1　Real Numbers
1　Preliminaries
2　Cuts
3　Euclidean Space
4　Cardinality
5* Comparing Cardinalities
6* The Skeleton of Calculus
Exercises
2　A Taste of Topology
1　Metric Space Concepts
2　Compactness
3　Connectedness
4　Coverings
5　Cantor Sets
6* Cantor Set Lore
7* Completion
Exercises
3　Functions of a Real Variable
1　Differentiation
2　Riemann Integration
3　Series
Exercises
4　Function Spaces
1　Uniform Convergence and C0[a, b]
2　Power Series
3　Compactness and Equicontinuity in CO
4　Uniform Approximation in Co
5　Contractions and ODEs
6* Analytic Functions
7* Nowhere Differentiable Continuous Functions
8* Spaces of Unbounded Functions
Exercises
5　Multivariable Calculus
1　Linear Algebra
2　Derivatives
3　Higher derivatives
4　Smoothness Classes
5　Implicit and Inverse Functions
6* The Rank Theorem
7* Lagrange Multipliers
8　Multiple Integrals
9　Differential Forms
10　The General Stokes Formula
11* The Brouwer Fixed Point Theorem
Appendix A: Perorations of Dieudonne
Appendix B: The History of Cavalieris Principle
Appendix C: A Short Excursion into
the Complex Field
Appendix D: Polar Form
Appendix E: Determinants
Exercises
6　Lebesgue Theory
1　Outer measure
2　Measurability
3　Regularity
4　Lebesgue integrals
5　Lebesgue integrals as limits
6　Italian Measure Theory
7　Vitali coverings and density points
8　Lebesgues Fundamental Theorem of Calculus
9　Lebesgues Last Theorem
Appendix A: Translations and Nonmeasurable sets
Appendix B: The Banach-Tarski Paradox
Appendix C: Riemann integrals as undergraphs
Appendix D: Littlewoods Three Principles
Appendix E: Roundness
Appendix F: Money
Suggested Reading
Bibliography
Exercises
Index