@@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.
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
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.
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.
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
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.
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.
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.
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.
If you stopped watching useless stuff you would stop complaining and feeling like a victim. UA-cam is not an evil organism that manipulates you to watch Andrew Tate and become a sigma male.
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.
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.
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
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!
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
Not just for maths, but for any more complex issues really. Simplifying isn't just being lazy, it's efficient and gets things done, since you're trying to make something hard more accessible to your mind so basically you can learn more by doing that. I think. Idk I'm just a linguistics student
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.
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😂.
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.
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 ...
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.
From experience, this is applicable for people who have done the grunt work and can do the math. Then you can start finding the short cuts. Before that you will have to practice . A lot.
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❤
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'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.
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
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:)
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.
@@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.
It's kinda funny how true this is. Or how true it seems to me, at least. In the first sections of a numerical analysis book, it is likely that you will find numerical methods to get solutions of random equations that don't contain derivatives or integrals. There is a great emphasis on speed of convergence: how fast does a method get you to an answer that's as close as possible to the real answer. Almost as if... The book was trying to progressively teach you ways to be lazy and get answers without having to spend so much paper on a single equation. Because, all methods will get you an answer with the problems that the book provides. The only difference is the complexity of the methods and the speed at with they give you an answer. The later methods really feel like some lazy person coming up with a complex method to avoid having to do the same thing over and over and over to get an answer.
They should implement this in schools this is amazing for students that understand anything but can’t skip the class because there are a few things they don’t know for example you know all of algebra 1 except polynomials and so you’re bored the entire time and you understand polynomials immediately as well but you’re stuck going over the same things so the rest of the class gets it “finding a trick” would be so much useful for those types of students
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.
I am a mathematician. I find ways to solve a problem because I think about how I can finish a task the fastest and easy way. People would it being lazy, but I call it being efficient and resourceful. Why do something the hard way when you could save a lot of time, energy, and resources doing it in a different way? Life doesn't have to be complicated and hard. I bet most of the world's problems would be solved if we didn't create the problem in the first place.
it really means do not be quick to Move the pen/pencil without having a second thought or comfirming what you are writing . it helps to solve hard problems.
This man is right, and teachers at school told students to use their complicated methods. For real even if my answers right they not accepting it if its not their method
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
My maths lecturer told me "find the pattern, know the solution.” 1,2,3,4,5....10 where x is the existent of the sequence, plus 1 = n, the novel of the sequence. Ergo, the pattern is n=x+1 Eg to follow the sequence if we know upto 5, then 5 is the existent of the sequence = x. To find the novel of the sequence we identify that the sequence is + 1 to the existent, so n = 5 + 1 = 6. Of course this is over-simplified, but the general principle stands where it looks chaotic the answer you need lies in a sequence Ergo, find the pattern, know the answer.
![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)
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 🤣
@@musashi.miyamoyo You are the guy who sees narsistic people everywhere.
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
😂😂😂
😂
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
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.”
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.
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???
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....
"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!
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.
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
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.
He is totally right. In this case, we might be lazy to not waste time. Time is money! Make every second count! That's intelligence!
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.
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 😂
Be creative that is one of the ways.
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. UA-cam is not an evil organism that manipulates you to watch Andrew Tate and become a sigma male.
If UA-cam is recommending junk content then that’s on you. UA-cam 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😅
Professor Maini! A great source of inspiration!
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
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.
It is great advice for everything. Imagine efficiency sky rocketed if everyone just follows this simple trick...
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
How many whiteboards do you need?
Him:Yes?
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... 😊
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 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
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!
"Inside being lazy we must be patience". Mariam Merzakhani. Fisrt woman who win fieldz medal.😊❤❤❤❤❤❤❤
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 UA-cam really notified me that a bot is spouting Christian brain rot nonsense
Not just for maths, but for any more complex issues really. Simplifying isn't just being lazy, it's efficient and gets things done, since you're trying to make something hard more accessible to your mind so basically you can learn more by doing that. I think. Idk I'm just a linguistics student
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 is life advice right here
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.
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
This is good advice for a lot of things in life. Not just mathematics
My father always told us :.
Observe the lazy people
Listen the wise ones
Study the hard workers
Combine them to your way
Fajr Zuhr Asar Maghrib Isha and Witr Namaz, Dua Qunoot ♥❤👌
Establish regular Namaz and Pay ZAKAT....
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.
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.
This is good advice for other things as well.
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.
Provided that you are ready to put lots of energy to think about the simpler way -- that is the hardest part, really.
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
I told my professor this.
He told me thats not an excuse for not turning in my assignment 💀
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.
Professor : you need to be lazy
Exam paper : prove the answer 💀
I know i'm doing something wrong when solving when it takes me so long 😅
From experience, this is applicable for people who have done the grunt work and can do the math. Then you can start finding the short cuts. Before that you will have to practice . A lot.
As a math's teacher..i can confirm ...its true 💯
I would argue that the first way is the lazy way
While what he called being lazy is creative and efficient
this is very helpful when dealing with complex integration problems like forier, good lecturer 👍
"Don't crunch the numbers like a madman"
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.
😂😂😂❤😊😊😊
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❤
"if u see a good move, look for a better one"
I dunno who said it, but he's got a point.
God is about to come through 🎉🎉🎉❤❤❤❤
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. 😁
Nice to know I'm already halfway to becoming a really good mathematician.
Dhanyavad 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
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.
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
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
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
plug it into the calculator and use the 'calc' function lol
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
You call it laziness, I call it "saving up energy".
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
"How the hell did he write on the upper boards..."💀💀💀
💀 spider man
He can pull the boards down 😅
Yet the Journey is what strengthens you
All of advanced math is basically clever tricks and shortcuts
😂
Stop yappin bruh
Professional yapper
@@jigglyCroissant?
@@syed3344 professional pp swallower
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.
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.
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.
Respect
It's kinda funny how true this is. Or how true it seems to me, at least.
In the first sections of a numerical analysis book, it is likely that you will find numerical methods to get solutions of random equations that don't contain derivatives or integrals.
There is a great emphasis on speed of convergence: how fast does a method get you to an answer that's as close as possible to the real answer. Almost as if... The book was trying to progressively teach you ways to be lazy and get answers without having to spend so much paper on a single equation.
Because, all methods will get you an answer with the problems that the book provides. The only difference is the complexity of the methods and the speed at with they give you an answer. The later methods really feel like some lazy person coming up with a complex method to avoid having to do the same thing over and over and over to get an answer.
And you also have to be creative
I like him. There are no tricks in math, only technique!
That's the only way to go with higher maths. Great teacher.
Professor’s version Lazy includes sitting back and thinking. Thoughtless Meditation is lazy gold.
To find the shortcut method you also have to work hard mentally.
A couple of girls from my class used to do this, so special and intelligent 😊
They should implement this in schools this is amazing for students that understand anything but can’t skip the class because there are a few things they don’t know for example you know all of algebra 1 except polynomials and so you’re bored the entire time and you understand polynomials immediately as well but you’re stuck going over the same things so the rest of the class gets it “finding a trick” would be so much useful for those types of students
I am so lazy to the point I do not want to even attempt solving the problem. I must be a GREAT mathematician.
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.
I am a mathematician. I find ways to solve a problem because I think about how I can finish a task the fastest and easy way. People would it being lazy, but I call it being efficient and resourceful. Why do something the hard way when you could save a lot of time, energy, and resources doing it in a different way? Life doesn't have to be complicated and hard. I bet most of the world's problems would be solved if we didn't create the problem in the first place.
Must be applicable to many other things irl such as business marketing. Thanks ❤
That's using your intellect and knowledge in an smart, optimal and effective way.
Can't ask that on YT.
Never thought about it in that way but i carried that laziness into my career in embedded software and became very successful
it really means do not be quick to Move the pen/pencil without having a second thought or comfirming what you are writing . it helps to solve hard problems.
Lazy and resourceful are two terms you don't want to have mixed up.
And this applies to all of life as well! You know this is a great lecture when it transcends beyond its own subject~
This man is right, and teachers at school told students to use their complicated methods. For real even if my answers right they not accepting it if its not their method
Saving time is not lazyness.
To live is a race against time itself
I saw this video before and didn't think much of it.
Oh, but how I wish I did.
Really smart advice...
This is perhaps the most important short I’ve ever watched
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
My maths lecturer told me "find the pattern, know the solution.”
1,2,3,4,5....10 where x is the existent of the sequence, plus 1 = n, the novel of the sequence. Ergo, the pattern is n=x+1
Eg to follow the sequence if we know upto 5, then 5 is the existent of the sequence = x. To find the novel of the sequence we identify that the sequence is + 1 to the existent, so n = 5 + 1 = 6.
Of course this is over-simplified, but the general principle stands where it looks chaotic the answer you need lies in a sequence Ergo, find the pattern, know the answer.