- 자료제공 :
- 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.