Intro Real Analysis, Lec 11: Continuity and the Intermediate Value Theorem (climbing Monk Story)

Lecture 11.

(0:00) Announcements.
(0:24) The Story of a Monk on a Mountain (will be at exactly the same point at the same time on two different days, by continuity and the IVT).
(5:23) The Intermediate Value Theorem statement.
(11:13) Outline of how to apply it to proving a certain polynomial has at least three real roots.
(18:32) Scratchwork to prove a fact about a limit of a rational function (it ends up being harder than I thought it would be at first and I end up just thinking about a special case).
(33:57) Epsilon delta definition of continuity at a point.
(38:25) The essence of continuity and ways a function can fail to be continuous at a point.
(43:12) Functions with holes come up in calculus.
(46:08) Continuity of arithmetic combinations of functions.
(48:06) Continuity of a composition (best proved using the relationship between limits of sequences and limits of functions).
(52:54) Theorems as work-saving devices for complicated situations.

Bill Kinney, Bethel University Department of Mathematics and Computer Science. St. Paul, MN.

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[Kiran_C_Nayak]

0:24 that monk analogy is simply amazing !!

[TheJProductins]

Wow that story made the property 10000 clearer OMG

[BillShillito]

This is an excellent series. I've been looking for a good video series for Real Analysis for a while, and I have very much found it. It's a refreshing deviation from the typical cycle, with discussions of why the material is useful in terms of understanding mathematics as a whole, as well as actual examples (which often seem to be absent from too many textbooks). It's amazing what a Mathematica graph will do in terms of SEEING the thing that you're trying to learn about!

Thank you for posting these!

[shivanisingla]

thanks for explaining the concepts without sounding them as" concepts"😅 plz if you can upload for modern algebra