Who came here from the short😂👇👇💯

I appreciate how much you point out how human advanced courses like these are. Hollywood likes to portray upper math courses like these as extremely cutthroat, sink-or-swim. But in reality these classes often involve a lot of collaboration, talking with professors openly and honestly, mutual curiosity in the subject, and lax grading. When I took quantum mechanics in my undergrad, everybody in my class ‘cheated’ by working together on our tests and quizzes. We did that because we all agreed that quantum mechanics isn’t something to be learned alone. We were just trying to understand the material the best we could. My second semester understood that very well, so he encouraged us to turn in assignments as a group, re-explain concepts on the whiteboard, take a stab at explaining things differently, etc.

The kinda sad thing is that lots of people never liked math or like math because of a bad teacher which can make everything seem like it’s much harder than it really is Edit: Dang I didn’t know this was that relatable

" as the letters turned into Hieroglyphics" got me rolling so bad 😂

Mid-way through the video, coming from someone that's learning college math right now, the lessons in Math55A are topics you would learn in year 1, 2 (Linear and Abstract Algebra respectively) and Representation Theory is something you're more likely to learn as a grad student. 55b's Real and Complex Analyses parts are something you'd learn in year 2-3, while Algebraic Topology is either 4th or in grad level

everyone: this is the hardest math class in the world me: I bet the professor is using hagoromo chalk

I’m a second year CS student in University, saying I love maths and physics is an understatement. Throughout my self study journey I taught myself Linear Algebra, Calc I-III, Differential Equations, working on Differential Geometry and Topology atm. Math 55 had always been somewhat of a dream of mine but unfortunately I’m not from the U.S nor have the budget for Harvard lol. Thanks allowing me to see for myself a glimpse of what I’ve always dreamed of 🙏🏻

Gohar you've transformed my high school experience, keep up the grind 🔥🔥🔥🔥🔥🔥🔥🔥

Math, especially higher level math, has this beauty that occurs when you're working proofs, like a giant jigsaw puzzle that comes together in the most wonderful way and almost always interlocks with other bigger puzzles. This class seems exactly like that. I was passionate about math in college, but also long past my time to go to college again thanks to how expensive it is, and sadly it's not that useful when building a career. I'll remember my time with math fondly.

All of Gohar’s videos are bangers

Gohar is such a great listener, pls consider making a video about something related, it'll wait help alot

Gohar thank you so much for your content. You have been absolutely lifesaving this year. I look forward to starting high school next year with a prepared study schedule.

Seifert-Van Kampert Theorem; Additional 5:00 Shown in an isomorphic (the part of the whole process of movement like a map) sense, though way clearer if simulated like a video/homotopy that's shown here. Isomorphic visualization: (you can draw it on paper to help visualize) [ Level 1: Imagine a point in a line Extend it until it reaches the goal Level 2: Now divide that line into 2 Extend those lines Level 3: Create 2 other points in those lines Imagine those points as A and B Duplicate Line A Draw the line from A to B (assuming its a perfect drag) And then multiple of those somewhere that can be any line (Also this man got this theory right) ] The algebraic expressions may seem like extremely hard unless you understand the language, you're all good. Overall, basic maths with funny languages, "we're still lacking tbh"

One of my longtime friends got into harvard this spring, and is planning to take this course. He has no math olympiad background and took calc bc in senior year, which is wayyy behind the other kids in this course, but I know he is going to do well. To do this course, it doesnt require really strong math skills, but hard work, determination, and passion for math Also after reading a lot of the comments, yall should understand that he is grinding over the summer. He is watching videos on all the concepts of multivariable calculus, linear algebra, and differential equations. Secondly, he is going over basic proof concepts to get a feel for the class. So he is not going into the class blind lol.

10:46 his voice is so calming.

Really enjoying this type of content…Keep it up!

Math is a language that some of us aren't taught correctly.

Love the hard work this guys dose and he helps get better at studying thanks Gohar❤

Hoping to take this course in September, this has made me feel like maybe it’s possible? Might eat my words though. Thanks for the great video!

Thanks a lot for your study tips in all your videos ❤❤

Thank you so much for such an insightful video ✨✨

It seems like this course is just a mix of algebra, topology, real and complex analysis using the language of categories. Some topics must be cut out to make it all fit into 2 semesters. Seems like a lot of fun for math majors

This was fascinating. Great job, thanks.

Huge respect to anyone taking this course😅. Quite intimidating tbh especially at an Undergrad level.

I cant lie bro, your really helping and doing amazing keep on going!!

best videos bro, not even Study Gpt understands it

Love the video and the content you got. Its so interesting to see what these people who love math so much have to share. The editing is great but I felt the excess jumpcuts were kind of messing up the flow at times

There is a very similar thing in Poland called MATEX, which is an experimental math program in the XIV Staszic highschool. Freshmen of that profile are often already finalists of math olympiads

발음이 너무 좋으시다!! 딕션이 귓속에 똭똭 박히게.

I’m a math major. I’ve taken abstract algebra, linear algebra, and real analysis separately in a span of three semesters. I can’t imagine doing all of these in 16 weeks.

Love this math video

This video has convinced me to try taking math 55 next year

My hot take is other universities have classes like this too, they just don't market the class the same way. I think UChicago has something like this. I'm an undergraduate student at Duke and took math 403 "advanced linear algebra" my freshman year, which is abstract linear algebra, point set topology, a bit of analysis and group theory, smooth manifolds, algebraic geometry, matrix perturbation theory, convexity, and a few more things I don't remember at the moment. The class was more so a tour of grad level math through the lense of linear algebra... and I took it as a freshman. Homework took around 35 hours to do for me per set, and I stressed a lot, but I made it. It was a highly collaborative and leniently graded class as well. It was a 1 semester course. So, it seems to me maybe other top unis just don't market their classes this way, even though they do offer them.

Gohar your amazing thnx for the amazing content

That looks really fun.

Great topic and nice editing.

I was thinking this was gonna be some otherworldy course, but then in 3:08 when the actual content was shown, it hit me. This is literally just a combination of all the courses I took in the span of 2 semesters back in 2022 as a physics undergrad.

This class is like a do or do not life scenario

7:32 this one gave me some real goosebumps like 5 times in a row. That's how i realize how fascinatingly big of a deal math is.

Great video. Thanks. Those hieroglyphics are why I preferred applied math. 🙂

What I hate is that it took the people who invented these proofs years to make them. yet we are expected to come up with the correct proof in a 2 hour long test to like 7 questions.

great and informative video

Those are literally my favorite concepts in math bc they are so foundational to higher level maths. Its awesome.

I recommend you look into the French system of the "classes préparatoires" (prep school), which condenses 4 years of undergrad math and physics into 2 years. Similarly to Math 55, all the problems we tackled were of insane difficulty, there was a strong sense of collaboration within the class, as well as competition versus other schools / classes préparatoires. These classes préparatoires prep you to apply to the "Grandes Ecoles" (the Great Schools), which are highly valued engineering schools and hard science schools (best among which the Ecole Normale Supérieure and the Ecole Polytechnique de Paris). In any case, I'm sure there's a good video or two to make about them! ;)

If this comment gets 200 likes I will attend math 55 Thanks for the 200, at the start it was kind of a joke not now I want to reach this goal. I will upload a short every day(starting tomorrow) until I get in to Harvard and pass math 55a.

Listening to this already hurts my head 😭😭😭

I love math & even decided to master it in my adult life to be fluent without needing a calculator. Particularly basic arithmetic operations; as they seemed to be the most practical to actually go through with learning for real world scenarios. For me to have knowledge stay in my head. It needs to have a relevance to my life, idk how the hell they can do these advanced mathmatics for fun.

8:15 my textbook at university proved something similar to problem 1, so here is a sketch of a possible solution: By definition, f is lipschitz continuous with lipschitz constant c, so it is also continuous. (Alternatively you can use epsilon-delta, just set delta=epsilon/c and continuity will follow immediately) Assume that there are distinct fixed points x,y. Then d(x,y)=d(f(x),f(y))≤cd(x,y) with c0 we can chose n such that c^n/(1-c) d(x_1,x_0)

I went to Harvard for undergrad and studied physics, so naturally I knew a lot of kids who took 55. I myself took the intro math class just one level below it in difficulty (Math 25). This video did a better job than I expected at depicting the nature of this class and separating fact from fiction. But some of the details could use better clarification or context. For one, Math 55 is solely for freshmen. Harvard has a large set of introductory Math courses for incoming freshmen who intend to study some STEM field and have already taken calculus in high school. At my time, I think there were around 6 such classes (19, 21, 22, 23, 25, 55). All of them more or less cover linear algebra and multivariable calculus. At the start of your freshman year, you're very much encouraged to "shop" these classes for the first few weeks to find the best fit for yourself in like an open enrollment period. Most students end up enrolling in 21, which is a very standard, non-proof based linear algebra and multivariable calculus series very similar to what you'd find at other schools (though still difficult because... well it's Harvard lol). The part Gohar gets wrong is that the mythical drop-out rate is mostly referring to the number of people who initially enroll in Math 55 first year during this open "shopping" period, then drop a level or two after a few weeks down to Math 25 or 23 once they determine they can't handle it. But of those who stay enrolled in 55a, of course they nearly all continue on to 55b. In my freshman year, I remember day 1 of 55a, there were upwards of maybe 80 people in the classroom. I went just for fun but wasn't serious about it. I think maybe around half so ~40 enrolled, and then at the end of the shopping period, ~20ish people remained in the class. They all took 55b the next semester, as far as I'm aware. Moreover, to add some detail, people who are more serious about math (math, physics, and computer science students, mainly) are encouraged to take 22 at the minimum. 25 is where things start to get *very* difficult, and the majority of Math majors at Harvard took it. Those assignments alone usually took me 20 hours. But 55 is special in that it far surpasses the material contained in the other courses; in fact, most of the students who take it probably learned linear algebra and multi on their own in high school. I appreciate Gohar's attempt to make the class seem more inviting and less exclusive, but it truly does deserve its reputation. The student interviewed in the video who had no prior competitive math experience is very rare, and he likely has other significant technical experience, probably in physics or computer science, that has given him the technical maturity to be able to tackle 55, as well as a great level of natural talent. Otherwise, there is no level of collaboration and wishful thinking that can get one through this course unless you are very very advanced and mature in math.

I'm new on your channel, but man i must say, your editing is nothing shortof impressive

Awesome video man

Hey gohar, I found your channel 2 years ago. I was a sophomore who had the worst study habits, now I’m a graduating student with far better grades, thank you man

Pretty neat.

The only major thing is changed that number of international students increased so that is why the class became smarter than in the past.

55b actually sounds like a blast

Great video to have a snowball effect with students & professors ❤

As an electrical engineering student at ETH, i could never create a deep and rigorous indirect proof of a "more complex" theorem, although i find the art and abstraction, but precision of proof based mathematics truly facinating. thank god engineering math doesnt depend on proof. we shall leave that to the mathematicians.

I forced myself not towards the long form video but you are short got me the other half❤😂

its best content please make this kind of videos

8:15 I wouldn't wish this on my worst enemy

first and I have a question, why didn't u do ur last live on Gohars lives?

w video. love your style

Pls make a guide on choosing a level subjects

This is a very fun video, I would love to see more videos like this

interesting video

Take a look in "classes préparatoires des grandes écoles" in France or Morocco and see how is the programme

Yo Gohar, can you make us a guide on how to study better and more efficiently?

I love this channel

cool video.

Great video

lmao gohar nodding his head during the interviews 😄

Who came here from the long😂👇👇💯

I don't even think this is Maths 💀

Do hardest english class next ik for a fact ill never find myself on this path but i like english

What I would say is that Math is my favorite subject even though its hard. I love math. The things you hate you are going to love those things. I never liked math But when I got to 8th Grade- 11th grade now I love math.

Talking of difficult math courses. I remember one graduate course in differential geometry and Lie groups I took at uni. The professor was a pole (in Denmark), who could hardly speak the language. He entered class and just began writing on the chalkboard without introduction. He made no references to the course book whatsoever. Nobody knew what the man was talking about at all. You had to complete assignments to pass, and they were difficult. You had to figure out yourself what part's of the book, that contained the tools needed. Most people had to team up to figure them out. I spend 2 days on a 4-page proof of a two line exercise, that I was the only one to do. It was a great course, where I did some great proofs!

4:38 I’m not too familiar with topology but is there a clear distinction between torus-es and filled in torus-es (donuts)? I know toruses have 2 holes, the obvious visible one and the one inside the torus. Since donuts are filled in, is the hole on the inside just nullified?

When I took this class I didn't know what a group or a set even was before joining the class. which made it even more difficult because I had to learn all the math notation on the fly.

Nice Vid!

Yeah idk, Im heading into high school next year and have already taken Algebra 2 and am hoping to take Pre-Calc as a freshman. I cant ever imagine myself being able to understand 10% of what theyre saying @8:15 lol, absolutely ridiculous

I am a grade 8 student in Canada , and I will soon be transitioning to high school. I am capable of studying and focusing diligently, no matter the circumstances. However, I am unsure about the direction I should take to be accepted into Harvard's MD program. Could you please advise me on the steps I should follow? Specifically, I would like to know which clubs I should join, what courses I should focus on, and any other activities or preparations and research projects I should undertake to enhance my chances of acceptance.

It’s amazing to have such an opportunity to learn math could a normal person have such opportunity

It’s about reasoning and logical explanation mostly for this kind of course. I took several higher division math classes back in grad school. It’s actually fun.

Me: Who can handle this class? 😰

10:46 That voice tho💀

UBC has math 257, partial differential equations, in the undergrad engineering program, and its pretty brutal.

If someone knows it so well they can teach it... Then if you feel up to the challenge, don't be too nervous to take it.

Why's it called Math 55?

Wonjae is one cutie pie

This course sounds super fun and interesting.

Hell no you will never see me taking a class like this lol. Math gives me so much anxiety , I barely survived college algebra ! But I commend those who do take it!!!

I'm taking it actually.

Bro is literally damaging his brain

Damn I learned some of this this semester that is crazy

Kinda cool, I didn’t even know they made crunch courses like this with legitimacy in college curriculum

Stopping children from saying first 👇

Here we go again….

I have insomnia, I hope they have that course at night so I could join.

3:58 slice/coslice, universal property of fibered product 4:15 oh yeah then the board makes sense but not a fibered product but its dual the "pushout" 5:23 no not at all, it says \pi_0 preserves aforesaid pushouts; it's beautiful 11:34 i love its idea, but you can keep going and build IUM/HSE in Massachusetts!

I know 99% of you won’t read it, but the 1% of people who are reading this... I strongly hope your parents and you live longer than 100 years with awesome health 🙏