Combinatorial Proof (full lecture)

[frontdesk]

She is so dramatic about teaching. 😄
I love it!

[artist]

Such a great film! To explain math is to tell a story, and these are delightful stories well told. Thank you!

[softcell]

It helped me so much with my combinatorial problems at the University of Wroclaw, thank you very much!

[calebpresto]

12:30 Isn't the intersection of A and X just {b}? And therefore this has cardinality=1? And then why are we using the intersection at all?

[chaytaninman]

Thank you! I like how you peel away the abstractions of words like permutation and combination and talk instead about the multiplication rule and the sum rule

[kshitijshekhar]

Can't really learn anything if I'm always distracted by her contagious smile

[RealWhiskerWonders]

Thanks mam 💕 I couldn't understand combinatorial proof written in maths Olympiad book. So I searched on YouTube and now feel blessed with your video

[Songvbm]

Respected Professor, I have one question to ask. How do you understand when to take one, two or more sets to solve a problem? What is the intuition behind it? I think choice of required number of sets is the key to write a combinatorial proof.

[encapsulatio]

Hi Dr. Valerie, what is your favorite book(from a pedagogical prowess) that explains and demonstrates practically double counting and the other proof techniques developed over the long history of math with great clarity and precision?

I am totally inexperienced with proofs and I'm just starting to learn about them but I can not find any good articles that give a good map of the terrain of what it means to master proof techniques exhaustively and if there is a spectrum of mastery or not.
Thank you!

[Jacquelinekarlsson_]

Thankyou so much for these lovely proofs. Helped me a lot in the understanding of how to write proofs :)

[chunlangong]

Thank you for this free video you made!
I love your teaching way!

[Measure_differentiable]

Thank ou Dr Hower. There are many proofs that make tons of mistakes.Yours is ckean.Thank you again

[manasimahadeshwar]

This is great video, i shared it with my friends. Thank you mam! 🙏🏻🙏🏻

[hopialozano]

Thanks for this ma'am. I am looking for a proof for the 2nd identity in this video such that we would use lattice points/paths instead of subsets or bit strings, it is possible tho?? I'm trying for 4 days now and I'm dying. I've read a hint which states

" For the lattice paths, think about what sort of paths 2
^n would count. Not all the paths will end at the same point, but you could describe the set of end points as a line."

and lol I dunno how.

[climitod]

12:30 I also dont understand this explanation