Introduction to Real Analysis
Calculus rebuilt on rigorous foundations.
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Real Numbers and Sequences
Completeness, suprema, sequence convergence, and Bolzano-Weierstrass.
Series with Rigor
Convergence proofs, absolute vs conditional convergence, and rearrangements.
Continuity and Uniform Continuity
Epsilon-delta arguments and consequences of continuity on intervals.
Rigorous Differentiation and the Riemann Integral
Mean value theorems and the construction of the integral.