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Big Picture of Calculus (2010) [video]

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Re: Big Picture of Calculus (2010) [video]

#41

Post by mindcrime »

alphajulietmike wrote: post #34
mindcrime wrote: post #30

Earlier 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. :-)

I'm learning linear algebra in tandem with Andrew Ng's - machine learning course on coursera. Challenging would be an apt description!

Yeah, 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.

Re: Big Picture of Calculus (2010) [video]

#42

Post by flor1s »

alphajulietmike wrote: post #34
mindcrime wrote: post #30

Earlier 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. :-)

I'm learning linear algebra in tandem with Andrew Ng's - machine learning course on coursera. Challenging would be an apt description!

Check out Linear Algebra: Foundations to Frontiers (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. 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).

Re: Big Picture of Calculus (2010) [video]

#43

Post by espeed »

mindcrime wrote: post #30
datainplace wrote: post #4

Now 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. :-)

Have you seen the Essence of Linear Algebra video series posted to HN a few days ago? Seeing the geometric transformations animated gives you intuition hard to develop otherwise:

Essence of Linear Algebra (visualized) https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

Re: Big Picture of Calculus (2010) [video]

#44

Post by corysama »

pknerd wrote: post #15

Thanks 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.

Re: Big Picture of Calculus (2010) [video]

#45

Post by huangc10 »

I 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.

Re: Big Picture of Calculus (2010) [video]

#46

Post by GregBuchholz »

alfonsodev wrote: post #7

Thank 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

Like a mind map?

https://www.freeplane.org/wiki/index.php/Main_Page

Re: Big Picture of Calculus (2010) [video]

#47

Post by mindcrime »

espeed wrote: post #43
mindcrime wrote: post #30

Earlier 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. :-)

Have you seen the Essence of Linear Algebra video series posted to HN a few days ago? Seeing the geometric transformations animated gives you intuition hard to develop otherwise: Essence of Linear Algebra (visualized) https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

Yep. Watched the first 3 or 4 of those right after they were posted. Good stuff. I'm not really focusing on Linear Algebra yet, but definitely looking forward to digging into those and the Gilbert Strang ones on LA.

Re: Big Picture of Calculus (2010) [video]

#49

Post by espeed »

mindcrime wrote: post #47
espeed wrote: post #43

Earlier quoted context omitted.

Have you seen the Essence of Linear Algebra video series posted to HN a few days ago? Seeing the geometric transformations animated gives you intuition hard to develop otherwise: Essence of Linear Algebra (visualized) https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

Yep. Watched the first 3 or 4 of those right after they were posted. Good stuff. I'm not really focusing on Linear Algebra yet, but definitely looking forward to digging into those and the Gilbert Strang ones on LA.

The course that follows the MIT calculus course is "Differential Equations" (which is like applied calculus):

MIT Differential Equations: https://www.youtube.com/watch?v=ZvL88xqYSak&list=PLUl4u3cNGP...

Don't overlook mathematical analysis -- real analysis, complex analysis, etc -- that's another big leg of the mathematical stool, with geometrical foundations underpinning it all.

https://en.wikipedia.org/wiki/Mathematical_analysis

https://ocw.mit.edu/courses/mathematics/18-100c-real-analysi...

As you self-study and progress into upper level math, you'll come across abstract and unfamiliar topics you didn't learn about in calculus/algebra -- and sometimes it's hard to pin down what category the topic falls under -- when that happens, the topic will often be related to analysis, group theory, or topology (courses taken by math majors but not as widely known).

See http://nada.kth.se/~axelhu/mapthematics.pdf and http://space.mit.edu/home/tegmark/toe.gif

Crosslinks for all MIT courses: http://crosslinks.mit.edu/topics/?query=subject18.100

Re: Big Picture of Calculus (2010) [video]

#50

Post by jacobolus »

stephengillie wrote: post #38

Having 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…

It’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/

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.

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