Thank you so much for sharing this great work!

This is true.

One thing that is different for me is that the research and "supervisor dating" had started from day one. I think this is case for most phds.

Worst explanation.

This story is completely misreported. To actually understand the math theory read this article: "Is a Trigonometric Proof Possible for the Theorem of Pythagoras? " Michael de Villiers RUMEUS, University of Stellenbosch

Well done Ne’Kiya Jackson and Calcea Johnson!!!

In Germany we start with Analysis in the First semester and it realy is something else having switch from school math to proving everything.

This is .. my (currently only) video, but better.. I'm sad xD good work. Too bad I only saw it now.

Hey man I really like the mindset of exploring prioritized over prize! I took on the conjecture and found a pattern all sequences might follow!! Take the stopping time (iterations to get to 1) minus 1. Then, subtract the number of right triangles formed by the graph (the graph is my little secret approach) and you will always get a number that, if smaller than 6, can be multiplied by something to get 6, or if larger/equal than 6, can be divided by 6 with no remainder. The product of the points along the hypotenuses of the triangles multiplied in order also always equal a number that can be divided by 6 with no remainder. When an idea of mine failed, I took another from the fountain of ideas. Check each idea off if it fails one by one until you strike gold!

Do we really want to know how some random clown failed at a mathematical problem that is considered to be one of the most difficult in mathematics? No, really not! I'll make a video soon: "How I peed past the toilet..."

IF I did not did well in my Ordinary Differential Equation class, do you recommend to take this class in my senior year?

It should be noted at 6:49 that if exactly one of the denominators s2, t2 is negative then it does not hold that s < t implies s1t2 < s2t1. However, the lemma still holds because if exactly one of the denominators is negative, we can take the -(s2t2) root of the inequality b^(-(s1t2)) < b^(-(s2t1)), and the rest follows.

I tried to learn from the video, but still too hard for me, so I read the textbook you referenced. It was excellent, I understood everything from page 1 to page 15, which answered the exact question I have in mind. But on page 15, it says: "The minimum mean square error is given by those weights that result in zero first derivatives of the kriging variance." I would like to know if you can do a rigorous proof on this claim. Thank you.

surely you didn't use Dummt and Foote for first year algebra? :o

The best book by all means in rigorous one variable, is Understanding Analysis by Stephen Abbott. It has classical proofs (triangle inequality, etc), well motivated and historically intuitive, shows strategies and skrach work of proofs (how to choose an epsilon and when to split it, when contradiction proof is better than direct and vice versa, etc), 10 exercises at the end of each subsections (and not at the end of the chapters), etc. It is very good for self-study and can be read even without an intro to proofs class as Abbott aims also to introduce readers to proofs writing and rigorous intuition (recognizing what in a definition can be used to justify cases). The final chapter introducing more variables cases and metric spaces. And just 300 pages. No solutions, but Abbott explanations are so clear that you can see if you are in the good of bad way ; and as the cases are very classic , every maths forum can tells you if you are wrong or not. With Abbott you’ll "Understand" Real Analysis.

dude your understanding is deep. wow

Finally, someone who takes a deep dive into the mathematical foundations.

Its difficult to understand, i was learning about resonant frequency and got into this rabbit hole

School name, please?

sorry to be that guy, but is this appliable to a finite number of measurements, say, R^n->R measurements? I've been studying functional analysis since last week, and I skim ahead to know what I'm getting to. I read real analysis up to hilbert spaces which was very brief. But my final objective is in optimization and machine learning, I moved from the math department to the CS department of college, but I want to implement advanced math into my formation as I like analysis a lot which is why I like your channel. I was reading Rudin FA, very fun first chapter until I hit completeness, which was very, very boring and unmotivated, admittedly I skimmed it and went to the next two chapters that are much more interesting IMO. But then at some point it hit me, isn't this way too general? Why am I even considering topologies where the local base could even be not convex if data comes from finite dimensional spaces? shouldn't I be already moving into optimization and machine learning after linear algebra and basic analysis (like PMA)? I want to keep going and study applied Hilbert spaces and analysis like you do at some point, but for the time being I'm trying to get the best use of my time to get something going in the CS department. I'm gonna write an undergraduate thesis and I wanted to put some of my math background, at first I thought just linear algebra and basic analysis, then I got ambitious, learned measure theory, L^p spaces and basic hilbert space theory, but since I'm reading Rudin (I like his style), I'm blindfolded to the applications. Love your videos man

Work 16 hours a day?

The peer review process finished this week. They submitted 10 proofs.

Can anyone give me an insight on how to use these for image classification?

I appreciate that you don’t edit out the sighs, the complaints about the environment, and even the unlucky moments.

Thank you so much!

Excellent channel! Really top tier content and presentation!

I have 1 question. How can we prove cos(2x) = cos^2(x) - sin^2(x) without using Pitagore theorem in the formula sin^2(x) + cos^2(x) = 1

50:22

I may be wrong but the KART seems to work for functions taking inputs in the [0,1] range, have I understood correctly?

I watched over and over as I did when I listened to metallica's kill'm all for the first time 40 years ago ...

Oohhh ... go home folks ... go home ...

Congratulations

WHATS THE BEST MATHEMATICAL PROOFS TEXTBOOKS EXPLAIN CLEARY, CONCEP AND CONTEXT AS WELL DEFINE THE SYMPOLS OF PROOF WRITING THANK YOU

falling asleep with baby rudin is all too real

maravilloso!!

4:12 That was quite a surprise for someone, who has never taken functional analysis (and any pure math classes beyond some minor self-study for that matter). Would have never thought there are linear operators that are not continuous, let alone that derivative operator (such a familiar example!) would be one of them.

I used baby Rubin 30 years ago for learning topology. Can’t believe it is still the gold standard up to this day.

This could allow the training of lower parameter models, and then scaling it up by adding more spline points, effectively creating greater resolution in the neural network

So cool!

would you consider KAN similar to ANFIS?

kzbin.info/www/bejne/gpi4c2qYmLKEepI

Actually it doesn't make sense to solve your equation for general nx+1 Because n=5, x=1 you end up with 421 loop but for n=5, x=5 you end up with another loop (26,13,66,33,166,83,208,104,52)!

"Reflexive"? Are you saying that our study sessions should want to become equivalence relations? 🤣🤣🤣

How did students in proof-based math courses get by before proof-writing courses and texts were available?

The prof who said do not visualize proofs should be fired . I don't understand where he is coming from 😹😹😹😹

Dirac was very active at international seminars, more after 1928 and more still after 1933. His work was widely discussed pre-publication, not just by peer review. Hard to show exactly what the notation's reach was early 1939.

You sure bud?

damnn such a great video and explaination🤩🤩🙌🙌, but so less views😥😥

Really helpful. one more thing, is it helpful to approach the professors?

I thought this was a video on cutting teeths