Introduction to Math Analysis (Lecture 1): The Need for Real Numbers

This is the first lecture in a course titled "Intro to Math Analysis". This is a test video, but with any luck, the full sequence of lectures will be published at some point.

[SteamPunkLV]

"Any idea what you signed up for"
*silence*

[bclan]

To make the "incommensurability crisis" more concrete, what the Greeks discovered is that there is no ruler, no matter how small its subdivisions, that can measure exactly both the side of a square and its hypotenuse (there will always be some remainder or leftover).
Equivalently there is no standard of length, no matter how small, that can fit evenly a finite number of times in both the side of a square and its hypotenuse.
Before the discovery of √2, the Greeks assumed that for any two line segments, represent them by 'a' and 'b', there exists some length 'c' such that a = c*k, b = c*m, where k, m are positive integers. That is, any two lengths are commensurable.

[vymann]

I've got a master in electrical engineering back in 1987, I've worked in electrical distribution for 35 years and didn't need any of the differential or integral calculation at wall.
I've also learned that the scientists and researchers are earning just a fraction of an engineer salary
However mathematical analysis is a beauty.

[kaizokulife]

Thank you very much for explaining the intuitive reasoning for getting the exact identity which shows there is always a number bigger than 'r'. I was dying to understand it. Thank you very much and thank you again.

[joeyphar]

I've been looking for a good explanation of how Rudin came about that number s (he calls it q in his book), and I thank you for showing it, unlike other lecture series using his book. It motivates me to come up with such simple yet brilliant arguments!

[victorsauvage]

Makes clear abstract notion of "number" or "space" -- profound but clear -- could teach the most abstract concepts to the completely unmathematical.

[greatloverofmusic]

It would be great if you uploaded lectures on methods of proof. Thanks. Great videos. Cheers.

[imraulemmaka]

please upload the full sequence of lectures

[duckyoutube]

Wow your website is very good. Thank you so much for the free education!!!

[EvaSlash]

Do you have any expertise in the field of statistics? Can a course in Real Analysis help understand statistics better? If so, how?

[galibrahman]

The audio from the GoPro is terrible. Perhaps use a separate microphone if you wish to use that device for recording lectures- but the camcorder used to the record majority of the video is okay.

[capybara-iypv]

Nice video.
At 16:10, if p | a*b then p | a or p | b, I think this is called Euclid's lemma.

[sayantan]

+Prof Etkin Hi I have seen you have a complete set of video lectures for "Analysis2" - which is more advanced ( metric spaces and all sort of things ), do you have similar video series for "Analysis1" -- I believe "Analysis1" will be more gentle by keeping the theorems and proofs restricted to Real line ---- It would be really helpful if you can please upload videos of your courses which are designed with this aspect

[llvallejoll]

Is there a chance to upload subtitles?

[maxpercer]

Did you ever publish the full sequence of lectures, or upload the notes which you have on the projector.Thanks :)

[maxpercer]

6:57 by similar triangles we have b/1 = k/a, then k = ab

[arurukshu]

Could u recomend me a calculus I, II, III text? I want to take analysis in future. Which book will be best for calculus? I m self learning at this point.

[mathsbyankitb]

prof etkin 2 words for you "thank you"

[perplexedmoth]

My mind is still blown from the fact that that irrational numbers are everywhere, yet they do not exist. It may seem irrelevant practically in infinitesimal quantities/measurements, but when the magnitude or resolution of scale is too large (as in astrophysics, or quantum physics), how do they solve this ancient age-old problems?

[duckymomo]

Aren’t you the prof at Hunter? I never had a class with you but I had it with others

Finding good quality professors are rare and hard