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- Опубликовано: 28 сен 2024
- Here's a top tip for aspiring mathematicians from Oxford Mathematician Philip Maini.
Be lazy.
More advice (and maths) from Philip in his 1st year student lectures on Fourier Series, the latest we are making available to you all. • Fourier Series and PDE...
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I'd say this is great advice for more advanced students.
It's great advice for all students, being a good mathematician is being an efficient mathematician
@@olliecole7163for the lower levels I think "being lazy" is already emphasized too much. For example the emphasis placed on memorizing Formulas and Steps, over intuitive understanding.
But it seems the opposite is more common at higher levels.
@@shemmoirichards yes in grad school, finding the lazy approach is usually what's novel and interesting mathematically. But I agree, at the undergrad levels, hard work pays off when it comes to checking/showing your steps carefully.
For less advanced students, this advice wastes more time than it saves. If you don't understand well what you are doing, you are better off doing more work, trying to think of that lazy way might take time. It'll happen, but it'll be a while.
@@VeteranVandal this
Happens with me many times. While solving que finding clever ways is very satisfying and interesting but during tests since it became a habit of mine I tend to keep finding clever ways even when I know the proper way to reach the answer, and end up wasting some time.
That is not being lazy, thats being creative and efficient.
Right
Lazy people are creative they’ll always find ways you do thing easily without putting much effort.
@@vipul3967 Lazy people in general are neither creative nor find ways, let alone always.
@@raymondz595really depends on what type of lazy someone is. U can be lazy in a way and hard working in another at the same time.
Bill Gates: “I choose a lazy person to do a hard job. Because a lazy person will find an easy way to do it.”
"Why are you not cleaning your room!"
"I'm a good mathematician"
😂😂😂😂You are lazy!
😂
Fine a clever way toh clean your room faster
😂😂😂
😂
My lazy ass not even solving the problem:
LMFAOOO
@@paris6604Lmfao
HAAHHAHAHHAHHAH
This is gold.
Lmaooo
Bro was preaching "Work Smarter, Not Harder" to college students about to exit with mountains of debt in student loans. Bless his soul! 💯
Tsk tsk, you shouldve picked the rich parents option before starting life
This is Oxford University. Annual cost of tuition is around £9000, which can also be waived if you receive bursary. This is the UK, not one of the broken US universities where you have to pay a few hundred thousand dollars for education.
@@aeea3306 Yeah well, I ended up going single player mode with divorced parents of average income, then migrating overseas. The game has been alright so far :)
@@Archemik99 £9000 per semester is still quite up there once you convert the currency to any other in the world, especially that if it's given as a loan, it will continually compound.
if they're in a math class this advanced, they'll be fine.
Its flattering that youtube suggested this to me.
Greattttt comment
😂
I’m impressed you found a way to make this about yourself.
I still don't know how I survived algebra 🤣
@@musashi.miyamoyo You are the guy who sees narsistic people everywhere.
"How many chalkboards do you need in your auditorium?"
"I need ALL OF THEM!"
how does he write on the top one xD?
@@fri_punt_soyou can pull them up and down.
The point is to have what you previously wrote on the board stay for longer before you have to erase it
Correct answer "Yes"
Also must know advanced white board manipulation theory.
He's got none!
No chalkboards. No chalks.
Only whiteboatds and soft tip markers!
As an IT guy who heard this advice years ago I would definitely say that it doesn't apply everywhere.
Sometimes you just need to do something even if its a bruteforce approach before you're able to learn from it and do it better next time.
Laziness is something you can pull off when you have the knowledge and experience to be lazy.
Indeed , that's what I'm thinking
I struggle with this, my math teacher also always said to be lazy, and I took this advice into my programming. So now I often just sit there staring at my screen trying to think of a way I can do something easier, which is not necessarily a bad thing, but it is hard to not overdo it.
Sure, but you should at least regularly try to make this step backwards. If you don't see anything, you can still bruteforce
Lazy clean code beats spaghetti code any day. Same with physics and math.
That's exactly right. And this applies pretty much in field that uses math.
for those wondering in this particular example, when it comes down to fourier series, the function you're trying to turn into sines and cosines may be either even or odd, and in the case of fourier series, you decompose the function into its even and odd parts, however, if the function is just even, for example let's take f(x) = x^2, there are no odd components, so finding the b_n term, which is the sine component, sine is odd, and there will not be any odd component, so the integral with respect to x^2*sin(pi*xn) from -pi to pi for example is going to be zero due to there not being any odd component in an even function.
Wait - I was just going to say that
You beat me to it!
Nah, just kidding. As Homer Simpson would say: "What was all the stuff you said about the things?" 😂😂😂
@@YaNeK92 one day we will learn it 😿
@@mahyargharehdaghi9383 I don't think so to be honest. Much sooner will be in control of an Android AI powered bot who will use similar equations 😄
@@YaNeK92 we've gotta adapt and evolve faster to have any jobs in the future at this point 😂
How many whiteboards do you need?
Him:Yes?
This only applies after you have sat down and gone through the material very thoroughly. Only with a solid foundation can you bend numbers at your will. In other words, don’t blindly memorize formulas, methods, etc. Instead, you have to understand why they are how they are.
Great point. If a person is so steadfast on the problem. Instead as you say, is there ways to simplify, or to come at another way. Great video
Finally, decent content on this platform.
Bro youtube is just an algorithm, think twice before you watch/click on something and 90% of the time you'll get more decent content
If you stopped watching useless stuff you would stop complaining and feeling like a victim. RUclips is not an evil organism that manipulates you to watch Andrew Tate and become a sigma male.
If RUclips is recommending junk content then that’s on you. RUclips uses an algorithm based on your internet activity to make those recommendations.
there are LOADS of very interesting audiobooks and lectures on this app.. just look for them and you'll get more reconnected
Can any of you tell me that how is the whole class be a able to hear the voice.
No, sort of mic is looking there😅
Efficiency is not laziness. It saves time and energy for you to get more work done in less time.
The point is that lazy people tend to be more likely to look for workarounds so they don't have to do as much where hard workers may just throw themselves at the problem until it's done.
It's not literally "be lazy." It's "take a note from lazy behaviour - some of it works here."
This is not only the imp question class but also full concepts in short time class...with each and every ques we learn a concept
Thankyou so much sir❤
This serves for anything in life, brilliant❤
I used to say this to my students all the time. "Maths is for the truly lazy." If it weren't we would keep adding everything rather than multiplying. Continuously multiplying rather than finding a series. And so on.
Finding the simplification is the act of a person saying "oh I can't be bothered to do all that" and finding a clever workaround that then shows an interesting property you never knew.
For example when I myself taught Fourier Series I made a point of going back over Odd and Even functions and their properties when added, multiplied, and integration of a function which is odd or even about the midpoint of the interval. This was after doing the longhand method for a while, and someone ALWAYS protested me doing the odd/even stuff, until I gave my explanation about how this is the TRULY LAZY thing, and blow their socks off with the sorts of simplification you can make.
In my fourth year of High school, a teacher got a bit angry with me because I kept finding easier/simpler ways of solving math problems. First year,of college, the lecturer encouraged me to keep doing it.
@@wain___614You must be really smart...
@@wain___614I truly believe from an American perspective a few teachers from my highschool in Florida was like this and college was a breath of fresh air. Students should finish high school from home asap and go straight college or intergrate highschool into college
i was in a physics class last week talking about vectors. there was a point where i looked at the example we were working on that was taking like 20 minutes to get through. "... can't we just use the law of sines?" took like 5 minutes that way. especially bc of my primarily inattentive-type ADHD, i hate spending more time than i have to to get things done. 😂 i want more time to play games.
everyone is truly lazy
Professor Maini! A great source of inspiration!
This is good advice for a lot of things in life. Not just mathematics
Thank you, so much
If anyone is wondering, if f(x) is an odd function an (including a0) equals zero and if it's an even function bn equals zero.
This is how you know the value to the integral of sin(x)*e^(-x^2) dx, from -a to +a
Even though it isn't possible to do this integral in closed form.
His lazy and most people think lazy is different lazy. So listen people, please dont be lazy.
Yup. The lazy he means here is efficiency.
Don’t be “lazy”, but be “lazy”. Got it!
This is true for so much. Not just math, but excel formulas, work processes, programming... You don't have to aim to be a mathematician to take a step back and find an easier way to do work by automating it or condensing it
We can use the concept where the integration of odd function is equal to 0 where the limit goes from -π to +π
Odd function in symmetric domain, not necessary-pi to pi
And if your odd signal has quarter-wave symmetry, you can further simplify by integrating from 0 to T/2 and double the coefficient.
No that’s not true. When you are integrating to find the Fourier series, you multiply your function to a vector that is neither odd nor even. Therefore, it doesn’t apply in this case.
Never thought about it in that way but i carried that laziness into my career in embedded software and became very successful
this man speaks an universal truth, not constrained to mathematics. I think he knows it :-)
Don’t see his name anywhere. Seems disrespectful to just call him ‘this man’
@@sustainableliving6319 congratulations on the most nonsensical sentence of the day. Would you care to share yet another word salad? Your audience awaits ...
@@ololh4xx Thank you. I mean, what’s his name? We’re appreciating his work, should be credited with his name.
@@sustainableliving6319 professor maini
God is about to come through 🎉🎉🎉❤❤❤❤
This will definitely see you through life. I would use this Equation daily to solve issues
In engineering, we use rigid and fixed equation templates that we do not change, but we always try to find easy ways to solve problems and search for the most comfortable ways. Good advice.
"Don't crunch the numbers like a madman"
I would argue that the first way is the lazy way
While what he called being lazy is creative and efficient
thats not laziness thats being efficient
using trick can mean something many thins 😅
one of the things it can mean is breaking some laws.So, this doesnt work on all problems and you are kind of ignoring the idea and just calculating .
i think using trick is good when you are trying to understand the problem and the idea some times like a backdoor method😂.
You got the joke, congrats
If you weren't lazy you wouldn't necessarily think of a more efficient way
Yea but imagine doing that in an exam? Wouldn’t work
Or you can say working smart.
it's true not only for mathematics. in every aspect of life, you always gain a lot by stepping back and rethink your situation. it's even more lucrative in your personal growth.
I literally experienced this in school a few days ago. It’s a standard Mean Value Theorem problem with sin, gotta find C, which is the Secant line… wait, the Secent line is just essential the average value. Sin function goes completely horizontally. With that info alone, you can just safely assume the Secant line is 0 and save 2 minutes of calculations. Same for Cosine and Tangent functions, so long as they’re by themselves.
This is good advice for other things as well.
Nice to know I'm already halfway to becoming a really good mathematician.
The clever way usually utilizes some symmetry of the problem.
Professor’s version Lazy includes sitting back and thinking. Thoughtless Meditation is lazy gold.
That's the way classes should go. Students should be taught how to learn and not just be bombarded with raw theory and methods.
....you say as we see 10+ boards full with nothing but raw theory and methods which one will have to memorize for the exam
him: is there a trick?
me: immediately opens chat gpt
ChatGPT is actually really bad at Fourier Transforms. Which is the subject of this lecture.
that's why I always photocopied my friend's math assignment.
❤😂
mega lazy
😂
Works like a charm
....... until your friend becomes mega lazy and starts photocopying someone else's assignment
Must be applicable to many other things irl such as business marketing. Thanks ❤
Exactly my thoughts for a few days 🤩🦧
All of advanced math is basically clever tricks and shortcuts
😂
Stop yappin bruh
Professional yapper
@@jigglyCroissant?
@@syed3344 professional pp swallower
"How the hell did he write on the upper boards..."💀💀💀
💀 spider man
He can pull the boards down 😅
As a math's teacher..i can confirm ...its true 💯
integrate from 0 to pi and mulitply the whole integral by 2 instead of -pi to pi as the distance to the two points are equidistant
Respect
That's using your intellect and knowledge in an smart, optimal and effective way.
Can't ask that on YT.
For those who are trying to find the topic that sir is discussing, it's "Fourier Series" where expressing an algebraic function can be expressed as a sum of Series of sine and cosine.
The clever trick he is speak is about the utility of integral of odd and even function.
Just integrate it......5 minutes
Sit back and look at it...2 minutes. Then solve it the time saving way... 3 minutes.
Overall time...5 minutes.
Thanks professor
One of the best advices I heard. Can be applied to different stuff as well
This is right. But it's actually harder for most students to spot the simpler way. Many tend to overcomplicate things. And you won't really get it, until you've experienced both.
I'm so glad I never have to do Fourier series and transforms and PDEs by hand again...ever
A couple of girls from my class used to do this, so special and intelligent 😊
It's VERY GOOD, and it actually works 👌👌👌
clever way: integration by parts, buton cylindrical coordinates 😊
Wish my professors say something like this
This is perhaps the most important short I’ve ever watched
integration of a odd function from - infinity to infinity is 0 .so ,basically for a even function f(x) bn will become zero and for a odd function f(x) ao and an will become zero
Tried this in calculus II, had to retake it again the next semester
if only we all had great teachers
I never, ever expected this to come, especially after many years. Although I am still mediocre, I feel exuberant & exonerated. Thank you, gracias, xie-xie, merci, 🙏, on & on.
Omg I remember this guy - he was one of the best maths lecturers I had at uni.
Effective laziness is hard work...
As my math teachers taught us, "yes, there are shortcuts. No, you don't get to use them until you can prove them."
This advice fits extremely well for Programming.
I have this conversation with my students.
Good advice and good beard. Salute to you mr math, respect.
God bless you. This is the first Olympiad question I've ever solved. ❤🎉
to those who are wondering: the integral from -pi to pi of sin is 0, because it's an odd function
the integral of cos can also be simplified in a similar way
Its a great life advice we all can use 💜
a smart thing to say! most of our daily-use inventions are born out of the thought of "i really hate to do this..." and boom! effecient invention! washing machines and dishwashers are a great example.
This advice works particularly well in a game of chess, mostly a blitz or bullet format
Even my Math's teacher says the same (Be Little lazy) while solving the problems and btw he is a great mathematician
Most often setting a way of thinking blocks us to shift into the other way of thinking, maybe simply because as we set one way, we also put this thinking into an action, and theese actions would set back our thinking in a way that would provide answers in the action we do, in a way we think now. Its like searching for answers by thinking how to set things right in a field of thinking we decided earlier to approach
Yeah he is right. I truly believe what he said. I tried n I got the result too.
👏🏻 I cannot agree with your opinion EVEN MORE!! Sir.
That's all I do, I sit back & look at the problem until the exam is over.
Good reminder.
Any beginning calculus student should know how to recognize even and odd functions, and that the integral of an odd function over a symmetrical interval is zero. Pretty sure that's where he was going with his integrals of cosine and sine on the board.
Not only for mathematics but being lazy is the best gift we humans had that enabled us to advance not only science but also technology.
As he says, dont go straight lazy but to be diligent to be lazy next time you see something similar
Using the Brute Force method on all problems or Use a clever way by using other methods you already learned.
Another great NI Educator!
This is life advice right here
I think this only mostly works for people who are more advanced. Being able to create that "lazy" way needs great understanding and fundamentals on that subject
For those wondering, the trick here was to split the integral of the cosine into 2 parts and use cos(x + pi) = -cos(x) to get 2 pieces of integrals that cancel each other. Same for the sine integral with sin(-x) = -sin(x)
Also the lesson seems to be about Fourier decomposition of a function
This is not laziness, this is the technique to solve questions.
Why some of the most efficient people, are the Laziest. I don't want to deal with the same issue twice, so get it done ... and right.
😂😂😂❤😊😊😊
The “lazy” trick he’s describing is for Fourier series, to recognize that the cos or sin term can be ignored based on the parity of the given function.
If the function is odd, then the cos term is 0. If the function is even, then the sin term is 0. No need to calculate anything!
It’s both funny and scary this short is in my feed, considering I learned this trick a few days ago..
One of my friend in college wrote a wrong number in an equation, it was supposed to be zero. I pulled an eraser to offered him one, but instead he wrote /∞ below the number. That was when I understand what mathematician looked like.
Nice to know I'm halfway there to being a really good mathematician
Very wise words
this is the function with integration , i had so much interest in it , i once ask my sir , how to do in smart way , he grabbed my head and said this is all for exam , so 2months left, at that time i only concentrated in exam only.
I used to apply fast tricks to solve math problems, but always almost always my teachers punished me for not using their 20 step way
Same advice my teacher gives me vikas gupta sir
True for primary school children as well
I do this with some basic algebra/geo but sometimes teachers get mad that it's not the way they taught it and mark it wrong 😢 or say "show all the progress" tho its extremely simple mental math for me
Yeah yeah i did exactly that i solved questions in a way that my teacher didn't like eventhough the answers were right i failed the tests and i changed the stream and it turned out great
That's not laziness, that's being smart.