“Here is this homework assignment it should take you about 60 hours. I need it by tomorrow”

Good thing I will never have to worry about this class.

Something I’ve notice is that classes considered “hard” usually don’t tell you the background knowledge you should have before taking the class. I find this really prevalent within chemistry since nobody tells you how much a good grasp of physics concepts underly chemistry

My Asian parents would deadass throw me into this class expecting high grades

This is a whole new level of "Thanks for Learning with Us"

“There’s a class so difficult that 50% of students drop out” Sounds like most college courses

Me who failed pre algebra: yeah i could take that class ez 😎

I wanna sit in this class for a day just to see the faces the students make

wonder how the teachers feel when grading them

*half the students drop out* So... like litterally every stem course lol?

“im sorry..” “dont topologize” - Martin Gardner

I remember my ap math professor walking me through a third of a problem from this in high-school and saying this is what college was all about.

This makes Calculus look like 1st grade math 💀💀💀💀

sometimes class is hard because of awful teachers

No wonder Bill Gates droped out💀

1. To prove that the discrete metric is indeed a metric, we need to show that it satisfies the three properties: non-negativity, identity of indiscernibles, and triangle inequality. a) Non-negativity: For any points p and g in X, d(p, g) is either 0 or 1. Since distances are non-negative, this property is satisfied. b) Identity of indiscernibles: d(p, g) = 0 if and only if p = g. This property holds since the discrete metric assigns a distance of 0 only when two points are equal. c) Triangle inequality: Let p, g, and h be points in X. Since d(p, g) and d(g, h) are either 0 or 1, the triangle inequality holds. With the discrete metric, subsets of X are open if and only if they contain each of their points as isolated points. Every subset of X is open since each point in a subset is isolated. A subset of X is closed if and only if its complement is open. Since every subset is open in X, the only closed subsets of X are the empty set and X itself. Every subset of X is dense since every point in X is isolated, meaning there are no points in X that are not in any subset. 2. To prove that do is also a metric on X, we need to show that it satisfies the three properties: non-negativity, identity of indiscernibles, and triangle inequality. a) Non-negativity: For any points x and y in X, d₀(x, y) is defined as d(x, y) / (1 + d(x, y)). Since d(x, y) is non-negative, and the denominator is positive, d₀(x, y) is also non-negative. b) Identity of indiscernibles: d₀(x, y) = 0 if and only if d(x, y) = 0, which happens if and only if x = y. c) Triangle inequality: Let x, y, and z be points in X. We have: d₀(x, y) = d(x, y) / (1 + d(x, y)) d₀(x, z) = d(x, z) / (1 + d(x, z)) d₀(y, z) = d(y, z) / (1 + d(y, z)) Using the triangle inequality for d, we can show that: d(x, y) ≤ d(x, z) + d(z, y) Dividing both sides by (1 + d(x, y))(1 + d(x, z))(1 + d(z, y)), we get: d₀(x, y) ≤ d₀(x, z) + d₀(z, y) Therefore, the triangle inequality holds for d₀. A subset of X is open under the metric d if and only if it contains an open ball around each of its points. Since the metric d₀ is defined in terms of d, the same subsets that are open under d are also open under d₀. The metric spaces (X, d) and (X, d₀) may not be the same as metric spaces, but they have the same open sets. The metric space (X, d₀) is always bounded since d₀(x, y) is bounded by 1 for any x, y ∈ X, whereas (X, d) may not be bounded. 3. Let's examine the given options for defining a metric on R: i) d₂(x, y) := √(x - y): This defines the Euclidean metric on R, which satisfies all the properties of a metric. ii Just call me the thinker 😗

My freshman roommate took this and was one of the smartest kids in the class as a freshman. Crazy.

Imagine the final question is 1 + 2, It’d probably be something fun to lift off the stress of doing one of the hardest quizzes you’ve ever done.

at this point, they're probably asking you questions that they can't solve LOL

Not me being tempted to try and solve the problems knowing damn well I still count using my fingers

A 50% dropout rate just goes to show how poorly the class is taught.

My toxic trait is thinking I could pass this class with an A

"Im sorry, dont topologise" bro decided to put a pun in an excruciating task

"Im sorry" "Dont apologize..." Bro even the guy making the paper is a statement 😭

This is like calculus and algebra combined with honor. I'm good at math when I use calculator if not, I'm screwed.

"I'm sorry" "Don't topologize" mathematicians need some humor in their work or else they're gonna go crazy

And this is where Photomath comes in😂

This is what’s wrong with professors these days. They try to make it hard and never really focus on actually teaching you anything.

And I was literally out here struggling with grade 8 math💀

The fact that there’s an apology at the start of the assignment

Ooh metric topology was one of my favourites in undergrad! Those first two questions are pretty solid ones too, not too hard but definitely need a good understanding.

Harvard: So what's 2/2 Student (Sweating): Okay so let's start by integrating.....

Saw the word “math” and I’m already dropping out 😂

Luckily for us we only need 1 person that passed to put the answers on the internet

“I sentence you to a full semester in math 55”

Now this really makes me wonder. When would they use that knowledge in the real world

Well, this just gives me flashbacks to today and everyday for the next 2 years... cause a lil brat thought "oh, I like maths, so why don't I pick my nations hardest most intense maths program even though I hate homework"🥰

Dear brocolli, that is no longer math, that is wizardry

You know it’s bad when it has more letters than numbers

"take a look at these questions" _laughs in potato quality_

"Im sorry" "Don't topologize"

im sending this to my math teacher

My brain ain't braining anymore after seeing the questions

Those questions actually aren’t that difficult. I’m an engineer and honestly you learn the fundamental rulings it’s all good. Don’t let this intimidate you lol. You can do anything you put your mind too!

honestly, most math grad can do those questions. The course is challenging because it’s an intro course that compacts ~5 course topics. However, it’s not difficult overall

Having half your students drop sounds like something you shouldn’t be proud of as a teacher 🥶

And here I am suffering in algebra 1

I just showed this to my younger cousin(1st grade) and he said “where’s the math” lmao Edit: Thanks for 1k likes! I’ve never gotten this many :)

This kind of looks like my upper level abstract algebra class with some real analysis thrown in there

I’m having a panic attack just looking at the questions

they call it math 55 because that’s the average grade for people who take the class

I am the type of person who will take course just to see how hard it is and since I hate dropping courses, will stick with it. And well probably fail it since I am an idiot who took it even when others warned me.

As much as I liked my professor, this class was HARD. My university has three courses for Abstract Algebra, but I took AA 1 only. The class was difficult, but it's very interesting how you relearn the reasoning behind a lot of mathematical concepts. For example, one of the easiest problems I had once was to prove why any multiple of 10 is a multiple of 5 (groups and subgroups). Now the difficulty comes from how you do it. In Abstract Algebra, you can't use numbers, you use "elements" of a group with a specific operarion that represent numbers or things and still have a valid outcome when the computations are done. Another example can be the proof of even and odd numbers. This class is great, but it's difficult if the basic concepts of the course don't click for you (that was me for some time and then bum, magic). ❤

I love that there's a pun at the top of the paper at the end. Lmao

To everyone here who says that people drop out because of teaching - please don’t judge a book by its cover. Professor Harris has been a great teacher and mentor to me this term in math 55 - his lectures really help you gain a motivation and insight as to why the ideas he introduces are important in the field and we’ve seen some really cool fundamental results from abstract algebra from his lectures. Main reason people drop out after shopping period is simply they don’t want to spend that much time on maths in their freshman year - which of course is not a problem especially if they are doing other hard classes/ comping for clubs etc

" the class is called MATH 55" *Scrolls*

In my opinion, having a class like this is ridiculous and not a flex. I’m not sure how it is in America, but I’m Australia each unit should expect about 10 hours (including contact hours) of work weekly because 4 units makes a full time study load. That unit better be worth 4 times the credit for it to be worth taking.

I put some of the equations into a math solving ai tool and even the ai couldnt solve it 💀

Me: can't be that hard Guy: the class is called math- Me: damn ok he was serious 👀

And lemme guess, the final is a free for all showdown and whoever wins is declared king of math

When I was a kid I decided to major in math because geometry and computation were fun. Only thing I was good at. By the time I hit Mathematical Analysis in college (a math class where your TYPED homework answers with symbols looks like essays 🙂) it was too late to switch majors. That’s where villains are made, but I still earned my degree all the same~* if you’re a student mathematician at ANY level, keep pushing!!!!! Much like anywhere else in life, only the persistent last.

Rudin is a classic 👌🏻

Elementary me: "I FOUND A LETTER IN A MATH QUESTION!" High school me: "I FOUND A NUMBER IN A MATH QUESTION!"

This is how I felt when my AP Calc teach in highschool handed me Spivak’s first edition of calculus. But it grew me into a wonderful student and love of it. Currently a PhD Candidate!

Tbh Ive done those concepts and I passed each course that taught each topic with a really good grade but I can see how ppl might find it hard, it’s a lot, and also a lot of problems. I’ve had a similar class that the professor gave 1 assignment each week that was 15 double sided pages it was for a discrete math course it was so much work that I ended up dropping another class so I can put more time into that class

You know you’re dead when the homework starts with a quote

You can walk in that class, scream "Yo nerd" and everyone would turn their heads

Teacher: The test isnt that hard. The test: Jimmy has three apples, how many atoms are there in Saturday on Wednesday weekend.

I would 💀 myself when i saw that homework

*laughs in soviet maths curriculum*

"I am sorry" .."don't topolgize' I am dying😭😭

I believe this is an Introduction to Mathematical Analysis for most undergrad courses. It's not only in Harvard that's difficult. The overall subject is very challenging because it teaches you a complete new perspective of thinking in math and logic with strict set of rules crammed into 1 semester. It's insufferable class if you're a math or physics major but the rewards are worth it.

yes, that pun at the top will surely motivate me to do the homework

This short made me break into a sweat, sped up my breathing, and gave me hives.

As a maths student, not disputing that the course is indeed difficult, but the homework you showed is not the hardest shit ever, the terminology might seem odd for most people but once you know what a metric space is, it becomes quite easy. Not trivial but only not the most I would have suffered, my guess is that this homework is at the very beginning of the course since a lot of problems are solved by directly linking the definitions of isometries and metric spaces

Looks like we'll never figure out how many apples Johnny have in his pocket.

Honestly these homeworks look just like every university math homework...

“Half the students drop out” that’s every math class I’ve ever been in lol

okay let’s take a moment to appreciate the fact that atleast half of the students suffer the full semester 😃

Fun fact: Simpsons executive producer Al Jean also took this class.

My ego would force me to stay in the class, whether my downfall occurs or not.

Not only did they introduced the alphabet but they also introduced the whole english subject

My program has an 80% attrition rate, and it's never about the difficulty of the work, just the amount, it's basically a 9-5 except you're using your brain, not your body and homework extends into after class, for sometimes hours. I've made it this far thankfully, and I only have a year left

When you pause the video and finish the problems at the end Just to realise it’s been 7 years

I look at this every time I want to feel humble.

took one glance and said “hell naw”

Bruh, forget the class, I felt like dropping out of consciousness after I saw that sheet.

" U try it." Oh hell nah

I better get paid by doing this job

bro analysis is so fun though

" I'm sorry.." "Don't topologize" - Martin Gardner

When you finish an assignment in this class but then you realize you used a different formula than the teachers.

Me when I finally solved 1+1: 🎉😊🎉🎉😊😊🎉😊🎉😊 Me when I see this question:

take me there finally found my class

* Me having ADHD and taking 3 times as long to complete my homework assignments * *:Yeah I’ll pass…*

It’s doable, some people still get A’s in this course, it’s just that there will be sacrifices

Now chat gpt gonna make that class a cakewalk

That class is lightwork

Okay those homework problems are actually quite trivial for anyone who’s had a real analysis course or a set theory class (the definition of a metric space and it’s corresponding metric can be understood by anyone who’s had algebra 2). But this is homework 1, so I’m sure it gets way way harder

As an engineering school graduate, I feel sorry for anyone having to take that level of calculus and linear. Looked at the problems and noped out. Spending an evening trying to solve one problem of 10 is not very fun, never again.