ISBN: 97804864579235
Page Count: 368
Dimensions: 5 3/8 x 8 1/2
Written by a noted expert on logic and set theory, this study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Geared toward undergraduate and beginning graduate students, it requires minimal mathematical training. Numerous exercises and several helpful appendixes supplement the text. 1973 edition
ISBN: 9780486468945
Page Count: 192
Dimensions: 6 1/8 x 9 1/4
Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, it offers an accessible treatment that requires no previous knowledge of algebraic topology. 1963 edition.
Chapter 1. Knots and Knot Types
Chapter 2. The Fundamental Group
Chapter 3. The Free Groups
Chapter 4. Presentation of Groups
Chapter 5. Calculation of Fundamental Groups
Chapter 6. Presentation of a Knot Group
Chapter 7. The Free Calculus and the Elementary Ideals
Chapter 8. The Knot Polynomials
Chapter 9. Characteristic Properties of the Knot Polynomials
Appendix I. Differentiable Knots are Tame
Appendix II. Categories and groupoids
Appendix III. Proof of the van Kampen theorem
Guide to the Literature
Bibliography
Index
ISBN: 9780486468952
Page Count: 576
Dimensions: 6 1/8 x 9 1/4
This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition
The Elements of Perspective
The Extended Euclidean Plane
A Little Linear Algebra
Further Properties of the Extended Plane
Linear Transformation in II(subscript)2
The Axiomatic Foundation
The Complete Four-point and Complete Four-line
Conics
The Introduction of Coordinates
The Introduction of a Metric
Singular Metric Gauges
A Review of Determinants
A Finite Nondesarguesian Geometry
Answers to Odd-numbered Exercises
Index
ISBN: 97804864689843
Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. 1978 edition.
List of Symbols
1. What Is Symbolic Logic?
2. The Statement Calculus
3. The use of Names
4. Axiomatic Treatment of the Statement Calculus
5. Clarification
6. The Restricted Predicate Calculus
7. Equality
8. Descriptions
9. Class Membership
10. Relations and Functions
11. Cardinal Numbers
12. Ordinal Numbers
13. Counting
14. The Axiom of Choice
15. We Rest Our Case
A Proof of the Axiom of Infinity
The Axiom of Counting
The Axiom of Choice
Nonstandard Analysis
Bibliography
Index
ISBN: 0486468992
The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The first half presents a self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics. 1986 edition.
Part I. Basic Course
1. Calculus
2. Topology and Linear Spaces
3. Probability
Part II. Selected Applications
4. Stochastic Analysis
5. Hyperfinite Dirichlet Forms and Markov Processes
6. Topics in Differential Operators
7. Hyperfinite Lattice Models
ISBN: 978048646900X3
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties. 1987 edition.
Preface
Introduction
Introduction to FEM for elliptic problems
Abstract formulation of the finite element method for elliptic problems
Some finite element spaces
Approximation theory for FEM. Error estimates for elliptic problems
Some applications to elliptic problems
Direct methods for solving linear systems of equations
Minimization algorithms. Iterative methods
FEM for parabolic problems
Hyperbolic problems
Boundary element methods
Mixed finite element methods
Curved elements and numerical integration
References
Index
ISBN: 9780486469027
One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. Many helpful definitions, examples, and exercises appear throughout the book. 1975 edition.
Lagrangian Interpolates
Hermitian Interpolates
Polynomial Splines and Generalizations
Approximating Functions of Several Variables
Fundamentals for Variational Methods
The Finite Element Method
The Method of Collocation
Glossary of Symbols
Index