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The Number Systems: Foundations of Algebra and Analysis

Solomon Feferman
Publisher: 
American Mathematical Society
Publication Date: 
2003
Number of Pages: 
418
Format: 
Hardcover
Edition: 
2
Price: 
51.00
ISBN: 
978-0-8218-2915-8
Category: 
General
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

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  • The Logical Background: 1.1 Introduction; 1.2 Logic
  • The Set-Theoretical Background: 2.1 Sets; 2.2 An algebra of sets; 2.3 Relations and functions; 2.4 Mathematical systems of relations and functions
  • The Positive Integers: 3.1 Basic properties; 3.2 The arithmetic of positive integers; 3.3 Order; 3.4 Sequences, sums and products
  • The Integers and Integral Domains: 4.1 Toward extending the positive integers; 4.2 Integral domains; 4.3 Construction and characterization of the integers; 4.4 The integers as an indexing system; 4.5 Mathematical properties of the integers; 4.6 Congruence relations in the integers
  • Polynomials: 5.1 Polynomial functions and polynomial forms; 5.2 Polynomials in several variables
  • The Rational Numbers and Fields: 6.1 Toward extending integral domains; 6.2 Fields of quotients; 6.3 Solutions of algebraic equations in fields; 6.4 Polynomials over a field
  • The Real Numbers: 7.1 Toward extending the rationals; 7.2 Continuously ordered fields; 7.3 Infinite series and representations of real numbers; 7.4 Polynomials and continuous functions on the real numbers; 7.5 Algebraic and transcendental numbers
  • The Complex Numbers: 8.1 Basic properties; 8.2 Polynomials and continuous functions in the complex numbers; 8.3 Roots of complex polynomials
  • Algebraic Number Fields and Field Extensions: 9.1 Generation of subfields; 9.2 Algebraic extensions; 9.3 Applications to geometric construction problems; 9.4 Conclusion
  • Appendix I: Some axioms for set theory
  • Appendix II: The analytical basis of the trigonometric functions
  • Bibliography
  • Index
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