1. Algorithms and Computation 

Sounds like youre thinking of changing majors 😆

@@randyt700 lol

+1bro , this hits me deep 😂😂

same but with finals week

Are you acquainted with Pasta Sempai?

@@elhermeneutico "But before you leave, do you recognize these things?" Jk, that's a beautiful comment and is amazing that this knowledge can reach the whole world.

THIS!! im from indonesia we dont exactly have the best education in the world so this channel has been a blessing for me

@UCTPCE7ckUioWlMK1nBThsfg lol that joke you're an a hole but funny af.

love to see this

You must be a genius then :-)

I'm not gonna say how lucky you are cuz i can realize how much worked was required to achieve such a thing!

Chop andu

How did you like signal and systems course?

Via Online?

They really are amazing. I always fantasize of how the world would be, if they were the decision makers of our country.

@@inamahdi7959 They teach the decision makers of the country, who go on to use these principles to sell your attention to advertisers.

great

Thanks

Thank u mate

I find this guy hard to follow?

@@gp10020 for me , I think it is because I not familiar with prerequisites of the course

but u of t courses easy to get bored

@@jackmiller9829 See dat dare cumpooter? Sheez go'n to uhlauh uss to proagram. At least that's how my family from down there sounds.

lmao he's so unprepared he couldn't express the concept or answer the questions clearly enough. And what is this 1980 style presentation 1/10 precious time wasted on writing and deleting the blackboard.

@@CP-jk3tc Much more engaging than what Princeton provides for free, which was made by the writers of the Algorithms book, so... MIT is doing it better, IMO.

@@CP-jk3tc Beg to differ mate - a bit of a rant, pardon! This method actually results in better processing and retention of the content being taught, by the human brain. Maybe a waste of 1/10 precious time, but those paying top dollar to actually learn there are getting their time and money's worth! For us online ones - it's actually free! Watch at 1.5 the speed and save all you want! 🙂But do not underestimate the power of 1980 method, and dismiss it in favor of modern, but lesser lasting ones! The prof also drew the learners logically into the inductive reasoning and WORD-RAM model, instead of just throwing it out there. Engaging IMO. Must laud the prof. Am already liking these lectures over the 2011 class. However Erik Demaine remains that one constant that defines passion, and is always a treat to watch. What a humble guy, to have earned PhD at just 20 years old, but being so accessible! MIT FTW!

It is very knowledgeable thanks. I need the way to make a dashboard for a mining activity (trucks, scoop, jumbo, solo, Excavator, Loader....)

Sooo good.

self learning algorism

until you spot that the teacher doesn't know induction xD

Is there anywhere this course completely uploaded somewhere already? Like from past years, but not too old?

@@quasa0 There is both 2011 and 2008, you can find them linked at this courses page (description)

which one do you think is the best, in terms of quality of instruction? 2008, 2011 or 2020?

@@mickeymacke1780 I would say 2020, but if you want to improve on Algorithms, then problem solving is vital, and also don't forget to checkout problem sets

@@ehza Do we get solutions to the problem sets?

thearshblog.blogspot.com/2022/09/beating-youtube-algorithm.html how to beat RU-vid Algorithm 👆

I think I am walking in your footsteps too. My chances are slim but I'd still give it a shot.

@@therealb888 definately try. if you can do some olympiads and win a good medal then you have a good chance of joining MIT.

@@therealb888 unfortunately i know one guy who got rejected by MIT accepted to Harvard so it's not the end of the world

Lies again? Serie A Leader

Bro just grab a book and read why do you think being in a different building will change anything

Me too, I don't want to read code so I am watching the course for relaxation!

Data Structures: - If the CPU fundamentally takes constant time to operate on a constant amount of data, how can we efficiently process inputs of arbitrary size that don't fit in a constant number of words? - Data structures provide efficient ways to store and access large amounts of data to enable certain operations on that data to be performed quickly. - Different data structures optimize different operations. Choosing the right data structure is key to designing an efficient algorithm. - The first part of the course focuses on data structures like arrays, lists, stacks, queues, dictionaries, sets, and various tree structures. Overview of Topics in Rest of Course: - The first part of the course focuses on data structures and sorting algorithms - The second part covers graph algorithms and shortest path problems - The last part delves into dynamic programming, a powerful general design technique for optimization problems - Most computational problems are solved by either: 1) Reducing them to a problem with a known solution (often involving sorting or searching data structures) 2) Designing a custom recursive divide-and-conquer algorithm - The course teaches different algorithm design paradigms to attack different classes of problems Diving Deeper Into Key Topics Covered: Asymptotic Notation: - Used to classify algorithms based on how their running time or space requirements grow as the input size n grows - Big-O notation gives an upper bound, big-Omega a lower bound, and big-Theta a tight bound on the growth rate - Exponential growth O(2^n) quickly becomes intractable while polynomial growth O(n^c) for constant c is generally considered "efficient" - Logarithmic growth O(log n) is even better than polynomial - nearly as good as constant time for large n - Big-O ignores constant factors and lower order terms, only focusing on the growth rate of the dominant term as n gets large - Allows comparing algorithms in a implementation and machine independent way to see how they scale Induction and Recursion: - Induction is used to prove propositions that assert something is true for all natural numbers n - Proves a base case, then the inductive step which shows if the proposition holds for some number k, it must also hold for k+1 - This allows conclusions to be made about arbitrary sized sets, key for analyzing general purpose algorithms - Recursion solves a problem by solving smaller subproblems of the same type and combining their results - Recursive algorithms are often simple and elegant, leveraging induction to prove their correctness - However, naive recursive solutions can often be inefficient, requiring optimization techniques like dynamic programming Word RAM model: - Assumes modern random access memory (RAM) hardware where any memory word can be accessed in constant time - Memory is byte-addressable, with 64-bit words being the atomic unit the CPU can operate on - Abstracts away low-level details of a specific computer architecture while still being realistic - Allows analysing algorithms in a implementation independent way by counting fundamental word operations - Enables use of data structures beyond just arrays by assuming any word can be efficiently retrieved - However, still requires accessing n words to fully process an input of size n Arrays: - Contiguous area of memory storing a fixed number of equal-sized data elements indexed by contiguous integers - Constant time access to any element by index using simple address arithmetic - Constant time to add/remove elements from the end, but linear time to insert/delete from middle as shifting is required - Inflexible since size cannot change, but space efficient with minimal overhead Linked Lists: - Stores elements non-contiguously in nodes containing the element and a reference to the next node - Access to an element requires traversing the references, taking linear time - But constant time insert/delete just by updating references, and flexible since grows/shrinks easily - Tradeoff of greater overhead and poor locality compared to arrays, but gains flexibility Stacks and Queues: - Restrict access to elements for certain patterns. - A stack is LIFO - last-in-first-out. Can only add/remove from one end called the top. - A queue is FIFO - first-in-first-out. Add to the back and remove from the front. - Both support operations in constant time using either an array or linked list as underlying structure. Dictionaries and Sets: - A dictionary stores a collection of key-value pairs and provides fast operations to insert, delete, modify, or lookup a value by key - A set is a collection of distinct elements that provides fast operations to insert, delete, and test membership of an element - Arrays provide O(n) implementation, but searching takes linear time. Sorted arrays enable binary search for O(log n) lookups. - Hash tables use a hash function to map keys to array buckets, providing amortized constant time average case for all operations. - Balanced binary search trees like AVL trees also support all dictionary/set operations in O(log n) time worst case. Priority Queue: - Stores a set of elements, each with an associated priority value - Core operations: Insert an element, and delete and return the element with the highest priority - Can be used for task scheduling, event simulation, graph algorithms like Prim's and Dijkstra's - Often implemented as a heap - a complete binary tree structure providing O(log n) insert and delete-max Graphs: - Graph G=(V,E) consists of a set of vertices V and set of edges E connecting pairs of vertices - Edges can be undirected or directed, unweighted or weighted with a cost to traverse - Can represent many real-world problems like maps, networks, dependencies, transition systems - Key representations are adjacency matrix and adjacency list, allowing tradeoff between simplicity and scalability - Two core graph search algorithms are Breadth-First Search and Depth-First Search, used as building blocks for many graph problems Shortest Path Algorithms: - Given a weighted graph and a starting vertex s, find shortest paths from s to all vertices - Key algorithms are Dijkstra's for graphs with non-negative edge weights, and Bellman-Ford for graphs that may have negative weights - Dijkstra's iteratively grows a set of vertices for which it has found the shortest path, using a priority queue to select the next closest vertex to add - Bellman-Ford iteratively relaxes all edges, propagating shortest path estimates until they converge - Both have many applications like navigation systems, network routing, AI pathfinding Dynamic Programming: - A powerful algorithmic technique for optimization problems, especially where naive solutions have exponential runtime due to repeatedly solving the same subproblems - Works by building up solutions to larger problems from solutions to smaller subproblems, filling in a table to efficiently look up and reuse common subproblem solutions - Makes problems tractable by turning exponential brute-force searches into efficient polynomial time solutions - Can solve a broad range of problems like combinatorial optimization, graph algorithms, string algorithms, and resource allocation Algorithm Design Techniques: - Brute Force: Try all possibilities (e.g. combinatorial search). Simple but inefficient, usually takes exponential time. - Divide and Conquer: Recursively break down problem into smaller subproblems of the same type, solve them, then combine results to solve overall problem. - Greedy: Make a locally optimal choice at each stage, hoping this leads to a globally optimal solution. Often efficient but doesn't always produce the optimal result. - Dynamic Programming: Fill in a table of solutions to subproblems and use them to build up an optimal solution to the overall problem bottom-up. Efficient for optimization problems with optimal substructure and overlapping subproblems. Computational Complexity: - P is the class of problems that can be solved in polynomial time O(n^c) for some constant c. Most "easy" problems are in P. - NP is the class of problems whose solutions can be verified in polynomial time. All P problems are NP but some NP problems are likely harder than P. - NP-Complete problems are a set of "hardest" problems in NP. If any of them can be solved in polynomial time, they all can, and P=NP. - Many important real-world optimization problems are NP-Complete, so study of approximation algorithms that efficiently compute near-optimal solutions is a major research area. Conclusion: This introductory algorithms course focuses on teaching how to solve computational problems and rigorously argue the correctness and efficiency of the solutions. It starts with fundamental data structures and builds up to powerful techniques like dynamic programming that can tackle seemingly intractable problems. Along the way it dives into key areas like sorting, graphs, and shortest paths that have many practical applications. It provides the conceptual tools and analytical frameworks to approach the design and analysis of algorithms for a wide range of computational problems. Mastering these techniques opens up a powerful toolkit for developing efficient, elegant, and provably correct solutions to real-world computational challenges.

Thank you!

The quality of the instruction decreased with time, unlike the video quality.

We need 4k

thearshblog.blogspot.com/2022/09/beating-youtube-algorithm.html how to beat RU-vid Algorithm 👆

It’s a good definition if the algorithm is deterministic.

@@andrewzhang5345 who cares about the defination

@@JUST_C0DE In practice you wont find that many deterministic algorithms.

@Barry Allen lol

People don't use blackboards anymore and thus the students knowledge doesn't last forever, the tike of writing taken by teacher and given time to take down the content make student grasp things better rather than using PowerPoint presentation with endless slides and meaningless content🤣

@@aishwaryadharmadhikari7165 Can't tell if you're being sarcastic 😂. Anyway there are probably more objective points that support a white board & power point presentation with an e pen. Blackboards do have their own charm and feeling in addition to giving more time to the student to digest the information. Not to mention the classic classroom environment. The best parallel for this is EVs vs ICE vehicles. Gas does have some advantages like range & refill time but they can be achieved in the future by EVs with advancements. Similarly, we should be able to transfer the black board advantages to newer learning technologies through advancements. I know I over analyse stuff, I'm self aware 😂.

@@therealb888 I totally agree with you, but, I won't change my opinion though 🤣 . It's been 2 years since the online education program has started in India where students are learning on mobiles and I dont think this has been any benefitable to anyone. Not students nor teachers not the institutions! Show me results😆😂

@@aishwaryadharmadhikari7165 I totally agree with you as well 😂. Where has been the results right?!. But the answer lies in your comment!. Watching on mobiles with distraction on the same device not to mention the small screen & eye strain. I think the results lack because of improper usage. If you look at IITs/MIT/ any top university, there are slides & these videos in addition to problem sets & notes/study materials that are available online. These online resources are absent in most small colleges in India. Online education is also the preferred way for all working professionals. The nice thing about this is that you get a backup of the resources & can pace yourself. Online resources like this should be a supplement to classroom learning in more Indian colleges. Out of curiosity what are you studying? It's cool to see more Indians here. Do you have plans for any form of higher education in USA?

Do you mean MIT is doing this primarily for Harvard students to catch up with them?! LOL

@@enisten No brother, but I think so sometimes.

The Harvard CS courses seem more concerned with the grandeur of their lecture halls than the depth of the content it self

You can do that with algorithms. :)

​@@AlpGuneysel Oh, I forgot, this is MIT

Absolutely, people today are so lucky.

There's a 50% chance your not.