makes me rather sad that the top comment has nothing of value to say or even any relevance to the video aside from how this guy thinks he sounds💀 people find interest in the most useless stuff sometimes
As a mechanical engineering student, sometimes when I run into hard differential problems. I watch these videos to appreciate how much harder math can be lol
Man we share the exact same mindset. I am a physics postgrad. And my roommate is a postgrad in commerce, his assignments and workloads always remind me what a tough path I am undergoing by comparison. The more I think about it the more I get demotivated. then I always come to these videos to get "motivated". seeing what an actual math postgraduate is dealing with makes me feel the things I am struggling with is just a walk in the park lol
This guy is iq high level they say oh I just study because I like it, you can learn if you commit to it They don't really think they are superior but they genuinely are than a lot of us, yes all people can study all people can remember but I don't think I will never and if there is a possibility that I would prolly understand it, it would take fricking years They don't intend to lie but the truth is not all people can do it
I used to be a high school math teacher. I can honestly say that it feels like I know nothing about math when I am watching this video. I love that feeling of being humbled knowing that expertise is sometimes relative. I am the top math expert at my old high school for all the students AND teachers yet if I walk into your class, I would be the most confused one there. This video made me smile. I wish you the best !
yeh its crazy theres higher level academia people out there with so much knowledge and intelligence. i watch them to know that my course work is nothing compared to theirs
Just imagine that this kind of mathematics is like teaching about the dot product to high school students for you. Some of my teachers in grad school didn't even have to look at the book once, when proving giant theorems in functional analysis or C* algebras. We students just struggled with the definitions and they were just proving those big theorems like nothing. I still miss it a lot. Nothing like trying to wrap your head around mathematics that were developed by absolutely talented geniuses.@
Go learn the terminology its not hard..... you are lost because terminology is being used that you do not know. The actual math is not really complex at all it just uses terms you have never heard of which makes it sound complex. You taught highschool math... cool... you were humbled by this? Yet taught people.... I mean realistically I was more intelligent than most of my math teachers and they were not really needed as well... highschool math is common sense. Geometric math like this man is doing.. is almost useless to be blunt lol.
The whole time I was just thinking: "what?" but somehow seeing people do things that seem foreign to me is absolutely fascinating. It's amazing to think that there are humans out there that can comprehend this level of stuff and have the capability of solving it as well. Most of them, not recognized by myself and majority of the general public as a whole, but hiding among us like gems waiting to be found. Kudos to you, sir!
I like this comment, I was wondering what perspective you were looking at this video from. Could I ask what major you are taking if you are in college?
@@grayson8566 i mean, ur "concept" literally allowed to build our entire world as we know it today and learn everything we know, but okay sure just a concept lol, hope u realize how ridiculous that claim is U sound like someone who'd believe in illuminatis because he saw a triangle with an eye in the street
@@xxneweraxx7422 I typed 5 words. You sound like someone who dumped his life into one field and is now defensive, bitter, and insecure. I agree, math has taught us much about our world, but apparently it cannot teach us how to conduct ourselves as adult men.
@@grayson8566 Such reflexion already is witness of your honest stupidity. Let's took a simple look at your beautiful reasoning and see what comes of it. After all, as you said, i'm just an insecure guy, surely I shouldn't be able to analyse simple stuff and will probably proceed to get mad and insult you over it, right? Anyways, you start your sentence with "I typed 5 words". And? I'd like to know exactly the connotation in which that plays a role, because I sure as hell don't see it here haha. Should i remind you that some of the biggest essays in human history literally came from simple questions of affirmations that are within that range of words? If I ask you the question "what is life", or if i type some pathetic attempt at explaining a concept in the wrongest way possible, what exactly is preventing you from typing an entire essay to answer it? Is it some kind of unwritten rule that I have to keep my answer short as hell simply due to you not wanting to elaborate more? I don't think so, so, that's out of the way, it honestly sounds stupid as hell. Now, obviously, comes the beautiful insult where you feel obligated to grace us everyone with your best interpretation of a useful enumeration. I apologize, mister, but calling me "bitter, insecure, and defensive" over stating how stupid your original point was honestly just sounds like a reflexion of someone who is very bratty pissed that I decided to answer to your original statement, which, i'll say again, is stupid as hell. Now, I won't even ask the link between me saying you sound stupid, and you saying I "dumped my life into one field", because that honestly makes no sense at all, we both know you are just resorting to random insults instead of actually stating why would my opinion be stupid, because that's the best you can do I guess. Now, your last sentence is even dumber. I could firstly perfectly ask you to describe what the fuck you mean by "conduct ourselves as men". What is the context, what is the scenario, what is the connexion? Now, obviously, your answer to that will be something among the lines of "being mature and not getting mad and insulting people over one opinion", or something like that, but, not only let me state again, your "opinion" is honestly dumb as hell on top of still not being in the slightest justified, but in that demonstration of lack of reasoning you provided me with, you also decided to throw in some free insults! So, exactly, what the hell are you trying to imply here if you can't even formulate proper sentences and must resort to "childish" insults, since apparently your definition of man must be something axed around that in this context. Not only that, but the statement in itself is pretty dumb, once again. Maths can and absolutely do help us conduct ourselves as "men" if that's the term you wanna employ. Indeed, any near-braindead idiot with a little bit of thinking can absolutely understand the concept that maths, through working and practicing, and through learning new things, will absolutely help us mature and transit from a "boy" to a "man". Now, if you wanna argue the definition of a "man" because you don't have anything better to actually say, sure, go ahead, I literally won't give a damn tho, because i'm just employing the term you decided to use to demonstrate how little of a point you can actually provide us with. So, there you have it, i'm providing my point of view based on analyzing your sentences. Now, will you be able to do the same? Viewing how you responded to the first comment, I doubt so, but the shot is still yours. But, i'll still go ahead and suggest my personal point of view : please do shut up, you make little to no sense and are just getting irritated over stupid stuff. Once again, "it's all just a concept" is a stupid opinion, because this concept translated into reality on a universal scale, considering maths gave us the ability to create and approximate pretty much everything we know today. So, once again, provide me with some actual thinking if you decide to come back, but in the meantime just shut up. (Oh and obviously, lastly, you can try to argue if you want that i'm just getting mad, but that'd just be the proof you don't even wanna try to elaborate an actual response because of how annoyed you'd be at me providing some simple reasoning. So far, you are the one out of us two that spat out the most insults.) Thanks!
@@grayson8566 It's a >cool< concept. Most of applied math today used to be theoretical concepts back then. Imagine what the theoretical stuff today could be used for in the future when technology gets even better.
I've been watching for a little over a year now and you been one of the big reasons i've resolved to study and go for a phd in math. You're journey has actually been so eye opening. You are amazing
@@elevatexd Josh essentially listens to videos made by the struggling grad student while at the gym. A supportive and motivating comment was written, suggesting that more videos be produced for Josh to watch while working out. I hope Josh's initial response was made clearer.
Man, at least in my engineering classes difficult physics and math problems usually had some sort of real-world application. At this level it just seems like theory and proving abstract concepts. Glad it still interests you
Well all of the things we do as engineers that have real world applications started as theory. Math is only theoretical and abstract until it finds its use in the real world.
Funny thing your "real world application" is using a formula for a already deduced problems of math people I an engineer student too we have a lot workload but not much logic land/or problem solving load, everytime I ask a question about a formula almost all the teachers says:idk we don't deduce the formula or go into details of it, just use it, it works, that's work for math major or PhD engineers
Fourier Analysis has tons of real world applications (you see it a lot in audio engineering). Although when things are on a Complex space, or X-space it definitely starts to leave the world we live in lol
No clue how but I have been watching your channel since under 900 subs and WOW you are doing great!!! You have improved so much since your first couple of videos. Doing this while pursuing a PHD in MATH is commendable. My hats off to you sir ✌️
For #7, you should be motivated by the general principle that regularity decay of Fourier coefficients, and that the Fourier coefficients of a convolution are the products of the Fourier coefficients of the factors. The Holder condition implies a small but polynomial rate of decay (*), and so convolving sufficiently many times you can get an arbitrary polynomial rate of decay, in particular enough to satisfy the sufficient condition to lie in C^3. (*) For C^1 regularity, recall you can prove O(1/n) decay of Fourier coefficients by integrating by parts. For alpha-Holder regularity you can no longer do this but you can still manipulate difference quotients in a way inspired by integration by parts (in the sense that you can pass difference quotients from one factor of the integrand to the other). Doing this in a slightly clever way, you will get O(n^(-\alpha+\epsilon)) decay.
Never thought I'd say this, but I miss grad school when I see this. Spending an entire day being stuck on a tough problem, hearing stories about how Stefan Banach developed functional analysis by my Polish professor. Life was good. IT pays well, but it will never be mathematics.
@@skydivenextwork would be yo time consuming, he said in his post that he would take DAYS for a tough problem, to be successful in his PhD program, a lot more time would need to be allotted to it to be successful
@@skydivenextnot only did this person say they were in grad school, but you have literally no idea who they are or what their life is like. you’re actually insufferable
@@skydivenextwhen you see someone talking about their enthusiasms, appreciate them rather than criticize them. love is all that makes this world bearable. to discourage love is evil.
@@wolfaww2726 I mean without criticize it wont be good since just apreciatin would be just accept their feelings and not think about it is like I really wanna play football but im not child anymore like old days you can play football but im not child but you could but not child and the cycle will continue wthout critic, you have make suggestion and criticize your behaviour or else you never grow
Master’s student here: I find it funny how I show my work to someone in the MA program for math, and we are equally puzzled at each other’s work. He cannot fathom the complexity of the essays I write, and I can’t even begin to understand the geometric formulas that he proves. Lol, just shows that we each have something we are good at.
Hi! I am also currently taking a Fourier Analysis course! A clean way to do #5 is to realize that if the required statement is false, then by Bounded Inverse Theorem there exists C>0 such that || f ||_1
I'm so glad calc 1 is going to be my last math class. I'm currently struggling with pre-calc, so seeing this gives me a profound level of respect for your ability to do math. I don't think I could learn this math even if I wanted to.
I used to think most math was difficult, but then I realized I was just psyching myself out. If you go into it thinking it's hard, you'll think everything is hard. If you go into it telling yourself it's easy and you'll be able to handle it, you probably will. This has worked very well for me, and now taking Calculus 1 seems like a walk in the park. I suppose the only thing this wouldn't be able to solve is sheer stupidity.
Imo pre-calc is harder than calc 1. Pre-calc is more about hammering in your algebra skills in case your previous teachers weren't the best at teaching (which was the case for me and a lot of people). Calc 1 is not that bad, some concepts are weird but there are plenty of math people on youtube that can break it down way better than most teachers.
@@juanshaftpatel7488 i have 3 associates - 1 in math, 1 in cs, 1 in physics. i literally just took classes required for transfer while going for the cs associates then a counselor told me i can qualify for all 3. itd be interesting if i can go for two bachelors in math and cs
I did my undergrad in Math and MS in Stats. I know very little about fourier transforms but this video reminded me a lot of the theoretical stuff I did in my pure math classes. Good stuff, I'd say I miss those days but I do not miss the stress of academia.
I love math, which is why i got an bachelors in it, but I've realized I don't actually love doing math. Just reading about it. Also I love the Cortex drawing. Makes me feel like a kid again
This was a cool video to watch, I’m in an engineering program right now, but I never took an interest in maths until my final math course in ordinary differential equations which I finished recently. I understand this isn’t really a hard course when compared to other math courses but it sparked an interest into what other courses I would have been taking if I decided to major in Mathematics or something else instead. It’s a bit of a shame that I won’t be delving deeper into the subject for my career.
higher level math courses are all proofs and theorem classes. not much applied like differential equations. just accept that the rules and theorems already exist and are proven to save yourself the trouble lol
i took functional analysis at my 3rd year in university and it was a mess. Our professor was literally insane but a kind fella, he was a soviet bro who took respect and hardworking to the top of all else. i was literally working my brain till it exploded at each lecture, trying to process what i was given. I didnt understand anything, couldnt even get the tasks done in the right manner. Time came and our quiz is %50 of our grade and the final is %50 also. I was shivering to my thighs. Before the quiz i didnt sleep 4-5 days, i lost time. Then it came the big quiz, professors look-after was there to gave us papers, as i have seen them i thought "oh, ok i can do this (maybe?)" , to my surprise i couldnt. i got 5 out of 50. Then the exam came, what a surprise it was worse. I did what i could. Then comes the part which is popular in russian universities (explain how did you do that!) i can say he was like: "now explain" - "ok you dont seem to understand this question you may leave!". Thats how everyone left. Some passed, some didnt. I was sent to retake with 15 days given to me to pass it (ps"if i dont pass ill be expelled by the university because it was a main class"). That was the hardest 15 days ive studied in my life, then i passed at retake by the favor of professor. I wish all our fellow mathematicians out there good luck. Its neither mentally or physically easy for us. Take care!
They somewhat forcefully put me into robotics and machine learning, even did my internship with projects like delivery bots with ml capabilities. but i pursue full-stack development as my future job because its fun.@@dhruvacharya2602
That's sad, you shouldn't be a math major how you gonna fail then pass by retake, the teacher prolly lowered the level for you to pass I beg you to never teach please or atleast teach low level math, is usually the people that don't do well in college, the worst at teaching That just my experience sorry My teacher alway said I barely passed test then all made sense how he was worst to ever teach in college BUT teacher that know a lot sometimes don't know how to teach lol so idk, I had another teacher that went to a lot of countries had masters TWO freaking PhD and still talk it like eeeeeh this theorem is eeeeeh well if you do applied eeeeehhh well then eeeeh
i am not a math major neither a candidate i studied computer science. took functional analysis and was forced upon me like at that time many of my computer and programming classes at the same time. for the last part i dont believe a teacher needs to be perfect student to teach thats nonsense and biased.@@skydivenext
Just started my maths/further maths a levels and plan to persue maths after; its so cool to think that in a few years I too should be able to solve problems like these.
My homework from my PhD stats classes (linear mixed models) are laughable compared to that lmao. And as someone with a biology background (plant genetics) I still struggle sometimes. However we don't get graded for the HW, they apply tests, which sucks imo.
Haha I’m a first year sciences student and I’m taking my first calculus course right now. 😂 I’m so impressed by what other people’s minds are capable of
quick question: did u have a huge passion for mathematics in highschool? and if so, has pursuing a phd in math ever made you feel burnt out from the subject and not enjoy it as much? its been a fear of mine ever since ive set my mind on the possibly of studying for a math phd
I've always been interested in STEM subjects but 8th grade was when I started to prefer mathematics. There are days that I get burned out but typically the next day I get back into it. Granted there are subfields of math I don't much care for. There's no real way of knowing if you will get burned out from doing math daily until you actually do it, which is unfortunate. But that is true for most things in life. My recommendation is to pick something you know you like (or at least tolerate) and fully commit to it. Michael Jordan probably had days where he hated playing basketball but still gave 100%. Not that we all have to be like Michael Jordan, but it is something I think about whenever I lose interest in math.
I've personally always been passionate about art, started drawing since I was like 4. However, I became a CS major 2 years ago after trying some basic coding online for a couple days. 3 reasons: 1. I found that I enjoyed it because I like the problem solving aspect of it. 2. I don't want to starve in the future as an artist because it is an oversaturated field of work. 3. I prefer to keep it as something I can do on my free time to relaxe and just let myself go into a piece of paper, or whatever medium I'm using. It is simply a fact that a job will be stressful at times, especially if it's a job that doesn't pay well and you end up struggling financially. I don't want that to happen to me with art. I do want to sell stuff on the side, but I don't want to depend on it to live because then it loses its "magic" ig u could say. Also, I find that when I spend a lot of time doing logic based stuff with math hw and coding projects, I end up craving to spend time creating art. And when I have lots of free time, I end up playing video games or doing anything other than what I want to make myself do, art. So just wanted to give my perspective on the matter. Some people have multiple interests and it's hard to rlly decide what to focus your time on and what to depend on for income. I also rlly like guitar but I haven't been able to learn much cus I have to prioritize school and art. It's also good to push yourself to explore other things. You'd be surprised what you can end up enjoying or being very good at. It happened to me with cs. For years, I dodged every opportunity to learn something about coding, simply cus I thought it looked very boring. When I finally tried it, I quickly realized that I actually found it enjoyable. So yeah, imma shut up now lol. Gl to everyone!
@@dynamicdingus If you're young, and you truly have a desire to become an artist, I would do that. If you're older, like over 30, smart, and you need money, CS might be something to consider.
I'm a sophomore in college taking discrete for a cs degree. I've thought discrete to be somewhat difficult (math is not my strong suit) but this math has just made discrete seem like nothing. Truly impressive.
The skill leap between discrete math (pretty much the first pure math course math majors take) and the level in the video is as big or larger than the leap between arithmetic and calculus.
every symbol and the their connections to others is so complex yet so simple, you could spends weeks unpacking all the information and still be totally baffled by those equations.
i kinda wish i took a course that really covered fourier analysis. only time i saw it was when i took a course in post-quantum cryptography. im hoping ill be able to fit some math courses into my phd, and i could make the argument that "these are relevant to my research because i am theoretical computer science and these mathematical methods may help me in solving some problems", but we'll see. i'm not doing anything with signal processing, so it might be slightly harder to justify. in another universe i was a math major anyway because where i went for undergrad didn't have pure math as a major
ODEs and PDEs are a lot more fun than this imo, although theyre actually somewhat related as the fourier transform is used in solving many differential equations
Well at least I recognized a couple of the symbols :). I'm in first-year math right now (going into engineering), I'll have to bookmark this video and come back in a couple of years to see if I can understand any more of it.
Freshman who just finished my second week of stats, this is awesome. What classes have you taken to get here? And what is your particular favorite subjects?
My brain likes to pull a particular practical joke on me with regards to difficult math classes. When I'm in one, I feel a lot of suffering, but as soon as I'm out I feel a desire to try an even harder one. Well in my case, I only got as far as abstract alg and Dicrete math II. Things just started to feel too magical for me. At some point it just felt like I was pattern matching to existing solutions without understanding deeply. It's fun to see these problems though, and though I don't understand them the format does feel familiar lol
Statistics is the one subject that is common basically in every discipline of higher level studies. I don't know what stats course you took, data mining and those type I'd also drop in an instant. But experimental design and analysis, that is useful even outside of academia.
These look like problems from my engineering course work, specifically my DSP course... In engineering, there are concrete reasons for all this math (actually solving a real world problem. ie filtering noise out of a signal so a communication system will work) ... but mathematicians always seem to do all this work for the pure joy of the abstract math. I would die.
Ive learned the insane cartoon math symbols are real. Good greif, thats some scary stuff to look at as someone who could barely get through algrbra 2 haha. Over the years ive found that i am much better at applied math, i can kind kf look at it as a puzzle i need ti solve, and i can easily recognize when ive solved it!
i'm in algebra 2 (highschool sophomore) and this is all straight up another language to me super cool though. maybe someday i'll think about majoring in math
@@PhDVlog777I prefer thousands of times the titans games rather than the original ones, except maybe Twinsanity. Maybe nostalgy makes me bias, but I don't get the hate.
I'm really curious about this class structure. Can each problem only be claimed by one student or do multiple students solve the same problem at the board over time?
So the class favors more skilled students, and less skilled students will be left with the hardest problems? Seems unfair, but maybe that’s the point to weed them out
There are many excellent books on real analysis, but if you are looking for an book (and have already taken some math classes, e.g calculus) then I have a particularly wonderful recommendation: Understanding Analysis by Stephen Abbott. I still keep it in my bookshelf.
i started with Abbot's understanding analysis. it was ok but questions were hard. then i moved to Ross analysis. it became hard as i reached Lim Sup Lim Inf topic in sequences. i have been struggling since 2 years and lost my interest. now i am looking for number theory.
Abbott is an absolutely amazing book for beginners, he explains everything perfectly, a highschool student with calculus knowledge can easily pick up real analysis using abbott's book! it's such a well written book with really good explanations and good exercises. It is the perfect introduction to pure mathematics :D Dont stop when the problems get difficult, that's exactly the point when you start learning more and you expand your understanding of the subject. it might take an hour or two hours or even several days to do one exercise, but that's good! All that time you spent thinking isn't time wasted, I recommend watching a 3 minute snippet from an interview with Alaine Connes titled "How a mathematician works" that explains what mindset you need to approach pure mathematics with.
What previous courses do you need to take to know how to solve these types of problems, and what are the applications of this stuff either in the real world or in research
Hi, engineering stud here, how do you manage time? I have difficulty working because I know that when I work with math, I also should have worked with 3 other classes
So, and please don't take this the wrong way I'm very dumb, but what is the goal or point of interpreting these problems? Like I understand the pursuit of complex problems as they pertain to complex practical applications with like, aerospace or whatever, but the way you describe these seems almost... Recreational maybe? Is that the word I'm looking for? Like I'd assume these courses work toward some larger goal, but like what is the macro quest here for these? Is it working toward problems that haven't been solved yet? If that's the case, do those have some application with which it's important, or is it all more or less for the sake of academia?
These types of courses might fall under the category, "can't see the forest for the trees." Fourier analysis has many wide reaching applications in signal processing, statistics, oceanography, digital image processing, and many other fields. But it is not at all apparent how these problems apply to these fields. My take away is that these problems serve more to help students develop tricks that can be used to solve hard problems later down the road.
@@PhDVlog777 gotcha, thanks for the insight, I hadn't thought to consider applications in data processing like you mentioned, and that's definitely interesting to think about.
![АЛАУДИНОВ у Скабеевой: эти их ВСУ нас НЕ ДОГОНЯТ 😁 [Пародия]](http://i.ytimg.com/vi/an0anqU4WGQ/mqdefault.jpg)
You literally have a nerd voice lol
You wouldn't have what you have if it wasn't for freaks and geeks.
bars damn
@@spreadneck2063
@@spreadneck2063 Facts unending
@@spreadneck2063 1980s ahh response
makes me rather sad that the top comment has nothing of value to say or even any relevance to the video aside from how this guy thinks he sounds💀 people find interest in the most useless stuff sometimes
As a mechanical engineering student, sometimes when I run into hard differential problems. I watch these videos to appreciate how much harder math can be lol
i do the same with looking at engineering maths lol
Man we share the exact same mindset.
I am a physics postgrad. And my roommate is a postgrad in commerce, his assignments and workloads always remind me what a tough path I am undergoing by comparison. The more I think about it the more I get demotivated.
then I always come to these videos to get "motivated". seeing what an actual math postgraduate is dealing with makes me feel the things I am struggling with is just a walk in the park lol
@@_HJ_K life was tough even for Picasso. Choose the difficult path, and life will become easy...
This guy is iq high level they say oh I just study because I like it, you can learn if you commit to it
They don't really think they are superior but they genuinely are than a lot of us, yes all people can study all people can remember but I don't think I will never and if there is a possibility that I would prolly understand it, it would take fricking years
They don't intend to lie but the truth is not all people can do it
@@skydivenextwhy not?? How do you know for sure? I could never ever admit I'm not a genius it.woupd.ne too depressing and infuriating.
I used to be a high school math teacher. I can honestly say that it feels like I know nothing about math when I am watching this video. I love that feeling of being humbled knowing that expertise is sometimes relative. I am the top math expert at my old high school for all the students AND teachers yet if I walk into your class, I would be the most confused one there. This video made me smile. I wish you the best !
yeh its crazy theres higher level academia people out there with so much knowledge and intelligence. i watch them to know that my course work is nothing compared to theirs
Just imagine that this kind of mathematics is like teaching about the dot product to high school students for you. Some of my teachers in grad school didn't even have to look at the book once, when proving giant theorems in functional analysis or C* algebras. We students just struggled with the definitions and they were just proving those big theorems like nothing. I still miss it a lot. Nothing like trying to wrap your head around mathematics that were developed by absolutely talented geniuses.@
Go learn the terminology its not hard..... you are lost because terminology is being used that you do not know. The actual math is not really complex at all it just uses terms you have never heard of which makes it sound complex.
You taught highschool math... cool... you were humbled by this? Yet taught people....
I mean realistically I was more intelligent than most of my math teachers and they were not really needed as well... highschool math is common sense.
Geometric math like this man is doing.. is almost useless to be blunt lol.
what maths is useful for an average person?@@user-ll4on9my7h
@@user-ll4on9my7h get your head out of your ass you're not him💀
The whole time I was just thinking: "what?" but somehow seeing people do things that seem foreign to me is absolutely fascinating. It's amazing to think that there are humans out there that can comprehend this level of stuff and have the capability of solving it as well. Most of them, not recognized by myself and majority of the general public as a whole, but hiding among us like gems waiting to be found. Kudos to you, sir!
I like this comment, I was wondering what perspective you were looking at this video from. Could I ask what major you are taking if you are in college?
@@joesh8213 Yes i give you permission to ask
@@davy1220 thank you
Us humans have created such impossibly complex things through the sheer power of our minds.
It’s all just a concept
@@grayson8566 i mean, ur "concept" literally allowed to build our entire world as we know it today and learn everything we know, but okay sure just a concept lol, hope u realize how ridiculous that claim is
U sound like someone who'd believe in illuminatis because he saw a triangle with an eye in the street
@@xxneweraxx7422 I typed 5 words. You sound like someone who dumped his life into one field and is now defensive, bitter, and insecure. I agree, math has taught us much about our world, but apparently it cannot teach us how to conduct ourselves as adult men.
@@grayson8566 Such reflexion already is witness of your honest stupidity. Let's took a simple look at your beautiful reasoning and see what comes of it. After all, as you said, i'm just an insecure guy, surely I shouldn't be able to analyse simple stuff and will probably proceed to get mad and insult you over it, right?
Anyways, you start your sentence with "I typed 5 words". And? I'd like to know exactly the connotation in which that plays a role, because I sure as hell don't see it here haha. Should i remind you that some of the biggest essays in human history literally came from simple questions of affirmations that are within that range of words? If I ask you the question "what is life", or if i type some pathetic attempt at explaining a concept in the wrongest way possible, what exactly is preventing you from typing an entire essay to answer it? Is it some kind of unwritten rule that I have to keep my answer short as hell simply due to you not wanting to elaborate more? I don't think so, so, that's out of the way, it honestly sounds stupid as hell.
Now, obviously, comes the beautiful insult where you feel obligated to grace us everyone with your best interpretation of a useful enumeration. I apologize, mister, but calling me "bitter, insecure, and defensive" over stating how stupid your original point was honestly just sounds like a reflexion of someone who is very bratty pissed that I decided to answer to your original statement, which, i'll say again, is stupid as hell. Now, I won't even ask the link between me saying you sound stupid, and you saying I "dumped my life into one field", because that honestly makes no sense at all, we both know you are just resorting to random insults instead of actually stating why would my opinion be stupid, because that's the best you can do I guess.
Now, your last sentence is even dumber. I could firstly perfectly ask you to describe what the fuck you mean by "conduct ourselves as men". What is the context, what is the scenario, what is the connexion? Now, obviously, your answer to that will be something among the lines of "being mature and not getting mad and insulting people over one opinion", or something like that, but, not only let me state again, your "opinion" is honestly dumb as hell on top of still not being in the slightest justified, but in that demonstration of lack of reasoning you provided me with, you also decided to throw in some free insults! So, exactly, what the hell are you trying to imply here if you can't even formulate proper sentences and must resort to "childish" insults, since apparently your definition of man must be something axed around that in this context.
Not only that, but the statement in itself is pretty dumb, once again. Maths can and absolutely do help us conduct ourselves as "men" if that's the term you wanna employ. Indeed, any near-braindead idiot with a little bit of thinking can absolutely understand the concept that maths, through working and practicing, and through learning new things, will absolutely help us mature and transit from a "boy" to a "man". Now, if you wanna argue the definition of a "man" because you don't have anything better to actually say, sure, go ahead, I literally won't give a damn tho, because i'm just employing the term you decided to use to demonstrate how little of a point you can actually provide us with.
So, there you have it, i'm providing my point of view based on analyzing your sentences. Now, will you be able to do the same? Viewing how you responded to the first comment, I doubt so, but the shot is still yours. But, i'll still go ahead and suggest my personal point of view : please do shut up, you make little to no sense and are just getting irritated over stupid stuff. Once again, "it's all just a concept" is a stupid opinion, because this concept translated into reality on a universal scale, considering maths gave us the ability to create and approximate pretty much everything we know today. So, once again, provide me with some actual thinking if you decide to come back, but in the meantime just shut up. (Oh and obviously, lastly, you can try to argue if you want that i'm just getting mad, but that'd just be the proof you don't even wanna try to elaborate an actual response because of how annoyed you'd be at me providing some simple reasoning. So far, you are the one out of us two that spat out the most insults.) Thanks!
@@grayson8566 It's a >cool< concept. Most of applied math today used to be theoretical concepts back then. Imagine what the theoretical stuff today could be used for in the future when technology gets even better.
I've been watching for a little over a year now and you been one of the big reasons i've resolved to study and go for a phd in math. You're journey has actually been so eye opening. You are amazing
You are too kind, thank you 🙏
I like listening to these videos in the gym. Keep it up brother!
Same!
Get them gains! 🏋️♀️
What??
ayoo?@@PhDVlog777
@@elevatexd Josh essentially listens to videos made by the struggling grad student while at the gym. A supportive and motivating comment was written, suggesting that more videos be produced for Josh to watch while working out. I hope Josh's initial response was made clearer.
Man, at least in my engineering classes difficult physics and math problems usually had some sort of real-world application. At this level it just seems like theory and proving abstract concepts. Glad it still interests you
Well all of the things we do as engineers that have real world applications started as theory. Math is only theoretical and abstract until it finds its use in the real world.
Funny thing your "real world application" is using a formula for a already deduced problems of math people
I an engineer student too we have a lot workload but not much logic land/or problem solving load, everytime I ask a question about a formula almost all the teachers says:idk we don't deduce the formula or go into details of it, just use it, it works, that's work for math major or PhD engineers
Fourier Analysis has tons of real world applications (you see it a lot in audio engineering). Although when things are on a Complex space, or X-space it definitely starts to leave the world we live in lol
That's the fun of it!
No clue how but I have been watching your channel since under 900 subs and WOW you are doing great!!! You have improved so much since your first couple of videos. Doing this while pursuing a PHD in MATH is commendable. My hats off to you sir ✌️
For #7, you should be motivated by the general principle that regularity decay of Fourier coefficients, and that the Fourier coefficients of a convolution are the products of the Fourier coefficients of the factors. The Holder condition implies a small but polynomial rate of decay (*), and so convolving sufficiently many times you can get an arbitrary polynomial rate of decay, in particular enough to satisfy the sufficient condition to lie in C^3.
(*) For C^1 regularity, recall you can prove O(1/n) decay of Fourier coefficients by integrating by parts. For alpha-Holder regularity you can no longer do this but you can still manipulate difference quotients in a way inspired by integration by parts (in the sense that you can pass difference quotients from one factor of the integrand to the other). Doing this in a slightly clever way, you will get O(n^(-\alpha+\epsilon)) decay.
(The same principle will also lead you to an example for #8.)
Well said. I concur.
what do you do for a living?
It's so interesting to read things like this as a high school student because none of this makes sense to me
@@sam_9228i’m 26 with a college degree and it doesn’t make sense to me either 😂
Never thought I'd say this, but I miss grad school when I see this. Spending an entire day being stuck on a tough problem, hearing stories about how Stefan Banach developed functional analysis by my Polish professor. Life was good. IT pays well, but it will never be mathematics.
I just find it funny, you could litterally get a phd while you work but you wont lol, you clearly not missing it just the nostalgia factor kicking in
@@skydivenextwork would be yo time consuming, he said in his post that he would take DAYS for a tough problem, to be successful in his PhD program, a lot more time would need to be allotted to it to be successful
@@skydivenextnot only did this person say they were in grad school, but you have literally no idea who they are or what their life is like. you’re actually insufferable
@@skydivenextwhen you see someone talking about their enthusiasms, appreciate them rather than criticize them. love is all that makes this world bearable. to discourage love is evil.
@@wolfaww2726 I mean without criticize it wont be good since just apreciatin would be just accept their feelings and not think about it is like
I really wanna play football but im not child anymore like old days
you can play football
but im not child
but you could
but not child
and the cycle will continue wthout critic, you have make suggestion and criticize your behaviour or else you never grow
As an aspiring PhD student I love the bts of how homework can look ! Thank you and I continue to wish you the best
bts v
@@andrewyu4069bts stands for "Behind the scenes"
His "chillax" environment would defiantly be my anxiety nightmare.
As aerospace engineering student, I thought I had it hard. But this is on another level.
Master’s student here: I find it funny how I show my work to someone in the MA program for math, and we are equally puzzled at each other’s work. He cannot fathom the complexity of the essays I write, and I can’t even begin to understand the geometric formulas that he proves. Lol, just shows that we each have something we are good at.
Masters student in what?
You write your homework solutions like you're writing a textbook and it is beautiful.
Problem #9-10 reminds me of divisors in algebraic geometry. Then again, I've never studied math.
Wish you would have just gone back to sleep rather than sharing that hallucination.
I really like the format of the video where you're saying out loud and explaining these complex math problems.
Hi! I am also currently taking a Fourier Analysis course! A clean way to do #5 is to realize that if the required statement is false, then by Bounded Inverse Theorem there exists C>0 such that || f ||_1
Thats exactly what I was gonna say. Man you kinda took the words out of my mouth
@@Ayyouboss sure he did
I'm so glad calc 1 is going to be my last math class. I'm currently struggling with pre-calc, so seeing this gives me a profound level of respect for your ability to do math. I don't think I could learn this math even if I wanted to.
Of course you can don’t be silly
I used to think most math was difficult, but then I realized I was just psyching myself out. If you go into it thinking it's hard, you'll think everything is hard. If you go into it telling yourself it's easy and you'll be able to handle it, you probably will. This has worked very well for me, and now taking Calculus 1 seems like a walk in the park. I suppose the only thing this wouldn't be able to solve is sheer stupidity.
NOOOOOOOOOOOO~ That would be my literal definition of hell. Calculus is where mathematics starts to become really fun!
cal 1 is so easy lmao what are you on; what part of precalc is so difficult for you?
Imo pre-calc is harder than calc 1. Pre-calc is more about hammering in your algebra skills in case your previous teachers weren't the best at teaching (which was the case for me and a lot of people). Calc 1 is not that bad, some concepts are weird but there are plenty of math people on youtube that can break it down way better than most teachers.
As someone with only an associates degree in Mathematics and another in Physics, this is fascinating and inspirating. Good luck with everything.
whats the point of your degrees? where do you eork? burger king?
@@juanshaftpatel7488 no, they were byproducts of the degree im pursuing in computer science and engineering.
@juanshaftpatel7488 💀
@@juanshaftpatel7488 i have 3 associates - 1 in math, 1 in cs, 1 in physics. i literally just took classes required for transfer while going for the cs associates then a counselor told me i can qualify for all 3. itd be interesting if i can go for two bachelors in math and cs
@@juanshaftpatel7488if nothing else its done for yourself. Have you ever done anything to better yourself?
I’m glad that I finished my PhD a few years ago… Such a tough struggle, but so incredibly rewarding.
me too
As an aspiring pure maths doctorate I appreciate the honesty and openness provided. I know you're gonna crush your thesis
well good luck with y'alls worthless degrees!! try something useful for the economy and yourselves!!
For no reason, I really like your videos I’m a business major lol😂 . Keep doing your thing!
I did my undergrad in Math and MS in Stats. I know very little about fourier transforms but this video reminded me a lot of the theoretical stuff I did in my pure math classes. Good stuff, I'd say I miss those days but I do not miss the stress of academia.
I am so far removed from math yet I still watched this video. I understood absolutely nothing. Great video!!!
I love math, which is why i got an bachelors in it, but I've realized I don't actually love doing math. Just reading about it.
Also I love the Cortex drawing. Makes me feel like a kid again
oh man, this made me miss my math lectures at uni.. it‘s been so long and i have forgotten so much 😅
This is my nightmare, I don't know why it's recommended for me. Thanks youtube.
This was a cool video to watch, I’m in an engineering program right now, but I never took an interest in maths until my final math course in ordinary differential equations which I finished recently. I understand this isn’t really a hard course when compared to other math courses but it sparked an interest into what other courses I would have been taking if I decided to major in Mathematics or something else instead. It’s a bit of a shame that I won’t be delving deeper into the subject for my career.
higher level math courses are all proofs and theorem classes. not much applied like differential equations. just accept that the rules and theorems already exist and are proven to save yourself the trouble lol
i took functional analysis at my 3rd year in university and it was a mess. Our professor was literally insane but a kind fella, he was a soviet bro who took respect and hardworking to the top of all else. i was literally working my brain till it exploded at each lecture, trying to process what i was given. I didnt understand anything, couldnt even get the tasks done in the right manner. Time came and our quiz is %50 of our grade and the final is %50 also. I was shivering to my thighs. Before the quiz i didnt sleep 4-5 days, i lost time. Then it came the big quiz, professors look-after was there to gave us papers, as i have seen them i thought "oh, ok i can do this (maybe?)" , to my surprise i couldnt. i got 5 out of 50. Then the exam came, what a surprise it was worse. I did what i could. Then comes the part which is popular in russian universities (explain how did you do that!) i can say he was like: "now explain" - "ok you dont seem to understand this question you may leave!". Thats how everyone left. Some passed, some didnt. I was sent to retake with 15 days given to me to pass it (ps"if i dont pass ill be expelled by the university because it was a main class"). That was the hardest 15 days ive studied in my life, then i passed at retake by the favor of professor. I wish all our fellow mathematicians out there good luck. Its neither mentally or physically easy for us. Take care!
Damn bro…may i ask what do you do now?
They somewhat forcefully put me into robotics and machine learning, even did my internship with projects like delivery bots with ml capabilities. but i pursue full-stack development as my future job because its fun.@@dhruvacharya2602
That's sad, you shouldn't be a math major how you gonna fail then pass by retake, the teacher prolly lowered the level for you to pass
I beg you to never teach please or atleast teach low level math, is usually the people that don't do well in college, the worst at teaching
That just my experience sorry
My teacher alway said I barely passed test then all made sense how he was worst to ever teach in college
BUT teacher that know a lot sometimes don't know how to teach lol so idk, I had another teacher that went to a lot of countries had masters TWO freaking PhD and still talk it like eeeeeh this theorem is eeeeeh well if you do applied eeeeehhh well then eeeeh
i am not a math major neither a candidate i studied computer science. took functional analysis and was forced upon me like at that time many of my computer and programming classes at the same time. for the last part i dont believe a teacher needs to be perfect student to teach thats nonsense and biased.@@skydivenext
Just started my maths/further maths a levels and plan to persue maths after; its so cool to think that in a few years I too should be able to solve problems like these.
My homework from my PhD stats classes (linear mixed models) are laughable compared to that lmao. And as someone with a biology background (plant genetics) I still struggle sometimes.
However we don't get graded for the HW, they apply tests, which sucks imo.
Good luck to you. I'll be doing Advanced Statistical Methods next year (behavioral genetics)
As a senior year high schooler, all I hear as enchantment table
Haha I’m a first year sciences student and I’m taking my first calculus course right now. 😂 I’m so impressed by what other people’s minds are capable of
I hate it when something fails the Dini Criterion.
Homework at Phd level, I can't
I came here to amplify the nice feeling of relief knowing I don't need to do this kind of work
Looks like my discrete math course on steroids
Alot of steroids
quick question: did u have a huge passion for mathematics in highschool? and if so, has pursuing a phd in math ever made you feel burnt out from the subject and not enjoy it as much? its been a fear of mine ever since ive set my mind on the possibly of studying for a math phd
I've always been interested in STEM subjects but 8th grade was when I started to prefer mathematics. There are days that I get burned out but typically the next day I get back into it. Granted there are subfields of math I don't much care for.
There's no real way of knowing if you will get burned out from doing math daily until you actually do it, which is unfortunate. But that is true for most things in life. My recommendation is to pick something you know you like (or at least tolerate) and fully commit to it. Michael Jordan probably had days where he hated playing basketball but still gave 100%. Not that we all have to be like Michael Jordan, but it is something I think about whenever I lose interest in math.
I've personally always been passionate about art, started drawing since I was like 4. However, I became a CS major 2 years ago after trying some basic coding online for a couple days. 3 reasons: 1. I found that I enjoyed it because I like the problem solving aspect of it. 2. I don't want to starve in the future as an artist because it is an oversaturated field of work. 3. I prefer to keep it as something I can do on my free time to relaxe and just let myself go into a piece of paper, or whatever medium I'm using. It is simply a fact that a job will be stressful at times, especially if it's a job that doesn't pay well and you end up struggling financially. I don't want that to happen to me with art. I do want to sell stuff on the side, but I don't want to depend on it to live because then it loses its "magic" ig u could say. Also, I find that when I spend a lot of time doing logic based stuff with math hw and coding projects, I end up craving to spend time creating art. And when I have lots of free time, I end up playing video games or doing anything other than what I want to make myself do, art. So just wanted to give my perspective on the matter. Some people have multiple interests and it's hard to rlly decide what to focus your time on and what to depend on for income. I also rlly like guitar but I haven't been able to learn much cus I have to prioritize school and art. It's also good to push yourself to explore other things. You'd be surprised what you can end up enjoying or being very good at. It happened to me with cs. For years, I dodged every opportunity to learn something about coding, simply cus I thought it looked very boring. When I finally tried it, I quickly realized that I actually found it enjoyable. So yeah, imma shut up now lol. Gl to everyone!
@@dynamicdingus If you're young, and you truly have a desire to become an artist, I would do that. If you're older, like over 30, smart, and you need money, CS might be something to consider.
I'm a sophomore in college taking discrete for a cs degree. I've thought discrete to be somewhat difficult (math is not my strong suit) but this math has just made discrete seem like nothing. Truly impressive.
Funny I took discrete math just this last school year.
nah discrete can get very hard too
The skill leap between discrete math (pretty much the first pure math course math majors take) and the level in the video is as big or larger than the leap between arithmetic and calculus.
i made it 6 minutes before i accepted that I understand none of this
I feel like a drooling neanderthal watching this. Crazy smart
Seeing math like this is like reading a foreign language but 10000 times harder to understand
My face watching this:🥴, I’m barely in calc1😂 good luck man!
im a junior in high school and this makes me feel so much better about my AP physics homework :) thanks for taking one for the team!
every symbol and the their connections to others is so complex yet so simple, you could spends weeks unpacking all the information and still be totally baffled by those equations.
Sometimes you can know just enough about a subject to know it is difficult, but not enough to know how far you are from understanding it.
Remind me to never try to get a PhD... I don't even have a clue what is happening on that homework lol
The writing on the white board should read "if cortex WERE an analyst."
i kinda wish i took a course that really covered fourier analysis. only time i saw it was when i took a course in post-quantum cryptography. im hoping ill be able to fit some math courses into my phd, and i could make the argument that "these are relevant to my research because i am theoretical computer science and these mathematical methods may help me in solving some problems", but we'll see. i'm not doing anything with signal processing, so it might be slightly harder to justify.
in another universe i was a math major anyway because where i went for undergrad didn't have pure math as a major
I finally passed real analysis.
Congrats! 🍾
Congratulations!
I’m in differential Eq rn, and this stuff is like a whole different language 😳
ODEs and PDEs are a lot more fun than this imo, although theyre actually somewhat related as the fourier transform is used in solving many differential equations
@@prodbyryshy interesting bro, I’m not gonna lie Diff Eq is not too fun rn, I would rank the math classes like this so far
Calc2
For an extra (and excellent) reference for Fourier Analysis I would recommend both of Grafakos's books (the proofs have all the details) on the topic.
I came for the Cortex drawing. I left thinking like Cortex.
And I'm out here struggeling in highschool-level math. I would guess almost everyone in these difficult classes got straight A's. I gotta work more.
You are one smart individual.
Well at least I recognized a couple of the symbols :). I'm in first-year math right now (going into engineering), I'll have to bookmark this video and come back in a couple of years to see if I can understand any more of it.
The man uses a pen for these insanely hard math problems, there's just no way.
I barely passed algebra. I only skirted by because another student did my homework.
thank you for sharing. everyone considering college must be aware what they are getting into.
Why i clicked this video when i knew that i won't understand anything 😓
THIS DUDE TAUGHT ME INTUITIVE CALC WTFFF
HEY PROFESSOR SHAW
Freshman who just finished my second week of stats, this is awesome. What classes have you taken to get here? And what is your particular favorite subjects?
The hardest thing is research, way harder than problem sets.
Love the reference to Crash Team Racing!! Also keep it up :))
Tell me you are a nerd without telling me you are a nerd. (Compliment Wise)
My brain likes to pull a particular practical joke on me with regards to difficult math classes. When I'm in one, I feel a lot of suffering, but as soon as I'm out I feel a desire to try an even harder one.
Well in my case, I only got as far as abstract alg and Dicrete math II. Things just started to feel too magical for me. At some point it just felt like I was pattern matching to existing solutions without understanding deeply. It's fun to see these problems though, and though I don't understand them the format does feel familiar lol
My brain hurts looking at that lol here i am struggling with intermediate alegebra in online college ill need to keep studying in order to learn more.
im in computer science 2nd year and im taking calc 2 without ever having done trig or precal and its a struggle but your videos keep me motivated.
You better get your foundations down if you plan to take Calc 3 in the future. I feel it's a hellhole if you don't know the fundamentals by heart.
howd they even let u take calc 2 without precalc
Engineering 2nd year. I took pre-Calc and trig but I’m still struggling in Calculus 2 this semester with you
what do you guys study in calc 2?
integration, differential equations, sequences and series, and parametric equations and polar coordinates.
Statistics is the one subject that is common basically in every discipline of higher level studies. I don't know what stats course you took, data mining and those type I'd also drop in an instant. But experimental design and analysis, that is useful even outside of academia.
These look like problems from my engineering course work, specifically my DSP course... In engineering, there are concrete reasons for all this math (actually solving a real world problem. ie filtering noise out of a signal so a communication system will work) ... but mathematicians always seem to do all this work for the pure joy of the abstract math. I would die.
Ive learned the insane cartoon math symbols are real. Good greif, thats some scary stuff to look at as someone who could barely get through algrbra 2 haha. Over the years ive found that i am much better at applied math, i can kind kf look at it as a puzzle i need ti solve, and i can easily recognize when ive solved it!
youre doing beautifully. and even if you werent at school.
this is beautiful i don't understand a thing but i watched it whole
i'm in algebra 2 (highschool sophomore) and this is all straight up another language to me
super cool though. maybe someday i'll think about majoring in math
You might be at a higher level than me at studies, but do you know that mitochondria is the powerhouse of the cell ?
Lmaooo
From what I've been told, for Masters or PhD, you need to study 12-16 hours a day.
Coincidentally I started playing Crash of the Titans again few days ago lol.
The game gets too much hate. Understandable, but I thought it was fun.
@@PhDVlog777I prefer thousands of times the titans games rather than the original ones, except maybe Twinsanity. Maybe nostalgy makes me bias, but I don't get the hate.
Nice!
Have you ever cried doing these problems bc I know I would
I'm really curious about this class structure. Can each problem only be claimed by one student or do multiple students solve the same problem at the board over time?
Once someone has answered the problem, it is removed from the list. So no one else may solve it.
@@PhDVlog777 are there enough problems that theoretically everyone can get an A?
@@whitneylevis yes, but there may only be hard problems at the end of the semester
So the class favors more skilled students, and less skilled students will be left with the hardest problems? Seems unfair, but maybe that’s the point to weed them out
@@jtfoog5220 Really mostly seems unfair, and kinda dumb. Just rate difficulty, and then require each student to pick one from each difficulty level.
What book would you recommend for a first course in analysis? Do you eat corn in rows or spirals?
Bartle and Sherbert is really good. Its been awhile since I've eaten corn, but I think I went by rows.
There are many excellent books on real analysis, but if you are looking for an book (and have already taken some math classes, e.g calculus) then I have a particularly wonderful recommendation: Understanding Analysis by Stephen Abbott. I still keep it in my bookshelf.
...looking for an introductory book...*
i started with Abbot's understanding analysis. it was ok but questions were hard. then i moved to Ross analysis. it became hard as i reached Lim Sup Lim Inf topic in sequences. i have been struggling since 2 years and lost my interest. now i am looking for number theory.
Abbott babbles on too much check out Pugh or even Rudin (since the proofs are shorter although harder, yes).
Rudin is no way...too tough for me@@kobemop
Analysis I by tao works for me , the fourth edition is available.
Abbott is an absolutely amazing book for beginners, he explains everything perfectly, a highschool student with calculus knowledge can easily pick up real analysis using abbott's book! it's such a well written book with really good explanations and good exercises. It is the perfect introduction to pure mathematics :D
Dont stop when the problems get difficult, that's exactly the point when you start learning more and you expand your understanding of the subject. it might take an hour or two hours or even several days to do one exercise, but that's good! All that time you spent thinking isn't time wasted, I recommend watching a 3 minute snippet from an interview with Alaine Connes titled "How a mathematician works" that explains what mindset you need to approach pure mathematics with.
I just curl into a ball when I think about Grad HW
As someone who dropped out of engineering because of Advanced Analysis, this is just mind-blowing to me lol
I"ve watched paint dry that has held my attention better than this video
That is very enthusiastic, but I recommend you to try and learn division by single digit.
What previous courses do you need to take to know how to solve these types of problems, and what are the applications of this stuff either in the real world or in research
genuinely so glad there are people in this life who can/would do this bc i sure as hell wont
Great homework PhD!!
Me thinking algebra is super easy...
I could not do any of these if my life depended on it
dude i wish i understood this but idk if i ever will
Wtf, Where the number bro? Is this math?
I saw a 3 but it was small and backwards
Hi, engineering stud here, how do you manage time? I have difficulty working because I know that when I work with math, I also should have worked with 3 other classes
intersting video, thanks for posting
So, and please don't take this the wrong way I'm very dumb, but what is the goal or point of interpreting these problems? Like I understand the pursuit of complex problems as they pertain to complex practical applications with like, aerospace or whatever, but the way you describe these seems almost... Recreational maybe? Is that the word I'm looking for? Like I'd assume these courses work toward some larger goal, but like what is the macro quest here for these? Is it working toward problems that haven't been solved yet? If that's the case, do those have some application with which it's important, or is it all more or less for the sake of academia?
These types of courses might fall under the category, "can't see the forest for the trees." Fourier analysis has many wide reaching applications in signal processing, statistics, oceanography, digital image processing, and many other fields. But it is not at all apparent how these problems apply to these fields.
My take away is that these problems serve more to help students develop tricks that can be used to solve hard problems later down the road.
@@PhDVlog777 gotcha, thanks for the insight, I hadn't thought to consider applications in data processing like you mentioned, and that's definitely interesting to think about.
Have you taken Differential Geometry?
Just what was covered in calculus.
Wow. Respect.