9 ms·
Big Picture of Calculus (2010) [video]
- sandyjames 10y agoI'm making over $7k a month working part time. I kept hearing other people tell me how much money they can make online so I decided to look into it. Well, it was all true and has totally changed my life. This is what I do... http://bit.ly/2jdTzrM http://bit.ly/2jdTzrM
- deleted 10y ago[deleted]
- datainplace 10y agoNow 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 https://www.youtube.com/watch?v=j9WZyLZCBzs The Exponential Function https://www.youtube.com/watch?v=oo1ZZlvT2LQ&t=100s https://www.youtube.com/watch?v=oo1ZZlvT2LQ&t=100s Vector Space https://www.youtube.com/watch?v=ozwodzD5bJM&t=36s https://www.youtube.com/watch?v=ozwodzD5bJM&t=36s Tree cutting fails: https://www.youtube.com/watch?v=JHZkR6UVegY https://www.youtube.com/watch?v=JHZkR6UVegY
- quakeguy 10y agoThat last vid made my day, expecting nodes and splitting algorhytms. You clever you! :)
- mcguire 10y agoFor those of you who don't know, felling trees is incredibly dangerous. They store immense energy in a not terribly structurally safe form. Don't do it if you don't know what you are doing.
- datainplace 10y agoI remembering learning that the most powerful force acting on a building or tree was inertia. Watching videos like this makes that much more clear.
- nothis 10y agoMy dad always insists on cutting them himself and watching it always gave me a heart attack. That vid is basically what I play through in my head the whole time. So far nothing happened but man.
- deleted 10y ago[deleted]
- mindcrime 10y agoYoutube 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. :-)
- alphajulietmike 10y agoI'm learning linear algebra in tandem with Andrew Ng's - machine learning course on coursera. Challenging would be an apt description!
- mindcrime 10y agoYeah, part of my motivation for doing a lot of maths study is exactly that I took that Andrew Ng class. You can get through the class without knowing multi-variable calculus and linear algebra and what-not, but that class made it clear to me that learning that stuff would be hugely beneficial.
- flor1s 10y agoCheck out Linear Algebra: Foundations to Frontiers (https://www.edx.org/course/linear-algebra-foundations-frontiers-utaustinx-ut-5-05x https://www.edx.org/course/linear-algebra-foundations-fronti...), it's being offered self paced by edx, and you can download the lecture notes for free at http://www.ulaff.net http://www.ulaff.net. When I took the course two years ago I liked how the lecturer will discuss basic concepts in the lectures but also gives additional material related to state of the art research being done in the field. There also used to be a course called Coding the Matrix, I'm not sure if it is still being offered online. The lecture notes form a book of the same title, which is available for less than 10$ (Kindle).
- 40acres 10y agoHey 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.
- agumonkey 10y agoI take more pride/pleasure by understanding through reading. Somehow I don't trust my brain not to go into a visual form of rote learning by replicating what the video said. Books are a bit more painful, but forces my brain to actually make sense of abstractions actively instead of passively (which is not always the case on videos, but a lot more probable). Also, libraries are a good place to reflect.
- seycombi 10y agoIf you want to get into the details of Calculus Professor Leonard https://www.youtube.com/user/professorleonard57 https://www.youtube.com/user/professorleonard57 Herbert Gross MIT Calculus Revisited: Multivariable Calculus https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B https://www.youtube.com/playlist?list=PL1C22D4DED943EF7B Herbert Gross MIT Calculus Revisited: Calculus of Complex Variables https://www.youtube.com/playlist?list=PLD971E94905A70448 https://www.youtube.com/playlist?list=PLD971E94905A70448 Herbert Gross MIT Calculus Revisited: Single Variable Calculus https://www.youtube.com/playlist?list=PL3B08AE665AB9002A https://www.youtube.com/playlist?list=PL3B08AE665AB9002A MIT 18.02 Multivariable Calculus, Fall 2007 https://www.youtube.com/playlist?list=PL4C4C8A7D06566F38 https://www.youtube.com/playlist?list=PL4C4C8A7D06566F38 MIT 18.02SC: Homework Help for Multivariable Calculus https://www.youtube.com/playlist?list=PLF07555F3CC669D01 https://www.youtube.com/playlist?list=PLF07555F3CC669D01 MIT 18.01 Single Variable Calculus, Fall 2006 https://www.youtube.com/playlist?list=PL590CCC2BC5AF3BC1 https://www.youtube.com/playlist?list=PL590CCC2BC5AF3BC1 MIT 18.01SC: Homework Help for Single Variable Calculus https://www.youtube.com/playlist?list=PL21BCE50ABFF029F1 https://www.youtube.com/playlist?list=PL21BCE50ABFF029F1
- diimdeep 10y agoHerbert Gross MIT Calculus Revisited - is one of best lectures I have seen, and it is recorded way back in 1973.
- Meegul 10y agoProfessor Leonard is really great if you need some extra help learning something. He moves slowly enough with the material that it's difficult to get left behind, however that might be too slow for most HNers.
- mindcrime 10y agoSecond the recommendation for Professor Leonard. He does a really nice job explaining things and making it accessible.
- santix 10y agoI would also add these great lectures by Theodore Shifrin: University of Georgia - Math 3500/10: https://www.youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujGcvumjCFPHbrd https://www.youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujG...
- alfonsodev 10y agoThank 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 https://www.khanacademy.org/exercisedashboard
- GregBuchholz 10y agoLike a mind map? https://www.freeplane.org/wiki/index.php/Main_Page https://www.freeplane.org/wiki/index.php/Main_Page
- hyporthogon 10y agohttps://arxiv.org/abs/gr-qc/9704009 https://arxiv.org/abs/gr-qc/9704009 p2 (fig1) is pretty nice
- Miserlou57 10y agoI 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 to the top
- loblollyboy 10y agoI just had that idea this weekend - also like a github branch-diagram of math/physics history
- brightball 10y agoWhat 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.
- brootstrap 10y agoSay you want to measure how much energy is hitting the top of our atmosphere in a given day? Triple integral from infinity (the sun) to top of the atmosphere (call it 0). Examples with classic physics problems are good too. How about F=ma => F=m*dv/dt. Everytime you apply a force to an object calculus magic is there to mathematically describe the process.
- jhck 10y agoIn a book review from 1988 [1, p. 892] the mathematician Underwood Dudley claimed: > First-semester calculus has NO applications. That said, the central ideas of calculus are firmly grounded in daily life (as Strang points out in the video): Differential calculus is about investigating speed (or, more generally, rate of change), and integral calculus is about investigating area. [1]: http://www.maa.org/sites/default/files/0002989051112.di991736.99p03667.pdf http://www.maa.org/sites/default/files/0002989051112.di99173...
- SomeStupidPoint 10y agoThrowing things is estimating calculus: you pick the velocity to counteract the accelerations the object experiences to get the displacement you desire. Acceleration from air resistance is a function of velocity. Also, you can measure boobs with integrals and model their jiggle with differential equations. ...I may have been a teenager when I was first learning. But modeling boob motion is apparently serious science and actually gets extremely complex when you try to model the interactions of the different constituent tissues.
- umanwizard 10y ago"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.
- pknerd 10y agoThanks 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.
- billyzs 10y agoGilbert Starng also has an excellent series on Linear Algebra on MIT opencourseware [https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...]
- mrcactu5 10y agoI was a teaching assistant at UC Santa Barbara for 3 years, I can tell you, students might slug through the calculations , but none -- or a precious few -- really get the big picture. Mostly, it is that calculus pedagogy is a disaster. And it hasn't been updated to include recent advances in technology (such as Data Science) Strang is an amazing lecturer. I can tell you, that far into your Masters and PhD these same basic issues resurface. There's at least one project I can think of where the entire problem hinges on taking one derivative.
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- stephengillie 10y agoHaving had a non-traditional route through learning various math topics, I'd like to advocate the teaching of calculus (the understanding of the accumulation of infinitesimally-small changes) before the teaching of trigonometry (the relationships between different geometric shapes, and the resulting association with waves). In my (humbly biased) opinion, it's easier to learn how trigonometric concepts operate with a calculus background, than with merely an algebra-and-geometry background. Trigonometry complicates calculus education - knowing trigonometry may facilitate better calculus understanding to some, but not knowing trigonometry doesn't necessarily complicate learning calculus concepts. The trigonometry-first tradition in math education reflects a "number-phile" bias, not the most optimal route for humans to ingest and retain concepts. Edit: The "number-phile" bias is clear - we want our teachers to be people with passion on the topic, as we're more likely to get a better understanding of the topic. Understanding sine waves as the result of an integral was much easier for me to understand than as the result of a complicated calculation.
- jacobolus 10y agoIt’s somewhat misleading/unfortunate to use angle measures as the basic characterization of an angle/rotation, when just trying to solve basic geometry / triangle measurement problems. It’s almost always easier to use a vector representation, written in terms of explicit coordinates if necessary (e.g. as a complex number). http://www.shapeoperator.com/2016/12/12/sunset-geometry/ http://www.shapeoperator.com/2016/12/12/sunset-geometry/ Where angle measures and sines/cosines start to be useful is with uniform circular motion, which as you say is a calculus problem. The key to understanding the form of trigonometry courses is to understand the context for their creation. Namely, all calculations (e.g. for astronomy, navigation, engineering, mapmaking, ...) used to be done by hand by humans, which was very expensive. It was important to have someone with fluent knowledge of trigonometric identities simplify formulas to a form with as few arithmetic operations and table lookups as possible to save money, or just to match the available function tables. Today in a computer age, extensive memorization of trigonometric identities is an anachronism, and spending lots of time on practicing their manipulation is okay algebra practice but not anything directly useful per se.
- effie 10y ago
- huangc10 10y agoI 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 down, think, and understand.
- adeledeweylopez 10y agoKeisler has a introductory text book (available free here: https://www.math.wisc.edu/~keisler/calc.html 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.
- rahimnathwani 10y agoLooks similar to this book, which I bought after a recommendation here: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mathematics/dp/0486428869 https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Ma...
- peetle 10y agoI love Gilbert Strang, but _by far_ my favorite book on calculus is "Calculus Made Easy" by Silvanus Thompson. It supplies a very elegant and powerful set of tools to derive many of the "fundamentals" of calculus.
- shaftway 10y agoHonestly I couldn't slog through the video. It started off with "let's use letters" and immediately got to things like "the right letters for this case are 'df' and 'dt'". This just feels like "here's a bunch of magic that you'll just have to memorize". Reminds me of my favorite quote: > And then Satan said "put the alphabet in math". When I learned the basics of calculus it was via simple problems that we wanted to answer. And for a while we estimated the answers by brute forcing approximations. I still drop back to this when I can't remember how to do something and need to re-discover parts of calculus.