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i like how your first example the proof is trivial straight from the definition of ideals and rings. And it's taken from a graduate math textbook where the people read are surprise surprise graduate students. Sure you can make this criticism of lang and bourbaki in general, but they don't claim to write "very easy" or well motivated books.

Same with info sources online like wikipedia, applies to tech and most science stuff as well.

and dude if you have a problem with mit ocw, I am sorry, math isn't for chimps

if only you had a pen and paper to work, sadly we don't have pen and papers anymore

And this, ladies and gentlemen, is the result of an entire generation being educated with CZcams tutorials. It used to be like "Here's your paper, pencil and sliderule, go invent the radar because the Nazis are bombing the crap out of us" but now they want someone besides them to grab them by the hand and lead them through life while they complain that free resources from MIT like Open Courseware are broken and that reading is hard. Can't wait to see what the new ChatGPT generation has in store for us.

during lecture: "the proof of this is really important so make sure you know it, but i won't be going over it since it's detailed in the course book (that i wrote and change a few numbers every year to charge top price again)" in the book: "the proof is left as an exercise to the reader" thanks teach, real classy

LINEAR ALGEBRA, MY QUEEN!!!!!!!!!!!!!!! (I literally did the moistcritical meme I got excited, I love linear algebra, cool ass shit)

Finding a good book on a mathematics subject is such a joy because of this.

problem with many old people expect anyone to be already godly skill already, like where's the learning when they ain't even showcasing the whole thing.

Skill issue

You spend an hour figuring it out, concluding that it is indeed trivial, just to come back a week later and have no idea how to solve it again

mckinsey has to be the biggest group of pseudo-intellectuals in the world

The absolute worst part is when they ask you to show all your work, but then skip steps in the first example... Like, am I supposed to reinvent the wheel after you show me the final result? This isn't critical thinking, it's reverse engineering. High school math was just the rosetta stone tactic.

Galois theory? Complex analysis? Topology? Basically all of this besides real analysis is required for an engineering major. How can you be a math major without taking abstract algebra?

In my country textbook is made by some random ass company that have outdated science from like 90'.

I literally only use textbooks for the assignments that you're given in them. Otherwise nobody shows their work in those books its insane

bro, r u me?

Linear algebra sucked

For some reason I learn more from textbooks than lessons......

I have this same problem ! Omg are you studying statistics/ machine learning. I’m trying to go from probability to Stocastic processes and I’m having so much trouble.

You should try topology before yoloing your life savings in crypto!

Brilliant drawing skill

You are growing as F

Lol 😂

bro thought he shot a blockbuster movie

Spend maximum amount of effort to make the most buzz that makes an impact on the majority of the people where most of the company's value comes from (clearly not you since you're smarter than average so obv not the target audience) they don't ever do technical things for PR they just show their past results so the talks are basically propaganda Then when it's down to real business they will make the overworked interns do everything professionally and actually deliver on their promise Smart people already know what mckinsey is capable of and if that's useful for them or not so they don't actually give a shit what they say in public the public bit is just a formality among the competition at this point to make sure they exist in the public's brains basically the last bits in their long checklist The people there are very rich for a reason they maximize influence on the stupid majority to spread their name so it can easily reach the smart minority's doorsteps and it works As sun tzu once said "If your enemy looks like a coke addict focus on their strategy not on how they look"

Math books are the most explaining

There is generally one really good textbook for every major area of mathematics that you should read, and the rest you can safely ignore. Analysis has Rudin, Abstract Algebra has Dummit and Foote, Topology has Munkres, and Linear Algebra has Strang. Physics texts have terrible notation, I recommend applied maths texts in optimization or dynamics over physics texts any day. More modern fields generally have monographs or unpublished draft texts that are often (surprisingly) well laid out. Since the early 2000s interactive visualizations and math pedagogy has been improving drastically, any modern text is like to be miles better than its older competitors

Seems like you can get away with anything in mathematics if you do that Like you can just go around solving so many conjectures and unsolved problems by just making up a bunch of equations and having a schizo rant, and then saying, "the proof is trivial and left as an exercise to the reader" at the end Someone must've done it already and whoever did that must be the greatest genius in the history of the world

All the McKinsey employees do is suggest to hire more McKinsey employees in every business. There's a thing called the exponential McKinsey problem due to this lol.

It's crazy to me that people still believe this company can help them. In the 1980s during their heyday when American companies were just run a lot worse, they could help a lot. But now most big American companies are at about the same level as they are.

Ignore the supporters

Khan Academy gives good and stepwise math teachings.

God bless CZcams vids

On the first img on ring theory the proof is actually trivial though, it's literally not worth the ink to put on there (just finished my ring theory exam today)

tEACH

what they ACTUALLY do is get paid to do nothing or recommend a layoff would be the general sentiment

If learning is easy it isn't learning. And also if you take math step by step it is actually pretty clear. Not always easy but fairly understandable

The issue is that consultants’ incentive structures are rarely aligned with the interests of the business. Their goal is either to say what management wants them to say in order to justify what management had already decided to do before they were hired, and/or it’s to convince the company to hire them again for more consulting work. There do seem to be some consultants that focus on long-term impactful service to business, but good luck telling the good ones from the goofballs.

It's a math book, it has problems and i hate it

Day in the life of a McKinsey consultant: In the morning you get a bunch of new grads and have them cook up a presentation about renewable energy and then present it to the government of french guinea. You dont know what you are talking about, so you make shit up on the go, just some classic improv. At noon you help Jacob Zuma to squeeze all the money out of their national infrastructure companies. After dinner (obviously a business expense) you do coke and help companies to break some international sanctions and take some client to a lap dancing bar (also business expense). After 10 years of doing this you have an extensional crisis and decide to start a startup where you manage climate projects and sell carbon credits.

it feel like every company nowadays does this.

i worked with ex mckinsey consultants. the best of them are amazing, these oversimplifications might make you feel good because you're ignoring the complexity of reality...whatever helps you sleep at night

Now try to explain that to academic teacher. That you understand CZcams explanations better than explanations in the books. It is almost impossible.

All the math teachers I had made it just like the books: oversimplify explanations. I always tough I was not smart for not "getting it" but today I know that, for being an asperger, I need COMPLETE AND VERY SPECIFIC DETAILED EXPLANATIONS before reason over a subject. Is not that I am "dumb" but quite the opposite: I just came to realize that my tough process is deep and requires lots of details before drawing conclusions or coming to a understanding.

all i knows is that they make hella racks

I feel you. Here in Romania we are forced to study in highschool everything from simple algebra to differentiations, integrals, matrix and more. As someone who is just about to finish the final year with a really good degree in math I can tell you one thing. Some of those textbooks can be that bad. Especially if they have really abstract exercises you will see no use for. And that's why I hate how they teach us math. Because they only make us memorise the theory, not understand it. There is an entire difference once you understand how complex numbers are used, how differentiations can be found everywhere or how those stupid composition laws we are forced to learn are the base for quaternions which are used everywhere you need to use rotation in 3D. Thanks god I had access to the internet.

Consultancy jobs just suck tbh, it's like (they employed us, so were gonna employ you)

There is a whole Last week tonight episode about McKinsey which might answer your question. But long story short, McKinsey gives an excuse to whoever hires them to make lousy and unethical decisions. I am sure they have some smart people there doing some interesting stuff, but recruitment events tend to be more for advertisement and brand recognition than to actually tell you what companies do

I bought a statistics book and I didn't know what any of the symbols or math notation meant, so I was able to get very little out of it. Having a teacher explain it was a world of difference. That's just me though.