required or encouraged to take courses in statistical methods. This book is intended to serve as a text for such courses. The book requires no mathematics beyond algebra, however, mathematically oriented students will still find the material in the text challenging.

ISBN: 0-12-088597-2 Book/Hardback
Line Illustrations: 84
Measurements: 7 1/2 X 9 1/4 in
Pages: 464
10 March 2006

E. A. Maxwell

Fallacies in Mathematics

Paperback (ISBN-10: 0521026407 | ISBN-13: 9780521026406)
Hardback (ISBN-10: 0521057000 | ISBN-13: 9780521057004)

January 2006

As Dr Maxwell writes in his preface to this book, his aim has been to instruct through entertainment. ‘The general theory is that a wrong idea may often to exposed more convincingly by following it to its absurd conclusion than by merely announcing the error and starting again. Thus a number of by-ways appear which, it is hoped, may amuse the professional, and help to tempt back to the subject those who thought they were losing interest’. The standard of knowledge expected is fairly elementary. In most cases a straightforward statement of the fallacious argument is followed by an exposure in which the error is traced to the most elementary source, and this process often leads to an analysis which is often of unexpected depth. Many students will discover just how mathematically-minded they are when they read this book; nor is that the only discovery they will make. Teachers of mathematics in schools and technical schools, colleges and universities will also be sure to find something here to please them.

Contents

Preface; 1. The mistake, the howler and the fallacy; 2. Four geometrical fallacies enunciated; 3. Digression on elementary geometry; 4. The ‘Isoceles Triangle’ fallacy analysed; 5. The other geometrical fallacies analysed; 6. Some fallacies in algebra and trigonometry; 7. Fallacies in differentiation; 8. Fallacies in integration; 9. Fallacy by the circular points at infinity; 10. Some ‘Limit’ fallacies; 11. Some miscellaneous howlers.

Edited by Andrew Ranicki

Noncommutative Localization in Algebra and Topology

Series: London Mathematical Society Lecture Note Series (No. 330)
Paperback (ISBN-10: 052168160X | ISBN-13: 9780521681605)
January 2006

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

Contents

Dedication; Preface; Historical perspective; Conference participants; Conference photo; Conference timetable; 1. On flatness and the Ore condition J. A. Beachy; 2. Localization in general rings, a historical survey P. M. Cohn; 3. Noncommutative localization in homotopy theory W. G. Dwyer; 4. Noncommutative localization in group rings P. A. Linnell; 5. A non-commutative generalisation of Thomason’s localisation theorem A. Neeman; 6. Noncommutative localization in topology A. A. Ranicki; 7. L2-Betti numbers, isomorphism conjectures and noncommutative localization H. Reich; 8. Invariants of boundary link cobordism II. The Blanchfield-Duval form D. Sheiham; 9. Noncommutative localization in noncommutative geometry Z. Skoda.