4 ms·

These have been a great help in my self-learning already. They definitely fill a huge void in intuition building that rote-style-learning generally ignores. Tha

by bpchaps 11y ago

These have been a great help in my self-learning already. They definitely fill a huge void in intuition building that rote-style-learning generally ignores. Thanks! :)

vinchuco 11y ago
It is sad that Mathematics is often taught either as narrow examples that miss the big picture or abstract definitions which are more general but feel artificial. The best teaching often jumps back and forth between the two. Mathematics can be thought of a simulation of properties of the world inside people's brains which verify the result. Sadly, there's no shared comprehensive framework outside our brains for visualizing [1] and organizing all of it, since it's very flexible [2]. And thus most people miss out on experiencing the beauty of many results. I sometimes wonder if LaTeX augmented by context (and visualization) would help, and I wish Mathematica was open source to aid this. At the same time, we are faced with incompleteness results that put into question any formal organization of mathematics [3]. [1] https://vimeo.com/36579366 https://vimeo.com/36579366 [2] www.jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ [3] http://inference-review.com/article/doing-mathematics-differently http://inference-review.com/article/doing-mathematics-differ... Sorry for the long rant.
- JadeNB 11y ago
  > I wish Mathematica was open source to aid this. Rather than wishing for this that will not happen, let's work to make Sage, particularly SageMathCloud (https://cloud.sagemath.com https://cloud.sagemath.com), the lingua franca of CASs.
- bpchaps 11y ago
  I actually deleted a rant that completely says what you just said. I 100% agree. It's mind boggling how much intuition is available to explain maths. It oddly just... makes visual sense. It's "simply" an explanation of what's around us. Yet, when discussing it, <i>while learning</i> with math folk, it's usually met with "You don't have a degree" or "That's not a formal understanding of the definition, come back". It's completely exclusionary and killed much of my math passion until recently.
  - stuxnet79 11y ago
    It seems a lot of concerns about math pedagogy tend to be killed off with "you don't have a degree", "you don't have the math gene" kind of rhetoric which is a pity. I discovered I really liked math waay too late for my tastes and it was mostly because I was being taught math by people who didn't really know math.

by bpchaps 11y ago

These have been a great help in my self-learning already. They definitely fill a huge void in intuition building that rote-style-learning generally ignores. Thanks! :)

vinchuco 11y ago

It is sad that Mathematics is often taught either as narrow examples that miss the big picture or abstract definitions which are more general but feel artificial. The best teaching often jumps back and forth between the two. Mathematics can be thought of a simulation of properties of the world inside people's brains which verify the result. Sadly, there's no shared comprehensive framework outside our brains for visualizing [1] and organizing all of it, since it's very flexible [2]. And thus most people miss out on experiencing the beauty of many results. I sometimes wonder if LaTeX augmented by context (and visualization) would help, and I wish Mathematica was open source to aid this. At the same time, we are faced with incompleteness results that put into question any formal organization of mathematics [3]. [1] https://vimeo.com/36579366 https://vimeo.com/36579366 [2] www.jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ [3] http://inference-review.com/article/doing-mathematics-differently http://inference-review.com/article/doing-mathematics-differ... Sorry for the long rant.

JadeNB 11y ago
> I wish Mathematica was open source to aid this. Rather than wishing for this that will not happen, let's work to make Sage, particularly SageMathCloud (https://cloud.sagemath.com https://cloud.sagemath.com), the lingua franca of CASs.
bpchaps 11y ago
I actually deleted a rant that completely says what you just said. I 100% agree. It's mind boggling how much intuition is available to explain maths. It oddly just... makes visual sense. It's "simply" an explanation of what's around us. Yet, when discussing it, <i>while learning</i> with math folk, it's usually met with "You don't have a degree" or "That's not a formal understanding of the definition, come back". It's completely exclusionary and killed much of my math passion until recently.
- stuxnet79 11y ago
  It seems a lot of concerns about math pedagogy tend to be killed off with "you don't have a degree", "you don't have the math gene" kind of rhetoric which is a pity. I discovered I really liked math waay too late for my tastes and it was mostly because I was being taught math by people who didn't really know math.