Ive finished school, finished studying and got a job. I dont use or need to know about complex numbers, BUT this guy is such a good teacher and makes learning so interesting that im watching this stuff out of fun. Honor to you
By an actual mile, complex numbers were favourite maths classes. Such an interesting subject and watching this video again brings it all back. Good job. 👍🏻
I watched a couple of your videos thanks to TH-cam’s decision to present them to me. You are a fantastic teacher. Your students are very fortunate and they seem to recognize that too. Thanks for sharing your classroom.
The reason to more accurately model reality (atoms as opposed to primordial elements) is that it gives you greater power over reality. If you can predict how it'll behave, you can make it do what you want under the correct conditions. (This is also the general answer to "why science?"). If I understand how leverage works, I can lift very heavy objects (for construction, for example) with much greater ease. If I understand how atoms work, I can use the knowledge to generate effects like electromagnetic communications, create things like transistors, etc.
This video is much clearer than the older videos, due to the improved microphone, and placement closer to the instructor. It could be improved further with a shockmount or foam placed underneath the stand to help avoid the footstep noise. Also, noise removal processing could easily remove the background noise.
I think it would be much more straightforward to use quantum mechanics to motivate complex numbers than string theory. Quantum mechanics matters. String theory doesn't (yet?) have that status.
It seems that anything involving rotation, periodicity, phase relationships, or oscillation is analyzed using complex numbers. Are there any examples where this is not true?
I am just looking at the Glock.. either it’s am or pm, that topic is not maid for this time of the day 🤷🏻♂️😅 Great vid tho, I wish you were my prof back in the days!
I have two questions about complex numbers, can you help me? Let Theta be a root of unity. Assuming n an integer and let m be order of Theta ^ (n), with m multiple of n. How can we define the order of Theta? Let Theta be a root of unity. Assuming p prime and let p ^ (j) order from Theta ^ (p ^ (i)). How can we define the order of Theta?
Is it right to call string theory a "theory" in the scientific sense? I know that mathematically it holds together but has it made any predictions or agreed with any observations?
Quantum mechanics is a separate framework of physics from classical mechanics. You get string theory from applying the quantum mechanical framework to gravity. Thus, string theory is essentially the theory of quantum gravity. Based on my very limited knowledge of the subject, it shows that subatomic particles such as quarks and electrons are comprised of vibrating strings that produce various properties in particles. Although, I am not sure if string theory can predict/produce decent approximations of what properties are produced from these vibrating strings.
John Doe that’s true, in general theory encompasses family of hypothesis, backed by statistical evidence, but one example can threw it all. That doesn’t mean theory is useless. I was going for more rigorous approach
@@pontikipsito46 i was going for distinction between what is considered Theory in mathematical logic vs Theory in science, theory in mathematical logic better be non-contradictory, i.e there can't exist statement S such that you can prove S and negation of S, however this is not the case for science. because when we see that Newton's Mechanics fails when we consider quantum phenomenas where planks constant cannot be regarded zero , i.e we found statement or example in which `Theory` fails, however that does't immediately mean to reject the so called scientific theory, however rigorously it can be considered correct by further assumptions, for newtons case its planks constant to be zero, (which we know it's not)
Why arent complex numbers introduced with quadratic equations and further Algebra? Complex numbers are part of the fundamental theorem??? Rediculous we wait so long
I just think he got a little confused with the numbers of how many people know complex numbers exist. My country has more than 200 million people and everyone that went to high school saw at least a little bit of complex numbers.
What. The best theory we have is quantum field theory which has been rigorously tested with experimental theory agreeing with the mathematics. String theory has failed to create testable predictions... Complex numbers are literally just 2d vectors equipped with a sense of multiplication that produces rotation. They are not the atoms of mathematics. They don't describe 3D rotation (in fact that requires a generalisation of complex numbers called quaternions). To me, the "atom" of abstract algebra is probably the group, although others may talk about groupoids (see link to many algebraic structures which are far more basic than the complex numbers): . Two group operations acting on the same set (where 0 doesn't have a multiplicative inverse), and behaving according to some distributive laws, can be used to create a "field". Complex numbers form a field, and different from the reals because of they lack ordering. Complex numbers, in this sense, are like molecules. I think with the amount of exposure that you get, that you need to properly research things, as you have a lot of misconceptions, and erroneous pop science that you like to spout out. www.cs.cas.cz/portal/AlgoMath/AlgebraicStructures/StructuresWithOneOperation/OneOperationStructures.htm#:~:text=The%20simplest%20algebraic%20structures%20is%20a%20set%20endowed%20with%20one%20binary%20operation.&text=a%20binary%20operation-,.,symbols%20are%20also%20used%2C%20e.g.
Eddie. THIS is what I needed every time I asked my teachers "yes, but WHY do we need to know this?"... This was well before this kind of content was a big thing on the Internet though, so it was harder to look it up. Everyone needs an Eddie teacher!
How interesting that in math certain formulas increase toward infinity while in other cases they decrease toward zero but never actually getting there. Likewise, as we explore more and more of the universe we find that it is ever expanding and inversely as we dig deeper and deeper into the building blocks of life we find that things get smaller and smaller, approaching infinitely small entities like atoms, then protons and electrons, then quarks, etc. Infinitely small or infinitely big, *the limit does not exist...*
According to modern belief, there is indeed, a smallest part, it is called the Planck distance, the Planck time. The universe is thot NOT to be infinite. Llook at the implications of something that is infinite: If the Universe were infinite, then there wojuld be infinite number of planets that are EXACTLY like Earf, and an infinite number of human beans EXACTLY like me (and you). Now, naturally, it would be very nice to have an infinite number of people exactly like me, in actuality, the idea is absurd.
Dik Hed well the universe is finite in the sense that it has a defined size, but at the same time it is constantly expanding...not so finite or infinite after all
if a teacher has such an energy during a lecture, any student will automatically start loving the subject, i would still still for his lecture even if i would not be a student of mathematics .
Ive finished school, finished studying and got a job. I dont use or need to know about complex numbers, BUT this guy is such a good teacher and makes learning so interesting that im watching this stuff out of fun.
Honor to you
i can't believe a math teacher like him exists, i feel so blessed to have come across these videos on youtube!
By an actual mile, complex numbers were favourite maths classes. Such an interesting subject and watching this video again brings it all back. Good job. 👍🏻
I watched a couple of your videos thanks to TH-cam’s decision to present them to me. You are a fantastic teacher. Your students are very fortunate and they seem to recognize that too. Thanks for sharing your classroom.
The reason to more accurately model reality (atoms as opposed to primordial elements) is that it gives you greater power over reality. If you can predict how it'll behave, you can make it do what you want under the correct conditions. (This is also the general answer to "why science?"). If I understand how leverage works, I can lift very heavy objects (for construction, for example) with much greater ease. If I understand how atoms work, I can use the knowledge to generate effects like electromagnetic communications, create things like transistors, etc.
This video is much clearer than the older videos, due to the improved microphone, and placement closer to the instructor.
It could be improved further with a shockmount or foam placed underneath the stand to help avoid the footstep noise. Also, noise removal processing could easily remove the background noise.
The analogy to the Matrix is great because the next line said after is "Show me" and we all know there gonna be a test here.
I didn't know it about 10 minutes ago, but this is exactly what I was looking for.
I love math ever since that's why i am very grateful of finding your videos on yt. Thanx
this class needs to lighten up geez
That’s some great teaching. Thank you sir!
I think it would be much more straightforward to use quantum mechanics to motivate complex numbers than string theory. Quantum mechanics matters. String theory doesn't (yet?) have that status.
Yeah my thought
you're absolutely awesome. Well done. !!
SHIIIEESH, avatar and maths, my two favourite things! Thanks for the amazing video! ily
most people do not exist - Eddie Woo
VadersMyUncle according to Michio Kaku we technically *should not* exist 😯
It seems that anything involving rotation, periodicity, phase relationships, or oscillation is analyzed using complex numbers. Are there any examples where this is not true?
I am just looking at the Glock.. either it’s am or pm, that topic is not maid for this time of the day 🤷🏻♂️😅
Great vid tho, I wish you were my prof back in the days!
My man just casually uses string theory to explain complex numbers
Yep, an unproven theory used to explain fake invented math.
very very enthusiastic sir
I have two questions about complex numbers, can you help me? Let Theta be a root of unity. Assuming n an integer and let m be order of Theta ^ (n), with m multiple of n. How can we define the order of Theta? Let Theta be a root of unity. Assuming p prime and let p ^ (j) order from Theta ^ (p ^ (i)). How can we define the order of Theta?
Is it right to call string theory a "theory" in the scientific sense? I know that mathematically it holds together but has it made any predictions or agreed with any observations?
In science all theories are hypotheses that may be disproved at any moment!
Quantum mechanics is a separate framework of physics from classical mechanics. You get string theory from applying the quantum mechanical framework to gravity. Thus, string theory is essentially the theory of quantum gravity. Based on my very limited knowledge of the subject, it shows that subatomic particles such as quarks and electrons are comprised of vibrating strings that produce various properties in particles. Although, I am not sure if string theory can predict/produce decent approximations of what properties are produced from these vibrating strings.
John Doe that’s true, in general theory encompasses family of hypothesis, backed by statistical evidence, but one example can threw it all. That doesn’t mean theory is useless. I was going for more rigorous approach
@@mishikookropiridze that is not true.
@@pontikipsito46 i was going for distinction between what is considered Theory in mathematical logic vs Theory in science, theory in mathematical logic better be non-contradictory, i.e there can't exist statement S such that you can prove S and negation of S, however this is not the case for science. because when we see that Newton's Mechanics fails when we consider quantum phenomenas where planks constant cannot be regarded zero , i.e we found statement or example in which `Theory` fails, however that does't immediately mean to reject the so called scientific theory, however rigorously it can be considered correct by further assumptions, for newtons case its planks constant to be zero, (which we know it's not)
Isn't the classes are taken in a school classroom?
Who takes classes at 7.50? Is it the AM or PM?
the class is empty lol
Eddie you canmot be an engineer or physicist without understanding complex numbers, they are everywhere!!! As certainly you're well aware
Why arent complex numbers introduced with quadratic equations and further Algebra? Complex numbers are part of the fundamental theorem??? Rediculous we wait so long
What happens at 6:03 was really funny
Is that clock correct? Who's in school at 07:50?
perhaps a night class?
In my old school in germany lessons started at 7.45 :)
In the Philippines, school usually starts at 7:00 or 7:30.
As a teacher, I bet there are no students in this video's class.
So quiet.
When I was a child morning classes start at 6.30.
I just think he got a little confused with the numbers of how many people know complex numbers exist. My country has more than 200 million people and everyone that went to high school saw at least a little bit of complex numbers.
when no one said avatar haha noooo i wouldve shouted it straight awat
me thinking why dis guy is teaching at 7:45 in the morning
What is the cube root of -1?
-1
Cube root #1 of -1 = 1/2 + sqrt(3)*i
Cube root #2 of -1 = -1
Cube root #3 of -1 = 1/2 - sqrt(3)*i
string theory is not really solid , so maybe wouldn't have been wise to include it
The bang noises in the room are so annoying
i know kongfu
What. The best theory we have is quantum field theory which has been rigorously tested with experimental theory agreeing with the mathematics. String theory has failed to create testable predictions...
Complex numbers are literally just 2d vectors equipped with a sense of multiplication that produces rotation. They are not the atoms of mathematics. They don't describe 3D rotation (in fact that requires a generalisation of complex numbers called quaternions).
To me, the "atom" of abstract algebra is probably the group, although others may talk about groupoids (see link to many algebraic structures which are far more basic than the complex numbers): . Two group operations acting on the same set (where 0 doesn't have a multiplicative inverse), and behaving according to some distributive laws, can be used to create a "field". Complex numbers form a field, and different from the reals because of they lack ordering. Complex numbers, in this sense, are like molecules.
I think with the amount of exposure that you get, that you need to properly research things, as you have a lot of misconceptions, and erroneous pop science that you like to spout out.
www.cs.cas.cz/portal/AlgoMath/AlgebraicStructures/StructuresWithOneOperation/OneOperationStructures.htm#:~:text=The%20simplest%20algebraic%20structures%20is%20a%20set%20endowed%20with%20one%20binary%20operation.&text=a%20binary%20operation-,.,symbols%20are%20also%20used%2C%20e.g.
String theory is not our best theory! Please do not spread this
Dude's a weeb, I'm not surprised.
This is, so far, one of the most beautiful classes that I ever saw
Eddie. THIS is what I needed every time I asked my teachers "yes, but WHY do we need to know this?"... This was well before this kind of content was a big thing on the Internet though, so it was harder to look it up. Everyone needs an Eddie teacher!
I have to click like a thousand times for this teacher
How interesting that in math certain formulas increase toward infinity while in other cases they decrease toward zero but never actually getting there. Likewise, as we explore more and more of the universe we find that it is ever expanding and inversely as we dig deeper and deeper into the building blocks of life we find that things get smaller and smaller, approaching infinitely small entities like atoms, then protons and electrons, then quarks, etc. Infinitely small or infinitely big, *the limit does not exist...*
According to modern belief, there is indeed, a smallest part, it is called the Planck distance, the Planck time. The universe is thot NOT to be infinite. Llook at the implications of something that is infinite: If the Universe were infinite, then there wojuld be infinite number of planets that are EXACTLY like Earf, and an infinite number of human beans EXACTLY like me (and you). Now, naturally, it would be very nice to have an infinite number of people exactly like me, in actuality, the idea is absurd.
Dik Hed well the universe is finite in the sense that it has a defined size, but at the same time it is constantly expanding...not so finite or infinite after all
What math class is this?
Watch the Magic of Tegonometrical Ratios in thus Video:-th-cam.com/video/dK6bDFSsM1I/w-d-xo.html
if a teacher has such an energy during a lecture, any student will automatically start loving the subject, i would still still for his lecture even if i would not be a student of mathematics .
As a teacher, I bet there are no students in this video's class.
So quiet.
in the student's defense, its 7:50 in the morning -_-,
quarks are definitely more important than string theory