Be Lazy  

I'd say this is great advice for more advanced students.

Its flattering that youtube suggested this to me.

That is not being lazy, thats being creative and efficient.

Finding the cleaver way to solve the problem is the hardest thing 😂

"Why are you not cleaning your room!" "I'm a good mathematician"

To be a really good mathematician you have to have at least 12 whiteboards

Finally, decent content on this platform.

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.

"How many chalkboards do you need in your auditorium?" "I need ALL 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.

Unexpectedly, I have so much potential to be a good mathematician!! Thank you, professor!

Efficiency is not laziness. It saves time and energy for you to get more work done in less time.

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.

The cool thing about this lesson is that it applies to things outside of mathematics.

Professor Maini! A great source of inspiration!

"Inside being lazy we must be patience". Mariam Merzakhani. Fisrt woman who win fieldz medal.😊❤❤❤❤❤❤❤

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.

One of the best teachers of maths on youtube. To the point teaching. Love it

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

I do that and my teacher will be like "you skipped a step"

His lazy and most people think lazy is different lazy. So listen people, please dont be lazy.

I do agree with this Sir 100% it brings back memories 😅

Sachin sir also give such advice ❤❤❤

This advice can definitely be used outside of the classroom as well!

This isn't laziness, this is time management.

thanks for this advice it can be very useful for me .

"Don't crunch the numbers like a madman"

thats not laziness thats being efficient

This is good advice for a lot of things in life. Not just mathematics

Thank you, so much

This is good advice for other things as well.

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 man speaks an universal truth, not constrained to mathematics. I think he knows it :-)

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.

Finding the "trick" is more work than just doing the question normally.

Nice to know I'm already halfway to becoming a really good mathematician.

if only we all had great teachers

always love it when respected community members say stuff like that

"if u see a good move, look for a better one" I dunno who said it, but he's got a point.

That's the way classes should go. Students should be taught how to learn and not just be bombarded with raw theory and methods.

My professors wish they had that board setup but with chalk not makers.

him: is there a trick? me: immediately opens chat gpt

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:)

that's why I always photocopied my friend's math assignment.

Yess optimistically I like to call myself efficient ✨️

Great advice❤. I actually do maths this way and it has been very effective over the years..

"How the hell did he write on the upper boards..."💀💀💀

All of advanced math is basically clever tricks and shortcuts

God bless you. This is the first Olympiad question I've ever solved. ❤🎉

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

Respect

to be really good in mathematics, you need a capybara 😭

I literally experienced this in school a few days ago. It’s a standard Mean Value Theorem problem with sin, gotta find C, which is the Secant line… wait, the Secent line is just essential the average value. Sin function goes completely horizontally. With that info alone, you can just safely assume the Secant line is 0 and save 2 minutes of calculations. Same for Cosine and Tangent functions, so long as they’re by themselves.

This useful advice not only for mathematics but for other things in life To Save Time.Thank you ,Sir.

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.

And you also have to be creative

A quick way to destroy mathematics is to skip proofs altogether. Just trust appeals to authority instead.

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

Fourier series of engineering mathematics nostalgic

I used to watch a mathematician who would ask "Wouldn't it be nice if...? Followed by a form of the question which would make it easier. This helped me tremendously.

Thanks for encouraging me

that's why I forward the short just to main points

We all love Professor Maini!!! 😊

Thank you sir for this helpfull information 😊

God is about to come through 🎉🎉🎉❤❤❤❤

I am so happy there's shorts like these

Your so right. !! Sometimes works.

This guy is wise, entire appreciation to u sir❤.

True for primary school children as well

Exactly my thoughts for a few days 🤩🦧

marvellous session ma'am 🎉🎉

God bless the math and Engineer brains. They make our world!

Omg I remember this guy - he was one of the best maths lecturers I had at uni.

Salute ❤

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 one common characteristic of clever mathematicians and good programmers!

The professor's advice is applicable for almost all aspects of life.😇

i admire those who can come up with ways to compute things with a piece of paper and not a computer

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

Good advice and good beard. Salute to you mr math, respect.

agree with this man being clever help you solve things

Very wise words

I TOTALLY RESPECTLY AGREE

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.

Thankyou so much ☺️❤️ sir for amazing explanation ✨

The ONE Thing ⭐

Thank you for a practical advise for smart work in math I'll use it well in a proper way

Fourier series...🤩 It is amazing topic...

I've been sitting staring the math problems for so long that no trick in the world could save me that time.

Work efficiently

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

Tried this in calculus II, had to retake it again the next semester

his experience speaks 🔥

Lovely lecture!!! 😁👌

that's really good advice

Great now am going to be stuck in after school classes because i choose to do maths the clever way Am not crying😢

Biggest thing that has helped me in chemical engineering and mathematics is that symmetry is your friend!

Oh! Thank you, God!!.... I always thought I was in the wrong for thinking this way!!

Great advice

I saw this video a long time ago. Thanks youtube for reminding me of it