# How to teach real analysis?

I am recently going to make a series of videos about real analysis and measure theory. I wonder if anyone can give me some suggestions on how to arrange the material of the course. Should I introduce abstract concepts(such as measure, $\sigma$-field, metric space, etc.)first, or can I start with some interesting examples?

My intended audience includes those who have already studied basic analysis course and know something about theoretical physics.

• Could you list a few of those interesting examples? That might help the advice you get here. Are these examples meant to surprise students about new concepts? Or show them something they didn't know about familiar items (subsets of real numbers)? Something else? – Nick C Jan 16 '18 at 23:29
• What background are you expecting your intended viewer to have? – David Steinberg Jan 16 '18 at 23:46
• Personally, I find that if I haven't taught a class before, the best strategy (for me) is to find a book that I like, and parallel their approach. As I become more familiar with the strengths and weaknesses of that approach, I'll make change where I see fit. In that spirit, I might recommend Royden, but suggest that you stay away from Folland (though, to be fair, I like Folland's approach, just not the pathological terseness). McDonald and Weiss is also an option, as they are more example-forward (though you might want to trim the redundancy of chapter 4). – Xander Henderson Jan 17 '18 at 3:23
• It may be foolish to make a series of videos like this if you have never taught the course to real live students. – Gerald Edgar Jan 17 '18 at 13:29
• @GeraldEdgar But bear in mind that NOT everyone has a chance to teach live students. – Ma Joad Jan 17 '18 at 22:11