LEARNING OUTCOMES

Conducting students to address mathematical development issues through a critically acclaimed understanding in a personal way.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

Foundations of analysis

Problems related to the concepts of convergence and continuity

Trigonometric series and uniform convergence

Riemann's definition of integral

Dedekind's construction of real numbers

Weierstrass's work

Cantor's Mengenlehre

The first steps

Non-countability of R

One-to-one correspondence between R and Rn

Cardinals and ordinals

The continuum hypothesis

Further developments

Well-ordered sets

The axiom of choice

The antonomies of the infinite

Genesis of measure theory

Hausdorff's work

The conundrum of "dimension"

Hausdorff's and Banach-Tarski's paradoxes

Zermelo-Fraenkel's axioms