Earlier quoted context omitted.
"Calculus" by Tom Apostol has lots and lots of simple physics applications. I cant think of any obvious applications of calculus to the average non-technical person's daily life. If that's what you mean, you're going to have a bad time, as I think it's a misconception of what math is supposed to be for.
Well, there's plenty of applications that may not be "daily life" but rather "you're likely to encounter this at some point". Take the relation between speed and distance traveled, or the difference between marginal cost and per-unit cost.
Big Picture of Calculus (2010) [video]
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Re: Big Picture of Calculus (2010) [video]
#52Earlier quoted context omitted.
I'm going to expand the definition of "daily life application" from things you actually use daily to things you experience daily. These could be engaging too! For example... what are sunspots? How does the plumbing around your house work? How does a car battery work? How does a microwave oven work? Another thought. If we are unable to find applications for a technique, should we place such an emphasis on teaching it?…
That's kind've where I was going with it. Basic understanding of the building blocks of society type stuff: power, water, gas, construction, radio, biology, growing food, vehicles, finances, etc. Thinking back, I just realized the main reason that I was bored to tears in high school wasn't so much that the subjects weren't worth knowing...just that at the time I was being taught formulas without any clear understandi…
Additionally, I think game development is a compelling way to teach math and science.
Re: Big Picture of Calculus (2010) [video]
#53Earlier quoted context omitted.
I'm going to expand the definition of "daily life application" from things you actually use daily to things you experience daily. These could be engaging too! For example... what are sunspots? How does the plumbing around your house work? How does a car battery work? How does a microwave oven work? Another thought. If we are unable to find applications for a technique, should we place such an emphasis on teaching it?…
That's kind've where I was going with it. Basic understanding of the building blocks of society type stuff: power, water, gas, construction, radio, biology, growing food, vehicles, finances, etc. Thinking back, I just realized the main reason that I was bored to tears in high school wasn't so much that the subjects weren't worth knowing...just that at the time I was being taught formulas without any clear understandi…
https://www.grc.nasa.gov/www/k-12/airplane/index.html
Obviously, it could use more work, but the kernel of something really good is there.
Re: Big Picture of Calculus (2010) [video]
#54I find that most people understand the general concepts of basic calculus. What's hard to wrap around is when you start getting into proofs (ie. delta-epsilon, trig, e,...and that's just some general ones). I suppose that's how they differentiate the good students from the just okay students. Personally, I don't think youtube videos will help that much when it goes down to the nitty gritty. You really have to sit dow…
I can't say how effective it is at that goal, but it is all mathematically legitimate, and has a nice intuitive appeal to it.
Re: Big Picture of Calculus (2010) [video]
#55What would be some practical "daily life" applications of calculus? I've been discussing a focus on teaching with applicable examples in a lot of subjects, but this is one where I've been struggling a bit.
Re: Big Picture of Calculus (2010) [video]
#56Thank you for this video, is there a platform that you could aggregate all this resources mapping them to certain knowledge tree ? So that you could have the big picture and then zoom in for specific topics videos. Something like Khan Academy's knowledge map[1], that you could customise to add you own contents, this video for example. [1] https://www.khanacademy.org/exercisedashboard
I worked pretty hard on something like this many years ago. I am not a coder so it was a formidable challenge and I never really got it polished or complete. The goal was to create a blank canvas where anyone could organize instructional content from the web (i.e. KhanAcademy, YouTube, etc) into their own class. Each class topic was structured like a subreddit for each topic, with the best results hopefully filtering…
Re: Big Picture of Calculus (2010) [video]
#57Now I know someone is browsing my Youtube history and posting to HN. Youtube really is the math teacher I never had. Probability Models and Axioms https://www.youtube.com/watch?v=j9WZyLZCBzs The Exponential Function https://www.youtube.com/watch?v=oo1ZZlvT2LQ&t=100s Vector Space https://www.youtube.com/watch?v=ozwodzD5bJM&t=36s Tree cutting fails: https://www.youtube.com/watch?v=JHZkR6UVegY
Youtube really is the math teacher I never had. Same here. I'm on a quest to run myself through the equivalent of a standard Calc I, Calc II, Calc III, Linear Algebra sequence, and I've managed to find great Youtube resources for all of those things (and more). It's times like these that you marvel at how awesome the Internet can be at its best. :-)
Re: Big Picture of Calculus (2010) [video]
#58Earlier quoted context omitted.
Youtube really is the math teacher I never had. Same here. I'm on a quest to run myself through the equivalent of a standard Calc I, Calc II, Calc III, Linear Algebra sequence, and I've managed to find great Youtube resources for all of those things (and more). It's times like these that you marvel at how awesome the Internet can be at its best. :-)
Hey I'd love to hear about how your learning experience is going! Care to share your experiences? I'm about to start a self-directed learning exercise focused on CS related math. I've never used online resources to learn / brush up on complex topics before so I'm a bit unsure what to expect.
I only took through Algebra II in high-school, but honestly, I went to Algebra II class maybe 4 or 5 times all year, never did any of the homework, and took maybe 1 test. Needless to say I failed it. That was the year I was too busy being "mr rebel badass guy" to worry about studying, plus I didn't need the class to graduate, so I just didn't give a flip. OTOH, I did really well in H.S. Geometry the year before.
Anyway, when I started college I needed some maths refresher, so I took 2 semesters of College Algebra, and 2 semesters of Pre-Calculus. I also had a 1 semester Discrete Math class. I started Calc I but I dropped out about halfway through that semester.
Fast forward about 6 or 7 years, and I decided to go back to school. Having forgotten all the maths stuff I had learned before, I took College Algebra yet again, as well as Discrete Math (I don't remember now why I took Discrete again. It might be because my earlier credit was too old to transfer).
Fast forward another 7 years or so, and I've again forgotten what maths I'd learned before. But by now Khan Academy exists and that's where the online stuff kicks in.
So I've fiddled around on KA a bit over the past few years, just trying to keep up some of the really basic algebra stuff that you forget if you don't use (rationalizing denominators, factoring, etc., etc.) But that was always kind of hit or miss and piecemeal, not really a focused thing.
Fast forward just a hair more and Coursera and the like have come into being. I started taking the Johns Hopkins sequence on Data Science, and I also took the Andrew Ng class on Machine Learning. That whole experience reminded me "I've always meant to get serious about this maths thing".
Notably I'd never taken a proper course on statistics and probability, so I wanted to fill that gap. So on Coursera I took the first 2 or 3 classes in that Duke "Statistics With R" sequence (I plan to finish the whole thing eventually) to pick up some basic stats knowledge. It also dovetailed well with the first few classes in the JHU Data Science thing, as both use R. And looking back on that, from where I am now, I highly recommend both the Duke sequence (which is more about the stats and less about R) and the JHU sequence (which is arguably more about R than stats). I think they complement each other well, and if you do both you'll learn a decent amount about basic stats.
This is also where I discovered Professor Leonard on Youtube. I was searching for some stats videos to complement the other stuff I was doing, and found his videos. I never did go through the entire Stats class he put up, but I was impressed enough with his teaching style to bookmark his channel for future reference.
Anyway, at some point I hit a lull in things and decided "now is as good a time as any to go back through Calc I with an eye towards working through all of Calc I, Calc II, Calc III and Linear Algebra". I started the MOOCulus course on Coursera, and while I like certain things about it, I feel like the content is too "choppy" since it's broken up into such short segments. That was when I went back to the Professor Leonard channel and started going through his Calc I class. And I'm just now about up to where I was at when I dropped out of school the first time. Only 20 years later...
Anyway, there was other stuff mixed in there too, including offline stuff with actual paper books. But as far as the online stuff goes, I also found Youtube channel called MathBFF that has some really good videos (at least for Calculus topics), and I also watched a chunk of the "Big Picture of Calculus" videos linked to above.
So from here out, my plan is to continue through the Professor Leonard series of Calc I, II and III (and supplementing the videos with problems from dead-tree books) and then move on to Linear Algebra, probably using a combination of Gilbert Strang's videos and the "Essence of Linear Algebra" ones that were posted on HN a couple of days ago. I might also consult the Khan Academy videos on some of this stuff.
And to go back to dead-tree books for a minute... I have this weird obsession with mathematics books. I kindof collect them. I guess because in the back of my head, all these years, I've had that "I'll get serious about maths one day" thing going on. So I'm forever buying maths texts at used bookstores, or on Amazon, or random places. I have shelves and shelves of books on all sorts of mathematics stuff to consult. So my self-learning definitely involves a heavy dose of both online resources and meatspace stuff.
If I had to summarize, I guess I'd just re-iterate that the resources you need to learn a LOT of maths is available online, mostly for free. I mean, there's a TON of stuff out there, including a lot I didn't mention above. And even though I'm mainly interested just in the stuff I need to for AI/ML, I did some poking around on Youtube out of curiosity and found that you can find videos on just about every math topic there is: abstract algebra, complex analysis, topology, group theory, measure theory, etc., etc. It really is an amazing time we live in. :-)
Re: Big Picture of Calculus (2010) [video]
#59I find that most people understand the general concepts of basic calculus. What's hard to wrap around is when you start getting into proofs (ie. delta-epsilon, trig, e,...and that's just some general ones). I suppose that's how they differentiate the good students from the just okay students. Personally, I don't think youtube videos will help that much when it goes down to the nitty gritty. You really have to sit dow…
Keisler has a introductory text book (available free here: https://www.math.wisc.edu/~keisler/calc.html ) that uses non-standard analysis, which he claims is easier for beginners to understand than the notorious delta-epsilon proofs. I can't say how effective it is at that goal, but it is all mathematically legitimate, and has a nice intuitive appeal to it.
Re: Big Picture of Calculus (2010) [video]
#60Thanks for sharing such an amazing thing. I am done with studies but should be helpful to understand it properly to teach my kids in future so that they just fill up pages with dy/dx without getting an idea behind it.
For kids I'm a fan of http://dragonbox.com/ and their http://www.dragonboxapp.com/ They do a pretty good job of teaching symbolic algebra to kids who don't yet know arithmetic.