10,000 Problems in Analysis

[@roseandvalerie1854]

Greetings from another struggling grad student in math. I love watching your videos and listening to you talk about these things. It's devastating when I struggle with some courses and other students comment that "they are not that hard". But you also make me realize that I'm not working as hard as you are. Thank you, and good luck with your graduate studies.

[@PhDVlog777]

Easy is a relative term anyway :) Good luck with your studies! We will be done eventually.

[@mathematicaleconomist4943]

​@@PhDVlog777 What sounds harder to your ears? 1. Masters Degree in Economics or 2. Masters Degree in Statistics?

[@PhDVlog777]

@@mathematicaleconomist4943 For me personally, economics. But I also don't know much about it.

[@mathematicaleconomist4943]

@@PhDVlog777 WOW! That's different. Most people think statistics!

[@mathematicaleconomist4943]

@@PhDVlog777 Please! Just one more comparison. I promise no more after that. What sounds harder to your ears? 1. Certified Public Accountant or 2. Masters Degree in Statistics?

[@timeisallitis]

i used to assess my studies by hours till now, this video gave me an idea to do it in number of problems you solve per day rather than counting hours.... thanks for it.

[@Aravestia]

I'm neither a grad student nor a math major, but these videos feel relatable to someone who wants to enjoy math but struggles with it. Love your videos

[@adokwuondoma37]

Good morning Sir, been watching you from Nigeria. I just want to thank you for your generous exposition to these things, because you have both re-ignited my passion to study and research math again. Watching your videos made me realize many things I should have done as a self taught but failed. I'm beginning to get confident again. I hope you realize how much help you are rendering. I think you'll make a great teacher, and I'm happy I met you now 'cos you'll be great someday. Your videos are worth a thousand class lectures. Thanks

[@aaAa-vq1bd]

I’m trying to self-teach up to algebraic topology, I think. Not sure yet exactly what I’m interested in- I’ve always had a passion for number theory and cryptography in general, I’m trying to read a book on Galois theory and cryptography, it’s super hard for me but also makes me want to learn enough to actually do the proofs and exercises. Anyways, my question: what were some of the blocks you ran into with self-study? Do you have any advice for someone who is trying to self-teach higher mathematics? Thanks

[@adokwuondoma37]

@@aaAa-vq1bd Hi, I guess we're both on the journey to achieve something great in mathematics, although I've never studied cryptography but since I've covered materials on Galois theory, I can assure you it's fairly easy to work through if you have enough time and a good textbook. For your question, personally I have big problems committing all the Theorems to memory because there are just too many of them. Also, the examples aren't really so much to give me enough confidence in solving exercises. As a result, after reading a topic I could barely solve all exercises. I don't know if it's the choice of textbook but I know my textbook was clear and easy enough. Whatever it is, I can't tell. Finally, sometimes when I get stuck in understanding a concept, I find it difficult to proceed, at times even after hours and days of research both on internet and other textbooks. Those are concepts that a tutor could have easily pointed out in a few seconds, e.g a line of reasoning in the proof of a theorem. I've observed somethings in his videos that I feel are going to alter the course of my studies again. Cheers

[@PhDVlog777]

Thank you for the kind words! I am glad I could help in anyway. I was not the best at mathematics as an undergrad and I only recently started self studying because it took time, and maturity to do it. Even though we have not met, If I can do it then I am positive you can too.

[@vincentzevecke4578]

Do not belittle yourself. It is an excellent quote from Bruce Lee. Never talk negative about yourself. The body do not know different from positive or negative self-talk. i took English Composition six times i finally pass it was C. .i have Trauma brain injury. I find out in 2009 that i finally got corrected diagnosed..i was 46 years old. I have believe in myself. Young man do not quit ever

[@renzostefanmp7937]

I'm an undergrad physics student and this semester I had the same plan, complete a certain number of Quantum Mechanics problems to get comfortable with the subject. Glad to find you are way into the challenge, and I'm not even officially started because of the job and university schedules. But it motivates me to see someone doing this so that I can emulate it.

[@nolanalexander8696]

Its nice that you are an optimist, my teacher in HS always said before giving us test or quiz: test for learning and not learning for test. Hope you are successful in your study and teaching. And I agreed with you, everyone will struggle, regardless how genius they are. I remember late Feynman said that genius people are people who dedicated lots and lots of time practicing, not some miraculous happenings. Good luck for you.

[@ichbindoofhihi1]

I like to watch people with powers that I will never have nor try to have. It gives me peace to know that there are people like you out there. I don't even know how to describe it. This, for me, is somehow more impressive than athletic features because you are stretching your mind to the outmost degree, I love it man

[@zorenrellauseyer5209]

Math is really difficult, especially if you are a beginner and no one is willing to assist or guide you on what and where you should begin to study with... You are all alone completely. Videos like these were a great source of light of hope and even push us to go over and continue our journey, there is no smooth journey in mathematics... The higher and the more the advance the subject the harder it gets... But I salute all of you out there!!! Great Motivation, let's keep up with the phase!

[@Jessica-kv2ob]

❤

[@Prometeur]

Hey dude, the very fact that you got so upset shows that you really care and that you really do love the subject. I respect it, plus you're like smarter than 99% of people on the planet haha

[@thetransferaccount4586]

i don't know why the hell your channel got into my recommendations but, feels nice to see other people struggling to pass a test and go above and beyond to get over it. nice determination

[@jakeman5825]

I love this idea! The best part is that it's a goal that's actually measurable and quantifiable. There is no progress bar to "Get Better at Analysis", but there is here.

[@sewinvicta9274]

9:08 百鍛千練? It's a phrase that dates back to 1100 AD in the Song Dynasty, suggesting the challenge within while attempting at mastering an art. Edit: Also, just like how the initial segment

[@NhuQuynh-nv7fp]

This is beyond comprehension for a normal person lol .

[@ToriKo_]

Fr. So so far beyond my comprehension

[@lugia8888]

A normal person does not know Analysis. No worries :)

[@JayOwinFull]

I never finished undergrad math. IMA II kicked my ass. I wish I had your dedication.

[@fredthechamp3475]

You could say the same thing for any special field. An Electrical engineer discussing a complex circuit sounds like Black magic to the “normal person”. A chemist talking about organic chemistry sounds like Black magic to the “normal person”. A physicist talking about quantum theory sounds like Black magic to the “normal person”. The list goes on and on. Don’t be too easily impressed.

[@abz7800]

At the end of the day this is purely copying some else’s work definitely requires effort and hard work but your not really do anything yourself your just copying what the real geniuses of humanity have developed over centuries

[@nomimino3414]

Hi, For some reason it's nice just hearing you talk about how you handle defeat... I wanted to get away from university mathematics so bad since the beginning, and it's like a challenge no one around me can relate to at all. I failed exams to the extent I lost my student apartment and had to move back home. I broke down, destroyed precious paintings as an outlet, and I haven't even told my dad. Not sure how to even say it. It's just torture. Some peeps at uni are bastards too, first thing that happened when I went there after a year was that someone decided it would be fun having me against a wall in a small room trying to scream out of me what I averaged in my courses and other just stood by. He looked just Evil, and afterwards he saught me down and told me to my face "I've never seen you before!" Biggest bully at my uni maybe? In spite of all this, I have to say I enjoy studying mathematics. I can't think of anything that would be more worthwhile, beautiful, useful, and intelligent. It's just so hard it's soul-crushing at times. (Also fitting into the academic setting of knowing how to act, I think I made an examiner hate me by sending in a joke as an assignment in order to get a completion. I did get the completion in the end, but he didn't find it funny. Humorless dinosaur.) Learning to write proofs, solving difficult problems, writing long academic reports about arbitrarily complex tasks with little to no guidance from anyone. And the rate at which you're expected to understand and complete tasks within new material is insane. Books aren't read; their content is gotten used to in my limited experience. Anyway, back to you. I find it so inspiring to see you struggle on. I wish to find some of your mental and emotional endurance color off on me. I watched the "Natural Born Talent vs Practice" video too, but honestly I don't see the point in worrying about a proposed factor I cannot control anyway. Is there mathematical talent? Maybe. Is it worth worrying about? I only find it disheartening so I don't. Thank you for your video, it was a pleasure to watch, and let's work towards a brighter future of mathematical understanding. And not forget to have some fun along the way correct?

[@AryaPhoenix]

I have a humble Analysis II midterm tomorrow (I'm not a math major or anything fancy, just taking some math classes to expand my study curriculum), it's comforting to hear you talk about your struggles and makes me feel less alone :)

[@spacetimemalleable7718]

These videos are great. You're a very candid and honest person. Failing a test is part of life unless you're a genius or fortunate enough to get ALL easy professors (rare!). Yep, life is unfair but adapt and move on.

[@bimrebeats]

Geniuses fail the most. They just fail upwards, in the sense that they see lessons in failures regular people don’t recognize

[@darkpikachu_.]

For measure theory you can try bogachev's monograph, it has like 854 total problems, over 100 in every chapter

[@PhDVlog777]

That Bogachev book scares me lol

[@sinclairabraxas3555]

my god

[@JoseRoberto-tc4vy]

Excelent video. Love from Brazil

[@anakbandel00]

Lately I just love watching your videos, that laugh of yours inside almost every video just really relaxing to hear, I hope you'll succeed on your Ph.D. greetings from Indonesia

[@fsflights4605]

What is genuinely amazing is that I'm hard to motivate, but hearing you talk about things I can vaguely kind of understand and casually state that you are thousands of problems into a topic you don't really like is perhaps the single strongest boost I need to get my diplomacy studies, which have nothing to do with math, underway. Keep up the good work!

[@douglasstrother6584]

"MY NAME IS GUNNERY SARGEANT HARTMANN, YOUR SENIOR DRILL INSTRUCTOR!" (Whispered voice) "Dude, are we in the right place?" (Whispered voice) "I guess. The sign on the door said 'Qualifying Exam'." "DO YOU CHATTERBOXES HAVE SOMETHING TO SHARE WITH THE GROUP?"

[@peeper2070]

1:01 I failed my university entrance exam and I am still extremely depressed over it, even now I am at another uni. And that was 16 months ago.

[@PhDVlog777]

After enough time, it will just be a learning experience. I think the famous mathematician Ahlfors failed his qual exam. So that puts things into perspective for me.

[@LucasDimoveo]

Were you able to find an answer key for these problems? How were you able to make sure that you had a true understanding of the subject? Self learning can be a pain without someone to nudge you back on track

[@anubhabbhattacharjee476]

It is more useful to students from a tutor or professor to give hint or some ideas to how to solve a problem rather than solving for them. More generally students can grow their ideas surrounding to the problem and the teacher should help them to give those students a proper direction.

[@pizzaface8140]

I just took my Analysis 1 final as a pure math undergrad and I really thought I understood things clearly but that final made me feel like I didn’t understand a single thing, so many things involved into one problem. I also just hate feeling like I lack understanding in a subject. I want to be better.

[@PhDVlog777]

I know your feeling. It takes time and a lot of effort. But it is 100% doable.

[@BrokenRecord-i7q]

I get you brother, this is so inspiration!

[@aladdinkayqubad1645]

Pilot G2s and Sharpies! Deadly Combo!

[@onlyonecjb001]

10,000 hours was made popular by Malcolm Gladwell.

[@kapoioBCS]

Wow I also want to do something similar in algebra. But on more advanced courses like commutative algebra, algebraic geometry, Galois theory, representations theory etc… Even though i find algebra somewhat easier in proofs than analysis, when I get stuck in algebra it is over, nothing unstuck me 😅

[@afzalsoomro7950]

Wow same. But i am very beginner😅 just in 2nd year of undergraduate. But i love Algebra.. will you give me some advice?

[@PhDVlog777]

The fortunate thing about algebra is that there is a wealth of resources and solved problems on the internet that analysis just doesn’t have. With the right Google search, you should find something very helpful. At least in my experience this was the case.

[@pursuitofnumbers]

@@PhDVlog777 Yeah but if you rely on that you will never be an independent thinker. I believe one should figure stuff out by oneself. But I would love to listen to your take on that.

[@Jessica-kv2ob]

I agree 100% with those final comments about time and copying from the internet.

[@helioliskfire5954]

We're not learning math unless it feels like we are banging our heads on a brick wall. Lolz. Looking at that problem takes me back. How we had to prove everything using the least upper bound.

[@elifsozen_]

I am writing from Turkey. My senior year of high school. I will take the university entrance exam in June. I don't understand your lectures because the math I see is lower level but I really like to listen to you. You make me feel that working is a good thing. Good luck my friend. ( ͡° ͜ʖ ͡°)

[@omoyne]

I did something similar to high-school geometry and it worked wonders.... Now I can even tackle Math olympiad problems and solve most of them completely on my own.🎉

[@vincent4578]

What a astonishing study journey! Also, I would like to ask is that really effective to learn by doing questions from internet. Though it's better than textbook as most of the textbook do not provide full solution.

[@Anamaria-ts6bf]

I love proof part in math even though it's mind destroyer lol.

[@aaAa-vq1bd]

Yeah the proofs are so hard but in the proof you see the guts and connections of the concept you want to understand

[@Anamaria-ts6bf]

@@aaAa-vq1bd Exactly, it's a great way of understanding the whole subject.

[@jackbrolin7709]

What are your plans for the future? Do you want to be a professor or do something else. Also, what does the timeline look like for taking these exams. Are you not doing any research whatsoever until you can pass? How does that work. Thanks!

[@PhDVlog777]

I would like to be a professor some day, or maybe just a college instructor. I’ve also considered going into finance. These exams are usually offered once a semester.

[@parrampampam]

Did you consider typing your solutions in Latex? Or even better in something like Coq or LEAN?

[@Jessica-kv2ob]

Love the proof of number 72 at 11:16 lol

[@jamiebaricaua4774]

I am a masters student and have to take my finals in real analysis. I want to do your challenge as well. This is good for me to grow as well.

[@johnnyq4260]

I strongly recommend that you type this up in Word as you do the proof, as I have been doing. Typing instead of writing is not as ridiculous as it sounds. It's not going to impede your thinking, and will make searching and organizing your work so much easier. Years later, you will be glad you did that.

[@galaxy5201]

Hi there, how do I prepare real analysis and abstract algebra for qualifying exam...please tell me the reference book and strategy.

[@zoommier8220]

What's beyond my comprehension apart from the mountain of analysis notes, is that how can you take so much notes and have no mistakes nor erasures?

[@davidskalak2908]

Your discipline is very impressive and inspiring. Graduate level math textbooks rarely present solutions for the exercises. I was wondering --- for those problems, how did you know your solutions were correct? Thanks and thank you for the video.

[@natnaelberhanu-i8w]

The fact that I passed this class is beyond me. I took the first part of this class fall 2018 got a D retook the class next fall with the same professor got a B- and then I took the second part of the class with the same professor and passed with a B. I remember the first exam I took for the second half of analysis I took it in a separate room from the students for extra time and my classmate told me what questions were going to be on the exam so I studied those questions before the exam. I got a 38/50. Not bad. I did not have a clear understanding of the proofs but the thing was my professor’s lecture proofs would end up being similar to the exam problems just with a different inequality or they would be the same exact problems as appeared on the exam so if you studied the lecture notes you might have passed the exams. Also, if it wasn’t for chegg solutions, my HW scores would’ve been piss poor.

[@asalamkamal6365]

We need determination and patience

[@hkrish26]

Please scan them and put them for public. Thanks

[@rsmith31416]

"I'm kind of a dreamer, I'm an optimist... and even like 5 minutes before they gave the test, I was like "I haven't failed yet". I will know if I fail as soon as they hand the test out to us and then they handed me the test "Okay I failed"" - Struggling Grad Student, 2023 😛😛😂😂😂

[@onlyonecjb001]

Fabulous videos despite the Mathematics is at a much higher level than I know. Still appreciate it though. What I find rather puzzling is why your instructor makes things so difficult to pass. Granted, people should not pass just for turning up but for all your Graduate students to fail a test seems to me to be very odd indeed.

[@ActuarialPost]

This is impressive and motivational.

[@devjyoti5614]

I am in Bsc i have come through this type of problems and it's nice to see। Btw I use bartle shebert and SK mapa

[@erickibernonsantos]

Could you scan this and publish for us here?

[@schrodingerscat7218]

I wish somebody would do this for GR, I have so many questions but especially some answers I would love to check. Like all the questions in Carroll.

[@afzalsoomro7950]

Wow . Impressive man.! I wanna do same with Algebra (Homological Algebra, commutative Algebra, Algebraic geometry, representation theory, Category theory etc) . Will you give me some advice

[@PhDVlog777]

Start with really easy problems that require little effort and gradually build up. And don’t be afraid to just look stuff up on the internet.

[@afzalsoomro7950]

@@PhDVlog777 Oh okay i understood. I will follow this. Thank you so much

[@Leo-uy6ok]

Thanks you for putting my thermo class into perspective😂

[@jacobmanning7983]

Would you mind mentioning which website you used to find analysis problems?

[@savageazn69]

I'm wondering how you stay organized without using actual notebooks... just looks like notepads all over the place lol

[@peterzeman2749]

Hi, that is quite a lot of problems. Do you have time to do any research? For me, PhD was mostly about research. By the way, have you considered using an iPad (or different tablet)? You could have all the notes and solutions in one place.

[@parrampampam]

How do you make sure you're not repeating an exercise? And when you come across an exercise that you suspect you've already solved, how do you look it up in your notes?

[@bedashrutiray8141]

Suggest me a book of real analysis where i find these types of problems and some answer soluyions

[@mattm9069]

Do they let you take the test as many times as possible?

[@joelwillis2043]

No, they show you the door.

[@Gaiwwie]

Is this useful for Data Science?

[@douglasstrother6584]

That's impressive!

[@mattm9069]

Looks like you already woke up from your spring break hibernation.

[@AndreusBins]

Can you share your p-set without the answers by chance?

[@chamocudno]

Where can you get those type of notebooks?

[@ToriKo_]

Good video thank you for posting

[@trs80model14]

Hang in there! Not uncommon to fail a prelim or two!

[@andreab6053]

DId you just copy the solutions or actually solved them that cleanly on the first try? it usually takes me multiple attempts to solve even a simple exercise 😂

[@barryram2605]

That's way more problems than Jay-Z had

[@feram3]

qualifier for what?

[@Ramanarajacademy1986]

Thanks Sir

[@calculus8399]

What book would you suggest for real analysis as a beginner

[@PhDVlog777]

Real Analysis by Bartle and Sherbert

[@Mahmood42978]

Are you at Mizzou?

[@InoceramusGigas]

Very inapiring video! I am an engineering graduate student transferring to an applied math graduate program in the fall, and have been self studying 14-20 hours a week im preparation. Keep up the good work

[@hamma-fm4wh]

Are these problems that you solved by yourself? before looking at a hint how much do you spend on an issue? thanks for your videos

[@PhDVlog777]

Most were exercises from text books that had solutions and examples. There were also old homework problems I had solved from from undergrad and masters level grad school. Others I had found on the internet. Others I had done solo.

[@69erthx1138]

The Paul Erdos of note taking?

[@williamschacht]

Lebesgue's framework!!

[@KartikayKaul]

I was failing theory of computation or I thoughtI was.... i still havent done space complexity part yet. I got a B. Dont ask how tf I got it.

[@wrathcs]

thanks

[@johnthelander1770]

This is a very difficult language to understand and learn, for sure.

[@broytingaravsol]

being tired of the number 10000

[@GabeDT567]

All this math hurts my brain.

[@bottlecap6169]

Why do you use pen?

[@revooshnoj4078]

10,000 is overkill lol

[@JaspreetSingh-zp2nm]

You are missing Royden in your stack

[@abdulmajidnematallah3357]

Do you ever take mechanics math

[@jagatacharjee3526]

Bro recommand some good Easy to understand , book on set theory for undergrad math stud

[@revooshnoj4078]

reminds me of grinding leetcode lol

[@AUSWQPCV]

Do 10,000 more and maybe you'll succeed this time

[@tear728]

Any comment on gpt4 proving math olympiad questions? I don't see why it couldn't be doing math beyond our ability in the "near" future

[@zakariatelmoudi2391]

well gpt-4 is humanity first AGI prototype lol

[@lordhenry2965]

Yes, we all will starve to death.

[@zakariatelmoudi2391]

@@lordhenry2965 we will end up suspended in gelatinous cocoons of liquified organic matter, with a sole purpose of generating Joules for the ominipotent machine. Farewll Lord Henry.

[@vaheakli4551]

I don't see why it could be doing math beyond our ability By the definition of how gpt works.

[@joelwillis2043]

um...large language models are terrible at logic

[@mihaihuluta2427]

How do you check the results for correctness?

[@PhDVlog777]

Many came with solutions. Other problems were old HW problems I had done. Mostly through internet searches but I have asked my instructors for help if needed.

[@alejandroromansanchez5368]

🥵

[@fahad_hassan_92]

I wish I could take BS Math but due to circumstances I have to take CS instead. I like CS too though

[@santafanta6108]

Okay but what is the point of that. We both know you're never looking at those notes, it just looks "nice".

[@PhDVlog777]

To git gud.

[@Singlton]

Do you have telegram or discord group?

[@Will-Ch]

wow 10 000 ?? really ?