Mathematics at MIT
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- เผยแพร่เมื่อ 24 มิ.ย. 2014
- Mathematics has played an important part at MIT since the founding of the Institute. Mathematics occupies a core intellectual position at MIT, an institution that is well known for its leadership in Science and Engineering. (Learn more about the MIT Mathematics: math.mit.edu/index.php)
Video: Melanie Gonick, MIT News
Music sampled from: Her breath (freemusicarchive.org/music/ari...)
Artist/Composer: Arizono Kazuhiro
/ arizono-kazuhiro
creativecommons.org/licenses/b... - วิทยาศาสตร์และเทคโนโลยี
mathematics is not about numbers , equations , computations or algorithms , it is about understanding
-William Paul Thurston
tom srivastava It's also the language of the universe. Math is the science of numbers, shapes, quantities and the relationship between them.
I must concede with what you've stated. Mathematics is another expression of life, an expression that quantifies phenomenon and events. Furthermore, Mathematics is also an explanation to the "nothing makes sense" kind of world all along =)
Hoak Like Galileo once said, "Mathematics is the language with which this Universe has been written"
All science is either physics or stamp collecting.
tom srivastava tell this to all school teachers, none of them will understand
“Professors do math, students do meth”
- someone very high
ooooooooooooouuuuuuuuuuuu
Imma cook meth for Heisenberg 😂
@Ranker's Journey chemist😂
@Ranker's Journey lol what kind of physics inside a meth
hahahahha
"The ability to appreciate meth lies in everybody"
Lmao
@@aarohgokhale8832 its not a joke!😂
Math*
@@arnavjain7566 No I did mean "meth"
i felt thet
I remember the good ol' days 1+2
simpler times
HAHAHAHA
Ah yes, the good ol' days, when we learned that the natural numbers (excluding zero) form a semigroup under addition, and a monoid under multiplication. Good times.
F
😂😂😂
I recall as a freshman our analysis prof said something like: "Many people believe math is hard... that's because it is." I thought that was more honest than the usual attempt to lull people with this fake soft crap. Ironically that guys lectures were some of the easiest to follow and most helpful I've ever attended...
Max E Its not though
It just takes getting used to!
Um for me Abstract Algebra was literally an atomic bomb in my college years. And analysis.
Max E t
Max E must see Channel Nikhil Nirmal Magic Unbelievable Wonderstrucks Geometry Theorum of18°72°90°
I love maths it's just that it doesn't love me back :( lol
Wow
Lmao same bro 🤣🤣 jk I think it do love me back
It is the only case where Newton's law does not work
Lol
Don’t worry, we all think that at times, but in reality it does love us all back; it’s just a tough love that will reward you at the end. You just got to put up with it till then. Just remember that even the smartest mathematicians can struggle at times; it’s all natural :)
I think after completing my Master's in maths I knew one thing about myself, which I doubted my whole life, I am good at analysis. I scored around 95 percentile from real analysis upto functional analysis. Mathematics came easy to me and it shown me the world of data science.
For me maths is not calculation, I am pretty bad at those but its all about analysis and connecting dots.
Maths is not just queen of all subjects but it is god of knowledge provided to humans on this earth.
Very well said!
hey i am currently in 11th std and i have opted pcm can you please tell me how do i start learning it or how do i understand it is there any different way other than just learning formulas simplifying the questions untill i can apply any specific formula in it to get the solution PLEASE HELP
Math isn't hard on itself, it's just that most teachers suck at explaining it.
not only that but add unnecessary amounts of stress by assigning work and grading it
@@revolution545 without grades, i wouldn't have touched math in the first place.
Agreed. I just asked when the tests would be .. knew I'd be better off learning on my own. I think very few people teach mathematics well.
Then my dear you haven't taken real analysis. It can get as hard if you don't take theory seriously, as theory is 80% and numerical part is 20% so for any undergrad it is hard at first but if you seriously study it make proper notes then in my opinion it is simplest subject in maths for me it was Machanical Dynamics as the more I study it the more confused I became. Who says a person needs to be good at physics if you good in maths? For me maths, chemistry and bio are much more easier than physics anytime of the day.
@@kanikahasija3537 aanalysis gave me ptsd
Being good at math doesn´t mean you understand it. I am good at math and I uderstand what I work with, how does it works and why it happens, but I don´t undertand where it comes from. For example, I understand the Laplace Transform and the Nabla Operator but I simply can´t undertand what a genius it takes to develop these concepts from scratch, or how did euler come to e=2.71, or how did they come up with so much more abstract concepts.
Even though this, I still love and enjoy doing math.
+xtheslipknotmaggotx i dont know they development that thing but i must pass the test first
+xtheslipknotmaggotx Euler's proof is actually pretty easy, just take the Mclaurin series of e^x and subsitute x for 1
+xtheslipknotmaggotx None of them started from scratch by the way. They all built upon the works of their predecessors and combined whatever they felt suitable for their problems.
+xtheslipknotmaggotx Yes, I agree 100%.....it must've taken pure genius to have been the first one to have developed these concepts because each one of these unrecognized relationships required one to take a leap and think out of the box.
+xtheslipknotmaggotx Exactly! Being able to relate to mathematics and understand the origins of those, especially the logical steps and proofs, help people to unravel more aspects of the mundane world. Like the distribution of plants, probabilistic proximity and various algorithms, all these are mathematics beyond papers and graphs. For Euler, it's very fascinating as during that time, I don't think there are many people who really understands group theory. Nevertheless, e = 2.71 can be proved from the original definition and from geometries. What's more important, is Euler's Formula, e^(pi*i) = -1 . This can be formed from usual Trigo forms of Maclaurin's Series and then combine them to form e^(pi * i) = -1. Like the joke where people cracked, asking how many people are needed to fix the light, as a mathematician, you'll say e^(pi * i), which is equal to -1. From what I know, geniuses tend to observe and question the reality. Their minds are always searching for answers to imagined questions. Just like how some people came up with conjectures and then went on for lives to discover and sort out the proofs.
I got C+ in calculus 1, can I apply in MIT?
Yeah, as a janitor.
ThePanzerFreak5 and I will end up like matt damon in good will hunting movie? awesome!!
Only If you did that in 6th grade
Hello Irun Mon, do you know Bot Min?
Of course you can apply. Make a clock like some guy in USA ( i think his name was ahmed). MIT will kiss your feet and accept you. And dont worry about your C+ or MIT if you really want to improve calculus then buy some books on calculus (there are lot of good books) stay away from internet for some days and you will be good at calculus , you dont need MIT .
Before junior year, I saw math strictly as numbers. I’d wire my brain to only understand it as numbers. By the time I got to junior year, I took ap Calc AB. For the first time I saw math as using common sense instead of just applying numbers. I saw that math took more reasoning than it did memorizing skill.
Same, my first calculus class was the turning point for me. Never went back.
it's frustrating to feel like humanity has achieved so much but somehow, it feels like we're not even close to finding what we're looking for
Because we are ruled by idiots
Watching this made me feel even worse over my terrible mathematics abilities.
Genetics and most of these kids started early
WKT must see Channel Nikhil Nirmal Magic Unbelievable Wonderstrucks Theorum of18°72°90°
@Chigozirim ᴖᴥᴖ I think he means overall I.Q. which is determined mostly by your genetics. Genetics determines the outcomes of your traits and that includes intelligence to understand math like this.
@@Stiggy- man hard work beats natural talent
Start learning using khan academy
What I loved about math in high school was there was only one right answer - biology, chemistry, physics asked questions on describing concepts and theories - and math didn't. I loved that.
Well then you would probably hate real mathematics.
cdsmetalhead99 aw man :(
27kdon That doesn't mean you shouldn't try it. Often there is one right answer (either something is true or it's not), but there are many different ways to arrive at that answer. Mathematics requires a lot more creativity than many people would think.
27kdon that's exactly what I hate about math lol
Heavenly Hamster lol
"You either get it, or you don't." This is such a dangerous idea. What I have loved about math is that it rewards practice and creativity with understanding. Suggesting that any level of understanding or misunderstanding reflects your actual mathematical potential is exactly the discouraging attitude that keeps many people from sticking with it and really diving into the gaps of what they've learned
Lies again? MRT MIT
@@NazriB ?
I think what she was going for was “The answer to any concept is clear and unambiguous. It cannot be indefinite, like it is in many other endeavours”. When dealing with non-native speakers, things can sound more absolute than they are. No matter how proficient one is, it takes a certain amount of brain power to retain coherence in a foreign language, especially when one wants it to sound natural, like she did.
I've never liked math.. But as I'm graduating this year something just clicked and I'm getting really good at it and trying to understand it, even excited to study it sometimes. Especially imaginary/complex numbers (even though I don't study them and am not required to).
Basically what I'm trying to say is even if you don't really like this subject (or any subject really..) maybe try and look further. Try and find an aspect, a topic, a formula, an idea, a theory. Anything that you may find interesting and look into it then see how it links with other ideas and eventually you'll start to understand it better and start liking it.
Hope this helped anyone struggling with a particular subject
"Either you get it, or you don't get it." I say, "either you get it, or you don't get it yet."
The better version 😇
But the truth is harsh
If u simply dont have the capacity and interest no matter how hard you try u wont get it this is not negative thinking but harsh reality
@@dhruvavikas1632 interest can be made and capacity of a human being is not as constant as you seem to think.
F
Thanks MIT from the deepest of my heart for your open course ware, that's something that shows that human from all nations in this globe need knowledge and have the right to get it. thank you very much
I seriously enjoy listening and watching geniuses and intelligent people so I came here
Levi 🔥
"To me an equation has no meaning to me unless it expresses the thought of God itself."-S.Ramanujan
Dont misquote a legend
Great
@@yashuppot3214 f
Misquote?
Prime Numbers in Holy Quran and Nature --- th-cam.com/video/E3u4NnkPbMk/w-d-xo.html
Yes, mathematics is universal and it can make for a better world. Sadly, politics, money, and special agendas always seem to get into the way of great ideas, and the optimistic child-like mind of unbounded imagination and dreams eventually stumbles upon reality. Side note: I miss Walter Lewin's lectures; he was a great physics professor at MIT.
I feel your thoughts. We'll go beyond those "recurring plagues" one day.
"Better world".
"... was a great ..." Wait what? Why did he leave????
@@heh2393 He was ousted due to a 'scandal' he was allegedly accused of doing; 'sexual harrassment'. I think it was more to do with an over-reactive 'metoo' student who didn't get the grade she had wanted. However, I am not entirely sure if the story has merit, but he left MIT following the allegation. I am sure there is more to this story than I care to investigate.
1:16 the limit definition of the derivative is written incorrectly...
What is wrong with it...
There is an extra equals sign, between "lim h-->0" and "[f(x+h)-f(x)]/h"
oh lol didn't see that
ah, good one!
moremoki First Principle
This is so confusing to a person like me. Props to these people for being passionate and patient.
I'm in 9th grade currently. MIT has been a dream of mine forever and I would love to take these courses when I'm older. I'm studying Basic Calculus right now so if/when I get in, I will be only a little behind.
It seems everyone in their own fields calls everything is just whatever their field is. Like this mathematician says that everything is just maths, then some physicist calls everything is just physics and so on.
Very true. People tend to find a lot of patterns relating things that at first seem to have no connection. That's how the brain works... not saying they're wrong, there is probably a lot of connection between everything that we just usually don't see.
Well Physics and Math do overlap a lot...
Dhiego Bersan well yeah, but even some chemist, biologist and geologist say so
Typically, the more abstract it is the truer it becomes. Mathematicians have the honor of being the most correct when it comes to this, lol
TheArnoldification yeah true. but then again, maths is humanity's product, not some thing out of nature right?
Well here I am. A high school senior and I still don't get Algebra 1...
Robert Trujillo Class of 2017; next summer.
+Jayden Rise Why not? You can learn anything if you decide to. Long time ago I thought the same, that math wasn't "my thing" and now I get every topic I study. Keep working, remember: no pain, no gain👌🏻😬 regards.
There's a trick that I used since Primary 4. Just imagine algebras to be like apples and oranges being mixed around with certain functions that place them in respective places. =) Eventually you'll see the patterns and form "shortcuts".
Fuck Algebra. I failed my high school Algebra 1 class. But here I, somehow managed to get to Calculus 3. Still don't really like Algebra, but after you use it in other concepts it's a not a big deal. Funny how that works eh? Learn the basics of a subject and it looks like morse code, then go deeper into that subject and you ask yourself how was it not this simple when I was learning lmao.
I'm 27 studying chemistry, and physics on my own. I had to go back and learn algebra, trig, and geometry to get to calculus.
Going through a precalculus book is SOOO easy if you just read the section and do all the problems. Put some thought into what you learn as you go along.
When you get an answer wrong ask yourself "why?"
Come up with your own examples.
A little extra work goes a LONG way.
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
At age 28 I graduated Cal Poly with a degree in Ind Eng and had completed Differential Equations.
As a Process Eng. at Weyerhaeuser Co. I tried to figure how to use calculus to determine the size of core that would produce the optimum number of studs from the veneer lathe. I solved the problem using descriptive geometry.
I helped solve a bearing problem on the Boeing 737 wing using a cut away bearing model to explain along with a comparison to a problem solved on a fish cleaning machine in Alaska.
As Chief Engineer for a manufacturer of wood processing machines, I converted steel fabrication techniques into servo controlled burners. The parts were drawn to scale and the thickness of the line was the kerf.
As an inventor, I have designed wheels and tracks that make the ground better by driving on it. The mathematicians and engineers working for the corporations that I approach with my white papers evaluate based on software and they reject my ideas. I have created a data base by building and testing five prototypes.
I qualified on the Boeing FCS Program (50 billion over 5 years ). It was cancelled in 2009 with no results.
I believe our schools are creating virtual engineers who do not believe in learning by correcting mistakes.
Iguana
You are great sir
What I enjoy about math is there is (generally) one good answer and you know when you have it. For physics, biology, or chemistry there is often a long developed answer where you're not even sure if you're right.
2:05 I found Waldo!
Now, tell me his location coordinates with reference to a fixed point. =D
James Zhang (0,0,0,0) his position is the origin, everything else is in reference to that point :D
LOL, so I wasn't the only one.
Hahaha....too good !
Growing ( still am ) up math and science has/had been my fave subjects. Though, funny thing about it was how I'd always Excel in eLa and social studies instead. I mean, the lowest I got in math was a C, but that was back in 3rd grade. After that it was either a B or an A. Then later on mainly A's
I'm currently going into sophomore year in the most advanced and rigorous math course offered at my grade level (Algebra 2-Trig) and I remembered in 8th grade when I'd suck at math. I was doing Algebra 1 at the time and I'd get so flustered and frustrated as to why I wasn't getting the concepts as quickly as everybody else, and I would get pretty bad grades. However, part of that wasn't taking school seriously and I told myself to never give up as mathematics was always (and still is!) my favorite subject. I started doing better and as 9th grade came along, geometry was just another step forward. I struggled a bit in the beginning, but I grasped the concepts much easier and I ended the class with an A. To those who hate math or think they are terrible at it, Never EVER give up!
Gonna cook some math, I need a mathlab. Guss, you there brah?
you need a matlab
It’s Gauss not Guss
Hahaha so funny!
A R it's Gauß
He's attending his brother's funeral. He'll get back to you, soon
"It's all mathematics"
-Mos Def - Mathematics
I am not really good at maths but a deep understanding even of basic maths is so satisfying.
*”MIT is a trade school!”*
_#SheldonCooper__ Quotes_
Thank you MIT, I hope to see you soon and work on the problems that we can solve together, peace and love, Doug.
did you reach mit?
@@teratrox4685 Unfortunately, MIT is not a sentient being so he hasn't been able to see him soon.
dafuk is that gasping at the end? lol thought i didnt close pornhub
let's do some math on that
Mathematics is synonymous to thruth. At any scale, place it remains unchanged.
I completely agree, I used to really dislike mathematics. It was about 3 years ago that I decided to give it a try, after that day I was completely changed. I am now in year 9, seeing mathematics around me, and have been doing mathematics whenever I can, it inspires me and helps me understand the world around me. Already I am nearly halfway through a calculus excersize book, I can't wait to get a hands on experience in making/learning/ helping other people with maths. It is funny for me to think about it know, it all commenced with an understanding.
People can achieve amazing things when they dedicate their lifes to their passion.
wow
Nailed me with that thumbnail, for a moment I thought it was something I haven't seen.
I used to hate maths but when i grew older i find in interesting to see how mathematics works and how big it can be
One thing I've learned when it comes to any subject the instructor will be the one that will help you hate it or love it depending on how they teach.
Fuck this, i'll be a stripper.
so why haven't you? :)
but i'll be safe if i stand on my head if that ever happens.. right?
does anyone know the ranging income of a stripper?
+Andy Shi
Or the "optimal tip-to-tip efficiency" and "mean jerk time"
therocksolid strippers need maths too though
I'm not good at maths but i still like it because when i am not able to solve a problem i became curious that how this will be solved
In 1956 math courses were labeled as M, M11, M12, M21, & M22. Then they changed to 18. 18.01, 18.02, 1803, & 18.04. That cov e red the first 2 years, 4 semesters through differential equations. Next was 18. O 5 and 18.06 Linear Algebra and Advanc e d Calculus for Engrs.
MIT 1960 Course 10 chemical engineering.
I'm not a mathematician but I love it very very much! I wish I have a shop from MIT for me to prepare a mathematic department in a little community I live in in Cambodia. I am actually doing it. I see many great talents here which I want to help them
Michael Sipser's tie says something about symmetry in mathematics
mathematics is a form of universal communication in life.
Hahah no.
Ever heard of music?
@Jojel salamela it isn't a form of communication at all
@@whateveryh211969
@@kingarth0r music is subjective. math isn’t.
mathematics is the basic subjects and it brings the real world to you
imagine the joy of studying math like this,,,, ugh the dream really!! especially in MIT!
'everything is just mathematics' my ears are bleeding, and so my heart.
Mathematics is life💜
You are sure 😂
Communicating Mathematics. Love it! Very interesting and very very very useful!
Thumbs up for Dr Sipser. His book theory of computation is absolutely the best exposition on the subject.
That undergraduate nerd is over exaggerating
@Kick Jowkowski Where is the link?
HAHAHAHHAHAHAHHAHA
Which one?
That is because I have heard(this is not in my experience by the way) that undergraduates are very idealistic, and then become more pragmatic, and some unfortunately go cynical.
@@robertmorrison1657 well said!
I'm preparing for engineering exam and I don't even know what is BODMAS ?
I'm in class 12th ... I opted mathematics...
Hello MIT
wth , this video was uploaded 6 years ago and youtube recommends to me NOW!!!!
I have a history exam tomorrow.
I was looking up videos to explain the renaissance, how did I end up here?
Why am I like this
One of the things that makes math difficult is that it is "build upon knowledge". Unlike other things like history, you have to understand algebra, if you want to even start with calculus.
I freakin love Math. It was/is/will always be my first love (literally my 1st love)
I would love to be good in math , but im bad
An interesting analogy of Pythagoras theorem by ax2+by2+c equals zero while bringing out -b+/- sq root of b2-4ac,/2a graphically swing between left and right side of X axis as y value equals a quadratic equation.This as X2+y2 = c2 as hypotenuse will traverse a circle of radius c a locus of vector traversing a circle in between X and y axis giving an information on rotating vector.
Beauty in mathematics lies in the freedom it gives you to believe only after you have used your deepest judgement.
The conviction you feel then is surreal..
2 plus 2 is 4 minus 1 that's 3 quick maths
get out
maffs*
*mafs
It's one o'clock in the morning. What am I doing?
same here
2 o clock
Same ....1 : 03 am.😂😎
mathematics is just about knowing what you are doing because truly speaking when I am working unlike any other subject I understand it because this is were most of my ideas are seen through
I had to switch majors from CompSci to IT because I flunked Precalc twice lmao
Mathematics is universal language 🚀..
True
Ou 🚀
Avunu
Even I am not that good in Maths…but totally agree…🎉
Agree, taking a math minor now with my che major, beautiful and useful subject.
What a beautiful place.. Hope I get to atleast visit it someday
Not sure what these guys are talking about. But without math, there would be no computer or internet. Which is what you are using to watch this video.
Person514cs I am actually using a baked potato with chicken strips connected to the 6th dimension which lets me view all the information there is.
Person514cs you are probably a troll , but I just wanna know who are the 21 dumb twats who liked your comment
23*
So, making a statement makes them a troll?
ok, sure, why not
2:55 right blackboard "Agenda: SWAG preservation"
This is so insightful without making any sense
The ultimate question in a test that I would make would a really beautiful question which ends with a step from like 4-6th grade just to get the ans
In my own philosophy of life. I strongly believe every machine such as cars, industrial robots and eletrical generators.. they are all moving numbers and mathematics.
Fun fact: Everyone who applies to MIT knows the answer to 1 + 1
everyone who gets accepted to mit you mean. when i get child ill apply them immediately to mit to prove u wrong
It looks simple
But theres gonna be that one question that want to make it harder than it seems
@@shybound5905 imagine going out of your way to have a child and then applying to mit with their name just to prove a random youtube comment wrong
I envy so much those people that talk about math with such passion
Wow!!they r all expert in maths grt professors👏👏
Me: math looks interesting
Also me: Too many knowledge brain hurting
*meth
Is there such a thing as a perfect measure, perfect in the sense of being consistently even?
There are the planck units,
although that's physics
This vid just hyped me up for decision day tomorrow
Mathematics illustrates a multi-agent system, and variables represent agency of that multi-agent system.
Education system in India is much difficult than others, as we learn many such difficult topics in our Class XII,but our coaching industries for preparation of IIT is making us a robot, and thus I am also becoming slowly-slowly a robot.
Cuz yall poor bois cant be in international schools and go abroad
@@darkblade3636 that’s mean.
Well ya know why just keep working hard and you’ll be amazed.
@@michaelterrell5061 I'm doing the iB in india nothing tough
@@darkblade3636 Hm...interesting.
3:38
no, you do in fps
we do it in mks way
Mit finally got it right on what I'm seeing connecting the dots
In Mathematics, you don’t just understand equations and concepts. You get use to them. -John Von Neumann
Therefore, explains why practice exams are provided before each exam.
I love math, it's honestly my favorite subject, just ahead of bio and chem. I'm looking at MIT because it seems like a place where I'm a good distance from my family and a place where I'll be able to express myself and ultimately find things that I enjoy, maybe even drop some bad habits like procrastination. My family has honestly been holding me back from so many opportunities, being in a far right household while personally being an extreme leftist does that. I love them, but I hate their ideologies and actions.
Two more years, and we'll see if I can make it.
Did u make it ?
John had a pineapple. He decided to make a smoothie with AN APPLE SQUARED PLUS SQUARE ROOT OF NEGATIVE ONE PLUS A ROOT TWO PI MULTIPLIED BY E USING C IS 33 TO THE ORANGE CHICKEN OF 79. And then she used some kale.
😂😂
out of all math topics, combinatorics and probability are undoubtedly, the most interesting
i love your vid, keep it up
mathematics is an endless language
It makes smiling to see that I can't be there
Am doing research in Stanley's depth of different graphs and interestingly Stanley was from MIT
Mathematics is a way of communicating through your knowledge and applying it in real life.
Hi Massachusetts Institute of Technology =),
I would like to say, thank you, for taking the time and effort to both upload and share this video with the youtube family. I hope you have a nice day! =).
@@jeerdace8625 dicks*
meanwhile in Yale... "This is not about creating an intellectual space, it is not!" just kidding. I understand if you're nitpicking you can do the same to any school.
I love math. This video just motivates me🙂
I want to meet those profesor one time as a bsc math undergraduate student
ha undergrad math major calling himself a mathematician lol , you aint seen nothin yet kiddo
LMAO