Introduction to Higher Mathematics - Lecture 8: Relations

In this lecture we build relationships between sets, which can represent many of the mathematical relationships we know.

[samiazaman]

Why do I feel like crying out of gratitude for being able to watch these videos. I'm seriously not trying to be lame or stupid.
Thank you so so much !
I feel that every point you ask us to note pulls just the right triggers.
*Indulgence hour*

[jashgala]

This is perhaps the best series on higher discrete mathematics on youtube comparable only to nptel.

[ArbitraryZer]

Archie's Weird Mystery reference has made my day, so much nostalgia. Best Maths lecturer on youtube hands down! 

[davidwhittle]

This is a great series of lectures. I'm working my way through them all.

[blabla]

Really fantastic lectures here Bill. I'm getting a lot of good information out of them. Thank you for taking the time to make them.

[ChiRhoFTW]

Most clear explanation of equivalence relations I've heard yet. Thanks!

[robertmartinez]

Love the whole series!!! A series of subsequent lectures that went deeper into each subject would be greatly appreciated and much anticipated... keep creating AMAZING CONTENT!!! thank you

[demonic]

Bill thank you so much for these videos, I am really getting this stuff I think, and my confidence is going through the roof. I never had much opportunity to study maths in school, focusing on other subject areas instead, and always felt a chip on my shoulder about "what the maths students were getting." Now I see it! And it's all actually very similar, just a different language! Awesome stuff +1x10e1000 :D

[duncan]

Great stuff! This is giving me a clearer angle on things than my own course materials.

[mcawesome]

Your videos are so clear that I will most likely pass discrete mathematics only thanks to you!!!

[chomk]

Wonderful! Please keep creating lectures.

[crazyboii]

DUDE! Thank YOU so much from the bottom of my heart! This is GOLD! SUBBED!

[baileyhulsey]

I love these videos! Two questions:
1) Are matrices built from Cartesian products? Like it seems like there could be an "index set" for matrices that is the set of all row x col coordinates. Maybe that "index matrix" is the Cartesian product of two index sets?

2) Is cards example at 5:36 really a Cartesian product or were you just using it as a loose example? In particular, it doesn't seem like the order of suit or rank would matter, so R x S = S x R. Is this a special kind of Cartesian product, like a "combination vs permutation" distinction?

[LearnwithMinti]

Thank you so much...Well understood...

[fuzzeline]

At around 19:47, wouldn't it be a more general description of equivalence relations to write [a] = {x *E* A | (a, x) *E* R}?

[matthewpendleton]

I've had a fascination with the way logic and mathematics come together and how they differ. There's also the interesting aspects of logic and language. I wonder: could you make a video explaining the general form of propositions according to Ludwig Wittgenstein in proposition 6 of his Tractatus Logico-Philosophicus? Also, I like how 30, 000+ people viewed your first video, and now on the eighth lecture only 4, 000 people have viewed it. >>

[ManigandanRajasekar]

Altenatively we can represent a point lattice, which is the set of of all ordered pairs of integers, such as on a "____"?  6:20-6:30 Did anyone else get that word?

[DeltonMyalil]

Great Lecture. Also, we share birthday - March 26

[cheukchan]

I think there is a mistakes made in 19:40 slide. An equivalence class should be [a] = { x A| x~a }.

[Viviansiren]

Is there a ppt available for download? Thanks a ton!