16:56 At the bottom of the page, after taking the gradient, I then take the absolute value, and the -1 can be dropped after applying the triangle inequality. Other than that, I believe the estimates are fine provided the proper adjustments are made.
This video just gets in the right time for me. I am also pursuing a math phd and it is taking me some time to adapt. Being surrounded with so many smart students is sometimes frustrating and cant stop comparing myself. I have to accept that we have different strengths and weaknesses. My mentality is to learn about what they do and maybe take one or two techniques that will help strengthen my weaknesses. It is good to know that I am not the only one with this feeling and I have a lot to work on to become a more mature person and potential mathematician. Thanks for the video !!!!
Math is such a complex activity with so many pieces! Saying "I suck at math" is useless because you can't improve at "math", that's too abstract. Saying "I often make algebra mistakes when I'm not careful" or "My proofs are often not rigorous enough" or whatever points you in the correct direction. I'd say lots of people in academia also have the opposite problem of what you discuss: they suck at many aspects of math but no one is telling them because everyone is being too polite! Hence they wander around without making any self-improvement efforts, and at some point they hit a wall and can't find a job or whatever. The best case scenario is one where you can receive consistent criticism on your shortcomings from very smart people and improve on everything you're told little by little. It's very hard to improve by yourself, certainly harder than if you have good advice.
Hey, I don't normally comment on videos but I had just gotten back into school this semester after leaving years ago due to addiction issues. I'm in a introductory linear algebra course and thought I had studied really hard for my midterm (at least compared to how I studied in addiction.) Anyways I didn't get the grade I wanted and I've been really down on myself. This video helped me see that its just an opportunity to see what my flaws are and now use this time to prepare to correct those issues before my final, so thank you. .
reduction of ego can be awesome. I was (am) very insecure about myself in general, i could dish out friendly jokes and never mean it, but as soon as the same joke was pointed at me id get defensive by default. Realizing that and laughing at my own mistakes was a huge step forward! Love hearing about your journey man
You got to have guts to recieve and accept criticism . But problem is often there are many profs who'd make fun of you rather than giving constructive criticism .....
Thank you for this video - it's always good to hear that others, especially those who may have progressed more than oneself, have had to deal with issues that one is encountering right now. It truly helps, so thank you for it.
I don't know if there is one already but I kind of on this topic I think a Struggling Grad Student discord would be very helpful, especially for people on a self-study journey outside of institutions. Could one be set up relatively easily, or does it already exist or is there another one that people use?
do you have any original thoughts or conjectures that come to mind that you try to investigate when you are working out through the exercises of your books or understanding a certain proof of a theorem?
Well, usually when I an doing problems or proving theorem from a text book, I only try understand what the statement is staying and what tricks were involved in proving the claim. The conjectures typically come later when I am daydreaming and trying to come up with examples.
You wrote x,y in R, aren't x and y vectors in R^n ? Maybe this is a specific problem with n being 1 but I'm very unfamiliar with the use of the notion of "gradient" in this case.
a more familiar notation for what he's doing is estimating the partials ∂/∂x and ∂/∂y. so it's ultimately a estimation on the first derivative of K_phi in terms of information on K and phi
We all suck that’s the secret, as you said, it’s a collective effort towards something greater, some new discoveries, new ways to go further in math and science in general, no one knows everything and if you think you now enough there’s always a new way to interconnect different branches of science and humanities in general so big ups for your video it made me reflect in my personal life and also bug ups y’all keep working and keep getting better, enjoy the ride cuz it ain’t another one in this life at least.
"Sometimes the planets will align just to take a fat dump on ya" Well, if that aint the truth i dont know what is. That should be on a t shirt in your future merch collection.
This is a nice sentiment. I’m taking topology this semester and my professor has been really explicit in acknowledging that what we’re learning is difficult and/pr confusing and there is a period for every math student where you feel like you suck at math. I’m there especially after taking my first real analysis course and barely getting by but it gives me comfort knowing that this experience is universal.
Hey SGS, I love how you warm us up with anecdotes before getting into the technical disassembly of the proofs because it feels like you build for us a safe space to systematically go through challenging problems without the small "Give up because you're am idiot" voice that often perches on your shoulder that prevents you from using logic and reasoning to understand things step by step. Because of you and some other RU-vidrs, despite failing Math in high school, I'm now able to understand and follow along what gets discussed in these videos despite a lack of formal education. P.s. I do a lot of reading and free time study, and am gaining formal/informal learning via MOOC's and textbooks in prep for my MSc in AI coming this Sep.
Just flunked my Waves and Optics exam in physics. I'm used to getting A's. The exam revealed the truth, which is that I just flat out did not have a good grasp of several topics covered on the exam. So I needed to hear this. it's been painful to look over the graded exam, with all the red ink, and try to improve.
Hey, commented a while ago asking about if one exam goes particularly bad and I really appreciate your advice. The exam actually went okay (I passed) and they had to give people extra marks due to the difficulty of the exam. As for the rest, they went really well and I got one of the top grades in real analysis and I want to pursue analysis in the future. Again, I really appreciate the clarity and I continue to enjoy your videos!
I bumped into this after basically feeling embarrassed that I couldn’t figure out how to plot and calculate some data (pharmacokinetics) my friends got it and the way they figured it out was so creative but so hard for me to understand obviously proving their understanding. I felt so stupid and wanted to give up and didn’t want to submit the work which is due tomorrow because I didn’t want to face confusion and feeling uncomfortable with humility. Ever since starting this degree I have never felt so dumb and failed so much in my life that I basically pull myself into depression. Like you mentioned strengths mine is writing and reading not so much the actual application of math. I literally searched what to do when you feel crappy cause you don’t know math and this popped up. Honestly this really helped me cause 1 my mindset has changed 2 I finished the assignment even though it’s midnight I understand it now and managed to get through it even though it hurt to see my weaknesses right in front of me. So thank you for the video and the honesty you helped a stranger today👍.
You need to realize too that isolated incidents are a blip of your overall math ability (i.e., things like your example are close to meaningless). Everyone has good and bad days. Even people who are really strong at math have days where they feel like they are useless when trying to solve even some seemingly basic problems. It's a nonlinear journey.
did the constant 1 in 1-Lip matter? if it did, it was in the last T.M., but that part was a bit of a whirlwind. but i guess you probably you could've replaced the 1 by any constant either >= 1 or
could you contextualize your problems? they're interesting to watch, but i don't know where these estimates come from/why you care to make them. the only clue in this video is the (calderon-zygmund) on the side
I feel like with higher math its different because of how different proofs can be. In lower math you’re used to routine calculations/ideas and eventually learn some tricks, versus trying to squeeze Arzela’s theorem / Stone-Weierstrass theorem in some problem in Real Analysis. Completely different ways of thinking
You sound like a good guy. Please remember not to fall into the masochism trap of academia. It doesn't matter if you solve a problem or how long it takes as long as you are still enjoying the process. Being surrounded by smart people all day distorts your reality.
I have absolutely no idea what you are talking about in the math part, this is so far above my level, still interesting though. I'm like at, learning integrals so still pretty fun. Your stories were interesting!
Love your content, I generally enjoy Math and like learning about it intuitively. I bounce back from setbacks without a second's thought because I've learned to take feedback in accordance with what I do not who I am, I always welcome feedback but acting on it has been such a weakpoint. Since I've been in uni it takes me far longer to actually find a viable method or solution to a problem. There's this fatigue I have of even answering simple questions, I want to be better and I guess this comment is just me taking responsibility for my ignorance and laziness. Maybe my mindset is flawed, maybe I need to seek more clarity and maybe it was curiosity that fueled me in high school. Thanks nonetheless, your transparency is highly appreciated.
Although the problem was written in the video as it was given in class, it should have been stated that we can differentiate phi(x) with respect to x when taking the gradient. Or at the very least, we are only interested in the points (x,y) where taking the gradient wrt x exists. But you are right, it should have been stated.
