This course is a gem. Dr. Devlin is a pioneer in offering MOOCs (massive open online courses), and he did so with a belief that education should be accessible and free to everyone ... and once MOOCs became commercialized and for profit, he was morally compelled to dissociate himself from this commercial enterprise. So, seeing these lectures online again, after all these years, is a delight. Every high school student on their way to college ought to enjoy these talks by Dr. Devlin.
we are all truly blessed to be able to go online and pretty much learn anything. I want to be a master mathematician, so I am starting with this course.
This course is a rip off from coursera I highly doubt coursera has released the rights to this course This channel is trying to get money for offering ripped off content There is also a book associated with this course
@@stultuses But remember, Dr. Devlin developed and offered this course when Coursera was a nonprofit, and he did everything for free, and content to be offered to free ... the working model at the time was that all those MOOCs were open access ... When these conditions changed, he did not accept that students will be charged for the course, and he stopped offering the course on Coursera. I don't know what the copyright laws would impose, but morally the only one with a copyright to this content is Dr. Devlin himself, and everyone else is sponging off him. Dr. Devlin wrote a blog explaining his reasons for dissociating himself from the for-profit Coursera., and affirming his commitment to open access (free) education to everyone.
Lecture 1. Introductory Material 8:43 Lecture 2. Analysis of Language - The Logical Combinators 38:06 Lecture 3. Analysis of Language - Implication 1:26:33 Lecture 4. Analysis of Language - Equivalence 1:58:14 Lecture 5. Analysis of Language - Quantifiers 3:35:04 Lecture 6. Working With Quantifiers 4:55:46 Lecture 7. Proofs 6:23:54 Lecture 8A. Proofs Involving Quantifiers Part A 7:46:32 Lecture 8B. Proofs Involving Quantifiers Part B 8:22:30 Lecture 9. Elements of Number Theory 9:00:38 Lecture 10A. Beginning Real Analysis Part 1 10:01:50 Lecture 10B. Beginning Real Analysis Part 2 11:15:36
When he said - "schools focus more on the formulas and procedures, without conveying the exact big picture or applications", thats when i knew that this course is for me.
_Greek Mathematical Thought And The Origin Of Algebra_ is the title of a book, considered by some to be the most important of the 20th century. You don't have to read it, but if you want to understand how modern mathematics became what it is and what its origin was, you really ought. By Jacob Klein.
We tend to attribute many things to "the Greeks" because we desperately want to avoid attribution to Arabs, Persians, Abbasid, or Muslim scholars and mathematicians in general, and Andalusians in particular. Babylonians and Pharonites are safely distant and genuinely lacked the abstraction characteristic of modern mathematics that we can safely attribute to them a primitive precedent. Cultural studies have not yet touched upon the history of mathematics, concepts and practices, in a meaningful way.
@@MyWissambro forgot india's brilliance in fields of mathematics. Hidden gem. A lot of ancient scriptures were stolen and burnt by mughals. Such a shame. And they were beyond the thinking capability of even arabs and all of them people you mentioned. Lmao but it probably did not have much application in fields of real world. But it had many in quantum mathematics and physics.
Hi, I am a first year engineering student and I really feel what you said about courses like mine steering towards learning processes rather than mathematical thinking. My goal has always been understanding, so it is really frustrating when the lecturer will skip over the heavy mathematical understanding, straight to the formula we can plug numbers into for quick and easy answers. Speaking to PHD students, they all say that you can be a good engineer just doing processes but, to be a great engineer, the mathematical thinking you speak of is needed. I hope to be a great engineer one day :)
Great attitude, seek and spend most time to understand the fundamentals , then ensure you pass and time permitting go back and play with the material you learned. Good luck !
@kez5729 i think that same problem goes with me also i use to think pure conceptually and became to know farther tht i have to make this thinkings also
I recently got a PhD in theoretical physics. Over my career, I thought I was hot shit and tried to sit in on advanced math courses, but they have always puzzled me beyond measure. Idk what it is, something like measure theory is so complicated with all the definitions and theorems that you have to keep in your mental RAM at the same time. If you don’t think mathematically, as described in this video, it’s not going to work out for you. I think they probably explained this stuff in earlier math classes but I tried to skip it all :D
Just found this series. Part of my difficulty absorbing mathematical thinking has been that my exposures have been time-limited: timed tests, classes of a fixed length, etc. A suggestion that I "slow down" will be appreciated if that's what's really going to happen.
Just the first five minutes would have been invaluable when I started college. My high school math was not only inside the box, but with one particularly awful teacher, the real rules were 1) be on time 2) be in your seat and 3) don't ask questions. If you violated any of those rules even the tiniest bit, you were punished and humiliated. Many years later I took up math again and had to shake off the inside-the-box mindset.
Bro...does high school mathematics include CALCULUS....? ASKING coz from where i am high school means 10th grade.... 11& 12 grade include stuff of PRECALCULUS AND CALCULUS....
@@AyushMishra-do5hk My rural American high school, in the late 70s, had a fair amount of precalculus, but only the briefst intro to limits and derivatives, with no real attempt to explain them. This was in my senior year. Even so, math education was almost entirely a matter of memorizing tricks rather than understanding concepts.
@@AyushMishra-do5hk my boy yes there be pre-calc and sometimes calculus. Depends on the school. There are other math courses like statistics or college algebra as well.
I am just trying to change my thinking process. Faced dilemma throughout my life while making decisions. Always had problems looking the bigger picture. Basically I always went head first.
Thats a good insight! Often what you want to do in learning, that might seem counter-intuitive due to our failed educational systems, is figure out the big picture first before adding on all the details.
Excellant idea of focusing on mathematical reasoning.I feel even for graduate students there should be some such courses that emphasize the reasoning behind various theorems in different branches of mathematics.This would help the student to be able to distinguesh between 'what it means to follow the ryles if mathematical reasoning and when doing out of box reasoning nd developing new theirems, laws or new branches of mathematicsme.g.,Matrix algebra,complex numbers,set &measure theories,topology etc I
Answer for problem at 1:24:00 - 4mph walking and 2mph walkway. - You can walk on the walkway (ie. 4mph + 2mph = 6mph). - The walkway always moves along no matter what (irrespective of whatever you may be doing). - When you stop to tie your shoes, your walking stops (whether you're on still ground or the walkway). So, if you tie while not on walkway, you will lose walking speed (-4mph) and come to a stop. If you do this while on the walkway, this will occur too, however, the 2mph is still not lost. Therefore, to get to the gate in the fastest way, you should tie your shoes on the walkway.
Does anyone also have a problem with the buffering of this video? Anyways, to the uploader, thank you very much for this. I see that you've got great contents worth watching on your channel. I appreciate it. THANKSSSS
well i am ready for the champagne! i learned and saw it; though in my case apple cider will have to do; in fact as poets go i plumb the heart at midnight a proposition which is false and so of course seeings how i'm phi and prone to psi means it is therefore true. so thanks for this dr devlin belike your name is raphael for there is healing in your touch and magic flames in mine so here far apart study we; two beautiful minds.
Really liked this! It's soothing to me lol and the lyrics are pretty nice, plus I like the video! I pray you can keep getting well and healthy. 🙏 Father bless you 💚
Very good sir, Thanks for such type course. Before few days ago I have started to read your book "Introduction to Mathematical Thinking" also......How can I follow book and this course together...
21:17 since you can only die once, I would say (being german) the first sentence is also correct. "One American" cant mean the same person, but in the context it can not. Dying again and again, almost once an hour. If the first sentence were "one american wins the lottery almost every day", again nobody would suspect it's the same person. Against all likelihood. "one american wakes up every day in his bed": yeah, here the same person would wake up again and again, every day, in his bed. Context.
For sure this thinking began before the symbolic representation of mathematics. Remember counting developed from notches made on surfaces, and prior to that use of the digit(fingers), hence digits in computer circuitry. Do not count the antiquitious bushman as inconsequential, as modern societies tend to do. I am a descendant.
5 minx... even back in school i met w problems that didnt work by any template ive learnt for that topic on maths... & that was hell confusing for someone not used to think mathematically...
Why doesn't question 8 at 1:07:17 invalidate the "clever" infinite number of primes proof? Here we have pn=13 < 59 < 509 < N where N=30031 "is not always" prime. So (p1..,pn)+1 is not necessarily prime but was stated as such in the infinite number of primes proof? Thanks
The assumption is different. The Euclid proof assumes that there only exists a finite number of prime numbers, which is p1, p2,…pn, and given this assumption since p1*p2*…*pn+1 is not divisible by all the assumed existing prime numbers, it must be another prime number, thus contradictory. The proof at 1:07:17 does not assume there is a finite number of prime numbers, which is the case in reality, and thus of course you can find a case in which p1*p2*…pn+1 is not a prime. Mathematics is all about what you assume and what you are trying to prove. If you can’t understand this fundamental difference then you need to redo the practice problems in the course again.
Also notice that the number we found by p1*p2*…pn+1 at 1:07:17 is NOT found non-prime due to any p1, p2,…pn. It is a bigger prime number that doesn’t exist when first timing all the first n prime numbers together, which should be another proof for Euclid’s proof because there always exist a bigger prime number than the existing ones we know.
A person on another site convinced me the proof is correct, even though the product of primes plus 1 may not be prime (e.g. pn=13), as some TH-cam videos imply. In the proof, for Q=(p1*p2*...*pn)+1, this is assumed to be the entire list of primes. But Q is not evenly divisible by any of the primes in this alleged complete list. Thus, it must either be prime or be a product of primes all greater than pn. So pn can't be the last prime.
A masochist can beat himself, but gets no pleasure from it. He only enjoys it if a sadist beats him. Write in mathematical terms, Keith said sadistically to a dungeon of masochists eager to learn..
Error at 11:25:48, and really shows how mathematical thinking is hard. x\mapsto(x+1)^2/(2x+1) is not an increasing function, it is decreasing on natural numbers.
But is it not increasing on natural numbers? When x=1, (1+1)^2/(2+1) = 4/3, and x=2 is (2+1)^2/(4+1) = 9/5, which is certainly greater than 4/3, and so on. Also, it's graph shows otherwise, so im a little puzzled by what you said.
@@GuruCodeWriter Yeah, my bad. After 11.5h of watching, I was a little tired, I guess. :-D I mixed up (x+1)^2/(2x+1) with what was estimated at that point, (2x+1)/(x+1)^2. Sorry for the confusion.
"Keith cycles only if the sun shines." if the sun is shining I can expect Keith to be cycling. If I see Keith cycling, then wouldn't I already know that the sun is shining?
hello i am a jee aspirant who love mathematics and want to master it , can this video increase my complex porbolem solving and overall mathematical thinking ??
Why jee then there are so many Institutes dedicated to mathematics in India Try their exam For eg :- isi, cmi, imsc, ima bbsr etc etc Try their exam bud forget jee
Does infinity exist in a finite universe? If not, and it cannot be proved either way, whether infinity exist or not, then why does consciousness permit the human intelligence to imagine such a thing as infinity does or might exist?
im still confused as to how the infinite prime proof works. Assume like if our humanity only knows so far some finite primes and we multiply all of them together lets say 2 * 3 * 5 * 7 * 11 * 13 * 17 then its gonna be equal to 510510 + 1 = 510511 which is divisible 19 which is the undiscovered prime? Could anyone explain that to me pls
Every number is either prime or not prime . There is no third category. Now let's say humanity knows only prime numbers up to 17 ,and multiplying we get 510510 as you mentioned , adding 1 , why ? Cause 510511 is either going to be a prime or not prime , so now we are sure of 2 things 1. If it's prime -that means humanity just discovered a new prime which will be 510511 but we need to check every number between with 2 and 510511 if it's really prime which leads to second thing 2.if it's not a prime that means there is a prime number by which 510511 is completely divisible and it's not in our known prime numbers as here remainder will be 1 as we added it first and it's greater than known prime number. But now we know there must be a prime number which we do not know leading to the conclusion there are infinite prime numbers. Main thing to understand here is that every number is made up of multiplication of prime numbers or it itself is prime number
@@sanketjadhav3.14 oh ok i see it now. The first time I watched it was a bit of a stretch for me to grasp but when i came back as soon as u posted the comment and rewatched the proof, it came clear to me now. Thanks a lot!
This course is a gem. Dr. Devlin is a pioneer in offering MOOCs (massive open online courses), and he did so with a belief that education should be accessible and free to everyone ... and once MOOCs became commercialized and for profit, he was morally compelled to dissociate himself from this commercial enterprise. So, seeing these lectures online again, after all these years, is a delight. Every high school student on their way to college ought to enjoy these talks by Dr. Devlin.
Thanks.. I didn't know the term MOOC. I knew there should be one. I just didn't know it.
we are all truly blessed to be able to go online and pretty much learn anything. I want to be a master mathematician, so I am starting with this course.
This course is a rip off from coursera
I highly doubt coursera has released the rights to this course
This channel is trying to get money for offering ripped off content
There is also a book associated with this course
@@stultuses But remember, Dr. Devlin developed and offered this course when Coursera was a nonprofit, and he did everything for free, and content to be offered to free ... the working model at the time was that all those MOOCs were open access ... When these conditions changed, he did not accept that students will be charged for the course, and he stopped offering the course on Coursera.
I don't know what the copyright laws would impose, but morally the only one with a copyright to this content is Dr. Devlin himself, and everyone else is sponging off him.
Dr. Devlin wrote a blog explaining his reasons for dissociating himself from the for-profit Coursera., and affirming his commitment to open access (free) education to everyone.
@@MyWissam where can is use MOOC's by Dr. Devlin? Is there a site for it?
Lecture 1. Introductory Material
8:43
Lecture 2. Analysis of Language - The Logical Combinators
38:06
Lecture 3. Analysis of Language - Implication
1:26:33
Lecture 4. Analysis of Language - Equivalence
1:58:14
Lecture 5. Analysis of Language - Quantifiers
3:35:04
Lecture 6. Working With Quantifiers
4:55:46
Lecture 7. Proofs
6:23:54
Lecture 8A. Proofs Involving Quantifiers Part A
7:46:32
Lecture 8B. Proofs Involving Quantifiers Part B
8:22:30
Lecture 9. Elements of Number Theory
9:00:38
Lecture 10A. Beginning Real Analysis Part 1
10:01:50
Lecture 10B. Beginning Real Analysis Part 2
11:15:36
Thank you. You are awesome for this
Thank you
You are the best
When he said - "schools focus more on the formulas and procedures, without conveying the exact big picture or applications", thats when i knew that this course is for me.
Lecture 1. 8:43
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Lecture 2. 38:06
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Lecture 3. 1:26:33
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Lecture 4. 1:58:14
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Lecture 5. 3:35:04
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Lecture 6. 4:55:46
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Lecture 7A. 6:23:54
- -
Lecture 7B. 6:46:19
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Lecture 8A. 7:46:32
- -
Lecture 8B. 8:22:30
- -
Lecture 9. 9:00:38
- -
Lecture 10A. 10:01:50
- -
Lecture 10B. 11:15:36
Could someone pin this
Good job! Thank you.
Thank you
million tnx
You, my friend, are awesome!
Wow just 11 hours to change my entire brain. Press play
Did you finish it?
My dad (and brother) were engineers. I'm here to see how much of it stuck with me.... and what didn't.
You gave me some hope 😊
@@robertcampomizzi7988I got none because I suffer from ADHD 😔😒
@@robertcampomizzi7988distraction happens
😅
_Greek Mathematical Thought And The Origin Of Algebra_ is the title of a book, considered by some to be the most important of the 20th century. You don't have to read it, but if you want to understand how modern mathematics became what it is and what its origin was, you really ought. By Jacob Klein.
Do not forget Egypt's role in mathematics as well. There is a tendency to do that.
We tend to attribute many things to "the Greeks" because we desperately want to avoid attribution to Arabs, Persians, Abbasid, or Muslim scholars and mathematicians in general, and Andalusians in particular. Babylonians and Pharonites are safely distant and genuinely lacked the abstraction characteristic of modern mathematics that we can safely attribute to them a primitive precedent. Cultural studies have not yet touched upon the history of mathematics, concepts and practices, in a meaningful way.
Do not forget Ancient India's role in mathematics as well.
Do not forget Ancient India's role in mathematics as well.
@@MyWissambro forgot india's brilliance in fields of mathematics. Hidden gem. A lot of ancient scriptures were stolen and burnt by mughals. Such a shame. And they were beyond the thinking capability of even arabs and all of them people you mentioned. Lmao but it probably did not have much application in fields of real world. But it had many in quantum mathematics and physics.
Hi, I am a first year engineering student and I really feel what you said about courses like mine steering towards learning processes rather than mathematical thinking. My goal has always been understanding, so it is really frustrating when the lecturer will skip over the heavy mathematical understanding, straight to the formula we can plug numbers into for quick and easy answers.
Speaking to PHD students, they all say that you can be a good engineer just doing processes but, to be a great engineer, the mathematical thinking you speak of is needed. I hope to be a great engineer one day :)
That’s awesome. It feels amazing to finally understand and use that knowledge practically or in conversation.
Bless your hope, and don't procrastinate 🙏
Great attitude, seek and spend most time to understand the fundamentals , then ensure you pass and time permitting go back and play with the material you learned. Good luck !
@kez5729 i think that same problem goes with me also i use to think pure conceptually and became to know farther tht i have to make this thinkings also
Only the how of mathematics is taught in college, never the why. Motivation is never taught.
I’ve always wanted to learn how to read mathematical formulas thank you so much I appreciate you sharing this with the general public🎉
I recently got a PhD in theoretical physics. Over my career, I thought I was hot shit and tried to sit in on advanced math courses, but they have always puzzled me beyond measure. Idk what it is, something like measure theory is so complicated with all the definitions and theorems that you have to keep in your mental RAM at the same time. If you don’t think mathematically, as described in this video, it’s not going to work out for you. I think they probably explained this stuff in earlier math classes but I tried to skip it all :D
Its about thinking, not about learning/remembering something.
so right 👍
It was a Coursera course. Thanks for provide it on Yt.
Just found this series. Part of my difficulty absorbing mathematical thinking has been that my exposures have been time-limited: timed tests, classes of a fixed length, etc. A suggestion that I "slow down" will be appreciated if that's what's really going to happen.
I took this course with him in Coursera by Stanford University. Thanks to share it in TH-cam!
Holy crap, this might be exactly what I need for my senior project, and I didn’t know I needed it until now…thanks in advance!
in what field?
@@Shivam-il2om Linguistics, though it’ll be interdisciplinary, so I’ll be branching out to programming and biochemistry as well.
This right here is a true blessing....
Just the first five minutes would have been invaluable when I started college. My high school math was not only inside the box, but with one particularly awful teacher, the real rules were 1) be on time 2) be in your seat and 3) don't ask questions. If you violated any of those rules even the tiniest bit, you were punished and humiliated. Many years later I took up math again and had to shake off the inside-the-box mindset.
Bro...does high school mathematics include CALCULUS....?
ASKING coz from where i am high school means 10th grade....
11& 12 grade include stuff of PRECALCULUS AND CALCULUS....
@@AyushMishra-do5hk My rural American high school, in the late 70s, had a fair amount of precalculus, but only the briefst intro to limits and derivatives, with no real attempt to explain them. This was in my senior year. Even so, math education was almost entirely a matter of memorizing tricks rather than understanding concepts.
Don’t ask questions is insane
not asking questions? that is not a teacher, just a man who got a job because of some piece of paper.
@@AyushMishra-do5hk my boy yes there be pre-calc and sometimes calculus. Depends on the school. There are other math courses like statistics or college algebra as well.
This is a rare precious gem!!👏👏
Thank you for providing high quality course for free😌
I promise that Im going to put a lot of effort into my STEM work.
I don't recall having a lot of time in University Math and Physics courses to master understanding over method.
Unexplainably underrated
11 hours to change your life impressive work
I am just trying to change my thinking process. Faced dilemma throughout my life while making decisions. Always had problems looking the bigger picture. Basically I always went head first.
Insight is the first step to advancement
Thats a good insight! Often what you want to do in learning, that might seem counter-intuitive due to our failed educational systems, is figure out the big picture first before adding on all the details.
minding opening. great lesson to unbox what i leant. Math is not about who is quicker.
Excellant idea of focusing on mathematical reasoning.I feel even for graduate students there should be some such courses that emphasize the reasoning behind various theorems in different branches of mathematics.This would help the student to be able to distinguesh between 'what it means to follow the ryles if mathematical reasoning and when doing out of box reasoning nd developing new theirems, laws or new branches of mathematicsme.g.,Matrix algebra,complex numbers,set &measure theories,topology etc
I
I follow this very interesting course in 2014. Brighlty thought by the excellent Prof Keith Devlin. Thank you.
This is my 1st time. And I hope to enjoy it.
feeling smart just by clicking on this video.
Answer for problem at 1:24:00
- 4mph walking and 2mph walkway.
- You can walk on the walkway (ie. 4mph + 2mph = 6mph).
- The walkway always moves along no matter what (irrespective of whatever you may be doing).
- When you stop to tie your shoes, your walking stops (whether you're on still ground or the walkway).
So, if you tie while not on walkway, you will lose walking speed (-4mph) and come to a stop. If you do this while on the walkway, this will occur too, however, the 2mph is still not lost.
Therefore, to get to the gate in the fastest way, you should tie your shoes on the walkway.
BUT, it depends on the length of the walkway.
Does anyone also have a problem with the buffering of this video?
Anyways, to the uploader, thank you very much for this. I see that you've got great contents worth watching on your channel. I appreciate it. THANKSSSS
That is what I've looking for loooong while. Thank's for sharing!
Stanford is genius college. The Stanford course on Special Relativity on Coursera is crystal clear, step by step.
Who cares about general relativity
@@unikat-kmnkmn2799 I do
@@unikat-kmnkmn2799 i do
Great video 😊😊🎉🎉
Loved it
Respect from India ❤
This is flat out awesome
Totally awesome dude.
Love it. beautifully explained
Hi Dr. Devlin, where is "Finding your way around the course website"? Is there a link?
Hey Thanks..You have some amazing courses here on this channel.
day 1 - 33:01
This is pure mathematics
Unfortunately I'm more into Applied mathematics 😊😊
Even if you're in applied mathematics you need to know this. This is basic stuff past secondary school
I dont need to learn this but im doing it cause why not
Imma listen this while sleeping... 😴
I'm trying to understand math since I'm getting interested in it but I can't even do basic math
Great work ! Congratulations
Mr. Keith Devlin is a great teacher. Try to negate this sentence using a wobbly false table.
Aapko pranam hai gurudev 🙏
I haven't even watched it but I wondered why I haven't subscribed yet.
well i am ready for the champagne! i learned and saw it;
though in my case apple cider will have to do;
in fact as poets go i plumb the heart at midnight
a proposition which is false and so of course
seeings how i'm phi and prone to psi means it is therefore true.
so thanks for this dr devlin belike your name is raphael
for there is healing in your touch and magic flames in mine
so here far apart study we; two beautiful minds.
Thanks a lot for this life saving course!:) Can we say that @1:09:01, -infinity
Really liked this! It's soothing to me lol and the lyrics are pretty nice, plus I like the video!
I pray you can keep getting well and healthy. 🙏 Father bless you 💚
Thanks for uploading good course
Mathematics is the study of numbers in the abstract.
Required advice, sincerely!
What makes humanity move ahead!
So should we live, think and reason like mathamathicians or like engineer's?
Very good sir, Thanks for such type course. Before few days ago I have started to read your book "Introduction to Mathematical Thinking" also......How can I follow book and this course together...
Mind-blowing video 🎉❤
Is Introduction to Mathematical thinking course in college comes before College Algebra, it is easier than College Algebra ?
i hope this will help me understand mathematical fundamentals so i can use geometry nodes better
21:17 since you can only die once, I would say (being german) the first sentence is also correct.
"One American" cant mean the same person, but in the context it can not.
Dying again and again, almost once an hour.
If the first sentence were "one american wins the lottery almost every day", again nobody would
suspect it's the same person. Against all likelihood.
"one american wakes up every day in his bed": yeah, here the same person would wake up
again and again, every day, in his bed.
Context.
Are the solutions to the assignments provided anywhere?
Perfect! Thank you (October 2023)
The "9:30" statement is very valid.
Maths course with no maths. Hell yes baby.
I wanna see a math course with a lot of kung fu or juggling!! 😁
thanks a lot, i really needed it
This is the main thing. Templates in high school means the different examples which i didn't exactly do in that way so might not be my case
3:06:48
For self
Mathematical thinking in today's world: Whenever there is a problem, count to 10 before reacting.
Will Smith has never watched these videos 🤣
OMG 11 hours. love it
Im finishing this today
What do you want. Why do you want it.
Ah, the British accent! Wonderful!!! Mathematik ist schön! Ausgezeichnet ❤
Wow you’re still alive
Thanks a lot.
You have a new sub, good man¡
Man prepare a course on number theory and other applied math courses please
th-cam.com/play/PLtS8Ubq2bIlXO4qEM5BOsBy6xWQNVFu8l.html
@@Nerdslesson Thanks man🙏🙏, have a good and safe day💝
NO problem bro , happy learning
@@Nerdslesson Happy Learning💝🥳
We had no clue when humans started thinking mathematically. Hence it is better to avoid such a definitive timeline for it…
For sure this thinking began before the symbolic representation of mathematics. Remember counting developed from notches made on surfaces, and prior to that use of the digit(fingers), hence digits in computer circuitry. Do not count the antiquitious bushman as inconsequential, as modern societies tend to do. I am a descendant.
5 minx... even back in school i met w problems that didnt work by any template ive learnt for that topic on maths... & that was hell confusing for someone not used to think mathematically...
Why doesn't question 8 at 1:07:17 invalidate the "clever" infinite number of primes proof?
Here we have pn=13 < 59 < 509 < N where N=30031 "is not always" prime.
So (p1..,pn)+1 is not necessarily prime but was stated as such in the infinite number of primes proof?
Thanks
The assumption is different. The Euclid proof assumes that there only exists a finite number of prime numbers, which is p1, p2,…pn, and given this assumption since p1*p2*…*pn+1 is not divisible by all the assumed existing prime numbers, it must be another prime number, thus contradictory. The proof at 1:07:17 does not assume there is a finite number of prime numbers, which is the case in reality, and thus of course you can find a case in which p1*p2*…pn+1 is not a prime.
Mathematics is all about what you assume and what you are trying to prove. If you can’t understand this fundamental difference then you need to redo the practice problems in the course again.
Also notice that the number we found by p1*p2*…pn+1 at 1:07:17 is NOT found non-prime due to any p1, p2,…pn. It is a bigger prime number that doesn’t exist when first timing all the first n prime numbers together, which should be another proof for Euclid’s proof because there always exist a bigger prime number than the existing ones we know.
A person on another site convinced me the proof is correct, even though the product of primes plus 1 may not be prime (e.g. pn=13), as some TH-cam videos imply. In the proof, for Q=(p1*p2*...*pn)+1, this is assumed to be the entire list of primes. But Q is not evenly divisible by any of the primes in this alleged complete list. Thus, it must either be prime or be a product of primes all greater than pn. So pn can't be the last prime.
thankyouu so much for this🩷
A school dropout because of dyscalculia here...hope this helps me...
should i know trigonometry stuff before starting this course?
No.
Is this class for a person who is bad at math?
What if you flunked algebra 3 times, but finally made an A in it after high school?
Not (I totally understand) And ThatImplies (I will be rewatching)
Firstly, fine work. HD reupload would be nice though. My eyes hurt
A masochist can beat himself, but gets no pleasure from it. He only enjoys it if a sadist beats him. Write in mathematical terms, Keith said sadistically to a dungeon of masochists eager to learn..
thanks
Can this be taken by someone who is starting math courses again?
Error at 11:25:48, and really shows how mathematical thinking is hard. x\mapsto(x+1)^2/(2x+1) is not an increasing function, it is decreasing on natural numbers.
But is it not increasing on natural numbers? When x=1, (1+1)^2/(2+1) = 4/3, and x=2 is (2+1)^2/(4+1) = 9/5, which is certainly greater than 4/3, and so on. Also, it's graph shows otherwise, so im a little puzzled by what you said.
Wait, what?
@@GuruCodeWriter Yeah, my bad. After 11.5h of watching, I was a little tired, I guess. :-D I mixed up (x+1)^2/(2x+1) with what was estimated at that point, (2x+1)/(x+1)^2. Sorry for the confusion.
@@vekyll Interesting. To safe face, I usually argue to the contrary, then agree at an appropriate time gracefully.
Where can I find the quizzes for this course, "Introduction to Mathematical Thinking" by Keith J. Devlin
On coursera
11 hours 27 minutes? that's a lot of thinking.
Better than 4 years of college
Watch the reboot of “Battlestar Galactica” or the whole series of “The Sopranos” in one sitting and you’ll change your perspective.
3:11:25 how come Team wins is antecedent because here consequent is “team wins” and condition is Karl plays. Please correct me if I am wrong.
"Keith cycles only if the sun shines." if the sun is shining I can expect Keith to be cycling. If I see Keith cycling, then wouldn't I already know that the sun is shining?
Just started video. Will it help me deal with people going 30 in a one lane 35?
hello i am a jee aspirant who love mathematics and want to master it , can this video increase my complex porbolem solving and overall mathematical thinking ??
Why jee then there are so many Institutes dedicated to mathematics in India
Try their exam
For eg :- isi, cmi, imsc, ima bbsr etc etc
Try their exam bud forget jee
OMG discrete MATH!!!
Timestamp: 05:00
44:00 isn't this iff ( if and only if example??)
Where to find the background reading pdf?
where can I find the link for supplemental reading?
in the description now! not sure if it was there before
Does infinity exist in a finite universe? If not, and it cannot be proved either way, whether infinity exist or not, then why does consciousness permit the human intelligence to imagine such a thing as infinity does or might exist?
You can imagine anything you like, that doesn't make it real though.
51:10 guys i cannot understand why the statement is wrong
please help sir
Outstanding!
im still confused as to how the infinite prime proof works. Assume like if our humanity only knows so far some finite primes and we multiply all of them together lets say 2 * 3 * 5 * 7 * 11 * 13 * 17 then its gonna be equal to 510510 + 1 = 510511 which is divisible 19 which is the undiscovered prime? Could anyone explain that to me pls
Every number is either prime or not prime . There is no third category. Now let's say humanity knows only prime numbers up to 17 ,and multiplying we get 510510 as you mentioned , adding 1 , why ? Cause 510511 is either going to be a prime or not prime , so now we are sure of 2 things
1. If it's prime -that means humanity just discovered a new prime which will be 510511 but we need to check every number between with 2 and 510511 if it's really prime which leads to second thing
2.if it's not a prime that means there is a prime number by which 510511 is completely divisible and it's not in our known prime numbers as here remainder will be 1 as we added it first and it's greater than known prime number. But now we know there must be a prime number which we do not know leading to the conclusion there are infinite prime numbers.
Main thing to understand here is that every number is made up of multiplication of prime numbers or it itself is prime number
@@sanketjadhav3.14 oh ok i see it now. The first time I watched it was a bit of a stretch for me to grasp but when i came back as soon as u posted the comment and rewatched the proof, it came clear to me now. Thanks a lot!