this was a great lecture thank you very much!

Wonderful- an example I think of when talking about Regular group actions is that if you combine a left and right regular group action together you form a Cayley table. Natural example.

I like the presentation of this obfuscated way to write vector a (36:00) using the delta tensor. Nice focus on entering a topic that a lot of beginners find a little hairy. P.S. The "alternating tensor" is also known as the Levi-Civita tensor (pronounced Lay'-vee Chee-vee'-ta). This is one person's hyphenated surname, not the names of two people. Both the tensor and its namesake have (of course) wikipedia articles, and the math one won't be useful for learning math from scratch.

I think there is an error in the notes (however a small one). “ This criteria is almost the definition of a homomorphism. However, here we do not explicitly require θ(g,·) to be a bijection, ) I think homomorphism should be replaced by isomorphism in this instance because a homomorphism is not required to be a bijection but a isomorphism is required to be one.

C9 hoodie goated

U the goat

This is the intuitive explanation i was looking for. Thank you ❤

This is the intuitive explanation i was looking for. Thank you ❤

At about 30:00 minutes are you taking about image and pre image?

Your explanation is great!!! Thank you

This was really helpful and broke down. Thank you!

You got some infectious enthusiasm about this stuff, thanks for making the videos man I don't think I've ever had a more compelling lecture

thank you

really cool

I really respect how nicely you write universal and existential quantifiers

Thanks a lot! WHat's after this series?

you're saving me.

Excellent work, I just found your channel today and this lecture is really enjoyable, thank you man!

Thank you

I enjoy your energy and commitment.

Youre a beast bro, thank you

Thanks for this !

Thanks a lot for this

thank you for this

Good lectures thanks

far too much hand waving and arm flopping .... should be talking about tensor calisthenics

34:10 cool identity

I think I missed the point for the last concept. Could you explain why it is named the Quotient Rule? It is comparatively much easier to understand why the derivative of f(x)/g(x) is called the quotient rule for example.

hie are you going to do type theory ?

Why in the textbook i have read wasn't talking about tensors?

Hello my friend

also an easier way to think about P implies Q is that what it's talking about is, "Does Q happen because of P (as well)?" or "Does P cause Q (as well)?"... So we really only need to care about when P is even relavent. For example, P(rained on ground) Q(ground got wet): if it rained and the ground got wet does that make logical sense? YES! if it rained on the ground but the ground didn't get, does that sound normal? NO! if it didnt rain, can the ground get wet? well YEAH! (cuz nobody said the ground can only get wet if it rains, we're not focusing on the ground getting wet (Q) but more so what does rain do (P); we're tryna see what happens if P happens, what happens when it rains basically, the ground though can get wet with or without rain). If it didn't rain and the ground didn't get wet, does that make sense? YEAH! OFCOURSE! so that's literally all it is, the focus is what happens if P happens, if P is false then that means it didnt even happen, it's not affecting Q aka the ground getting wet...but when it does rain? now thats where things get spicy, thats what we wanna know... when it rained the ground got wet so we know thats true and when it rained but the ground dindt get wet we were liek what the heck is going on and knew this cant be true. an easy example by chatgpt: "If you eat your vegetables (P), then you get dessert (Q)." If you eat your veggies and get dessert, that’s fair. ✅ If you eat your veggies and don’t get dessert, someone broke the promise. ❌ If you don’t eat your veggies but still get dessert, it’s fine because the rule wasn’t about that situation. ✅ If you don’t eat your veggies and don’t get dessert, it’s still fine because nothing went against the rule. ✅

Nicely explained

for De Morgan's laws, an easy way understand it is to consider a scenario where two people named Jack & Joe are competiting against eachother; let's look at the case where one of them wins and one of them loses to get both laws, for our example lets go with the case: Jack WINS & Joe LOSES NOT(Jack AND Joe): "It’s not true that both Jack and Joe win." -this is the same as saying that both jack and joe can't win at the same time which makes sense because Joe lost, therefore this statement is TRUE NOT(Jack) OR NOT(Joe): "Either Jack doesn’t win, or Joe doesn’t win." -this is the same as saying one of them has to lose which makes sense because Joe lost, therefore this statement is TRUE • Since both statements above are true, this means that to say that "both Jack and Joe cannot win at the same time" is the same as admitting that "one of them must lose" which makes sense. They are equivalent statements, you can say either of them interchangeably to make the same point. NOT(Jack OR Joe): "Neither Jack nor Joe wins." -this is the same as saying both of them lost at the same time which doesnt make sense because one of them (Joe) lost and one of them won (Jack), hence this statement is FALSE NOT(Jack) AND NOT(Joe): "Jack doesn’t win, and Joe doesn’t win." -this is the same as saying jack lost and joe lost which is not true because jack won, just think about it! joe literally cant lose if jack lost as well cuz theyre the only two competiting, one of them has to win in order for there to be a loser, hence this statement is FALSE • Since both statements above are false, this means that to say that 'both of them lost' is the same as 'jack lost and joe lost' both of which are false statements and logically equivalent, you can say either of them interchangeably to make the same point. from this you can also see how the placement of the parenthesis/brackets affects the scenarios: for example NOT(Jack OR Joe) is not the same as NOT(Jack) OR NOT(Joe) because saying "neither of them will win"/"both of them will lose" (when the brackets include both together) is not the same as saying "either one of them will lose"/"jack will lose or joe will lose" (there are no brackets grouping them together, one can be affected whilst the other has something completely different happen to it)... matter of fact, they're completely opposite if u think about it because one of them is true while the other is a false statement

so easy, simple, but effectively taught omd thank you so mcuh!!

Thanks ☺, keep doing sir.

finally understood what axioms are thankyouu

this was pretty good! I think I got most of the things covered but there is always something that you don't understand.😊

will you do ib next?

Your video is amazing

It's no coincidence I discovered your channel on Christmas. 🎁 🎄

appreciate your content sir