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Foundations of Modern Mathematics - Table of Contents

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