ISBN: 9780486469034
Page Count: 400
Dimensions: 6 1/8 x 9 1/4
Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.
Topological Space
Convergence
Separation Axioms
Topological Concepts
Sup, Weak, Product, and Quotient Topologies
Compactness
Compactification
Complete Semimetric Space
Metrization
Uniformity
Topological Groups
Function Spaces
Miscellaneous Topics
Appendix, Tables of Theorems and Counterexamples
Bibliography
Index
ISBN: 97804864691313
Page Count: 384
Dimensions: 5 3/8 x 8 1/2
This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics. 1996 edition.
Part One: Preliminaries
Chapter 1. Building Proofs
Chapter 2. Finite, Infinite, and Even Bigger
Chapter 3. Algebra of the Real Numbers
Chapter 4. Ordering, Intervals, and Neighborhoods
Part Two: The Structure of the Real Number System
Chapter 5. Upper Bounds and Suprema
Chapter 6. Nested Intervals
Chapter 7. Cluster Points
Chapter 8. Topology of the Real Numbers
Chapter 9. Sequences
Chapter 10. Sequences and the Big Theorem
Chapter 11. Compact Sets
Chapter 12. Connected Sets
Part Three: Topics from Calculus
Chapter 13. Series
Chapter 14. Uniform Continuity
Chapter 15. Sequences and Series of Functions
Chapter 16. Differentiation
Chapter 17. Integration
Chapter 18. Interchanging Limit Processes
Part Four: Selected Shorts
Chapter 19. Increasing Functions
Chapter 20. Continuous Functions and Differentiability
Chapter 21. Continuous Functions and Integrability
Chapter 22. We Build the Real Numbers
References and further reading
Index
ISBN: 9780486469140
Page Count: 560
Dimensions: 6 1/2 x 9 1/4
This convenient single-volume compilation of two texts offers both an introduction and an in-depth survey. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. 1976 edition.
Vol. 1: Linear and Multilinear Algebra
Elementary Matrix Theory
Sets, Relations, and Functions
Groups, Rings and Fields
Vector Spaces
Linear Transformations
Determinants and Matrices
Spectral Decompositions
Tensor Algebra
Exterior Algebra
Vol. 2: Vector and Tensor Analysis
Euclidean Manifolds
Vector Fields and Differential Forms
Hypersurfaces in a Euclidean Manifold
Elements of Classical Continuous Groups
Integration of Fields on Euclidean Manifolds, Hypersurfaces, and Continuous Groups
Index
ISBN: 9780486469195
Page Count: 272
Dimensions: 6 1/8 x 9 1/4
This three-part treatment focuses on elliptic and evolution equations. Largely self-contained, this volume concludes with a series of independent topics related to the methods and results of preceding sections and introduces advanced topics for further study. Geared toward graduate and postgraduate students, it also constitutes a valuable reference for professionals. 1969 edition.
ISBN: 9780486469218
Page Count: 192
Dimensions: 6 1/8 x 9 1/4
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Zermelo-Fraenkel Set Theory
The Consistsency of the Continuum Hypothesis and the Axiom of Choice
The Independence of the Continuum Hypothetis and the Axiom of Choice
References
ISBN: 9780486469317
Page Count: 272
Dimensions: 5 3/8 x 8 1/2
Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition.
Integers
Unique Factorization
Linear Diophantine Equations
Congruences
Linear Congruences
Fermat's and Wilson's Theorems
The Divisors of an Integer
Perfect Numbers
Euler's Theorem and Function
Primitive Roots
Quadratic Congruences
Quadratic Reciprocity
Numbers of Other Bases
Duodecimals
Decimals
Pythagorean Triangles
Infinite Descent and Fermat's Conjecture
Sums of Two Squares
Sums of Four Squares
x(superscript 2) - Ny(superscript 2) = 1
Bounds for pi(x)
Formulas for Primes
Additional problems
Proof by Induction
Computer Problems
Factor Table for Integers Less Than 10,000
References
Answers to Selected Exercises
Answers to Selected Odd-Numbered Problems
Comments on Selected Odd-Numbered Problems
Index