Please view the playlist titled 'Mathematics in this channel for the complete lecture series in a sequence. Note that the lecture number is given in the description of the video.
Thanks
NPTEL Web admin

Pertaining to 13:57. All he is saying is that if we can show there exists some n such that (2r/n + 1/n < 2-(r^2)) then it would follow that 2r/n + 1/(n^2) < 2-(r^2) since 1/(n^2) < 1/n. He ends the proof with an appeal to the Archimedean property to show the existence of such a n.

I think you mis-understood it. He says that if he can find an 'n" such that Y<Z is satisfied, then automatically X<Z will be satisfied. Hope it clarifies.

It is not possible to understand advanced calculus or complex analysis without understanding the structure of real numbers & analysis.
However, most of the calculus they teach constitute, application of formulas, few fundamentals, substitutions, logical steps, finding similarities & parallelalities.
Unfortunately, this & other presentations by Dr. Ray is not visible.
I urge him to present a clearer & visible version of his lectures.
Also, please give more examples on the number line.

Embarrasingly inept. Why bother videoing these lectures if 1/2 our time is watching Prof Ray writing indecipherable symbols on his acetate. He should have referred to pre-printed & readable lecture notes !!
Much better to read a textbook – this is a tortuous & deeply inefficient way to learn Calculus.

It has nothing to do with depth. I am referring to his pedagogical style. Amongst the worst I have seen. Complete geek unable to communicate or inspire. And wretched handwriting.

Ref: 16 to 17 minutes
In simple words, he is saying, between any two different real numbers, no matter how close together, there are infinitely many other real numbers. So there is no number larger than any number on the real number line or no number smaller than any number on the real number line

Nice teaching and the Kolkata accent was nice as well! Just one small correction at around 52.00 where he says any S which is a subset of R has a supremum. It should be any S which is bounded above has a supremum. For e.g N which is a subset of R does not have a supremum.

You must be in a very advanced high school 🙂 I learned some of this in my grade 12 (America), and have extended these ideas in my freshman year of college. My masters degree doesn't include this because it will already have been covered 🙂 More advanced/addictional topics will be covered than real and complex analysis.

It's not that hard to understand him or any of the IIT professors, just focus on what he is saying more. I have had 2 teachers with a heavy accent, so I guess I have gotten used to it

some people are so ungrateful. the lecturer is taking his valuable time to teach us for free but instead of being thankful, some viewers have nothing but negative things to say.

if you are getting a high paying job opportunity to work abroad or in a global company that deals with multinationals, would you turn it down or would you accept it and adapt to the accents?

please stop being so closed minded. if you cannot understand him, pause and play back but don't be negative or insulting.

HEY VIEWERS…Prof Ray is great but i fond another professor who is EXTREMELY GOOD when it comes to teaching CALCULUS if you are interested. copy and paste the following. trust me you won't regret it!……

But please see if you can improve the quality of the writing. The images are not very clear. If the visual form is good it is much easier to focus on the content.

@ ebunny5 we care and appreciate the proffs time only if it values us!!!! He is just an amazing guy in knowledge, but in teaching with the greatest of heart i could give him 35%. Students need real teachers not anybody else!!!
@alexlaur2007: listen we care a lil bit of the guy's accent since it deals with our understang and nothng more!!! If I am a real student i would personally give nothing towards his english if i understand him!!!! But the prob he complicates things thats all!!!!

I am not abl to express my gratitude to thes lecturers.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before………….

8:33
There is an error with the representation of the number 1/2 on the line. It should be between 0 and 1, but it is shown to be between 1 and 2 in the video.

I think at 10:20 he's trying to prove that the rationals don't have the completeness property; e.g. he takes a particular set of rationals and shows that it is not bounded above. He also states that this particular set is not bounded below, although he doesn't actually prove it.

@chpsanders
friend rationals are surely bigger set than integers because consider 3. 3 is an integer and at the same time rational _can be represented 3/1 which makes it rational……….

@psycool666, Math is a language and not just a way of solving problems. In mathematics sometimes you have to define very specifically what you are describing. sometimes it is convenient or necessary to bound natural numbers as all integers greater than or equal to 1 sometimes you need to describe natural numbers as all integers, sometimes all integers other than 0 is useful. it depends on what you are describing. you could say Alaskan winters are cold. or the killer was cold.

@psycool666
Negative natural numbers doesn't mean the negative part of the natural numbers. It means the negatives of the natural numbers. Also, names are nothing but convention, and at least in India we call the set of negative numbers the set of negative natural numbers,

I'm sorry If I sounded Cocky actually I'm a non-math student, and have been interested in math after my college, so a lot of self learning, It is just that these terms are a bit Confusing , Cuz I read that the number "1" was the lowest Natural number, and I definitely don't doubt on what an IIT professor is lecturing on – Cuz Im from India too, maybe it is just that these Terms aren't STRICTLY DEFINED to apply them Universally

@psycool666
Well your version of the definition is correct, and the smallest natural number is 1, but what I think the lecturer meant was the negative of natural numbers, so basicly its the set of elements -x, where x is an element of natural numbers

@ls600h1
But wouldn't set of " Negative INTEGERS " would have fit well rather than set of negative of natural numbers as INTEGERS already contain them as a part of their Complete Set – It is just that it is less confusing where we mention a SET which is already a part of it instead of Creating a Set that isn't actually there

WHY MUST I BE SO INEPT AT MATHEMATICS!? fuck i go to the most basic maths video on youtube and the first thing he says confuses me and i can't focus anymore. fuck!

dont try to see the starting concepts ..they are just the intro …see the ending of the playlist and then compare your 7th grade concepts with IIT…Seems as if you are another creep not getting into iit's !!!

Hi NPTEL, the video resources u offer r at least as good, if not better than MIT OCW. However, I do think it's a shame that there is a significant number of lecture series (including this 1) that r at such low resolution that I cannot read the lecturer's notes! is there any chance that u will b refilming those series with higher resolution?!

Can some one explain clearly what he means "Then I say that the proof is intuitively clear" at 14:22. How he says that r+(1/n) also belongs to the set A from the proof he gave

When i was taking a admission in local privet engineering college. I tought why the classes of iits do not recorded and uploaded for other students which dont have luck to study in iit. And now I found this. Thanks a lot of you.

can you give the lectures in a sequence ?..because it is hard to know which is lecture 1 and so on…..

Please view the playlist titled 'Mathematics in this channel for the complete lecture series in a sequence. Note that the lecture number is given in the description of the video.

Thanks

NPTEL Web admin

Good video – thanks! You might want to take a look at 41:00; there is a technical glitch there where the writing doesn't appear.

Excellent summary of the basic properties of Real numbers and how they are derived as well as why they are important. Thanks again!

Pertaining to 13:57. All he is saying is that if we can show there exists some n such that (2r/n + 1/n < 2-(r^2)) then it would follow that 2r/n + 1/(n^2) < 2-(r^2) since 1/(n^2) < 1/n. He ends the proof with an appeal to the Archimedean property to show the existence of such a n.

Great lectures except that I can't read the darn thing. Too bad.

I think you mis-understood it. He says that if he can find an 'n" such that Y<Z is satisfied, then automatically X<Z will be satisfied. Hope it clarifies.

how is this relavent to calculus this is not calculus calculus is about functions people already know about natural rational numbers etc

really good video with good explanations but I couldn't read the handwriting 🙁

It is not possible to understand advanced calculus or complex analysis without understanding the structure of real numbers & analysis.

However, most of the calculus they teach constitute, application of formulas, few fundamentals, substitutions, logical steps, finding similarities & parallelalities.

Unfortunately, this & other presentations by Dr. Ray is not visible.

I urge him to present a clearer & visible version of his lectures.

Also, please give more examples on the number line.

and 1/3 is between 1 and 3.

Embarrasingly inept. Why bother videoing these lectures if 1/2 our time is watching Prof Ray writing indecipherable symbols on his acetate. He should have referred to pre-printed & readable lecture notes !!

Much better to read a textbook – this is a tortuous & deeply inefficient way to learn Calculus.

please read :"what is mathematics" book then you will come to know the importance…..

It has nothing to do with depth. I am referring to his pedagogical style. Amongst the worst I have seen. Complete geek unable to communicate or inspire. And wretched handwriting.

It was funny, but i'm not sure it's meant to be.

Ref: 16 to 17 minutes

In simple words, he is saying, between any two different real numbers, no matter how close together, there are infinitely many other real numbers. So there is no number larger than any number on the real number line or no number smaller than any number on the real number line

Forget waterboarding, we have a new form of enhanced interrogation!

guys is there a trancript of this lesson. He is a good teacher but his accent is killing me 🙂

For real number do you mean rational plus irrational?

Need help guys: Why does he introduce te relation 1/n2<1/n. I agree on the values but I don't see the logic of it.

Nice teaching and the Kolkata accent was nice as well! Just one small correction at around 52.00 where he says any S which is a subset of R has a supremum. It should be any S which is bounded above has a supremum. For e.g N which is a subset of R does not have a supremum.

strangely I can understand his writings but not his vocalisation. But I don't despair I'll get used 🙂 HAs someone post some notes of the course?

go to the nptel website , you will find a web course there too.

Yes, download them, open them in a movie editing program, and slow it down by a factor of like .9 or so 🙂 You can download them using DVD video soft.

You must be in a very advanced high school 🙂 I learned some of this in my grade 12 (America), and have extended these ideas in my freshman year of college. My masters degree doesn't include this because it will already have been covered 🙂 More advanced/addictional topics will be covered than real and complex analysis.

whats hee sayingggg

!!!!!!!!!!!

It's not that hard to understand him or any of the IIT professors, just focus on what he is saying more. I have had 2 teachers with a heavy accent, so I guess I have gotten used to it

some people are so ungrateful. the lecturer is taking his valuable time to teach us for free but instead of being thankful, some viewers have nothing but negative things to say.

if you are getting a high paying job opportunity to work abroad or in a global company that deals with multinationals, would you turn it down or would you accept it and adapt to the accents?

please stop being so closed minded. if you cannot understand him, pause and play back but don't be negative or insulting.

HEY VIEWERS…Prof Ray is great but i fond another professor who is EXTREMELY GOOD when it comes to teaching CALCULUS if you are interested. copy and paste the following. trust me you won't regret it!……

Calculus1 Lecture1

or if you are doing college algebra….

College Algebra – Lecture 1 – Numbers

you won't regret it!

Good and clear explanations.

But please see if you can improve the quality of the writing. The images are not very clear. If the visual form is good it is much easier to focus on the content.

This course is the equivalent of Calculus II & III right?

This course looks as if it will drop heavily off the deep end very quickly…

Wow, I never understood the contradiction in the proof of root 2 being irrational!

This guy is good :p

@ ebunny5 we care and appreciate the proffs time only if it values us!!!! He is just an amazing guy in knowledge, but in teaching with the greatest of heart i could give him 35%. Students need real teachers not anybody else!!!

@alexlaur2007: listen we care a lil bit of the guy's accent since it deals with our understang and nothng more!!! If I am a real student i would personally give nothing towards his english if i understand him!!!! But the prob he complicates things thats all!!!!

Ref [54:12] Archemidian Property Application (1): (small typo)

I think you meant (1/n < eplsilon) not the other way. (refer [35:16])

BTW: Love the lectures. Keep up the gr8 work

I had this confusion for l.u.b always but after after this lecture everything is very clear thanx a lot

Great video!

@pablito12sc lol

Very important basic proof at 10:20.

Does the set B = {q: q^2 <2 } contain a largest member? Nice job. Simple and clear.

I am not abl to express my gratitude to thes lecturers.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before………….

Thank you so much for this lecture sir. I am most grateful.

8:33

There is an error with the representation of the number 1/2 on the line. It should be between 0 and 1, but it is shown to be between 1 and 2 in the video.

I think at 10:20 he's trying to prove that the rationals don't have the completeness property; e.g. he takes a particular set of rationals and shows that it is not bounded above. He also states that this particular set is not bounded below, although he doesn't actually prove it.

Thanks for the lecture.

@chpsanders

friend rationals are surely bigger set than integers because consider 3. 3 is an integer and at the same time rational _can be represented 3/1 which makes it rational……….

Negative Natural numbers ??

—- but aren't natural numbers the ordinary counting numbers 1, 2, 3,…

(or)

is it that there is no universal agreement about which set of numbers is designated by the term "natural numbers"!!

@psycool666, Math is a language and not just a way of solving problems. In mathematics sometimes you have to define very specifically what you are describing. sometimes it is convenient or necessary to bound natural numbers as all integers greater than or equal to 1 sometimes you need to describe natural numbers as all integers, sometimes all integers other than 0 is useful. it depends on what you are describing. you could say Alaskan winters are cold. or the killer was cold.

Video is not clear

thanku sir.

If anybody is to grumble, it is about the quality of the video youtube provides.

@psycool666

Negative natural numbers doesn't mean the negative part of the natural numbers. It means the negatives of the natural numbers. Also, names are nothing but convention, and at least in India we call the set of negative numbers the set of negative natural numbers,

I Really Like The Video From Your Lecture 1 Real Number

@ls600h1

I'm sorry If I sounded Cocky actually I'm a non-math student, and have been interested in math after my college, so a lot of self learning, It is just that these terms are a bit Confusing , Cuz I read that the number "1" was the lowest Natural number, and I definitely don't doubt on what an IIT professor is lecturing on – Cuz Im from India too, maybe it is just that these Terms aren't STRICTLY DEFINED to apply them Universally

@psycool666

Well your version of the definition is correct, and the smallest natural number is 1, but what I think the lecturer meant was the negative of natural numbers, so basicly its the set of elements -x, where x is an element of natural numbers

@ls600h1

But wouldn't set of " Negative INTEGERS " would have fit well rather than set of negative of natural numbers as INTEGERS already contain them as a part of their Complete Set – It is just that it is less confusing where we mention a SET which is already a part of it instead of Creating a Set that isn't actually there

nice lecture!

awesome video…………….

WHY MUST I BE SO INEPT AT MATHEMATICS!? fuck i go to the most basic maths video on youtube and the first thing he says confuses me and i can't focus anymore. fuck!

Thank you to the government for such a greatest idea to make this type of lectures… from lectures…………….

lots of bayans from 12:03 and on

Where do you live? I don't know of any country in the world where this is 7'th grade material…

Do you really understand these concepts in 7th grade ? Do you really understand what analytical functions are ? I certainly did not.

wow!! this is a very good idea and i wish other countries in the world would adopt this.

I want video lectures of topology of metric spaces by

Professor S K Ray plz mail me the link

dont try to see the starting concepts ..they are just the intro …see the ending of the playlist and then compare your 7th grade concepts with IIT…Seems as if you are another creep not getting into iit's !!!

The lecture material and presentation are superb, but the graphics are hard to read/understand. But, still excellent coverage. -r.

The quality is not good but he explained very well…!!

There is no gaps in Real numbers?

What's the difference between math analysis and calculus? Why there is such distintion?

Hi NPTEL, the video resources u offer r at least as good, if not better than MIT OCW. However, I do think it's a shame that there is a significant number of lecture series (including this 1) that r at such low resolution that I cannot read the lecturer's notes! is there any chance that u will b refilming those series with higher resolution?!

Great.

Does he mention which textbook he's using?

only one lowpoint low resolution please try to reflm them

all here can't read notes can on subtitles

please sir visible clearly is not seen in online lecture .so,keep neccessory steps towards it.

i want at least 480 p resoltution

TYPOS AT 8:33 AND 54:12

what u write isnot visible sir ,

sir is that video and other related of this course is also useful for graduation?

The beauty of mathematics,……….in 240p( starts crying).

1/2 is between 1 and 2 amazing iit teacher

Not running on 360p&480p

Thank You so much sir !! 🤗

From..41:47 video is not working please fix it..I need this teacher so badly

got lost in 30 sec. back a few dozen steps now..

At 54:10 he made a mistake he said epsilon <1/n instead of epsilon>1/n

Can some one explain clearly what he means "Then I say that the proof is intuitively clear" at 14:22. How he says that r+(1/n) also belongs to the set A from the proof he gave

If root 2 is irrational how can it has finite length in Pythagoras triangle…..

bogus video quality

Video gets stuck at 41 min

Explanation is nice but video is worse

Is this is of bsc 1year calculus

When i was taking a admission in local privet engineering college. I tought why the classes of iits do not recorded and uploaded for other students which dont have luck to study in iit. And now I found this. Thanks a lot of you.