CODE 35288 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/04 TEACHING LOCATION GENOVA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW Language: Italian AIMS AND CONTENT 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 TEACHERS AND EXAM BOARD CLAUDIO BARTOCCI Exam Board CLAUDIO BARTOCCI (President) PIERRE OLIVIER MARTINETTI NICOLA PINAMONTI (President Substitute) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule HISTORY OF MATHEMATICS EXAMS EXAM DESCRIPTION Oral.