So essentially, you have some balls, you pick some of them, the balls grow to 3 times their size, and the balls create a family.
@squeezy7252
9 ай бұрын
You got it
@SpartaSpartan117
9 ай бұрын
This dude
@MyOneFiftiethOfADollar
8 ай бұрын
So essentially, you have oversimplified.
@HeavyMetalShredder
18 күн бұрын
There has to be a better way to phrase that
@noalsono393
9 ай бұрын
Congratulations man! Great to see this perspective of the process
@courtcat339
9 ай бұрын
I believe the last math class I took was a statistics class in freshman year of undergrad… I definitely do not understand a thing about this test or any of these problems, but your passion for the subject keeps me watching! It comes out in how you speak about it - you love this stuff. Good for you, man.
@minzreis4522
9 ай бұрын
Thank you for sharing your experiences and congrats on passing! I'm starting my maths major next month so your channel reminds me to work hard and do my best 👍
@Gaurav-um4oh
9 ай бұрын
Congratulations, man!❤
@kobemop
9 ай бұрын
Congratz my man. I feel kind of curious of wanting to try those questions myself lol.
@OscarRamirez-jv2hj
9 ай бұрын
Congratulations!!!
@cui348
9 ай бұрын
Thankfully, I only have to go as far as Calculus 3 for my major, but I am extremely proud of your success and passion for math.
@user-zj2wj6oo3c
9 ай бұрын
Congratulations! Keep going
@Djentstructer
9 ай бұрын
I dig the whiteboard that's been in these past few vids!
@briangronberg6507
9 ай бұрын
Congratulations!
@dorukme
9 ай бұрын
Congratz man!
@akeccunkaq
9 ай бұрын
For 3, I would take compact neighborhoods (closed balls) of all the rational points in U, their union is U. The image of each compact is compact, and then f(U) is a countable union of compact sets so it is a Borel set.
@frootylupus
7 ай бұрын
Congrats!!
@TranquilSeaOfMath
9 ай бұрын
Congratulations and best wishes. Fun analysis comic.
@bobbyking2490
8 ай бұрын
Well done!
@sev9042
9 ай бұрын
HUGE CONGRATS
@researchchannel1767
9 ай бұрын
🎉Congrats🎉
@christophernieves1328
9 ай бұрын
This is amazing, I’m currently in my Civil Engineering curriculum taking courses such as CE Statics and Mechanics of Deformable Bodies. I only took math through calc 3, and then differential equations and linear algebra. Just watching your videos is insane to me, and I can tell you put so much time into studying and broadening your intelligence towards these topics , congrats! I can’t ever imagine learning what you’re learning!
@mr.sloppytaco69
8 ай бұрын
Yo CE gang
@BadAss_691
4 ай бұрын
All engineering is maths so you're no less , don't underestimate yourself.
@captainchicky3744
9 ай бұрын
Congrats!
@williamangelogonzales148
9 ай бұрын
Loved these videos even though I don't understand the problems😅
@zhangkevin6748
9 ай бұрын
great job man, nice.
@RedionXhepa
8 ай бұрын
Congrats, I came to check this thing after I saw your first video.
@Qolee99
9 ай бұрын
Congrats
@loc_real
8 ай бұрын
lets go congrats man
@priyanegi2102
9 ай бұрын
Congratulations. I just came across your channel. I am a freshman in math major in an undergrad.
@KingOfSwedenIII
9 ай бұрын
I have zero interest in pursuing a PHD in math but I like this guy so I’m subscribing 🤣
@troybird8253
8 ай бұрын
You should input your information into an a.i. Prompt and charge for the file used in a compiler.
@etonalexandria341
9 ай бұрын
congrats
@0Clappy
9 ай бұрын
Congratulations on passing the exam. Would you mind throwing a video together really quick for number 5 on the real analysis?
@lugia8888
7 ай бұрын
bn is bounded on that interval so since an converges you can use ratio test
@robertschumann6977
9 ай бұрын
For 2. b): Assuming that a_k -> 0 (otherwise just set f_k = a_k) a typewriter-like sequence should do it, i.e. in the first iteration pick some n s.t. sum_{k = 1}^{n} a_k >= 1 and set f_1 = 1_[0, a_1], f_2 = [a_1, a_1 + a_2], ..., f_n = 1_[...] * 1_[0, 1]. Continue in this fashion so that f_k(x) fails to converge for any x. Just like a typewriter, the indicator function wanders from left to right along the interval over and over again.
@AshKetchumAllNow
7 ай бұрын
I don't agree with what you wrote but I think you have the correct idea. Let S_1 be the first time the partial sum is greater than 1 (so it is for the n you found). Then, the trick you did works until then: define f_1 = 1_[0,a_1], and f_k = 1_[summation until k_1, summation until k] (so that the interval length is a_k). For f_n, we can do the same thing, and notice that since summation k=1 to n goes outside [0,1], the interval is smaller than a_n, so the integral still holds. For f_(n+1), we should continue as before, but make sure to subtract S_1 (to map back into [0,1]. Eventually, we will go above 1 again, and have to subtract S_2, etc. There's no need to multiply by 1_[0,1] since the f_ks are defined only for that interval anyway.
@AshKetchumAllNow
7 ай бұрын
I think there should be a cleaner way to do this
@researchchannel1767
9 ай бұрын
Hey man any tips or advice how can i get into a IMO team and also how to learn Combinatorics, Geometry, Algebra and Number Theory fast lol like any website that is challenging and yeah worth it
@mikakee5154
9 ай бұрын
holy shit, congrats
@Scriabinfan593
Ай бұрын
I laughed every time he said balls.
@Qq-lp5xg
9 ай бұрын
fucking love your videos
@jonathangallagher3116
9 ай бұрын
Hey man... Congratulations... Not many people in your life will understand what a great achievement this is, but trust that we in the comments acknowledge the significance of such an accomplishment! All the best,
@jamesromano3288
9 ай бұрын
At the end of the week he will be broke AF..papi.....
@jonathangallagher3116
8 ай бұрын
@@jamesromano3288 you clrarlh don't know anything about job opportunities for math PhDs, cope + brainlet
@miraculous4104
7 ай бұрын
However he will be broke with a Phd while you will be broke without an education @@jamesromano3288
@paulcatterson1732
9 ай бұрын
congratulations! I've really enjoyed the videos you have been posting but I'm wondering what it is you want to do after you PhD, or have you not thought that far down the line.
@jamesromano3288
9 ай бұрын
He will be working at Home Depot, papi.
@orang1921
5 ай бұрын
@@jamesromano3288 why are you commenting so much about this guy going broke? why a random math phd student of all people? you're weird, man.
@OverwhelmedUndergrad
9 ай бұрын
Go Golden Flash!
@vqsilly
9 ай бұрын
this guy is the sam sulek of maths
@nilo866
9 ай бұрын
Lmaooo what a comparison
@joelfalco8735
9 ай бұрын
Every time the teacher said Balls in class, my whole friend group would start laughing. You wouldn't think we're math students lol
@joelfalco8735
8 ай бұрын
@@MyOneFiftiethOfADollar we're respectful and get good grades. having a little fun doesn't hurt anyone
@MyOneFiftiethOfADollar
8 ай бұрын
@@joelfalco8735 when you laugh at such crass humor as a reference to testicles, you are asserting your entertainment is more important than interrupting class. Save those type of jokes for your weekly circle jerks with your friend group clowns. Cheating is so widespread these days that reporting good grades is not particularly noteworthy.
@Dark_Souls_3
7 ай бұрын
@@MyOneFiftiethOfADollarno
@orang1921
5 ай бұрын
@@MyOneFiftiethOfADollar you're weird, man
@Youssef-Abotaleb
9 ай бұрын
What do you want to work after finishing your studies , like afyer your PhD and after you have evry certificate you want which field are you going to work in ?
@neerajnongmaithem392
9 ай бұрын
By the sound of it, I think he might continue to be academics as prof and continue with his post doc research
@Cyclically
7 ай бұрын
Interesting
@_mario_2985
9 ай бұрын
How much time did you get for these 5 questions in real analysis? Over 7 hours seems too much for me...
@kirkpetersjr
9 ай бұрын
I'm taking math grad RA right now, and these questions seem decent. I was surprised to hear you say hour seven. 😅
@anshsehgal7043
9 ай бұрын
I'm soo early that the vid isn't even loading lmaoo😅
@Blahcub
9 ай бұрын
New to this channel. What are you studying for? Academia or what job prospects are you using this math for?
@jamesromano3288
9 ай бұрын
He will be working at Home Depot, papi.
@Itzak15
8 ай бұрын
For me it's shocking that this is not a take-home exam. Everything we do is take-home because that is how you do it in research
@agni961
9 ай бұрын
For no.5 I used the Abel summation formula and then show the cauchy condition is true(by suitable bounding)....I think it works can someone verify?
@kelvinhoria5127
9 ай бұрын
yes. I think the key idea is to use Abel summation formula.
@robertschumann6977
9 ай бұрын
Yup, I got the same. I assume you meant using the integral test to show that `sum n^{-1.5}` converges (we need that sum |1/b_k - 1/b_{k + 1}| converges)
@agni961
9 ай бұрын
@@robertschumann6977 I rechecked my work..my bound for |1/b_k+1 - 1/b_k| was ugly...sum of 1/n^1.5 works fine.
@bobbypesch5220
8 ай бұрын
where do you go to school?
@jamesromano3288
9 ай бұрын
If I want to learn calculus,,,,,is all that trig stuff really needed, papi ?
@tiwariabhinay868
9 ай бұрын
Yeah it's building block, trig with you mean trigonometry na?
@dinglerdangler
9 ай бұрын
balls 1:23 , 1:26, 1:28, 1:38, 1:44, 1:52 , 1:55
@joelwillis2043
9 ай бұрын
standard for analysis but whatever
@dinglerdangler
9 ай бұрын
you think people who enjoy the simple pleasures of "balls" don't know analysis? how very assumptionous of you willy
@aleksandrb4635
9 ай бұрын
the *union* of the balls
@Devesteter252101
9 ай бұрын
@@joelwillis2043 pee balls
@user-ke5ux3sg4s
9 ай бұрын
Hey, im a second years math student (bachelor). Taking (real) analysis 2 rn and I feel overwhelmed by the proofs, do you have tips on how to study it? Also, would you be interested in reviewing my university's syllabus? They write the theory themselves and I feel like their expectations are a bit high for second years students.
@MyOneFiftiethOfADollar
8 ай бұрын
switch majors
@user-ke5ux3sg4s
8 ай бұрын
@@MyOneFiftiethOfADollar yeah im thinking of quitting math and cs and pursue a econometrics degree
@bennoarchimboldi6245
5 ай бұрын
Where do you go to college?
@user-ke5ux3sg4s
5 ай бұрын
@@bennoarchimboldi6245 Radboud University, the Netherlands
@jayloncarter7030
2 ай бұрын
Did you switch majors yet? If you made it this far to real analysis 2 then i’d say just stick with it. Re read and re do proofs over and over and over again.
@ethanbartiromo2888
9 ай бұрын
g(x) = f(x) + f(-x) is an even function if that matters?
@bedasrutiray1850
9 ай бұрын
Can you suggest me a good analysis book for problem. Solving?
@soyoltoi
2 ай бұрын
Pugh - Real Mathematical Analysis
@pak-keungdannychan3082
9 ай бұрын
For Q.3, it seems that we may try in this direction: Let $\{K_n \mid n\in\mathbb{N} \}$ be a countable collection of compact sets such that K_n \subseteq U and U = union of these compact sets. Then f(U) = \cup_n f(K_n), which is a F_\sigma set and hence it is Borel. I have not worked out the details for the construction of {K_n}. If the domain of $f$ is R, this is easy...
@CoolCatDoingAKickflip
9 ай бұрын
1:22 Haha, Bj 😂
@prempun5906
9 ай бұрын
hehe bawlz
@oo_rf_oo8824
9 ай бұрын
Is it that I'm delirium or 3 is probably the most easy one in the test?
@siddharthjain2127
9 ай бұрын
I'm assistant professor of mathematics I suggest you try question paper NTA CSIR MATHEMATICAL SCIENCE This is national Eligibility test in India for assistant professor certificate
@aryansaxena4978
9 ай бұрын
I tried to solve the third question for the case when n=m=1. If f is a real valued continuous fn. on R, prove that f(U) is Borel. Since U is an open set, we can write it as a countable union of disjoint open intervals, and since f is continuous it will map an open interval to some sort of an interval (maybe open, close, half-open, all of them are Borel that's what we care about). Therefore the image of U under f will be a countable union of intervals OR a countable union of Borel sets. Which is a again a Borel set. Is this the right approach?? How did you do it for general n and m??
@robertschumann6977
9 ай бұрын
Yes, that's correct for the 1D case (the rigorous argument would be that an open interval is connected and connectedness is preserved under continuous transformations, hence also its image will be connected and thus an interval). For the general case you want to argue by means of compact sets since compactness is preserved under continuous transformations. This means all you have to do is to show that an open subset of R^n can be written as the countable union of compact sets (e.g. dyadic decomposition).
@PhDVlog777
9 ай бұрын
@@robertschumann6977 this guy has it
@RandomGameClips27
9 ай бұрын
early view gang
@yanntal954
9 ай бұрын
These are easier than the exams I had as an undergraduate and we had way less time (2.5 hours for each exam) I am so confused 😢
@jeecrack3396
9 ай бұрын
Stop lying bro
@yanntal954
9 ай бұрын
@@jeecrack3396 That's most definitely not a lie, year 2 sem 2 here we have complex functions (which is complex analysis) and we go deep into this subject, we end up in conformal mappings and mostly talk about the Mobius mapping but also others. In year 3 sem 1 we have what we call "modern analysis" which is basically real analysis but we really go deeply into banach spaces and hilbert spaces as well of course measure theory. The exam had as question 1 literally to find a set of outer measure 1/2 that isn't lebesgue measurable and I think there was also a condition that it's in [0, 1] (I still have no idea what you were supposed to do there btw). Most integral problems in analysis you would use Tonellis theorem because its for some reason way more useful than Fubini for many problems and there were really difficult double integrals to prove things about using it!
@theflaggeddragon9472
9 ай бұрын
@@yanntal954What university?
@HopUpOutDaBed
9 ай бұрын
what was harvard like?
@magickauras
9 ай бұрын
At UofT i had exam problems that looked easy at first glance but ended up stumping me for an hour.
@robertgerbicz
9 ай бұрын
The fifth problem is quite trivial, without any integration: From convergence you have that for eps>0 there is N for that if n,p>N then |S(n,p)|
@uva1312
9 ай бұрын
worst math student is the one who uses trivial and trivially
@josephquinto5812
7 ай бұрын
“quite trivial” 🤓
@josephstalin5003
9 ай бұрын
Is this guy like Terrance Tao? I want to be like this how can I do this as quick as possible
@BboyKeny
9 ай бұрын
I think working through math books and daily practice. You can't really skip to much when talking about the fundamentals but after that all of math opens up for you. (pre-)Algebra -> Trig -> (pre-)Calc -> complex numbers. For analysis you need to know logic, sets and proof writing. Which is basically building math up from logic to proof the stuff you use in Calculus. There are many more subjects in mathematics but basically if you're doing Real Analysis and you understand the way of thinking then you are well equipped to tackle any other subject.
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