@@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.
Yeah, the main point was to dedicate to solving problems even if it means taking an unimaginable amount of time, akin to solving a book's problem without looking at manual solutions
@@spiderjerusalem4009Atleast u got the motivation from the laziness, after that it takes a lot process to solving the problem and then u gain the solution for the problem so u can more lazying urself lol
The hard part is spending the time understanding the mathematics and learning the tricks. I heard one guy described as knowing all the tricks in probability theory, things that are useful in proving convergence. You don’t get to that point without spending a lot of time using them.
I often say to my high school math students, "Work smarter, not harder. That is not being lazy; it is being smart!" Much of mathematics is recognizing patterns. With much practice, the math actually gets easier as you advance. Calculus actually possesses a beautiful elegance and simplicity once you arrive to that peak. The challenge is getting to that peak.
That is great. I was a slow-learner in early elementary school, but I ended up majoring in math (and tutoring college math) in my twenties. I studied many formulas and memorized quite a plethora of them.
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.
My math teacher in school was the same: What would you need to solve it elegantly? Lean back, think about it, dream a little, use your creativity.. Loved him. He made me appreciate and actually love mathematics.
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.
@@ИльяПавлов-ь4уWhen 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
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.
in a single problem, you are right. But if you need to solve 1000 problems, and you find a trick to solve them quickly, then you appreciate what he recommends.
So the next time u come across the same problem/same type of problem, u can save urself some time + allow urself to solve other problems more strategically and efficiency
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.
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.
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.
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.
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.
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.
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."
@LordDeuce-ul7my: And what does getting more work done do? Will you get a certificate for how much you got done at the end of your life? And is "efficient" work preferable over "effective" work?
@@Kyouma. It makes you worth more $. And it's fun when you apply yourself. You have to love what you do. And you have to have the motivation to want to be one of the best and to be worth the money.
@Kyouma. Efficient is effective. Inefficient is defective. You don't get a certificate for anything in life. Nothing matters. You can die right now and it makes no difference. Jus saying if you suck at construction it would be better for everyone if you do something else with your life.
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___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.
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
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.
This man isn’t teaching math, he is teaching life skills. Taking a break for a moment to reflect on what you are doing to then think. Is there a way I can make this better/easier/faster? And then doing it allows you to perform hastily.
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.
Jesus is the only way to healing, restoration and salvation to all souls. Please turn to him and he will change your life, depression into delight, soul heading from hell to heaven all because of what he did on the cross “Whoever calls upon the name of the Lord shall be saved” Romans 10:13
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.
@@sustainableliving6319 congratulations on the most nonsensical sentence of the day. Would you care to share yet another word salad? Your audience awaits ...
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😂.
This is a great advice not only for mathematicians but for life. 😁 I only know the basics, I'm not into math, but, yeah, I got what he said. Thank you, professor! And God bless you all guys! 🙌 Please, be lazy, solve the questions the easier way, and then teach us mortals. 😁
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:)
I wanna to say this speech to all people I think just keep going on your way and just laugh to other people who laugh at you and make you fun... don't listen them......................live and Loving❤
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.
@@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
for anyone wondering - it seems the trick is that cos bounds zero area from 0 to pi bc of its periodic nature. so the whole integral can be defined as zero
@@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.
I've been told I was good at math many times as a student and to be very honest all I did was I tried to solve every problem without having to pick up my pen and work it out. At first i was messing up but eventually i found tricks to solve stuff in my head and it saved so much time.
Yes! I just started Calculus BC a few months ago, and a few days ago I had an issue like this while reviewing related rates. I had an absolutely massive mess of an equation to solve, but my teacher showed me a way of thinking to reach the right answer SO MUCH FASTER and easier!!! Be lazy people!
As a quiz boy i know what he talking about. Looking at a quiz boy solve maths and science questions is soom amazing. No calculator and very quick answers.
Determine if the function is even or odd. If it odd eliminate the fourier sine series and just compute for the fourier cosine series. Vice versa if the function is even and just compute the fourier cosine series. But if the function is neither like e^x then back to the drawing board.
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
![Why you didn't learn tetration in school[Tetration]](/img/tr.png)
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.
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.
Yup. Laziness breeds efficiency. It's an important virtue to have.
😂😂😂😂😂
Yeah, the main point was to dedicate to solving problems even if it means taking an unimaginable amount of time, akin to solving a book's problem without looking at manual solutions
@@spiderjerusalem4009Atleast u got the motivation from the laziness, after that it takes a lot process to solving the problem and then u gain the solution for the problem so u can more lazying urself lol
The hard part is spending the time understanding the mathematics and learning the tricks. I heard one guy described as knowing all the tricks in probability theory, things that are useful in proving convergence. You don’t get to that point without spending a lot of time using them.
This feels like linkedin
My lazy ass not even solving the problem:
LMFAOOO
@@paris6604Lmfao
HAAHHAHAHHAHHAH
This is gold.
Lmaooo
"Why are you not cleaning your room!"
"I'm a good mathematician"
😂😂😂😂You are lazy!
😂
Fine a clever way toh clean your room faster
😂😂😂
😂
I often say to my high school math students, "Work smarter, not harder. That is not being lazy; it is being smart!" Much of mathematics is recognizing patterns. With much practice, the math actually gets easier as you advance. Calculus actually possesses a beautiful elegance and simplicity once you arrive to that peak. The challenge is getting to that peak.
I need to see that peak
Einstein probably reached that peak at like 7 years old
How can I get the peak ???
That is great. I was a slow-learner in early elementary school, but I ended up majoring in math (and tutoring college math) in my twenties. I studied many formulas and memorized quite a plethora of them.
@@daniellerosalie2155 can you tell me ur journey to get rid of the learning problem?specialy in a hard subject like math???
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? @@BunnyWatson-k1w
@@BunnyWatson-k1w48 for
@@BunnyWatson-k1w48 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.
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
My math teacher in school was the same: What would you need to solve it elegantly? Lean back, think about it, dream a little, use your creativity.. Loved him. He made me appreciate and actually love mathematics.
"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!
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
@@ИльяПавлов-ь4уWhen 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....
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.
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.”
Spend 2 minutes solving the problem ❌ Spend 2 hours finding a method to solve the problem in 30 seconds ✅
in a single problem, you are right. But if you need to solve 1000 problems, and you find a trick to solve them quickly, then you appreciate what he recommends.
@@timytidy60 and this thing is what we called engineering which is optimizing equations and apply them to more problems
So the next time u come across the same problem/same type of problem, u can save urself some time + allow urself to solve other problems more strategically and efficiency
Thats a lot of maths, find clever ways to avoid to do any work
By doing a lot of work beforehand ofcourse
It is great advice for everything. Imagine efficiency sky rocketed if everyone just follows this simple trick...
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.
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.
Thank you 🙏🏽
Professor Maini! A great source of inspiration!
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😅
Such a crystal clear teaching . Loved it sir. Sab samajh bhi aaya ❤❤
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?
Yet the Journey is what strengthens you
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
😂😂
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.
My math teacher always told me to work smarter not harder. Good advice
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."
@LordDeuce-ul7my: And what does getting more work done do? Will you get a certificate for how much you got done at the end of your life? And is "efficient" work preferable over "effective" work?
@@Kyouma. It makes you worth more $. And it's fun when you apply yourself. You have to love what you do. And you have to have the motivation to want to be one of the best and to be worth the money.
@Kyouma. Efficient is effective. Inefficient is defective. You don't get a certificate for anything in life. Nothing matters. You can die right now and it makes no difference. Jus saying if you suck at construction it would be better for everyone if you do something else with your life.
Trust me! My efficiency is a result of my laziness
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 : you need to be lazy
Exam paper : prove the answer 💀
"Inside being lazy we must be patience". Mariam Merzakhani. Fisrt woman who win fieldz medal.😊❤❤❤❤❤❤❤
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
this is very helpful when dealing with complex integration problems like forier, good lecturer 👍
I know i'm doing something wrong when solving when it takes me so long 😅
This is life advice right here
As a mathematician, I can say I totally agree. Often if a computation is too complicated I avoid it as much as possible trying to simplify it... 😊
This is good advice for a lot of things in life. Not just mathematics
I told my professor this.
He told me thats not an excuse for not turning in my assignment 💀
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.
This is good advice for other things as well.
"Don't crunch the numbers like a madman"
This man isn’t teaching math, he is teaching life skills. Taking a break for a moment to reflect on what you are doing to then think. Is there a way I can make this better/easier/faster? And then doing it allows you to perform hastily.
this is not being lazy but actually trying to save time and brain cells. aka not doing it the hard way but the smart way.
this is only works for advanced experienced practioner in any field, otherwise you will end up causing lots of harm
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.
Why is pi?
Jesus is the only way to healing, restoration and salvation to all souls. Please turn to him and he will change your life, depression into delight, soul heading from hell to heaven all because of what he did on the cross
“Whoever calls upon the name of the Lord shall be saved” Romans 10:13
@@HaroutBlack RUclips really notified me that a bot is spouting Christian brain rot nonsense
Be creative that is one of the ways.
Fajr Zuhr Asar Maghrib Isha and Witr Namaz, Dua Qunoot ♥❤👌
Establish regular Namaz and Pay ZAKAT....
As a math's teacher..i can confirm ...its true 💯
I saw this video before and didn't think much of it.
Oh, but how I wish I did.
Really smart advice...
Dhanyavad 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
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.
😂😂😂❤😊😊😊
Must be applicable to many other things irl such as business marketing. Thanks ❤
God is about to come through 🎉🎉🎉❤❤❤❤
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!
no
Provided that you are ready to put lots of energy to think about the simpler way -- that is the hardest part, really.
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
@@d7home2129provided the summation counter begins at 1, and not 0.
"if u see a good move, look for a better one"
I dunno who said it, but he's got a point.
A couple of girls from my class used to do this, so special and intelligent 😊
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
Nice to know I'm already halfway to becoming a really good mathematician.
This serves for anything in life, brilliant❤
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.
plug it into the calculator and use the 'calc' function lol
I like him. There are no tricks in math, only technique!
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
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
This is a great advice not only for mathematicians but for life. 😁
I only know the basics, I'm not into math, but, yeah, I got what he said.
Thank you, professor!
And God bless you all guys! 🙌
Please, be lazy, solve the questions the easier way, and then teach us mortals. 😁
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.
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:)
Whats his name
I wanna to say this speech to all people I think just keep going on your way and just laugh to other people who laugh at you and make you fun... don't listen them......................live and Loving❤
"How the hell did he write on the upper boards..."💀💀💀
💀 spider man
He can pull the boards down 😅
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
for anyone wondering - it seems the trick is that cos bounds zero area from 0 to pi bc of its periodic nature. so the whole integral can be defined as zero
All of advanced math is basically clever tricks and shortcuts
😂
Stop yappin bruh
Professional yapper
@@jigglyCroissant?
@@syed3344 professional pp swallower
And you also have to be creative
You have to be lazy ❌
You have to be clever✅
Respect
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.
My maths teacher already given us this advice many times in the class last year❤
This is perhaps the most important short I’ve ever watched
I will definitely implement these. Thanks for the precious advice Sir.
This is great advice thank you
teachers when you do this in school: 🙎🔪
I am so lazy to the point I do not want to even attempt solving the problem. I must be a GREAT mathematician.
And this applies to all of life as well! You know this is a great lecture when it transcends beyond its own subject~
To find the shortcut method you also have to work hard mentally.
One of the best advices I heard. Can be applied to different stuff as well
I love this man
I've been told I was good at math many times as a student and to be very honest all I did was I tried to solve every problem without having to pick up my pen and work it out. At first i was messing up but eventually i found tricks to solve stuff in my head and it saved so much time.
Clarity explained in a nutshell
For this case in Fourier series the smart way is to check if the original function is odd then a0, an=0
“Ok so how many whiteboards will you be needing?”
“Yes”
Yes! I just started Calculus BC a few months ago, and a few days ago I had an issue like this while reviewing related rates. I had an absolutely massive mess of an equation to solve, but my teacher showed me a way of thinking to reach the right answer SO MUCH FASTER and easier!!! Be lazy people!
Professor’s version Lazy includes sitting back and thinking. Thoughtless Meditation is lazy gold.
That's the only way to go with higher maths. Great teacher.
As a quiz boy i know what he talking about. Looking at a quiz boy solve maths and science questions is soom amazing. No calculator and very quick answers.
That's using your intellect and knowledge in an smart, optimal and effective way.
Can't ask that on YT.
That's not being lazy, thats being smart.
Instructions unclear, now i have a fleeting report card.
I'm so happy that all this time I've just been a mathematician
Determine if the function is even or odd. If it odd eliminate the fourier sine series and just compute for the fourier cosine series. Vice versa if the function is even and just compute the fourier cosine series. But if the function is neither like e^x then back to the drawing board.