I get to teach real analysis this year! So I’ve been making notes for my students. We are working from Rudin, and we began by building the real numbers using Dedekind cuts. Each set of notes has a rough learning objective at the top. You can find them here:

Lecture 1_sv

Lecture 2_sv

Lecture 3_sv

Lecture 4_sv 131

Lecture 5_sv_131

Lecture 6_sv_131

Lecture 7_sv_131

LEcture 8_sv_131

Lecture 9_sv_131

Lecture 10_sv_131

Lecture 11_sv_131

Lecture 12_sv_131 more compact properties

Lecture 13_sv_131 Connected and compact

Lecture 14_sv_Conv seq

Lecture 15_sv_131 cauchy conv seq

Lecture 16_sv_131 Completion

Lecture 17_sv_131 limsupinf

Lecture 18_sv_131_series tests

Lecture 19_sv_131 Absolute convergence

Lecture 20_sv_131 Continuity and limits

Lecture 21_sv_131_Continuity consequences

Lecture 22_sv_131_uniform continuity

Lecture 23_sv_131_differentiability

Lecture 24_sv_131_Taylor and Uniform convergence

Lecture 25_sv_131_Function convergence