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Foundations of Modern Mathematics - Table of Contents
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Preface
Table of Contents
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Offering: Foundations of Modern Mathematics
Titles: Foundations of Modern Mathematics
By Dr. Lee Keener
1. Basics
1.1 - Introduction
1.2 - Finite Geometries
1.3 - The Natural Numbers and the Integers
1.4 - Elementary Number Theory
1.5 - The Rational Numbers
1.6 - Exponentiation
1.7 - Sequences and the Real Number System
1.8 - The Complex Numbers
1.9 - Sequences and Series of Complex Numbers
1.10 - Fields
1.11 - Linear Spaces
1.12 - Continuity and Metric Topology
1.13 - Differentiation
1.14 - Integration
1.15 - The Fundamental Theorem of Algebra
1.16 - Countable and Uncountable Sets
1.17 - Irrational Numbers
2. Additional Topics
2.1 - Groups
2.2 - Rings and Euclidean Rings
2.3 - The Distribution of Primes
2.4 - The Weierstrass Approximation Theorem
2.5 - Inner Product Spaces and Fourier Series
2.6 - Graph Theory
2.7 - Brouwer's Fixed Point Theorem
2.8 - Measure Theory
2.9 - Geometric Constructions
2.10 - Euclidean and Non-Euclidean Geometry
2.11 - Non-standard Analysis
2.12 - Appendix I: A Summary of Axiomatic Set Theory
2.13 - Appendix II: Reading in the Literature
2.14 - Appendix III: The Greek Alphabet