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- Опубликовано: 19 мар 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...
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
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.
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 🤣
@@friday13michael You are the guy who sees narsistic people everywhere.
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.”
My lazy ass not even solving the problem:
LMFAOOO
"Why are you not cleaning your room!"
"I'm a good mathematician"
😂😂😂😂You are lazy!
😂
Fine a clever way toh clean your room faster
😂😂😂
😂
To be a really good mathematician you have to have at least 12 whiteboards
24 for a future Nobel Laureate.
Are you referring to Fields medal? @@user-og2wt3le4j
@@user-og2wt3le4j48 for
@@user-og2wt3le4j48 for
I just got my first one with wheels and it is reversible. I love it so much.
It's not an almighty chalkboard, but I can't clean the chalk effectively where I live.
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.
"Inside being lazy we must be patience". Mariam Merzakhani. Fisrt woman who win fieldz medal.😊❤❤❤❤❤❤❤
"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!
Finding the cleaver way to solve the problem is the hardest thing 😂
Wohi toh Sara khel h mathematician bn ne ka
Not if you're smart enough
Having a cleaver definitely takes care of problems for me
yh u cant simplify(lazy) something if u dont understand the thing
@@MonaLisa-jj3tb Regardless. Compared to finding the other solutions it's the hardest
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?
The professor is right in the sense that mathematicians avoid doing something over and over or doing it with brute force or by applying direct definitions. Mathematicians try finding patterns and developing formulas.
How long have this class been in?I mean year or month
While mathematicians in the past did piles of pure brutal calculations. And i guess most of this simplicity comes only after big calculations
@@user-fk2uj2vj3sWhen you ask a professor how they made it through hard classes and they're like "oh I just did every problem in the textbook" 💀. The academic life ain't for me son
Mathematicians do use computers to brute force
developing methods by induction, maybe....
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.
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❤
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😅
The cool thing about this lesson is that it applies to things outside of mathematics.
How ?
@@sitproperlywhilewatchingph423 How not?
I was just asking what are those things outside of maths that we apply , I have no idea
the way how math problems are getting solved can be applied to anything for me, its so cool
True, my dad once told me he thinks lazy people make good employees, because they devise ways to make the job easier. This can then be passed along to other employees, raising efficiency and effectiveness.
That's the theory at least. In practice I think it depends a great deal on the nature of the work. In many scenarios a lazy worker would simply produce less.
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.
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 do that and my teacher will be like "you skipped a step"
Typical if you use techniques more advanced than the level of the course.
"there goes your 1 mark"
@@idk-what-bruh😂💯
This aint high school buddy
😂😂
This is exactly what I need. I'm trying to calculate an equation that includes three given points on the plain. I've tried to do it like I have compass and straight edge. I have constructed the median perpendicular of two given points and the intersection point of two given straight lines and I need to combine them to make the center of the circle. The math already looks messy and complex. I need to see connections, not a mess.
Yess optimistically I like to call myself efficient ✨️
Unexpectedly, I have so much potential to be a good mathematician!! Thank you, professor!
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!
A couple of girls from my class used to do this, so special and intelligent 😊
God is about to come through 🎉🎉🎉❤❤❤❤
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.
Professor Maini! A great source of inspiration!
One of the best teachers of maths on youtube. To the point teaching. Love it
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.
"Don't crunch the numbers like a madman"
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
That's using your intellect and knowledge in an smart, optimal and effective way.
Can't ask that on YT.
One of the best advices I heard. Can be applied to different stuff as well
This is good advice for a lot of things in life. Not just mathematics
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
It is great advice for everything. Imagine efficiency sky rocketed if everyone just follows this simple trick...
He is absolutely right and this helps us enhance our analysing capacity too
But out of context he sounds so soothing and it feels like I am talking to a genius person
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.
This isn't laziness, this is time management.
I do agree with this Sir 100% it brings back memories 😅
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.
using definite integral properties, since cosx is even function it's graph would be symmetrical wrt y axis, hence it would be twice intg(cosx) from 0 to a; and sinx being odd, it's graph would be symmetrical wrt origin so that term would become 0.
Errr … yes?
Also the cos integral is zero because in this case it is -pi to pi
This is good advice for other things as well.
always love it when respected community members say stuff like that
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
him: is there a trick?
me: immediately opens chat gpt
"if u see a good move, look for a better one"
I dunno who said it, but he's got a point.
This advice is a game changer for real. I used to be pretty good at mathematics in high school (I’ve been an A+ student all my life), but my preparation for advance mathematics went downhill post that as I couldn’t figure out the trick to differentiate b/w high school math and the math that professor is referring to.
I finally get it now after a year!
This is the reason that why I was very good and best in math at my class because, I was the laziest student in my class.Thanks for your teaching😂
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
Nice to know I'm already halfway to becoming a really good mathematician.
This advice fits extremely well for Programming.
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
Finding the "trick" is more work than just doing the question normally.
But the end result doesn't just give you some number to look at, you learn something that can be applied to a problem somewhere else as well :)
The trick here is that cosx is an even function and you're integrating over [-n, n], in this case [-pi, pi]. Even functions are mirror symmetric so the left side of the graph, [-pi, 0] will cancel out the right side of the graph [0, pi] and the result is 0. Checking for this is waaaaayyyyy easier than doing the integral imo.
I saw the trick in 2 seconds lol, it's pretty standard if you do anything with mathematics
Once you notice a trick, you have more chance to notice it somewhere else. But a boring computation won't make you learn shortcuts like that.
@@jonathan3372 you don't know how long finding the trick will take. It can be equivalent to solving 1 question, solving 10 questions or solving 100 questions
I remember having him as a lecturer in uni, he was really good! Remember he wrote his lowercase “p”s quite strange so at the end of the year I got him a mug with all the times he’s written “p”s on the whiteboard and he liked it! Wonder where that’s knocking about:)
Fourier series of engineering mathematics nostalgic
We can use the concept where the integration of odd function is equal to 0 where the limit goes from -π to +π
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
All of advanced math is basically clever tricks and shortcuts
😂
Stop yappin bruh
Professional yapper
@@jigglyCroissant?
@@syed3344 professional pp swallower
Sachin sir also give such advice ❤❤❤
Biggest thing that has helped me in chemical engineering and mathematics is that symmetry is your friend!
"How the hell did he write on the upper boards..."💀💀💀
💀 spider man
He can pull the boards down 😅
Respect
I do this in class all the time and solve the problems before anyone and tell my method/trick to the teacher to always get approval later
Never thought about it in that way but i carried that laziness into my career in embedded software and became very successful
A quick way to destroy mathematics is to skip proofs altogether. Just trust appeals to authority instead.
Proof by intimidation
@@flsendzz Before you start writing your proof, you should ask yourself "why is this statement true/false", and have a good idea in your mind of how you would explain why or why not if you were asked that question by someone else. Once you've convinced yourself that the statement must be true or not, if that reasoning is rigorous enough, then that simply is your proof, and you can write it out in plain English or mathematics. Otherwise, if it's not all quite there but you have a general idea, start writing out your argument more mathematically and see what you can argue from there. In other words, have a solid idea of what your argument is going to be before trying to write a formal proof, and then convert that argument into the language of mathematics. At the end of the day, a proof is simply a rigorous explanation of why a statement must be true/false.
@@flsendzzI would recommend the book," How to Prove it" by Daniel J Velleman.
No proofs are must to clear concept 😂areu a arts student
Proof by faith.
And you also have to be creative
This is a great advice for programmers as well.
Taking a step back to reimagine the code and making it as simple as possible helps alot 👍 . A good abstracted code can save so much time and resources
The clever way usually utilizes some symmetry of the problem.
to be really good in mathematics, you need a capybara 😭
This will definitely see you through life. I would use this Equation daily to solve issues
He’s talking about integrating an odd function from -L to L where the definite integral will equal 0.
This is Fourier series and there are times where using basic properties will help the meticulous process of finding some coefficients for the approximations we’re looking for.
Screw Fourier series
@@loayahmed9605 indeed.
The second integration was calculated, since cos(x) isn't odd function
@Anonymous-fr2op I'm not sure what he was integrating, but you can multiply cosine with an odd function like x or x^3, resulting in an odd function and the property holds. But yea, you may be right, I just noticed he was working with Fourier series and is most likely teaching partial differential equations.
I've solved countless problems simply by looking at trivial cases. It's amazing how many people overlook them and find complications instead.
The most valuable life skill I’ve ever learned from math. That and, doing as much work as fast and as well as you possibly can buys you a lot of immediate stress and pain and a restful, rewarding future.
Omg I remember this guy - he was one of the best maths lecturers I had at uni.
Sometimes in math finding the creative way to save time takes more time than just do alot of work fast
This advice works particularly well in a game of chess, mostly a blitz or bullet format
This useful advice not only for mathematics but for other things in life To Save Time.Thank you ,Sir.
I would argue that the first way is the lazy way
While what he called being lazy is creative and efficient
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
Thank you, so much
For anyone wondering, the shortcut he is referencing here is the fact that cosine is an odd function so when you integrate it over the symmetric region -pi to pi, it will be 0
It looks like a combination of integration by part, power exponents, and shifts in graphs in trick ratios, which could be divergent or converged depending on the graph nature or involving infinite methods to analyze its complexity.
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
True for primary school children as well
Used to get bad marks in maths because I did zero homework. Prof used to give so many that you'd be busy for at least two hours to finish them. She saw I wasn't doing them so started giving me just one harder equation to do instead. Nailed it then
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
thanks for this advice it can be very useful for me .
25 years software engineer here and this 💯 true all the time
Saving time is not lazyness.
To live is a race against time itself
Tried this in calculus II, had to retake it again the next semester
I TOTALLY RESPECTLY AGREE
We all love Professor Maini!!! 😊
i admire those who can come up with ways to compute things with a piece of paper and not a computer
Marcus Du Sautoy talks about laziness and the avoidance of doing mindless work. Mathematics is about finding shortcuts.
This applies to almost all work. But lazy shouldn't mean compromise, but more efficient.
this I tell all my students since I started teaching.
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
Dhanyavad 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏