Lecture 1: Sets, Set Operations and Mathematical Induction

MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez

An introduction to set theory and useful proof writing techniques required for the course. We start to see the power of mathematical induction.

License: Creative Commons BY-NC-SA

[faizanmansoori]

I am crying right now. I am an economics student and I have been waiting for MIT OCW to release lectures on Real Analysis for so long. My whole mathematical economics training has been due to MIT OCW from calculus, linear algebra, differential equations to statistics and ML. Thank you MIT.

[vhiremath]

Wow this guy is an incredible teacher. Constantly states why things are important. Has a sense of humor. Builds up logic so that things flow vs. a spattering of random facts. 💯

[vinylflouring]

This guy has the style to teach this subject matter effectively. Best analysis content on YouTube

[lezeuvete]

After all theses years, MIT finally decided to post pure math videos.
I haven't thought such a day would happen...

[victorrodriguez]

after years and years of no well known university uploads a full course in this topic, it had to be MIT

Thanks Again MIT from Bolivia!

[Deliriummary]

This is incredible!! Thank you so much! You can’t even imagine how much I appreciate this. I would really love to see more pure math content like topology and abstract algebra!!

[preciouspetermasula]

being a maths major student, and lucky enough this course we are taking this semester, this is really helping me Dr.

[tuongnguyen]

I am an engineering student and I have been looking for this for such a long time. Real analysis, functional analysis. I hope in the future there will be complex analysis. This is extremely useful for digital signal processing stuff. One strange thing is that currently all the machine learning stuffs are not design for things that have complex number inside them

[digitalfroot]

great video. A discussion woth my dad about him failing real analysis is what played the seed of being a math major. We had that conversation probably 6-7 years ago and now i’m a junior in college pursuing a math degree. So happy to have this information at my fingertips. I get to watch these lectures in my own time and learn a lot by myself

[dtung]

Prove induction theorem by well-ordering property! Nice and clear.

[maxpercer]

I love this mathematician's logical way of thinking.

[yan-amar]

Don't feel too akward professor, there are people actually listening on the other side, maybe even more eagerly than some of the students that get to be there in person.

[mississippijohnfahey]

Hey MIT, thank you so much for posting this! If you want to improve the sound, try using an expander (a compressor set to a less-than-one ratio). To make the chalk more visible, the contrast could maybe be turned up. Come to think of it, the expander is just like audio contrast! After expanding, you may want to apply a maximizing limiter. The Waves L2 plug-in works great ($30), and you can do all this audio work in Ableton Live ($250 for students).

My mentor at work told me a few months ago I need to learn analysis. Since then, I went through 18.01, 02, 03, and 06 to refresh, and to see this lecture series up now is just perfect--thank you again!!

[saaqibmahmood]

O MIT OCW, please release videos onto YouTube of the 18.100B, 18.100C, 18.700, 18.701, 18.702, and 18.901 courses!!! And, also of the complex analysis courses taught at the MIT! Please do seriously consider this request.

[manoranjansahu]

I have been waiting for this for 10 years!!!

[vazn]

Thank you so much MIT for providing high quality courses like that OMG !

And i'm entering my math major next month, that's a GREAT TIMING😄

[diegolainfiesta]

I got dizzy by following the video, the cameraman is constantly following the teacher, instead of leaving the dashboard view. Because here are no students, he is writing pretty fast without any interruption. It is so say, I´ve been waiting this course. If you have the chance to fix it, it would be great.

[carlosmateosamudiolezcano]

Finally a real analysis video lecture series from the OCW :'). Thank you

[cswanson]

47:53 - 48:36 Chilling. Doesn’t want us to suppose the rules of logic are as obvious as they seem. And since he’s been quite sharp up til now, it kind of startles you to hear him warn of something “hairy” that stalks us. Kind of spooky, like we’re about to listen to a campfire tale.

It’s almost cinematic in a way, as uncertainty about the rules of logic creeps into his monologue, he wanders into a thicket of upturned chair legs.

[zukamakanesada]

I really appreciate this course and I hope complex analysis lectures will come out soon