Introduction to mathematical thinking complete course

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.
The goal of the course is to help you develop a valuable mental ability - a powerful way of thinking that our ancestors have developed over three thousand year
assignment and background reading : drive.google.com/drive/folder...
#intromathematical
#thinking
#stanford
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Link to PayPal donation www.paypal.me/nerdslesson
⌨️ This course is created in collaboration with Stanford University.

[@harrymon0]

Lecture 1. 8:43 - - Lecture 2. 38:06 - - Lecture 3. 1:26:33 - - Lecture 4. 1:58:14 - - Lecture 5. 3:35:04 - - Lecture 6. 4:55:46 - - Lecture 7. 6:23:54 - - 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

[@cheromkun2829]

Could someone pin this

[@TheCausticThinker]

Good job! Thank you.

[@AbhishekKumar-it7yp]

Thank you

[@Naji..]

million tnx

[@therese_paula]

You, my friend, are awesome!

[@MyWissam]

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.

[@robertcampomizzi7988]

Thanks.. I didn't know the term MOOC. I knew there should be one. I just didn't know it.

[@DanteTaviantzghfgh]

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.

[@stultuses]

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

[@MyWissam]

@@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.

[@juliuscaesar564]

@@MyWissam where can is use MOOC's by Dr. Devlin? Is there a site for it?

[@kevinbruna7114]

Wow just 11 hours to change my entire brain. Press play

[@kptrzk9398]

Did you finish it?

[@robertcampomizzi7988]

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 😊

[@arjunratnadev]

​@@robertcampomizzi7988I got none because I suffer from ADHD 😔😒

[@user-qp1jh5vm8m]

​@@robertcampomizzi7988distraction happens

[@sheisty1753]

😅

[@Scientist287]

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

[@kez5729]

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 :)

[@ok-kk3ic]

That’s awesome. It feels amazing to finally understand and use that knowledge practically or in conversation.

[@sebastianhlatshwayo6060]

Bless your hope, and don't procrastinate 🙏

[@das250250]

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 !

[@physicsloverr8563]

@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

[@markkennedy9767]

Only the how of mathematics is taught in college, never the why. Motivation is never taught.

[@StopWhining491]

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.

[@anhumblemessengerofthelawo3858]

_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.

[@normanhenderson7300]

Do not forget Egypt's role in mathematics as well. There is a tendency to do that.

[@MyWissam]

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.

[@dephones4032]

Do not forget Ancient India's role in mathematics as well.

[@dephones4032]

Do not forget Ancient India's role in mathematics as well.

[@Yashhh02]

​​@@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.

[@dannuttle9005]

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.

[@AyushMishra-do5hk]

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....

[@dannuttle9005]

@@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.

[@Dhruvbala]

Don’t ask questions is insane

[@jeremywinston1]

not asking questions? that is not a teacher, just a man who got a job because of some piece of paper.

[@TheMassacreOfTheBanuQurayzahQu]

​@@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.

[@lumieres369]

I follow this very interesting course in 2014. Brighlty thought by the excellent Prof Keith Devlin. Thank you.

[@amazagx]

This is a rare precious gem!!👏👏

[@Im-not-alone-Im-full-of-myself]

Its about thinking, not about learning/remembering something. so right 👍

[@RainbowBut81691]

I’ve always wanted to learn how to read mathematical formulas thank you so much I appreciate you sharing this with the general public🎉

[@classic_sci_fi]

I don't recall having a lot of time in University Math and Physics courses to master understanding over method.

[@dhrumitpatel2342]

Thanks for uploading good course

[@crazychaba9816]

Thank you for providing high quality course for free😌 I promise that Im going to put a lot of effort into my STEM work.

[@Andre_birds]

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

[@tcg10120]

minding opening. great lesson to unbox what i leant. Math is not about who is quicker.

[@rjrviudez]

Great work ! Congratulations

[@ismayonnaiseaninstrument8700]

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!

[@Shivam-il2om]

in what field?

[@ismayonnaiseaninstrument8700]

@@Shivam-il2om Linguistics, though it’ll be interdisciplinary, so I’ll be branching out to programming and biochemistry as well.

[@sciencefordreamers2115]

Outstanding!

[@Birobrata_Deb]

Love it. beautifully explained

[@grounded9623]

Totally awesome dude.

[@ashukalipahari9965]

Mind-blowing video 🎉❤

[@bhuvaneshwarjoshi3683]

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

[@sayantanmukherjee8198]

It was a Coursera course. Thanks for provide it on Yt.

[@TheRealGigaMind]

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.

[@john.8805]

Insight is the first step to advancement

[@IsomerSoma]

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.

[@BenoitMussche]

Stanford is genius college. The Stanford course on Special Relativity on Coursera is crystal clear, step by step.

[@rolandotorres9741]

This is flat out awesome

[@huseen25]

11 hours to change your life impressive work

[@CCc-ui7wb]

Thank youuuuuuuuuuuuuuu

[@unripetheberrby6283]

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 💚

[@LearnArabicwithTahir]

Hey Thanks..You have some amazing courses here on this channel.

[@Idonthaveanythingbettertodo]

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

[@justinkanas8477]

Thanks 👍

[@youraveragedude007]

Unexplainably underrated

[@hendryjay9306]

Perfect! Thank you (October 2023)

[@oldsachem]

Mr. Keith Devlin is a great teacher. Try to negate this sentence using a wobbly false table.

[@documentwithsachin]

Aapko pranam hai gurudev 🙏

[@oldsachem]

So the Real numbers are like Zero so far as the Reals beyond the Rationals were conceived to achieve the purpose of supplying placeholders to fill in the gaps in the Rational Number Line.

[@zikriaamjad4759]

❤👍

[@dharmendrasinghazadhindust7186]

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...

[@_casg]

i hope this will help me understand mathematical fundamentals so i can use geometry nodes better

[@Obylearns]

The "9:30" statement is very valid.

[@victorsauvage1890]

I enjoyed following the proof that there exists an un-limited number of prime numbers. Is there a book which has other such proofs? (Is there a simple proof of the proposition attributed to Gauss, that every number of the form 4n+1 may be written as the sum of two squares?)

[@sayantandasgupta242]

try "The book of proof" by Richard Hammack

[@elmacho7561]

Thanks a lot. You have a new sub, good man¡

[@anonimx3512]

🙏

[@charlesemehel2449]

Thanks a lot for this life saving course!:) Can we say that @1:09:01, -infinity

[@niveditajayaswal7615]

Hey thank you for this

[@Nerdslesson]

No problem!

[@shimaalcarrim7949]

My hero

[@samric2000]

thanks a lot, i really needed it

[@NoxAllan]

Im finishing this today

[@oldsachem]

Are the words perhaps and maybe equivalent to if, logically?

[@themantrah2359]

Whoa🔥🔥🔥🔥

[@ichbintupinikim]

Ah, the British accent! Wonderful!!! Mathematik ist schön! Ausgezeichnet ❤

[@mayanlogos92]

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...

[@gerrystevens9041]

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.

[@Starfish845]

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

[@holymallows7841]

thankyouu so much for this🩷

[@nitharsanam630]

We had no clue when humans started thinking mathematically. Hence it is better to avoid such a definitive timeline for it…

[@normanhenderson7300]

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.

[@FrankieGRAI]

Is Introduction to Mathematical thinking course in college comes before College Algebra, it is easier than College Algebra ?

[@frankfahrenheit9537]

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.

[@efaldykeyn8097]

OMG 11 hours. love it

[@oldsachem]

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?

[@StarsManny]

You can imagine anything you like, that doesn't make it real though.

[@harryyalomi219]

thanks

[@jsl1375]

Are the solutions to the assignments provided anywhere?

[@ivandrofly]

11:51 - Branches definition

[@sgct89]

Kinda reminds me of the books that Shane Parrish wrote

[@DEEWORLDX]

Hello, I’m here from April of 2024..

[@diamondwhite8550]

Me too

[@anoraktheblack]

Me three.

[@heartattackchuufromloona36]

me four ❤

[@stanslausJohn-sr2vr]

Me five💪

[@sadinbinabid5340]

Man prepare a course on number theory and other applied math courses please

[@Nerdslesson]

kzbin.info/aero/PLtS8Ubq2bIlXO4qEM5BOsBy6xWQNVFu8l

[@sadinbinabid5340]

@@Nerdslesson Thanks man🙏🙏, have a good and safe day💝

[@Nerdslesson]

NO problem bro , happy learning

[@sadinbinabid5340]

@@Nerdslesson Happy Learning💝🥳

[@steelbrotherhoodof2359]

Logica is also a major study field in the philosphy studies. Just like surrealaisme and nihilisme. Not every has this. Mathknobb nerfs have. It is really quit uniqueke too calculate or todo math for a normal person. Math is a language. With its unique logicle grammar. For any human is the fact that working with numbers greater then 10 is very hard. Like ducks. They can also count a limited amount of offspring. The cultural expectation is just theory and became never practicle. Made by a person who used too do mathamatics.

[@Sciencegrinds]

That's a really interesting point of view. "People are like ducks." 💚💚💚

[@karshamik708]

GOOD.

[@petercape2331]

Where can I find the quizzes for this course, "Introduction to Mathematical Thinking" by Keith J. Devlin

[@mikkel066h]

On coursera

[@glennlopez6772]

Required advice, sincerely! What makes humanity move ahead! So should we live, think and reason like mathamathicians or like engineer's?

[@akashsinha9924]

Please add time stamps.

[@bronsomccor2642]

I dont need to learn this but im doing it cause why not

[@oldsachem]

Among the universal domain of quantification of human beings, there is a narcissist who loves himself and only himself.

[@julians9070]

Mathematics is the study of numbers in the abstract.

[@bakurcaldor4816]

"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?

[@rajkumar-wg6ce]

feeling smart just by clicking on this video.

[@mewodall841]

Please add captions @nerds lesson to this video

[@abdullaaliyar9602]

8:34 where can i find the video....can someone provide me the link

[@andrewjames6676]

Hi Dr. Devlin, where is "Finding your way around the course website"? Is there a link?

[@ASIFKHAN-ur5jk]

Wow

[@delhianathalib8044]

😮

[@srxjan8485]

Can I have Timestamps pls? Thanks

[@fench1234567]

Mathematical thinking in today's world: Whenever there is a problem, count to 10 before reacting.

[@buitragom]

From the mathematical perspective what will be the difference between "does not imply" and "does imply not"?

[@_Cartographer_]

26:15 Why should the prime be bigger than Pn?

[@AdarshSingh-pk7ws]

You can think of (P1,P2,.......Pn) as a list of prime numbers in increasing order (although not necessary but for simplicity) and hence P1 is smallest (2) and Pn is largest in the list , so since we include all the prime numbers in increasing order , any new prime P essentially would be greater than Pn.hope it helps

[@fernandocortes1187]

11:00 patterns

[@wintur2856]

bookmark: 8:17

[@sneakerbabeful]

Yeah I never 'completed' high school math. I took statistics in college, because Triganomatry and Pre-calculus made no sense.

[@SocraticEngineer]

10:27:29 , 7-09-22

[@Alians0108]

3:06:48 For self

[@vekyll]

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.

[@GuruCodeWriter]

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.

[@thefunpolice]

Wait, what?

[@vekyll]

@@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.

[@normanhenderson7300]

@@vekyll Interesting. To safe face, I usually argue to the contrary, then agree at an appropriate time gracefully.

[@ChrisJV1883]

I love to learn, and have always hated 'school'. Also, you say you doubt AI can exist, and at the least, that it'll be *at least* a decade ... yeah. Like in 1997, it was clear it'd take 2+decades to sequence the genome ... a couple years later, it was done, by a fuck-up maverick.

[@indusingh6015]

Please tell me how to do the assignments

[@minformationcenter9351]

can u issue a cirtificate with this course.

[@nehemiemole3243]

Does anyone know if this video would be useful for a high school student? Seems pretty advanced?

[@Prachi_Singh]

i think the answer is no, im in 11th grade and i found this video too advance/complicated.

[@IsomerSoma]

This is very useful if you want to study mathematics. While not relevant much for highschool students it isnt advanced. Its very basic in the sense that you need almost no prior knowledge for it - highschoolers know more math than it is required as a prerequisite. It might seem difficult initially as it requires you to think logically and write formal symbols to represent the logic in a clean way. Imo this can very much so be consumed by a highschool student that is interessted in math. This is way more important for studying mathematics than what you learn highschool and in case you like calculation, but dont like this you probably shouldnt study mathematics.

[@jonathankolawole9850]

I haven't even watched it but I wondered why I haven't subscribed yet.

[@oldsachem]

Even times an irrational number is not even.