Tentative topics are: Real numbers (algebraic, order and distance structures); Archimedean property; Sequences and their limits. Bolzano-Weierstrass theorem; Cauchy sequences and completeness; Limit ...

Assuming only undergraduate real analysis and following the power series approach, it quickly and elegantly develops the basic theory through Cauchy's theorem for cycles, normal families, the Riemann ...

Real analysis: inequalities, the continuum property, induction, sequences, functions and limits, continuity, contraction mappings and fixed points, differentiation, mean value theorems and Taylor's ...