Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010
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- Опубліковано 15 тра 2024
- Lecture 1: Introduction and Proofs
Instructor: Tom Leighton
View the complete course: ocw.mit.edu/6-042JF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
Nothing like procrastinating by watching a *lecture* from 12 years ago on a course I have no knowledge on
I am doing the same thing
same here
Same here , bad place in life right now and im watching this
@@ahmedayad3261 tell me more - I'm a good listener.
i really thought i was a master procrastinator until i bumped into this comment...you have really taken procrastination beyond its natural limits where it is not that harmful for you because you actually learn something even though it might be useless to your life later on...truly admirable
when i see a professor ask his class ,have you ever seen a " for all " symbol, shows his dedication to make sure that every one understand what he is teaching
No kidding. I'm a history student and he explained it so even I could understand.
Wtf, this is MIT. I have been using this symbol for 3 years before college.
@@panoskre Everybody has knowledge gaps. It all depends on if whatever teacher you had in high school told you what it was or your parents did. Pointless to discuss when you learned something.
kurosaki ichigo Its just a notation, because mathematicians are lazy.
That's so true I don't know what to do with it.
The writing on the chalkboard and knowing i'm not paying for this class is so relaxing.
cause MIT is too high for u bro
🤣 thats a funny one. Would have been a disaster had you been paying
Mit is very benevolent so it has allowed us to see it's classes. Kindly appreciate their benevolence and kind nature.
Very true, Matt..
And I thought I was alone, in thinking that...😆😆😅
@@adeputri8601 Sometimes being humorous isn’t so bad.
I'm commenting here, so that my grandchildren will think their grandad is a smart guy
epic
Grandad, what do you mean you didn't use the Holodeck to learn stuff?
Relieved that I'm not the only one
I will join you in the archives of human history. ground zero google.
@@AngriestEwok No holodecks you just get a brain chip installed.
00:24 What's a proof?
02:02 How to ascertain truth?
07:30 What's a mathematical proof?
08:47 What's the definition of proposition?
09:50 What's '∀'?
10:10 What's a prime number?
10:43 What's predicate?
11:17 What's the universe of discourse?
11:29 What's quantifier?
16:27 What's "∃"?
28:45 What's "→"?
30:00 What's "↔"?
35:55 What's axiom?
40:34 What's consistency of axiom?
41:25 What's completeness of axiom?
you did a nice job.
Thanks bro 👍👩💻👩💻
laugh out loud copy and paster noob
holy shit thanks
good job dude you just saved me 40 min
These lectures are clear and comprehensible and you think to yourself, "I can do MIT". Then you read the recitations and homework assignments and realize why MIT is known to be so tough.
I couldn't agree with you more...sheesh these people
I read your comment and was inspired to give it a try, I did the first recitation, it was easier than it looked, just a fun logic puzzle. The problem set looks a bit harder, but if I took it one question at a time I think I could do it.
@FichDich InDemArsch you're so smart bro
@FichDich InDemArsch Though clearly not smart enough to know better than to claim that you're smarter than someone whom you know absolutely nothing about on the internet.
@FichDich InDemArsch Not really because my original comment wasn't intended to imply anything about your intelligence level, rather it was a shot at the arrogance of your comment.
I like this professor. He doesn't seem to put anyone down and looks to enjoy what he's doing.
I want to sit in one of theses classes just to raise my hand and ask " When drawing a "4" should I leave the top of it open or closed?"
rofl
thats why u arent there xd
Marcel right!
LOL
That is a personal preference. I always leave the top open when I write.
Thank you Professor Leighton. Your lectures got me an A in my Discrete Mathematics course.
Hmm billionaire professor
@@elonmusk352 Hmm billionaire technoking
guys where can i get the video recitation (the problem solving ) for this course?
Bruh I got a 10% in this course
It is a great pleasure to listen to this legend who is not only an extraordinary Math professor but also the co-founder of Akamai Technologies, a billion dollar company!! Regards from India!
More like 11 billion :P
@@K4inan isn't more like 111 billion?
@@elonmusk352 Isn't more like 1.11 trill.. okay I should stop!
guys where can i get the video recitation (the problem solving ) for this course?
Professors that take the time to write down a good deal of what they lecture on are highly underappreciated. This allows students sufficient time to think about the material during lectures instead of wasting their brain's resources in trying to figure out what is important enough to be written down. This is the first professor I have seen on MIT OpenCourseWare to do this.
Does anyone know of other professors like this? I truly dislike the professor who rambles on endlessly without writing a thing on the board and expecting students to figure out for themselves what is and what isn't important enough to be written down. It is basically their job to let us know what we should take note of and study to succeed in their course.
guys where can i get the video recitation (the problem solving ) for this course?
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018. Another great instructor if you are interested in data analytics
What a great man is this teacher.
All the teachings he gave are in the MIT Mathematics for CS book, but the interaction, the examples and the way he explains, are a good complement to the book.
This first lecture is a fine introduction to logic, proofs in mathematics and number theory. All these topics are huge in mathematics. Professor Leighton introduces these topics for each computer science student to think theoretical and analytical about this class and beyond.
Thank You for Your work, Professor Leighton, and thanks MIT for making this delightful lecture available to the public!
I'm in awe of these MIT OCW professors. They explain everything in such a coherent and understandable way. I love how they write their notes as they speak. If only any one of my professors were this good at their jobs, I'd be very happy.
They make ME understand such a complex yet interesting topic! It's amazing to see the results of great teaching skills.
For those of you who don’t know Tom is ceo of Akamai technologies, market leader in cdn, security and compute
Thank you for spreading the love for education! Helps us who can't afford college.
I am a senior high school student from Greece and just randomly stepped on one of the best "gems" I could find. This lecture indeed indicates how easy it is, but in reality difficult, to think and parallel everyday life with mathematics. It is really unique to see a very unconventional, for our country's educational standards, way of engaging mathematics in a more philosophical and applied manner than ever. I am truly glad to the man or woman that was assigned to list these lectures on UA-cam, it is a really beautiful and entertaining way for me to spend my free time. I often listen to consults that by thinking that you will never attend any such classes in person or be able to study them abroad you are only limiting yourself and your dreams. So seeing these is a true way of forgetting my worries for my future studies in Applied mathematics. Thanks again to anyone from filming this and capturing audio to the professor and the man or woman who uploaded this unique playlist.
Nice diagonal with the y's in the first couple of sentences.
What a fantastic teacher. This should be the standard. Top drawer!
can u give me ur mobile no. please...
Pradeep Singh, ”can u give me ur mobile no. please...” Why is it always indian people?
Pradeep Singh That... is the most pathetic comment I’ve ever read on this fucking site
I wish standard like this is applied.
guys where can i get the video recitation (the problem solving ) for this course?
You know the lession is great when you can learn not only maths but even more things from it
What an amazing professor! seems fun and that 44 mins flew by so I can
only imagine how quickly a 1 hour lecture would go. I'm a Computer
Science major and I review these lectures on top of my studies I truly
am thankful MIT makes these viewable.
guys where can i get the video recitation (the problem solving ) for this course?
I love this! Brings me back to my student days at Cornell from 1972 to 1977. Something comforting about that sound of a big piece of chalk on a slate board.
Being a Sociology and Poli Sci student, the beginning really refreshes my view on math courses
What a great teacher he is. What a level of dedication he has .
That's a great lecture. I normally get bored out of OCW lectures, but I didn't even mean to watch this whole thing, and I just did and really enjoyed it.
Strange this lecture was suggested by UA-cam on Thanksgiving. The world should be thankful for my childhood mentor & visionary MIT EE professor Dr. Jordan Baruch, in 1960 managed the computer center. At 9 had done analog & digital designs when one Saturday took me to the lab. Asked his students and the operators to show me the ropes. That day learned IBM 026 keypunch & Fortran. Then special night lectures like Grace Hopper Nanosecond, think it was E51.
A slight correction : Natural numbers starts from 1 and not 0
00:23 Proofs
02:01 Ascertaining truth
07:31 A mathematical proof
08:46 Definition of proposition
09:51 '∀'
10:11 Prime numbers?
10:42 What is a predicate?
11:16 Universe of discourse?
11:28 What is a quantifier?
16:28 "∃"
28:44 "→"
30:01 "↔"
35:54 What is axiom?
40:33 Consistency of axiom?
41:24 Completeness of axiom?
Thankyou 💥
He makes his lesson so easy to digest with interesting examples.
I wish i had this Professor. He makes things so clear. I have never studied whatever math this is but he makes it so clear.
Oh my god thank you. I understand him so much better than my current teacher. These videos make the world a better place.
guys where can i get the video recitation (the problem solving ) for this course?
This is just exactly the lecture I've always craved
guys where can i get the video recitation (the problem solving ) for this course?
Wow. So much clarity and an understandable presentation. I would have got an honors degree if this kind of lecturer was in my University.
I'm just watching this now over the summer I took Discrete math in the past @ a different university but don't remember the content much but this guy is heaven sent with his lectures. I am taking Computer Theory in the future + DSA , so discrete will help with the problem solving. Wish I seen this before
Wooow you are an amazing lacturer , everything is clear and you are explaining in detail , walking this journey with you will be the best thing ever, all the best to those who are studying with this man❤️
Hey! Is this useful for someone who is in first year cs btech ?
School: How many chalkboards do you want
Him: yes
I took an algorithms course and couldn't keep up. This is exactly what I needed. Thank you for sharing!
Thank you for making information available to the people who are hungry to learn it.
Thank you for posting this!
help what going on will take my time of life?
I’m in this class right now 🤦🏾♂️ this shih is hard
Update: I ended up with a C in here, but honestly it was solely due to my irresponsibility, if I retook it again I could see myself getting an A or a high B, the content itself is very well explained and honestly common logic and algorithms necessary for mostly computer science students. Good class.
F bro, so much respect XD
Thanks for the update haha
Lol the change in formality is funny
Great video thanks, refreshing to see this again after couple years
Love the way he teaches the subject. Clear, concise & evoking the intuitive reasoning part within me.
MIT and other private universities have such great professors .... the way he introduces his material is different than A professor just reading out the text book giving you examples .... I wish I was there for my Comp Science Degree Pursuit... Awesome Work
well the examples he gave were from his notes (the white papers he holds) , but yeah the lesson was smooth af.
wow...matthew mcconaughey is mit lecturer..
And a billionaire too
Coolest professor
He is more clear than most of my math profs. I watch a lot of these OCW lectures and I can follow all of them. However, the homework is often very challenging, but it’s doable.
This is something which everyone needs to know when doing mathematics. Those are the basic ideas.
Thank you for sharing this. Computer Science/Mathematics double major at UW here, and this is super helpful for my proofwriting class and I'm sure it will tie in with my Mathematical Principles of Computing course, too. The math jargon is way less evil than physics! :P
guys where can i get the video recitation (the problem solving ) for this course?
When a chemist enjoys this lecture, that tells you something! It was great!
I'm a Chemical Engineer who has fallen in love with these lectures too!
@@troychavez That’s probably because you love math :) Math was my favorite subject but somewhere along the way chemistry took over. :)
@@pexaminer The queen of science and engineering
@@troychavez Indeed...
this has to be one of the most interesting talks I have ever watched and listened to.
You don’t go much on the internet now do you!? Lol
@@Santalucesguy 🤣 Right
Excellent- would love to see more of these lectures!
wow i wish i had this professor at my college :'(
me too... i guess that`s why he`s an MIT profesor.. i wonder what the collective IQ is in that room... no wonder why the USA is the most advanced country in the world... lots of intelligent people.
Yeah, I hope to be going there at some point in my life. If not for my undergraduate degree, then I will definitely pursue this school for my graduate degree. Also, I concur that the U.S is advanced; however, China's infrastructure is much better in ways.
The USA got some very good universities. But if you look at the AVERAGE. It's not high. Then Finland tops it by far. Just like you got a big diference between rich and poor in the USA. You got a big diference between shit education and good education. For a country as a WHOLE, it's better to have high average quality than some little peaks which can only be afforded by the rich. The USA does contain smart people but not super much, or more than other countries. And the USA is not the most advanced country at all, it only looks like that because of movies. What is advanced? If we look at the future and best societies are very social, then you need to look at the nordic countries of Europe as being MORE advanced. Is not having properly organized healthcare and it being very expensive very advanced? Many things in the USA are actually looking the opposite of advanced.
Seeing as being poor correlates highly with being an immoral abhorrent person in many categories that we can see actively observe and quantify - no, I'm not saying having wealth makes you more virtuous; or that the more wealth you attain, the moral you are - what trickles down from the 1% to everyone else is a sign of advancement AND social (though not in the degenerate sense that you put it as). Not only that, but making things accessible to all or even most for the benefit of 'society' is a both a myth and unnecessary given trends between demographics of people. Hell, the very stratification you THINK you're arguing against is the only means by which things become accessible for the few disenfranchised individuals who will properly utilize it --the EXTREME exception, not even at 5-25% discrepancy
And that's even without getting into the immoral sense of stratification that's necessary to make it financially plausible for all of us to take advantage of all the virtues modern technology provides us at the rate and distribution that's required; or is sweatshop """labor""" not slavery cos history says whenever it involves Asians, it doesn't count?
The EU has practically been on the dole, and have bevied that same dole onto people even worse than them for a long time now. The academic output there is outweighed by far from what modern atrocities they commit on human freedoms that they set precedent to possibly occur in the rest of the world. And hell, even when speaking on health care, what skin is the EU putting out there to lose themselves. Its easy to give stuff away when its the enterprise of others (read: not lazy degenerates) that pioneer the gibs for you to take and give away. And you're enough of a mook to believe in the Robin Hood/Christ myth under a different veil cos if there's anything Europeans need to distance yourselves from, its the tract they take their dogmatic, borderline retarded morals from. Have fun with all that debt that'll be accrued over time while CHINA railroads over you via Africa since they don't give a flying fuck how they treat their own CITIZENS, much less Baizou.
The problem lays with your Assumptions. You assume GIBS. But we regulate that you cannot just get everything. Also everything has to be paid for. So the Socialwelfare in which contains also Schooling & Healthcare are funded here partly by Tax and a small montly fee. This fee can decline based on your situation. But generally most people pay the full fee because they have no problems. Can you please look at the "Costprice" of healthcar of the USA compared to the EU. The costprice of the USA is at least more than two times higher than in the EU. The policy of USA that capitalism is good for everything. Then why isn't capitalism working in the Healthcare taking prices down? Explain. Capitalism is also very important in the EU. The EU is #2 global market.(china #1, USA #3) But we actually make a decision on when something is part of Capitalism free market, and when something is NOT. The USA policy of cripled free market with strange regulations with full capitalism on every aspect isn't working out so well for the quality of life of the average American cittizen. It's not a group thinking. It's selfish thinking of the people in the USA that makes them weak as a whole. As they say: The whole is greater than the sum of its parts. The funny thing is also. You are starting out about debt. But the DEBT to GDP is after 2008 only declining here. And the debt to GDP of the USA is increasing. Trump is doing a terrible job in decreasing American's debt. EVEN WHEN THE ECONOMY IS GOING WELL. What would happen if the economy didn't go well? Damn, the USA is lucky the worldwide economy is going well at the moment.
can you imagine that you are literally most probably seeing current brilliant scientists sitting in their benches and studying just like a normal fellow?
Natural numbers starting from {1,2,3--------------n}
Will I do my own work? No I won’t. Will I watch a MIT lecture of a class I had no idea existed? Yes I will.
I absolutely loved this lecture. I'm currently writing my thesis in political science and I regret putting not enough effort in / having not enough motivation for Maths. I consider doing a bachelor in Computer Science now :D will follow-up on the next lectures.
did you end up taking a bachelors in computer science or going further in the subject other ways?
This is totally facinating
Watching this after the military school during winter vacation , feels good and calm to finally get some stuff in my head xD
where do I can find similar videos like this one but for Algebra and Geometry for computer science D:!!!
I’ve been programming for about two years. Python is my martial art of choice.
I know basic math but seeing normal programming paradigms and statements expressed in plain mathematics is just beautiful. It helps me teach better too.
> _seeing normal programming paradigms and statements expressed in plain mathematics_
umh, what are u referring to?
@@yash1152 for loops, while loops etc.
@@webknowledge9989 aah 'kayh, but those things felt quite normal to me in C too - alteast after looking at the flowchart for those blocks... but anyways.
Excellent instructor. I literally stumbled on this video and was able to follow the whole thing.
I hope all my college math professors are like this...!! He's awesome. :)
Are there people who dislike videos for living?
+Boshen Gao Yep
what dislike definition is for a living while liking okay living is?
😂
Yes , yes there are
Yes , yes there are
Watching a lecture from a university incredibly far away from me to avoid watching my own university's lectures lol
Amazing lecture. Wish I could be there, but happy that I can watch through the screen!
That professor is worth straight up a quarter of a billion dollars. Amazing the people who've come through MIT.
And his salary is 1 dollar LOL
"That other school down the street" is he referring to Harvard?
Vimal Sheoran pretty good sense of humour!
thought the same thing hehe
Liberal Arts School, in Mass Ave.
It's there in ThomasLeighton's book.
@@subhradipsaha9518 Could be, I don't really know I just made a guess I don't live in that area.
I’m a primary school teacher and this gentleman is one of my role models
Wow, I couldn't stop watching it. I now understand why MIT has always been the top university.
Is it just me? -- Prof. Tom Leighton looks like Matthew Mcconaughey
+Apurva Dubey just u and the 8 people that liked this
+GreyFace Yes! The first time I watched the lecture, I was like "what is this guy from True Detective doing here". On a separate note: MIT students are really lucky to be taught by amazing teachers like Prof. Leighton. I have gone through all lectures of this course -- MIT has done a great service to humanity by making this material available.
He looks like him lol
Alright, alright, alright already 😂😂
Apurva Dubey
He sometimes kinda looks like Martin Freeman.
Prof is CEO of Akamai.
H
wow
Thanks so much for the video! Amazed about the Goldbach's conjecture! :-O
Thank you for providing us such a wonderful content.
Great lecture.
5:45 "With Donald Trump as your boss you better agree or your fired." :)
and this video is from 2010
such innocent times back in 2010
O' the days of ignorance, how I miss thee.
everyone knew and they didn't tell us
Trump2020
He is a good teacher. I like the way he reacts to the contributions from the students and guides them into the answer set. I was taught that zero was not a natural number, although it is a whole number.
sometimes 0 is used as a natural number and sometimes it is not. you just have to be aware about how the naturals are first defined in any context. Ive take real analysis twice: one time we included 0 and one time we didnt.
THE JUESITS BLOW THIS GUY AWAY
10:15 I think zero is not a natural no. but fantastic explanation, loved it.
I also think the same
Natural numbers are those numbers which are used for counting
0 is a whole number
"If Donald Trump is your boss, you better agree or you're fired". How true...
So prophetic considering this was in 2010 and we all know how the orange presidency went...
@@SimGunther better than the current one at least
@@danielj5650 I totally agree!!
@@SimGunther thanks for the $60 gas tanks
To all those viewing this video, have a nice day, help others, help yourself, live in the present, and most importantly set a goal to watch the whole course !
Great lecture, like it!
如果猪能站着走路，我可以用脚趾写代码，这个在逻辑真值表里面是真值呢。。
***** hm.
I'm learning and watching this so that I understand MIT6.006 properly.
What an amazing teacher! Seems like a great man :)
math for CS. otherwise known as making sense of shit that goes through the heads of computer scientists (formal language). I like the weave of history into the material. Cheers.
10:12
Wait a minute, they are whole numbers right ?😅
Yeah man
I think much better than 2015 version and Professor Leighton is a very good educator, thanks Internet... This is awesome!
This person is a great teacher let's hope these kind of people are in india also.
At 33:24 I was saying aloud " Sir you made a mistake, its True!" 😅
Is that a stenographer in the front row?!
Natural numbers is the set of {1, 2, …, n}, zero is not included in the set.
if you were intrigued by the first 5-10 mins of this lecture, go look up some videos about epistemology. it's the domain of philosophy that deals with how and why we "know" things to be true or false.
5:46 really aged well
Do I need to know precalculus prior to learning this course or is college algebra good enough ?
Blood1397violet You need to know single variable calculus for this course (also know as course 18.01 on MIT OpenCouseWare ocw.mit.edu/18-01F06). College algebra is not sufficient.
***** Your response is valuable, thanks!
Blood1397violet all you need is algebra 1 to understand the concepts in discrete math tbh. they may use concepts from other branches of math for specific examples, but they have basically nothing to do with discrete math itself. it has very little to do with continuous math.
+Blood1397violet the site has a prereq for a module. this is the link to that module ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/
+SANKET RAI Man, it's an example and introductory class that just requires course 18.01, what did you want? Look at all introductory classs in the first or second year of undergratued and they are very easy, but afterwards get more difficult
Really appreciate for sharing these awesome lectures.
I am from India 🇮🇳 ina poor village I live. I did not get good education here.. But i found these MIT courses for free.. Now there is a hope I will be a good mathmatical physicist... 😊😊so thanks Mit for doing this for free...
5:44 I didn't expect to hear Trump's name in 2010 lol.
I got visual cancer when I saw the 0 is included in the set of natural numbers.
No veo realmente cuál sea el problema.
@@abdulalhazred5924 si estudias álgebra, aprendes que el conjunto de los números naturales son el conjunto intersección de todos los conjuntos inductivos, y un corolario sería que ni n es natural, n>=1, por otra parte, se llaman número natural porque fueron los primeros en ser usados por el hombre y los intuitivos a nuestra comprensión, son los de contar cosas.
@@casidiablo665 supongo que sí, pero son menos que del uno en adelante, pero es mas por una cuestión histórica que creo que los naturales no deben incluir al 0
@@lucasdepetris5896 en la sciencia de computadora. los naturales tienen 0
not sure who this professor is, but i wish there were more like him
He is Tom Leighton, CEO of Akamai Tech. He is worth millions of dollars
I was required to take this kind of course in my first year of University. I actually enjoyed it somehow.
my method of acertaining truth - health, fitness, and nutrion. great teacher :)))
is this same as discrete mathematics ? because when i search for discrete mathematics this video shaws up
+sAMA SAMA This course covers elementary discrete mathematics for computer science and engineering. For more information on this course MIT OpenCourseWare at ocw.mit.edu/6-042JF10.
what amazing way to doe this?