What is the number "e" and where does it come from?
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- čas přidán 22. 02. 2015
- e (2.718281828...), also known as Euler's number, is a critically important number in mathematics. It forms the basis of the exponential function and the natural logarithm, and like π it crops up in innumerable places (even where you wouldn't expect it).
Besides the accent, the way you know this is an Australian classroom is by how casually someone swears in front of the teacher
"HOLY SH!T!"
@Prashant Kumar it's not. try again.
@Prashant Kumar nope
timestamp?
@Prashant Kumar no he didn't
No math teacher ever explained how the value of e is derived to me in all my years of schooling.... until now
69 likes...nice
school doesnt usually teach you that
i learned it in a 'math for engineers' lecture
@@quaffie but to be fair you cant just throw of an transcendental number and expect to know what the hell it's supposed to mean
Sorry but this is just an approximation of e only. Not e! This value doesn't exist unfortunately!
Probably because my maths teachers didn't know.
Society needs more teachers like this guy. Young, smart, relatable to youth and able to convey complex subjects in a simple way.
He's such a good teacher. I wish I had him as one of my teachers :(
Society in most of the US has decided teachers like him are needed only if they have an Education Degree (as opposed to a math or other STEM degree) and if he is a teachers union member.
I wish this was my math teacher, cause my math teacher makes us do these terrible projects focused on graphing, which we did for the entire year. Also she explains stuff in confusing ways and says we should have learned something we didn’t.
and handsome too
Idk about the young part
Still amazing 4 years later.
Also, that class in the background sure is engaged.
4:36 "Shut up. Shut up."
4:31"Holy shit that was fun!"
7:57" Whooaa-
2:30
Lol
😂😂😂😂😂
Great teacher stuck with fricks
Luigi at the end there😂
5:10 whoever said 365.25 - I like you
+FinnShack Leapyear?
Ynox Yeah, average year length
well 365.25 isnt exactly correct either. a year is about 365.2425 days
UbererSK Close enough for a quick answer;
+Fin Koya 365.2422, that's what i memorized xD
This guy is just brilliant... I was speechless.
He made maths so fun and interactive, something almost no teacher does. It's not all boring formulae and stuff, this guy actually involves the class and explains stuff extremely well. Hats off!
Mind blown..... I wonder my lectures 12 years ago like him.... :-)
Maybe our Aussie teachers need to take a leaf from his book, passion cost nothing!!
actually teachers like these are really costly because they are rare and usually they are really qualified thus they find it easy to explaim
NO OFFENCE INTENDED. Actually he is teaching in such a way so that even the weak minds(about +97℅ of the human population) which might be considered as good by those +97℅ people but the truth is that by this way mathematics (in the known sphere of humans) won't evolve and that's what is happening we have not told about any new discovery (in this field ) since 3 to 5 decades
NO OFFENCE INTENDED. Actually he is teaching in such a way so that even the weak minds(about +97℅ of the human population) which might be considered as good by those +97℅ people but the truth is that by this way mathematics (in the known sphere of humans) won't evolve and that's what is happening we have not told about any new discovery (in this field ) since 3 to 5 decades
The single best way of explaining "e" by anyone, anywhere. And I believe this is how the number e was originally discovered. Truly excellent teaching. These students have no idea how genuinely lucky they are. Around the world literally a billion people have learned the number e and how to use it in calculus and other maths courses, and have been using it for years with still no clue how this mystical thing came about. These kids will have no fear of using it and will totally get it's significance and be able to teach it to anyone. Bravo Eddie Woo.
I remember when I asked my Math TA why is the derivative of e^x still e^x? I was just asking for the answer, but she thought I was getting all philosophical so she spent 5 minutes explaining this concept hahaha. Now that I'm older and wiser, the simple explanation is what Eddie said: "The rate at which something grows/decays is proportional to itself". THAT'S why the derivative of e^x is itself...
The way e was discovered is because of Calculus. Mathematicians wanted to find a function where it would be it's own derivative. So you have to solve the differential equation f(x) = f'(x), and out pops e if you do some complex mathematics. All of the rest are then discoveries afterwards.
@@yami_the_witch that is not at all how it was first discovered
Yes!
Exactly!
The students who are lucky enough to be taught by teachers like this one will find it easier to live in this world. Too bad there are very few teachers like him.
Yes, too bad, but in most of the US it is not coincidence. State licensure requirements, supported by unions, mandate college degrees in education. As a general rule, talented math students will not put up with simplistic education courses. As a well known writer explained, when visiting colleges he saw STEM majors working on problem sets, while the education majors were cutting letters using safety scissors on poster board.
They go into better paying jobs, and where they don't have to deal with constant student harassment.
@@veramae4098 and constant pointless beaucracy
That's why CZcams is here!😁
i could watch this guy teach maths all day
Nataly RAW he's got a CZcams channel for a reason...
what do you think I'm doing right now?
Math*
Hi
919 subscribeer without any vedio hats off to you
Passionate teacher:) Well done! Way to engage the class.
+Aidan Davis Cool teach, cool class.
+Aidan Davis Well, hes young.
Aidan Davis I was first
Is there even a class? Or were the students' voices dubbed in to make you think he's teaching a class ;)
@@andrewcbuensalida ok
Einstein's right when he said, "If you can't explain it simply, you don't understand it well enough". Some people cover how shallow their understanding is by throwing jargons in class.
You notice how Einstein's is becoming Jesus exponentially?
people like this should be famous, they actually make a difference in our life.
Totally agreed. Meanwhile, other CZcamsrs who call themselves influencers or "content creators" don't know the difference between content and garbage!
@@virajnagpure because those content creators provide entertainment which may not serve as much utility but increase happiness instead which is arguably just as important. An unhappy individual is generally less productive and their ability to learn and perform goes down. Not saying a youtuber is more important than this guy by any means, just that they're not innately useless, I don't know where i'd be without some of the "content creators" I watch. Big fan of Eddie wu though lol he was at my mum's uni graduation and filmed a miniseries at my school, his videos helped me through my HSC and definitely contributed to my grades
He is
Dude, I'm a secondary teacher (in my second year now), you are literally my inspiration. You're now my reference point for how good a teacher I can be.
If you wanna be a good teacher; just take the following as a rule: Let the students interact with you & the subject in class, and let them witness how beautiful whatever subject you're teaching is. And afterall don't be too boring yourself, have a good sense of humor. Wish you luck with your fourth year!
@@user-lc6jq1hi1r'll also say watch how he holds discipline in the class too. Not apparent in this video but in others he does have to call students to account and he is brilliant IMHO at that too.
@@Raysnature exactly, something ive also noticed lately
Just apply the maths you are teaching to a real world situation, job done. Everyone is interested.
Mark, you certainly are a good teacher, too, because you recognise and try to imitate a good teacher. Good luck.
I love how he explained everything in only 8 minutes, my teacher was talking about this for 3 and a half hours, and nobody understood the formula, we all just memorized it... Congratulations!
Atleast your teacher had taught you about this unlike my teacher.
@@arsiveparkour6251 at least you had a teacher.
atleast you have a life
@@MikaelS5 at least you have a.. Oh damn it I think you won that battle
yeah dude, it's so hard to memorize e^x
Eddie: "It's a number that exists in reality just like Pi does."
Student: Surprised Pikachu Face
Unfortunately that's not true. I'm sorry but these numbers doesn't exist!
He said that because he doesn't really know either.
@@manwork6545 Yes it does, it's how radioactive material decays.
@@manwork6545 define what you mean by not existing.
I can measure my weight, say, to the nearest 100th of a pound. However, my exact weight is an irrational number that's decimal places stretches on to infinity, just like pi or e.
Does that mean that the exact value of my weight doesn't exist?
@@scarmackd1498 yes
I love watching this teacher's lectures. And while I am not much of a mathematician, this was both crystal clear and mind blowing. So cool.
4:36
Some guy: it's 2.2......
Girl:Shut up!!
😂😂😂
Nah dood i bet that's a Rachel
And they wonder why math isn't popular..
I almost shouted 225 at my phone. It's fun
Every math class has “that student”
I had a teacher like this for my first Calculus course in high school. She was brilliant and engaging and taught us the reasons behind doing things... instead of just "do them because I say so". To this day she is the reason I enjoy mathematics and get excited about learning new facets of the science. I credit her with my SAT Math jumping over 100 points inside of a single semester. The right teacher is something you just can't put a price on. Bravo, man!
Learning the logic is critical. Kudos to your teacher.
I remember learning that pesky limit as a formula and always wondering why it was e. This is eye-opening. I suppose this is what a mathematical epiphany feels like; it's an incredible feeling!!
He teaches his student the most basic thing which are never taught in a school and school make student an intelligent donkey..... Huge respect for him
"you and your feeble units of measurement!"
Physicists feel attacked
👌
@@saimnaqvi7169 They are.
Such a line !
😂
hey, who's your math teacher ?
-It's Eddie
yeah but Eddie who ?
-yes
...
anyways great teacher
did you just...?
chocolatechocochoco ahahah
chocolatechocochoco no, woo
Mildly racist. Wildly funny!
Who?
Great explanation. Just want to add that the key principle here is *compound interests* and letting _the interests generated earlier to produce higher results_ , e.g. generate interest after one semester rather than one year, generate monthly instead of semesterly, etc. This allows the principal itself to grow as the base for the next interest calculation. E.g. after 1 semester 50% (0.5) interest generates a result of (principal 1 + interest 50%) and then this result combined immediately generates a new interest; "the clock starts ticking" immediately the next day after one semester, no need to wait until one year (read: increasing the value of n). This compound interests on smaller timeframes (increased n) are resulting in dynamic base values, therefore the growth becomes *exponential: the growth is given on previous growth* .
This channel is singlehandedly turning my CZcams consumption from "very distracting" into "very productive".
I'm in my differential equations class and I never knew where e came from. I wish my teachers in high school taught me this.
Drake Aure Read the chapter on exponential functions in Spivak, Calculus. It gives a rigorous definition. Then read from a complex analysis that extends e to complex numbers and reveals a relationship between pi, e, the pure imaginary number i, 1, and 0.
There are some videos on youtube that help you visualize and better understand Euler's identity [e^(pi*i)+1=0], if they are of your interest
you were studying calculis before you were taught what e was?
Me too, I'm in 12th grade, we are doing limits and functions analysis and I ALWAYS wondered where that number came from, I asked my teacher but she couldn't explain. You can also find it in physics like in capacitors formulas etc, very very interesting and odd number
@@JensenPlaysMC He said he was using it in diff equations before he knew where it came from, not before he knew about it.
eMail is the growth of the number of mail messages I have after a year of spam.
lol
What do you mean
That doesn't even make sense
yes, if you keep replying to them...
Lol
I just don't have words. Beautifully explained. I just watched 8 mint video and didn't even got bored, that how amazingly it is taught. May ALLAH bless him and me with this type of teaching method. Ameen.
There's something about this math instructor that makes complex number concepts easy to understand. I'm getting back to learning all that I didn't in the past. Kudos to the instructor!
I'm not completely hating on my high school experience...but Goddammit, I wouldn't have been such a math delinquent if I had someone like you for a teacher! Your teaching method is utterly brilliant and engaging. All teachers should be like this.
JayGatzVFXsk8r pay close attention, this method is extremely dependant on the students' intrinsic motivation rather than only the teacher... if done right, the results are far greater than the regular methods though.
True in that it not only depends on the teacher but the students. My education system is like it begins to turn people into worker drones so the curiosity that could arise in maths classes barely exists. I wish I had passionate teachers
I already teacher like him
@@matiascabral1502 You're right, this method might not work at 3 pm on a Friday afternoon.
@@faithlesshound5621 Indeed, once the subject loses priority status, that's it.
This guy is actually a really great teacher, actually shows some enthusiasm in his work.
he seems very enthusiastic. He is an awesome teacher.
I can't believe I am 39 and watching this, getting entertained AND getting more educated at the same time. Kudos.
This lecture was absolutely engaging. You have an amazing talent. Thank you!
This is why CZcams is an amazing platform - allows teachers like this one to teach in such a fun and engaging way
at the end someone's mind was blown "woooaaah" ^^
Lol that was most hilarious part of the video for me as well.
Had to scroll too far down to find this lmao
waAaAaA
Eddie's enthusiasm is great but his examples are crisp and clear to a degree that makes him truly a fantastic University physics teacher.
Inspirational, authentic and unfazed in the face of funny remarks - brilliant teacher!
This guy needs to start working for khanacademy.org Thumbs up if you agree.
I vote for Khalid as well from betterexplained.com
I think khan academy should be working for Eddie instead
Lol ok
@@collin9143 true
@@zeidkazi3402 you misunderstood. He's not forcing eddie. He's just suggesting he should work for Khan academy because he would greatly benefit everyone's education
Sir Eddie Woo, you're just a amazing teacher. I'm brazilian and the professors here don't even get close to your foot. I just want to thank you for the amazing classes or part of it that you upload here on CZcams, I really enjoy them. Keep the excelent work you do, your students are so lucky. I hope someday I can watch one of your classes! Sorry about my English, I'm a little bit rusty.
This is the best explanation of Euler's number I've ever heard. Mr Woo, I will take your lesson's forward in my engineering life. Thank you.
I quit math when I was 14 due to a bad teacher and chose a branch of studies that didn’t include math because of that. One of the greatest regrets of my life. I so wish I had a teacher anywhere near Eddie. Superb didactics! His pupils have a treasure in him
Eddie, I have a graduate degree in physics but I still enjoy your videos because you have an insight I have never experienced in all my years of education and experience.
Wow- the best explanation I've come across- wish you were there to teach me in school! :D. Thanks a ton ! :)
i can not thank you enough, but really you are the best teacher. Mostly teachers here are trying to prove students that they are dumb but look at this awesome teacher who proves e instead of downgrading his students thank you man thank you again...
You give a completely different perception of thinking towards mathematics. I like it and i am liking it more. i wish i knew you while i was learning, but yes i am learning all over again. Hats off to you and whoever has taught you.
You are an excellent teacher!
I am Engineering Graduate . and All i can say is , I wanted you badly while those mathematics classes that i had during my childhood !! Still , It's never too late. Starting my Education once again ! Thanks a lot .
How my life, school reality, and my feelings towards math would be different if i met more people like yourself during my educational path. What you doing is just amazing.
Hello! I love your teaching style! I am an Engineering Post Graduate, I don't watch your videos to learn the concept but to witness the sheer brilliance of how you deliver the concept and i am always left wondering how much effort goes in preparing for each lecture. keep up the good work sir.
Great Teacher!He gave them the best intuitive answer possible.
A fun yet intelligent teacher always brings any sort of materials into comfort to embrace the students' thought
Eddie you are a marvellous teacher. I actually came first in 4 unit Maths in 1976 in NSW. The way that you explained the number e was so good. I was very impressed .
Excellent, I taught 40 years, now I realised how easy it is to prove the value of e
you sir are an amazing teacher ! .... respect
What a teacher! The world needs more teachers like him and then every subject would be beautiful.
I love the way you explain this concept. I have an engineering degree and never thought about this kind of stuff, but the way you explained it makes so much sense
I love this lesson so much! I keep coming back to it over the years. There's just something fascinating about the compound interest formula and e.
I really enjoy this kind of videos. I do love maths because, back in the years, I had a teacher who gave me this passion. If all the teachers could be like Eddie , I think students wouldn't see maths as a boring thing anymore
That was so brilliant. Building up the concept from simple beginnings.
Eddie, you're something! Very good. Makes me wish I was back in class. Reminds me of the time I mowed a lady's lawn and general cleanup and other errands for her every day except weekends. I made a deal with her that if she doubled the previous pay starting at 1 cent. So one cent for the first day 2 cents the second day 4 cents, etc. After working 10 days she started understanding what was happening. We stopped at the the 12th day.
I have no idea why he's popping up in my youtube algorithms 6 years after the video has been posted, but I'm freaking loving it. Great content and a great teacher.
Brilliant Eddie. You are a born communicator.
I didn't want this video to end...
I'm 60, an engineer, learned about e decades ago. But never REALLY learned it, like this. Mind completely, totally blown.
Keep this passion in teaching, and spread the enthusiasm to others. You inspire more kids (but not only kids) not to scare from math and science :) waiting to see more videos with your lectures.
Everyday I am having my eureka moments just because I watch your videos, and I am a computer science graduate with good background in mathematics. I studied all my life to pass the exams, I feel so terrible right now. I ended up being a well trained student and not well educated. Looks to me like I ll be going back to my books and I will read them with fresh perspective with a free and broad mind and asking why this why that at every point.
Thank You Mr. Eddie Woo, I am so glad you got selected in worlds top 10 best teachers for 2018
u iit?
"You and your feeble units of measure" new favorite qoute.
Loved his enthusiasm and clarity.....great teacher!
Fantastic...the best description of e that I've gotten so far...and I'm in my 50's and have had maths...up to college Calculus III. Thank you!
Him: "How about every minute"
Me: **breaks out in a song about love**
Unfortunately this guys video will only get few hundred thousands views, while perhaps it's most amazing, useful and beautiful video ever for ones knowledge.
While stupid bullshit gets millions of views...
As of right now, it is about "e" million, so.....exponential growth my friend
Simply amazing!!!
Exponential finally makes sense.
Compounding to a limit....
I really wish we have more teacher geniuses like Mr. Woo
Those students can easily ace any math test no prep needed - going to class is more than enough
Thank-you Eddie. This makes perfect sense! I may be grey-haired and retired and may never use this info, but to have it finally make intuitive sense is a delight!👏👏👏👏
This is the kind of man i want to be when i’m an adult.
Great video. A joy to watch teaching in action like this.
As usual loved it ..!!
Came here from Gilbert Strang's Lecture, he briefly taught this approach towards 'e' in addition to the calculus approach which he explained thoroughly.
I have never seen a better math explanation video, and this is live. Thank you for this.
4:31 "holy shit" :D
That 9GAG post will give you the views you deserve! Great teaching, will definitely browse through more of your content!
Eddie is so passionate
I wish every teacher had this passion and love for their job
Why didn’t I have you as my math teacher? So much energy and meaningful approach to concepts….. wow….. just wow.
“Bro what did I miss out while I was gone?”
“Yeah we started a new unit, and…”
“And? What.”
“It’s complicated”
6:46 - That infinity symbol was glorious.
Such a great teacher, with such a loud and undeserving classroom.
Thank you for an awesome, brief, clear, straight to the point explanation. :) I haven't done advanced maths since highschool 23 years ago, and most sources I found on the subject required me to start from page 1.
Title: what is the number ‘e’
Me: I thought ‘e’ was a letter
e = lim n -> INF (1 + 1/n)^n
+thethakuri that inf should be a sup as it's increasing
You can tell these young kids are super under appreciative and inexperienced to know how valuable this guy’s instruction is. It’s really funny and makes the video even more enjoyable 😂
I finally understand what Euler was going for. Thank you
I wish you were my maths teacher.
dude, thank you for the mind blowing experience. I understand this way better now. =)
Sir you are amazing. No one ever explained to me the real meaning of e ever. I wish to be in ur class one day.
My father is a great mathematics teacher but He is on another level. Just love to listen the concepts and still feel like a kid after even completing the graduation. Love from India
It simply blows my mind that mathematics and nature are basically two sides of the same coin. It’s freaky.
Maths was created to explain nature
Maths was created from nature
Thanks!!!! You made me smile at math e little more.
Never seen such a easily understandable teacher
He is a great teacher, he always explains the real meaning of math.
Many thanks to Eddie.
1:10 "the larger a population gets, the faster it can grow" - watching this amidst 2020 coronavirus pandemic 😂
"you and your feeble units of measurement!"
@@antonpap5540 Shut you mortal, you and your feeble units of measurement does matter
watching this in the first world amidst feminism
watching "things decay when they decay in relation to their own size"
The larger a lie is, the faster it will grow.
I laughed way too hard when he said “this is interesting” because it is literally interest-ing
Exactly. Interesting but not correct :) :)
I love your videos !!!! I showed this video to my math class two years ago when we were taking exponential growth and compound interest.
I really wish I had a teacher like you. I'm Mexican and even though I've had good teachers throughout years, I think I could've learned way more if I'd had a teacher like you. Congratulations you've got a new follower.