Another great YouTube math guy is Eddie Woo. They’re recordings of him teaching high school math, and he does such a great job at engaging his class (and viewers).
There is a bit in a PG13 movie where the guys says "Do you know that unless you’re willing to use the R rating, you can only say the ‘F’ word once? You know what I say? Fuck that. I’m done." I think the same is true for `from X import *` and code quality.
PowerPoint is a decent tool for creating lightweight animations.
With the right use of tools like morph transition etc. one can achieve pretty decent looking or even professional looking animations of concepts.
I have also used PowerPoint to create web application wireframes, design concepts, Logos and website graphics, icons, repeating fill patterns, arbitrary vector graphics, etc.
I guess one strong point is how easily / widely available the tool is, and therefore even if you don't have the same machine with all your design tools, or don't have admin access to install them, you can still edit your work later easily.
I recently built a fancy excel sheet with lot of formulas for a quarterly process. Now I am having a hard time delegating that work. Having to hand hold the new person multiple times :)
the most important thing for me in his videos is how he strives to explain the topic from a first principles thinking perspective.
if i had someone explain linear algebra the way he does in his youtube channel, i would have enjoyed and absorbed it much better than I did during my classes. while the professors did a decent job in explaining linear albegra and its usefulness among various topics around us, they did a poor job at explaining how thinking about these topics from linear algebra perspective makes so much sense!
I'm amazed of the amount of great resources available to students today to learn complex topics. I'm not even that old (late 30s) but the only real resources available when I was in school were other textbooks. There were some math blogs but they were mainly focused on higher-level mathematics.
His visualization of the Fourier Transform[1] actually enabled me to understand the how it was happening behind the what was happening with one of the most used algorithms in computing.
In terms of simple word-explanations, I've always thought of it as taking a flat strip of LED lights (imagine the eyes of Battlestar Galactica Cylon robots), then sticking a nail through the center and then spinning it around.
Depending on how fast you spin it, the resulting blob-o-light will have different shapes. If it's a simple oscillation and you spin it at exactly the right rate(s), you'll get a straight line again, whereas pure chaos will always make round blobs.
As someone much more effective at learning though text than by watching videos, I really appreciate the creators who do the additional effort of publishing a written version.
I've watched a number of Penn's videos and generally enjoy them but they really seem to be targeted to the math major types. I have a BS and MS in electrical engineering which did require some high level math but not to the degree needed to fully grasp what he's showing. Nothing wrong with that but people without college math study are usually going to be overwhelmed.
Some of it requires study I think, so not like just watch the video and yep it makes sense, but using them as lectures while also reading other texts on the same subject.
His differential forms playlist is great. Goes well together with eigenchris' lectures on Tensors for Beginners, I think.
And I was an engineering major but took a lot of math.
Another excellent math youtuber is the mathologer. He has humor, great graphics, clear explanations, all while expounding on challenging topics. Here is a representative sample
https://www.youtube.com/watch?v=LFwSIdLSosI
Seriously, his explanations on topics go well beyond the lectures some of my professors provide and could probably benefit a lot of students if given as a resource... If only academia wasn't so distrustful of those outside their circles...
But he's not even outside their circles right? Doesn't 3b1b have a PhD? I can tell you at least that we watched some 3b1b videos in my university undergrad math classes last year!
That's so encouraging to hear, I would've loved uni maths with some high quality videos like his to watch, even if just for after class to reinforce the topics.
Wikipedia thinks he has a Bachelors from Stanford[1]. That said, I love his videos too. I started with The Essence of Linear Algebra[2], which is just fantastic and really shaped my intuition for the topic.
I'll be the first to admit this is a little odd. The logo is a loose depiction of my right eye color. It has what's known as "sectoral heterochromia", meaning there are different colors in different sectors, which in my case looks like 3/4 blue and 1/4 brown.
In the same way that many channels simply share their name with the author, a younger me thought that a more genetic signature might be neat. Plus, the channel is all about seeing math in certain ways, so it felt fitting. The name is just a reference to the logo, factoring in a desire for something deliberately weird-sounding that stands out.
Another YouTuber I really like is Another Roof [1] -- the videos on Golay codes [2] using an icosahedron, and sporadic groups [3] are fantastic. There are some objects in mathematics that have pretty elementary definitions that a schoolchild can understand, but have secrets-of-the-universe level stuff behind them.
The interesting thing is that one of the Golay codes is isomorphic to a mathematical object called S(5,8,24), which is the set of 8-element subsets of a 24-letter alphabet such that any 5 elements occur exactly once. And that this is very closely related to one of the Mathieu groups, which are finite and sporadic: exceptional objects in mathematics.
Could anyone recommend a calculous book with lots of exercises (and their solutions)?
3Blue1Brown videos are great, but they're more for building the initial intuition. I'm looking for something that I can practice to "get used to" calculous.
I did a lot of research on this at one point, and these are what I ended up going with and was quite pleased. You can probably find them cheaper at abe books or somewhere, I'm just linking amazon for the ease (hopefully amazon links are allowed)
I love learning the intuition behind math concepts, but when it comes to practical things, often you have to deal with unruly and ugly equations in which intuition plays little role. For instance, as much as I enjoyed his Fourier transform videos, when it comes to actually calculating the Fourier transform for arbitrary functions, intuition is outta the window; it goes back to pure calculations again. That’s the part of math that I hated the most-not the beautiful intuitions.
If you don’t have a good intuition for and understanding of the concepts, how can you know when it’s appropriate to cut corners / use various approximation techniques on messy data? Or how can you combine a bunch of techniques for real world applications without doing something nonsensical?
Good point. I see what you mean and I agree that having an intuitive understanding of math concepts helps us choose the right tool for the job, but as soon as that decision is made, intuition doesn't play much role anymore. I really wanted to think that intuition (or even learning about the history of various math concepts) would be useful somehow, but every time I would end up getting lower scores than students who would just memorize the formulae and were able to calculate things quickly.
Well, I think I know what your mistake is, because I made the same mistake for a long time before I realized the error of my ways.
Intuition and deep understanding is important, and you won't go far without it. It's arguably the most important thing. But memorization / "knowing" things is important as well, and if you avoid doing that completely, you're just like a two or three legged stool. You need both, for true mastery.
I can't persuade you of this on my own, but if you ever trust something you saw on the internet without proof, hopefully this is the one thing! Haha.
OT - 3b1b did an interesting video on the epidemic modeling [0] that shaped my thinking a bit on the lockdown and caused me to lose a few friends to argue against the prolonged lockdowns.
I believe he used the same technique deployed by major media institutions and health organizations.
Basically the interesting conclusion was unless you apply a very rigorous lockdown (CCP style) the virus ultimately spreads. All you’re doing is spreading the time. As in “flattening the curve”.
As some might recall the initial lockdown was proposed as a way to flatten the curve and allow the medical system to cope better by having a more gradual influx of patients. Which makes me think everyone promoting the initial lockdown understood its limitations and its objectives.
However, for what ever reason “control demolition” of the economy to make Trump lose the election or who knows why it turned into a long term lockdown.
I know this is a controversial topic, but it shouldn’t be. This is a clear case that the science of pandemic modeling suggested one path and for political reasons we were pushed to follow a course that caused a lot of damage, some irreversible, to the society.
Yes, basically everywhere lockdown started as a “flattening the curve” and then at some point became “everyone needs to be kept out of harms way until everyone is vaccinated”.
That isn’t an American experience it was the same almost everywhere lock down was initiated.
So I am not sure it makes sense to blame it on Trump haters.
It's pretty impressive. A lot of work goes into these videos.
My other favourite YouTube math guy is eigenchris. His tensor calculus series is legendary: https://www.youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBk...
In complete contrast to 3b1b, eigenchris creates his videos entirely in PowerPoint, which makes me laugh even as I type this.