Analysis III - Integration: Oxford Mathematics 1st Year Student Lecture
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- čas přidán 8. 05. 2019
- The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the course to the mathematics our students have already learnt at school and develops that knowledge, taking the students to the next, more rigorous, stage. Like all good lectures, it recaps and points forward.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): • Oxford Mathematics Stu...
CZcams: Lets send everyone a math lecture
CZcams recommendation jokes in 2019. You may as well have commented "First!"
I like it
😂😂😂😂😂😂😂
Need to learn some math algorithms for the Rubix cube
thanks youtube
No one:
CZcams: Hey wanna learn some mathematics from Oxford?
Why not tho.. It is nice content.
Yes.
Me: FUCK YEAH YES
Someone who can explain this joke it's on all twitter and i can't understand even more than this video hahaha
Hel ye
Finally I can tell my friends that I attended at Oxford
RishIKesH MorE 😀😎
Attended at?
Nope, if you mangle language like that, you never went to Oxford.
Breyner Rivas Agudelo I think it should only be attended Oxford
Breyner Rivas Agudelo “was an attendee to Oxford.”
@@rbanerjee605 it's attendee thy art of Oxford conservation of happy
My favorite parts are when he says "and I think it's fairly obvious that.." like yeah bud sure is
If you know your maths and if you’ve done your prerequisites a lot of things like these are fairly obvious, or straightforward. Sometimes though lecturers cop out and say it’s “obvious”, when really they don’t want to do the problem, but I’m sure this isn’t the case.
Welcome to math at university, where nothing is obvious yet your prof tells you that it (read: everything you don't understand) is very obvious indeed every 5 minutes.
LMAO
@@Bibi_effin_Blocksberg same for physics, "i will skip the proof of this since it's obvious"
If you understand a little bit of open ball topology (open/closed sets, limit points, compactness), and a little bit of real analysis (sequences, construction of real line, convergence, series), and linear algebra (function spaces, vector spaces, etc.). Not saying I understand it all, cuz it’s hard for me too, but I’ve been exposed to the subject
Feels great knowing Oxford isn‘t teaching differently than other universities...
Their system of tutorials is a bit more unique because it's always very few numbers of students per teaching staff (usually max 3, sometimes even 1 to 1) but yeah the differences end there pretty much.
@@gooscarguitar ah ok. Yeah when I was younger I always thought of it as this super elite school where they show and teach you stuff you won't learn anywhere else...
@@gooscarguitar - You can see 15 students in the video - and those are only the ones that happen to have been caught by the camera.
@@yeahiagree1070
I know, they do tutorials as well as lectures.
I think lectures and tutorials are separate things. Don’t quote me on this, but from my understanding they have lectures with the whole class and then tutorials that take place at their college in groups of like 4 max. I don’t go there though, just what I gathered when I applied to Cambridge (and got rejected) for medicine. Assume it’s the same though.
not sure why this was recommended to me.
watched it anyway.
understand nothing.XD
Dan K. u r a literture student I think that's y 🤣😂
🤯
czcams.com/video/z_WsUNs6-iw/video.html
"And actually what's pie?
So we'll also be carefully defining pie."
Now it all makes sense.
@Paul Mallory but i feel like u are too weak in integration i'm from Bangladesh
Same
Appreciate that he’s writing all that without the need for any notes
My first thought
@Nathy V Actually no, they don't. In the UK it would be once a year, but even that would not be true in this case. Lecturers (at Oxford) tend to swap/change every 1-2 years. He's Ben Green, that's the 'because'.
Lua Exactly. Thank you
@Nathy V as a math teacher, i c what u said is absolutely right..
@Nathy V thank dear, for your appreciation.🙏
Oxford students : 1%
why it's on my recommendation: 99%
lol
Because people are not blocks of wood with labels like “students” nailed into them. It’s about spreading beyond the boundaries. I think it’s great.
My dream was to become a physicist and a mathematician but the conditions of life made me a doctor. Although I am a successful doctor, I still practice my passion for mathematics and physics. I love everyone who cares about mathematics and physics and my greetings to the great professor and all the Oxford students from Turkey
Mathematics is game of brave peoples
Thank you for sharing this. People like you are inspiration to the rest of us. Being a doctor and keeping your interest in mathematics. God bless you sir. Best wishes from Serbia
Poor you
You do not know how happy I felt to read your comment, especially since I study mathematics, but I feel despair because of the lack of interest in this great science in our Arab countries 😔😔😔💔💔💔
🤗🤗
I guess CZcams is recommending it since it’s exams season in England and students from Oxford are rewatching their podcasts in an attempt of being of able to prepare for exams lol...
Maybe !
That professor right there is writing the algorithm for recommendations of CZcams videos.
The Sad One 🤣🤣🤣🤣🤣🤣🤣🤣
Fucking underrated!!!😂😂
Mmm yes you must measure the precise derivative of the milk being poured in the coffee at the average integral rate for which the quantum mechanical principals must be applied, to ensure total accuracy.
This video make me want to drop out and I'm not even in college
😂😂😂 im dead
Hahahahahaha
I finished college 8 years ago and it makes me drop out, LOL
lol...good one
Its kind of easy actually xddd :v
2 + 2 is 4 minus 1 = 3 quick maths
@Youcef Youcef Non 1+2=2
*mafs
Everyday mans on da block
Cheeseburger stfu I go to oxford
great ehien yeah of course
How did I end up in the educational section? I was watching parkour deaths just a moment ago
CZcams had enough
First of all, the youtube algorithm
to calculate hours and days to parlour death lol
where the link at doe
😂😂🤣🤣😂😂 so you can calculate how much energy they hit the wall/rail/building/floor/old lady/ huh? with.
Honestly quite blessed that MIT, Oxford & other top universities put up their lectures online for noobs like me to watch
i just cried and had a mental breakdown while watching this and i’m NOT EVEN TAKING THE CLASS
What is he writing on ? It looks like a whiteboard but bends like paper.
White paper
Its a A0 paper
@@vettypasanga9955 But why paper ? What happened to black and whiteboards ?
Lol, it’s a rolly whiteboard. It gives double the space of a blackboard
I am a student at this university taking this course. These are flexible whiteboards which we can move up and down, and they kind of wrap around the whole board space, so what you see is only half of the available board space. To use more we can kind of rotate the board like you see there.
CZcams: our audience are oxford math students
CZcams is a men of culture.
@@yahooperfecto4470 man*
@@2014ax *men
@@symbolitical4158 *min
*maths
Most interesting thing about this whole video was those boards he was drawing on 😂
Ikr 😂😂
It bothers me how they crinkle when he pulls them up.
Anybody else disturbed by the sound it makes when he's writing? I can't stand the sound of that friction.
@@KDErkisi very much so
Wahi tho. Isse accha selate par likh leta
The board, the cloth board, is really annoying. Give him a solid board!
書き辛そうw
JoeL as a teacher, I think that board is DOPE!
Yeah, that's kinda weird to see)))
victor Channel なんでもない
@@user-rb5yd6uk3y すみません.日本語おわからないです.
Good sleep material, my insomnia is cured 🎉
Lol
LOOOOOOL
😂😂😂😂
Legendary comment
@@b.m.5068 seriously legendry commend.....😂😂😂😂
I’ve been watching this for 10 minutes before realizing who the lecturer is. This guy is a very famous mathematician. It is a privilege to get to see him lecture.
At oxford i would be feared to ask a question, because the Profs are that intelligent.
@@herbertdonermaier7459 They are human just like you. With strengths and weaknesses, don't be afraid to ask questions.
Who is it?
Jalees Ahmed His name is Ben Green, and he has won many awards in mathematics. You can read about him here:
www.maths.ox.ac.uk/people/ben.green
Actually I recognised him immediately.
Thanks. I took some good notes. I hope I get a win on fortnite
fornite is gei
@@jonchan252 petition to ban fortnite in united states
czcams.com/video/WJ21fTvjVwk/video.html
Teacher: I'm sure you all already know...
Me:
I finally know how to make my integral's notions rigorous.
Been bugging me for years, that has.
Nobody:
Annoying students: **when will we use this in real life**
@@mkalsterboy1234 true lol
Cheeseburger no I’m just making a joke about what students normally say about this kind of stuff
Cheeseburger oh I didn’t think it was coz I’ve heard loads of people in the past theorise that life IS LEGIT A SIMULATION lmao
Ahahahahahha
literally no one:
CZcams: it's time to learn some math!
Lol
It seems that CZcams's algorithm is feeling a little bit guilty: after years of burning our brains with «shit» and «stupid» videos, now it's trying to teach us something «useful».
@@MissRoux exactly! for years recommending me those Logan Paul shit...
666 likes
Thanks CZcams for not making me bored during my holiday time.
Literally no one:
CZcams: Lets learn about math problems for no reason
i nearly failed high school calc. why am I here?
I almost failed high school Calculus. There were just too many hot babes at my high school. But got an A in college.
To fix that ;)
It's explaining the theory behind high school calc, so you might give it another try?
@@Rorkazak weird flex but okay
lmao i just constantly came late to the lessons (since it is in the morning) and never even did the homework
Nothing but admiration for those who can understand and master this. Mathematics is the language of everything that exists.
Actually mathematics are a tool we created to make models about reality, but they are just models, reality is written in another language hahaha
@@rodrigoniveyro9763 I guess, but the fact that mathematics can be used to explaon pretty much ANYTHING with an equation/algo etc seems to suggest to me that mathematics exists independently of life.
But I'd defer to someone who's studied the subject.
@@rodrigoniveyro9763 You are wrong, in physics we use mathematics to "compact" descriptions of physical systems. But it is a coincidence that mathematics just "works" as a tool. What other language do you speak of since you find it so funny? I only know three languages, English, Spanish, and math. But I can argue that math is a discovery rather than an invention.
@@tinyspeaker Math by itself doesn't describe anything. It is a lot of substance with no function until a scientist, engineer, puts that substance in to something useful. In physics, chemistry, even in biology, it is very "suspicious" that math just happens to fit with our theorems. So I can agree with your last statement.
@@alexv5581 I think you made the point that I was poorly trying to myself, that maths is a discovery and not an invention. But interesting, I didn't see it from the perspective that its not describing anything.
Didn't know Oxford lectures this but I'm so glad I've watched this calligraphy course!
YES.... Yes of course! I get it now!
CZcams Recommendation at it's finest.
I am preparing for a math exam, they give me math lectures. Astounding AI, it can read minds!
Somehow CZcams algorithm recommends this video to me.
I see what you did here 😃👏
Wow! just what I want to see pop up in my recommenced after I finish writing my math final. Thanks CZcams :)
This is actually quite an interesting lecture and does add a greater understanding to integrals. I wish I had some qualifications that would allow me to study the full course
One of the weirdest things about Oxford is watching world-class mathematicians teaching basic first-year material. This guy is incredibly well respected and has collaborated heavily with Terry Tao
Do you know how much that would, on average, impart the spirit of world class mathematics to the juniors? I wish I had that sort of an opportunity when I was their age.
@@nahidhkurdi6740 I was lucky enough to have the experience myself. It has definitely been one of the most formative and important times of my life moving forwards, and a unique experience in its own right
I'm law student, don't know a thing about math, yet here I am.
Its an interesting subject. If you get a good grasp of calculus you can make predictions with a degree of accuracy given a set of statistics or values. Great for economics and science. Its the math of change.
Same
Politics too
Haha, I'm a Law student too
@@charbelhv yeah i gotta admit that now i don't know anything bout politics. i mean, i used to know pretty much of it, but as the course is getting rougher and rougher, i don't care a thing now, man.
He seams like such a chill and nice lecturer. I'm enjoying this so much more than my lecture on integration that I'm taking at my uni in germany^^
"This courses is about integration"
*My brain left the chat*
Me: *learned the circumference of a circle is 2pi radians in 11th grade*
This professor: "you should've know this since primary school"
I learned it in 7th, I guess everyone’s school is different idk
@@S0M3THING 7th grade!? I wish I was exposed to these concepts earlier. Yeah, North Dakota is pretty behind education-wise
I learned it in 5th
@@satanlucifer4437 if it makes you feel any better, I learned this in year 11 (UK)
Make a 100 slot wheel. We need giant ones we can walk on. Refer to percentages as slots. Et cetera is maths future.
That's a curtain not a white board
I've given seminars on these boards, they are *awful* to write on. No tension in the fabric at all.
@@rosePetrichorHear, Hear. I attended my friends PhD defense and the bloody board wouldn't shut up.
thats a projector screen
Hi, I really appreciate that you have put these lectures up, thank you so much!
No one:
Prof. Green: " [...] and that's pretty obvious"
What a struggle to write on this paper (he has to use both hands!?), bring back the blackboard.
It's not paper, it's a whiteboard...
Totally agree! Maybe promote #bringbacktheblackboard ? Hahah
Doesn't seem to me he has any problem at all; on the contrary he writes easily and rather beautifully. And he uses acres of space - doing that on traditional blackboards would be impossible without spending much time erasing and filling the atmosphere with chalk dust!
@@lsbrother You cannot be a mathematician without having chalk dust in your lungs :)
Chalk boards suck though.
Soy Venezolana y me siento orgullosa de decir que como estudiante de ingenieria los profesores que tuve le echaron un cerro de bolas para explicarnos esto mismo pero con muchisimos menos recursos, ojalá las universidades de mi pais algun dia lleguen a ser tan sofisticadas como esta. Honor a todos esos profesores universitarios que a pesar de las adversidades y del sueldo misero se esfuerzan por educarnos.
Was taking my break from Economics studies and found this, very good way to relax.
I think that's pretty clear - Oxford's profesor 2019
I don't even do Mathematics... I don't know why I'm here, but it's so interesting! 😂
Then you've skipped a lot of maths
But it's easy to understand this
@@marcioamaral7511 LOL, what? I don't do maths, it's got nothing to do with skipping...
😂
I'm still in high school
my feeling too
My high school math final exam was 4/10 . What do you want from me ?
Lol
Hahahah
Kak Wildan mine was 3/20 😬😎
4/10 would be a fantastic score in something like the International Mathematics Competition.
Anak pintar😂😂😂
2:50 “circumference of circle is 2pi”
Me: I understood that reference!
BluebearChu that’s literally the only thing i understood to...😭😭
OTAKU SAMA -amine right? He writing symbols and words I’ve never seen in my life 😭😭😂
"I understood that reference" (in Cap's voice)
Circumference of circle is '2πR'. NoT '2π' 🤣🤣🤣
Physics X I forgot to add radius 1 is 2pi 😭
without any notes ...amazing...and if he teaches likethat ...advance courses too...amazing
Daaaammmn you spend all day watching Khan academy for finals and the algorithm starts recommending this.
So, the point remains the same.. I should have done my homework before this surprise lecture from CZcams. Also, i didn't attend the first and the second lecture...
@John Wick I know
@John Wick what a day... John wick accepted Islam.... 😯
This is the first lecture. Analysis 1 and 2 are different courses.
Aula mais que perfeita ❤
Thank you CZcams, it's just what i was thinking about at 3 A.M.
Some people have a lot to say about the whiteboards but, it seems to me, the lecturer uses them easily and effectively and has no problems at all.
1am and here I am watching. Waddup people😂 i know im not the only person to who YT recommend this vid
Exams season
Yep happened to me too, horrifying!
HEY THANKS FOR THIS KIND VIDEOS! IT'S REALLY IMPORTANT! THANKS AND GREETINGS FROM Bogotá COLOMBIA!
His majorities are spot on!
Yesssss!!! Thank you thank you thank you thank you!!!!
I study maths in Germany. But we had the Riemann integral already in Analysis 1 or 2. Now I feel even "smarter". But good to know that these classes at this famous university are as "boring" as here :D
This is a first year course. So it was taught right at the beginning of their degree
I'm doing my bachelors in humanities and here I am watching this video
@The Media Norman what are you talking humanities means history sociology its not humanity
Me: am i suppose to take notes?
what an amazing video so entertaining and joyful its easy and fun
Glad to know CZcams looks out for me in moments of trouble
The sound of the marker relaxes me
This is going to be essential knowledge when we apply for work at Starbuck's.
The students in this video paying for this class when I’m watching it for free on CZcams 😎
Chip Skylark I wanna see you when you've got at least 1 question during the whole video 😂
Gerson Bernal what the hell are you even saying 😂
Chip Skylark i don't fucking know, 26 hours straight without sleeping, ok thank you
I remember when 3 years ago I have started studying chemical engineering and my first exam was analysis 1, now all of what he's saying it's obvious, but 3 years ago it wasn't :')
When i was over glad, i came to this video. To stabilize my emotion.
Isn't Analysis 3 generally considered to be a course on measure- and integration theory introducing the Lebesgue integral?
It is remarkable that he is writing without using any notes.
I’m a biological genetics student why am I here and why does he keep saying rigorous
abbie sharpe
Because u r also interested in those boards, which he is using😝😝😝
“Rigorous”
That’s a standard math terminology, I find it hilarious that of all lectures or math or stem related videos, this, pure math course, that few people know, got recommended to everyone. But, rigorous means, well what it’s defined as, extensive, difficult, longer, precise, rigor is used a lot in pure math. So in a regular course you’re taught that a function is continuous at a point c, if you can take the limit of the function from both sides. A rigorous definition would be that there is a delta greater than zero, such that |x-c| implies that there exists an epsilon greater than 0 that |f(x)-f(c)|< epsilon.
@@sedeanimugamez5418 shut up nerd
i'm a high chool student with a D in math i can relate
Can't help but click on this recommendation, after watching for two and a half minutes, that's it.
It's so good to know the equivalencies inBetween integrAl summaries and target sum(mation)s.
Especially when building a true
Quantum ConversationAl
Neuroholographic Network, entangled between quantum computers/reServers and FPGA chips reactive to topological error-correcting codes; stabilizer lanGuages.
So, we meet again random video
(Good thing this subject is not a concern anymore, except for Math Analysis II, next year)
Skips 10 minutes
"Yo, wtf"
More like: Skips 10 seconds
I talked to this dude once. He's extremely smart.
When he said step function...I was thinking of greatest integer function...then he changed the game by saying he don't bother about that constant value ....enjoyed the lecture...
This is not a weird recommendation for me... I suck in integration and it really cleared some of my concepts... 😉😉😉
These mathematics lectures go over the smallest details possible. Makes almost every engineer fall asleep.
Thus why they use math students and not engineers to do the math
@@lourensstrydom1502 Engineers do maths just fine. We just take the more practical approach.
@@howardlam6181 pi = 3
@@gooscarguitar e=3, pi=3, g=10, R=.1, Rj=8, fuck yeah.
And thats why i love the youtube recomendations
This is like a therapy for me 😊
It's ASMR for me.
日本人発見
how can he know this all by heart and still make less mistakes than my prof using his notes all the time
where can we find the rest of this course please?
'relatively easy'
Yeah that's spot on, bro!
Is that a reusable erasable board or one time use hmm
I hope it is, it would be a big waste of paper
Reuseable
@@alexhomovc8179 tru
@@ManagingVideo yeah, I'd assume so, thanks, material looks one time use lol
@@2PacPRNDL its whiteboard material, just without the solid board behind it
How does this board system work. I’m so confused.
Its basically a scroll
Have the next episode released online?
This is pretty good!
Do Oxford have a hand writing class... Just saying...
Being a med student this reminded me of my old wounds but dk why it was a pleasure to watch 😂😊
Hi baby
Afsar Ali wtf dude
@@czechmeoutbabe1997 😂😂😂
Awesome lecture!
Almost everyone making jokes about that recommandation iam not saying it is interesting but that prof. Ben green is seriously one of the intelligent mathematician he gave the famous GREEN-TAO THEOREM so give him some respect . I think he is calm and did't talk too much.
I'm dropping out of this class through the chrome backbutton.
Loser!
@@demetrius7184 Pretty true actually
if ana 3 is a 1st year course, when do the students take ana 1/2?
@@Kr46745 exactly
@@Kr46745 In Belgium we had Analysis 1: Real analysis and metric spaces, Analysis 2: Integration theory and functional analysis. When do you guys learn metric spaces and functional analysis?
Kr1ngou in italy we do integration at analysis 1 (in analysis 2 double and triple integration)
Niccolò Tommasi Im studying math in Germany. What is double and triple integration? 😅
Frank Grimes double integration is when you integrate a two variable function respect to the first then respect to the second one:
Eg: ∫∫(2x +y^2)dxdy = ∫[x^2+(y^2)x]dy =
=(x^2)y+x(y^3)/3
Geometrically it represent the volume under the surface of the f(x,y)
Triple integration is the same adding the variable z and so on..
CZcams reminding me its time to study
Thank you
Studying at University Of Oxford
That feels honoured realy very honoured