My semester on university: *Starts. Me: *Watches completely unrelated lectures from MIT.

Thanks to Technology. Im in Africa Uganda but I feel like as if Im at MIT. Thank you very much for the lecture.

I took Linear algebra, Algorithms, probability, and signal and systems at MIT. Thanks.

There is a big difference between learning what's going on under the hoods of algorithms, instead of just jumping directly to learn a programming language, it's a really explained architecture course, thanks MIT

I highly admire American intellectuals. Putting out free high quality contents for the rest of the world to learn. Thank you!

There is no way anyone can get bored in lectures like these, such a great professor

Always wanted to go to MIT, unfortunately I couldn't. Thank you so much MIT for giving us the opportunity to learn from the best from these videos.

Thanks a lot MIT. What you have done by sharing these resources for free to the whole world is beyond my skill of appreciation. May your institute and its glory grow and prosper!

The professor simplifies everything, Thank you so much for sharing this informative content

The professor is full of passion! Very clear structure, thank you!

0:00 intro, goals of the course 2:59 what is an algorithm 11:10 birthday problem 15:15 correctness of an algorithm 25:35 efficiency of an algorithm 36:50 model of computation 42:35 why use data-structures

Thank you MIT for these uploads. Love the way Ku teaches

This is fantastic I love their energy and enthusiasm which make the lecture fun and interesting

I can't believe I'm watching these type of videos for entertainment.

This prof.'s energy when he teaches is on another level.

Thank you MIT for these fabulous lectures!

After 10 years of open course finally video quality went from 360p to super high res in 1080p

Finally a refresher to a legendary course God bless

I think the teacher has set a goal on daily steps and tries to accomplish it while teaching. Which is a nice life hack.

This only video has much more valuable content than any entire Colombian computer science program. Thanks, MIT.

Thanks for bringing an updated version of this class back.

Finally!! I've been asking for this ever since I took course 6. Thank you.

This is an amazing lecture! Thanks for let me revise my algorithm and data structure knowledge after I become an engineer.

I love the sound those massive chalks make on those blackboards. Very pleasant.

MIT is sick. Its way better then my university course and I m not even a native speaker. Kudos to Jason Ku

The explanation on words (in the models of computation section, towards the end of the lecture) was excellent and has enabled me to understand the concept better than any previous explanations I've encountered - thanks! Jason did admit he couldn't spell; I'd suggest it's "arbitrarily-sized" (inputs), not what he wrote on the board 😉

Thank you MIT for these amazing lectures.

thank you for these videos, ilook forward to the rest of the videos in this course

I found happiness cause you see people like you who code and the talk about ideas.

this's an amazing lecture. love it professor.

these lecture series are so amazing! I am so thankful they're available to the public

high quality knowledge at the palm of our hands , what a time to be alive. thank you MIT.

Thank you MIT! Here we go let's learn! I'm a self-taught Developer hoping to improve my algorithm skills.

Introduction and Goals of the Course: - The goal of this Introduction to Algorithms course is to teach students how to solve computational problems and communicate that their solutions are correct and efficient. - Beyond just solving problems, the course emphasizes proving correctness, arguing efficiency, and communicating these ideas clearly. Students will do more writing than coding. - An algorithm is a fixed-size procedure that takes an arbitrary-sized input and produces a correct output. What is a Problem?: - A computational problem consists of a set of possible inputs and outputs. The problem specifies a binary relation mapping each input to a set of correct outputs. - Problems are usually defined using a predicate to check if an output is correct for a given input, not by explicitly listing all input-output pairs. - The course focuses on general problems that can take arbitrarily large inputs, requiring the algorithm to loop or recurse to process the entire input. What is an Algorithm?: - An algorithm is a fixed-size procedure that takes an input of arbitrary size and generates one of the correct outputs specified by the problem. - If the algorithm generates an output for an input, it must be a correct output according to the problem specification. - Algorithms are like recipes - a sequence of steps that will return an output for any valid input. Birthday Problem Algorithm: - As an example, consider the problem of determining if any pair in a group of people share the same birthday, generalizing to any "birth time" to make matches less likely. - A proposed algorithm is: Maintain a record of birth times. Interview each person in order. Check if their birth time is already in the record. If so, return the match. If not, add it to the record and continue. If no matches after checking everyone, return no match. Proving Algorithm Correctness: - With large inputs, we can't just test an algorithm on all possibilities to argue its correctness. Instead, we use induction. - The key is finding an inductive hypothesis that can be proven true for a base case and all larger instances. - For the birthday problem, the inductive hypothesis is: If the first K people contained a match, the algorithm would return a match before interviewing person K+1. - Base case: Trivially true for K=0. - Inductive step: Assume true for K. If first K+1 contain a match, either: 1) the match was in the first K and algorithm already returned it, or 2) the match includes person K+1, which the algorithm will find and return when checking against the first K people's records. - By induction, if a match exists, the algorithm returns it before running out of people to interview. If it interviews everyone without returning a match, then no match exists. Arguing Algorithm Efficiency: - An important aspect of an algorithm beyond correctness is its efficiency - how fast does it run and how does that compare to other possible algorithms? - Measuring actual running time is problematic as it depends on the particular input, the speed of the machine, and other implementation details. - Instead, we count the number of fundamental operations executed by the algorithm to get an input-size-dependent measure irrespective of machine or implementation. - The number of operations an algorithm requires as a function of input size n is used to classify it using asymptotic notation: - Constant time: O(1), runs in bounded time irrespective of n - Logarithmic time: O(log n) - Linear: O(n) - Log-linear: O(n log n) - Polynomial: O(n^c) for constant c > 1 (e.g. quadratic is c=2) - Exponential Time: O(2^n), considered "intractable" - In this class, "efficient" generally means polynomial time, with linear or near-linear time being even better. Exponential is considered inefficient. Models of Computation: - To measure efficiency abstractly in terms of fundamental operation counts, we need a model specifying what operations a computer can do in constant time. - The model used in this class is the Word RAM: - Assumes a CPU connected to a large random access memory (RAM) consisting of a sequence of bits - The CPU can read/write a word-sized block of memory in constant time (modern word size is 64 bits) - The CPU can do integer arithmetic, comparisons, and logical bit operations on a constant number of words in constant time - The word RAM allows any individual word in memory to be accessed in constant time. However, accessing all n words of an arbitrary-size input requires O(n) operations.

I define a problem as a question pertaining to an unknown variable or function, in the programing sense, but more abstract. I define a computation as a calculation. Therefore, I define a computational problem as a question pertaining to a calculation, or, in other words, a question about what algorithm is necessary to find a desired output.

2 years back I had the privilege to do an interview with Dr Ku for a high school project. He was wonderful, very warm and down-to-earth. I was honestly shitting bricks cos I was so nervous but his friendliness helped me ease into the whole thing. All around great guy.

Literally best instructor ever!!

I like to say that an algorithm is a set of instructions that will take you from the beginning to the end in a particular order so long as there are no errors.

Thank you MIT for sharing this to the public

Thank you MIT for publishing such video lectures

I am Form Bangladesh I liked the lecture very much, Especially Sir's Explanation was very nice

Timely upload, thank you, MIT

Thank you MIT!

I look forward to hearing more

Love the enthusiasm, thanks mit

thankyou MIT OCW, for these lectures.

Thank you very much for making this fabulous course not only for Harvard students but also for other students.

The teacher is the reason we love the subject. As a teacher I ve learned to be energetic

Thanks MIT, watching from Sri Lanka.

Nice to see that Michael Reeves is uploading again. Also I knew he was gonna go some places, but MIT... Congrats

Awesome, we have been waiting for this, thank you. Nairobi Kenya.

I always wanted to study in mit but i don't have money Now mit is uploading classes that's awesome

I am fortunate enough to live in an era which I can live in Sri Lanka 🇱🇰 and watch these valuable lessons from MIT

What a time to be alive thanks MIT 🎉

Absolutely spot on.

thanks to the mit for giving us oppurnity to learn interesting topics thank you

I believe an algorithm is not a function as functions have predefined output based on a set of sequential operations. It may be made up of multiple functions but Algorithm is more closely related to the technique to derive a function or procedure to find a solution to the problem.

Thanks for MIT, I am Iran and it is tough to come there for studying .it is pleasure to be able to learn via internet.

these teachers are amazing ..

What a blackboard. I love it.

Perfect start!!!

Because the speaker is always walking around, I think we have to thanks the cameraman, he's really doing well.

If MIT uploads all the lectures on youtube nobody will be deprived of eduction in this world.

Very good teacher, thank you Jason.

MIT, the one school where I can somewhat understand the expensive tuition of private universities. You get the professor like these to teach the students. Luckily for a broke student like me, I can partake in these amazing lectures.

Bring Video lectures of 6.045 Automata and Computation course to OCW pls.

Thank you very much for the lecture.

Thanks for the explicit explanation. From Nigeria.

Thanks to these lectures uploaded from 2020 I can watch these from 1994. Thank you so much.

The definition of the problem is also the definition for a mathematical function. Highly recommend taking a course of sets, relations and functions, proofs n induction in maths, along with an introductory programming course in C/ C++/Python to learn about arrays, strings, etc

thank you for this lecture!

Beautiful lecture

the fact that we are able to attend lectures online at one of the most prestigious schools in the country is amazing!

The materials on the website makes me feel like I am actually taking this class.

⏱Timestamps for this video! 0:00 - Introduction to the Algorithms Course 1:00 - Goals of the Course 3:24 - Understanding Computational Problems 9:38 - Definition of Algorithms 15:41 - Understanding algorithm correctness 26:18 - Measuring algorithm efficiency 33:00 - Understanding Running Time 36:31 - Model of Computation 43:18 - Data Structures 🧙‍♂✨ Generated with Houdini Chrome extension.

You guys have helped me so much ! I can’t believe this is free! God bless😊 subscribed

It's 1 am and I just clicked and now I m Loving it 🤣🤣

Thank u MIT ❣️

Ily Jason Ku and MIT

Thanks Sir And MIT Watching From Varanasi INDIA 🇮🇳🇮🇳🙏🙏🙏

Clear and informative. Just one small thing: it seems misleading to link 32 bit addressing with disk space limits, because disk space is addressable in sectors (generally of size 512 bytes), not in bytes as with RAM. HDD limits of 8GB, 128GB, 2TB etc. are due to limitations of CHS or LBA addressing modes for disks, and not word size (16, 32 or 64) used by the CPU. Keep up the good work! Many people are benefitting :-)

Information for free! Brilliant:) god bless you educators for such amazing knowledge you’re will to hand out to the world 😊 subscribed

Thank you so much MIT

I love this lecture. The teacher is excellent. Claps

Thank you so much for sharing

Thanks to MIT for rolling out this course. I feel like I study at MIT and I sit at his class:D

Wating for the next video.. tq MIT

ooo! yes my dream is to meet the mit chancellor some day really radical revolutionary institution. i love MIT

Really very fruitfull tutorials on DSA.

MIT...Pls provide course videos of Principles of Macroeconomics.

Im balls deep into these Open Lectures. Thank youz

I always wanna go to MIT. thank you

Great lecture sir, but it was hard to keep track sometimes because of the movement, maybe because I'm not accustomed to it :)

Thanks to technology, i can attand mit class from another side of the world😊❤

I'm a Japanese bachelor. Thanks to MIT ,and thanks to Technology. I will listen this lecture again and again. (Sorry, I'm not very good at English.)

nice course, helped me lot. thanks

Thank you!

nice work im happy to see it

Respect to mit thanks 👍🔥🙏

Thank you MIT