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
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!
My favorite book for beginning with proofs is Book of Proof www.people.vcu.edu/~rhammack/BookOfProof/. It is the textbook I use in this playlist. thank you!
@@DrValerieHower Thank you. I guess the one you are using in this video is your favorite. Thanks for confirming. From your experience as a professor do you know of anyone making(and finalizing) a resource that maps in a fine grained dependency graph, k1 to k12 math concepts? I have many holes in my math, I pretty much forgot everything since I never understood math in a conceptual way to begin with, I only memorized formulas because I had to and it's a bit frustrating to not be able to identify in a principled and precise way what concepts I do not understand properly. This kind of dependency graph would be incredibly useful, each concept having linked either written instruction or videos demonstrating that concept. We have thousands of k1 to k12 math videos on youtube from many channels but it's not like we can find with a youtube search the precise videos that explains one minor concept both in isolation and how it is used together with other concepts, how many concepts overlap in algebra, trigonometry, geometry etc and what concepts you truly only need when studying some particular small part of just one type of math like algebra. It's easy when you have a teacher that knows all high school math concepts and can guide you faster to pinpoint your weak areas but what do I do if I'm by myself in the position of not knowing what I don't know so no quick way to find what concepts I'm missing? I guess I could just follow a textbook that is somewhat structured but most textbooks I began and ended up abandoning seem to be more interested in teaching you this progression in an artificial way, jumping too fast to some other topic without making sure you truly mastered the one before. Too much focus on teaching generic algorithms, not teaching you the micro and mini skills to be able to come up by yourself with the final form of the formula. That's when you can say you understand the formula, because you independently can arrive at that formula. I guess i want to do math the generative way not the prescriptive procedural way. The procedural way is fine for most but that is the reason I always despised doing any math because I never understood how and especially WHY everything works at the low level.
@@DrValerieHower Thank you. I guess the one you are using in this video is your favorite. Thanks for confirming. From your experience as a professor do you know of anyone making(and finalizing) a resource that maps in a fine grained dependency graph, k1 to k12 math concepts? I have many holes in my math, I pretty much forgot everything since I never understood math in a conceptual way to begin with, I only memorized formulas because I had to and it's a bit frustrating to not be able to identify in a principled and precise way what concepts I do not understand properly. This kind of dependency graph would be incredibly useful, each concept having linked either written instruction or videos demonstrating that concept. We have thousands of k1 to k12 math videos on youtube from many channels but it's not like we can find with a youtube search the precise videos that explains one minor concept both in isolation and how it is used together with other concepts, how many concepts overlap in algebra, trigonometry, geometry etc and what concepts you truly only need when studying some particular small part of just one type of math like algebra. It's easy when you have a teacher that knows all high school math concepts and can guide you faster to pinpoint your weak areas but what do I do if I'm by myself in the position of not knowing what I don't know so no quick way to find what concepts I'm missing? I guess I could just follow a textbook that is somewhat structured but most textbooks I began and ended up abandoning seem to be more interested in teaching you this progression in an artificial way, jumping too fast to some other topic without making sure you truly mastered the one before. Too much focus on teaching generic algorithms, not teaching you the micro and mini skills to be able to come up by yourself with the final form of the formula. That's when you can say you understand the formula, because you independently can arrive at that formula. I guess i want to do math the generative way not the prescriptive procedural way. The procedural way is fine for most but that is the reason I always despised doing any math because I never understood how and especially WHY everything works at the low level.
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.
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.
Hi. here is an idea. Try latice paths from the origin: (0,0) with n steps where you can either step Right (R) or up (U). You can consider this as a list of length n of R's and U's of which there are 2^n such lists. Therefore, there are 2^n such lattice paths. Now, the hint is a good one regarding the end points. How many paths end at the point (0,n)? Exactly 1, which is (n choose n). This is the lattice path of n U's. How many paths end at point (n,0)? Exactly 1, which is (n choose 0). This is the lattice path of 0 U's (and hence n R's). Then for example how many lattice paths end at the point (n-2, 2)? Here you have (n choose 2) as these paths have 2 U's (and hence n-2 R's). I hope idea is helpful.
Capital B is A union one point: little b. Any subset of B containing more than 1 element necessarily will intersect A. I am not sure your question here. Thank you
![CAMPปลิ้น | EP.83[1/2] เปิดแคมป์หลอนต้อนรับ 2 ตัวพ่อแห่งวงการผี!](http://i.ytimg.com/vi/2uPuHYHgwiI/mqdefault.jpg)
![Combinatorial Identities via both Algebraic and Combinatorial Proof [Discrete Math Class]](/img/n.gif)
She is so dramatic about teaching. 😄
I love it!
Thank you!
It helped me so much with my combinatorial problems at the University of Wroclaw, thank you very much!
Wow that is so wonderful! You are welcome and thank you for the comment :). best wishes in your studies.
Such a great film! To explain math is to tell a story, and these are delightful stories well told. Thank you!
You are welcome. Thank you so much for your comment.
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
You are welcome! Thank you so much for your feedback.
Thanks mam 💕 I couldn't understand combinatorial proof written in maths Olympiad book. So I searched on TH-cam and now feel blessed with your video
You are welcome! I appreciate the feedback :)
YOUR CHANNEL IS AMAZING.
Thank you!! :)
Thankyou so much for these lovely proofs. Helped me a lot in the understanding of how to write proofs :)
You are welcome! I appreciate the feedback. Best wishes to you.
Can't really learn anything if I'm always distracted by her contagious smile
Thank you?? Though I hope you are able to learn!
Thank ou Dr Hower. There are many proofs that make tons of mistakes.Yours is ckean.Thank you again
You are welcome. Thanks so much for the comment and best wishes.
Thank you for this free video you made!
I love your teaching way!
You are welcome!! Thanks for the comment. I appreciate the feedback :)
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!
My favorite book for beginning with proofs is Book of Proof www.people.vcu.edu/~rhammack/BookOfProof/. It is the textbook I use in this playlist. thank you!
@@DrValerieHower Thank you. I guess the one you are using in this video is your favorite. Thanks for confirming.
From your experience as a professor do you know of anyone making(and finalizing) a resource that maps in a fine grained dependency graph, k1 to k12 math concepts?
I have many holes in my math, I pretty much forgot everything since I never understood math in a conceptual way to begin with, I only memorized formulas because I had to and it's a bit frustrating to not be able to identify in a principled and precise way what concepts I do not understand properly.
This kind of dependency graph would be incredibly useful, each concept having linked either written instruction or videos demonstrating that concept.
We have thousands of k1 to k12 math videos on youtube from many channels but it's not like we can find with a youtube search the precise videos that explains one minor concept both in isolation and how it is used together with other concepts, how many concepts overlap in algebra, trigonometry, geometry etc and what concepts you truly only need when studying some particular small part of just one type of math like algebra.
It's easy when you have a teacher that knows all high school math concepts and can guide you faster to pinpoint your weak areas but what do I do if I'm by myself in the position of not knowing what I don't know so no quick way to find what concepts I'm missing?
I guess I could just follow a textbook that is somewhat structured but most textbooks I began and ended up abandoning seem to be more interested in teaching you this progression in an artificial way, jumping too fast to some other topic without making sure you truly mastered the one before.
Too much focus on teaching generic algorithms, not teaching you the micro and mini skills to be able to come up by yourself with the final form of the formula.
That's when you can say you understand the formula, because you independently can arrive at that formula.
I guess i want to do math the generative way not the prescriptive procedural way.
The procedural way is fine for most but that is the reason I always despised doing any math because I never understood how and especially WHY everything works at the low level.
@@DrValerieHower Thank you. I guess the one you are using in this video is your favorite. Thanks for confirming.
From your experience as a professor do you know of anyone making(and finalizing) a resource that maps in a fine grained dependency graph, k1 to k12 math concepts?
I have many holes in my math, I pretty much forgot everything since I never understood math in a conceptual way to begin with, I only memorized formulas because I had to and it's a bit frustrating to not be able to identify in a principled and precise way what concepts I do not understand properly.
This kind of dependency graph would be incredibly useful, each concept having linked either written instruction or videos demonstrating that concept.
We have thousands of k1 to k12 math videos on youtube from many channels but it's not like we can find with a youtube search the precise videos that explains one minor concept both in isolation and how it is used together with other concepts, how many concepts overlap in algebra, trigonometry, geometry etc and what concepts you truly only need when studying some particular small part of just one type of math like algebra.
It's easy when you have a teacher that knows all high school math concepts and can guide you faster to pinpoint your weak areas but what do I do if I'm by myself in the position of not knowing what I don't know so no quick way to find what concepts I'm missing?
I guess I could just follow a textbook that is somewhat structured but most textbooks I began and ended up abandoning seem to be more interested in teaching you this progression in an artificial way, jumping too fast to some other topic without making sure you truly mastered the one before.
Too much focus on teaching generic algorithms, not teaching you the micro and mini skills to be able to come up by yourself with the final form of the formula.
That's when you can say you understand the formula, because you independently can arrive at that formula.
I guess i want to do math the generative way not the prescriptive procedural way.
The procedural way is fine for most but that is the reason I always despised doing any math because I never understood how and especially WHY everything works at the low level.
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.
This is great video, i shared it with my friends. Thank you mam! 🙏🏻🙏🏻
Wonderful! and thank you so much for your feedback.
love your energy!!
thank you!
Thank you!
You are welcome!
Thanks
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.
Hi. here is an idea. Try latice paths from the origin: (0,0) with n steps where you can either step Right (R) or up (U). You can consider this as a list of length n of R's and U's of which there are 2^n such lists. Therefore, there are 2^n such lattice paths. Now, the hint is a good one regarding the end points. How many paths end at the point (0,n)? Exactly 1, which is (n choose n). This is the lattice path of n U's. How many paths end at point (n,0)? Exactly 1, which is (n choose 0). This is the lattice path of 0 U's (and hence n R's). Then for example how many lattice paths end at the point (n-2, 2)? Here you have (n choose 2) as these paths have 2 U's (and hence n-2 R's). I hope idea is helpful.
@@DrValerieHower OM G, thank you very much ma'am. this helps me a lot. 😭😭 Forever grateful 😇🥰
You are welcome :)
I LOVE MATH!
I do too! :)
12:30 I also dont understand this explanation
Why would A be effected by x intersect A when A and b are disjointed
Capital B is A union one point: little b. Any subset of B containing more than 1 element necessarily will intersect A. I am not sure your question here. Thank you
you are sooo cute. Thanks for video
You are welcome!
Thank you!
You're welcome!