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Programming as a Way of Thinking

blogs.scientificamerican.com

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Re: Programming as a Way of Thinking

#111

Post by devoply »

shubhamjain wrote: post #5

> With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later. This is exactly how I understood it. Three years back, WebAudio API was a new addition in browsers and I decided I should make something with it. I settled on building a Whistle Detector using a ci…

I feel the same way about math and statistics. It makes much more sense if the knowledge is applied and makes it more interesting and worth learning.

Re: Programming as a Way of Thinking

#112

Post by j2kun »

bigger_cheese wrote: post #110

"With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later." The "Learn how they work later" part sends out alarm bells to me. I don't have a lot of confidence that students will be particularly motivated to dig into how an algorithm works after their proble…

Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and instead just translate pseudocode. I once had an interview where I was asked to explain why a piece of code (that the interviewer wrote) worked, because the interviewer did not know.

A benefit of the bottom up approach, of starting with the math and no reference implementation, is that you are less likely to implement it unless you understand it. And I should stress, these are tradeoffs.

Re: Programming as a Way of Thinking

#113

Post by aaachilless »

bryik wrote: post #105
aaachilless wrote: post #98

Earlier quoted context omitted.

In this case there's not really a naming problem either. The confusion comes from the idea that ((A -> B) && (A -> ~B)) is sometimes true. Capturing that subtlety in a name doesn't seem practical to me.

I'm not sure I understand. The problem with symmetric/antisymmetric is that the names make students think they are related and this can lead to misunderstanding (e.g. "since this relation is antisymmetric, it cannot be symmetric"). Arguably, this confusion would not exist if they were named differently.

I think maybe there's some confusion here regarding the definitions of symmetry and antisymmetry, because they're very closely related. Symmetry says "whenever A, then B" and antisymmetry says "whenever A, then not B". I.e, given a piece of information A, symmetry and antisymmetry tell you to draw opposite conclusions, which is why one is "anti" the other. The only time a relation can be both symmetric and antisymmetric is when the antecedent in their definitions is never true, which is the trivial case.

Re: Programming as a Way of Thinking

#114

Post by j2kun »

vlasev wrote: post #68
ccleve wrote: post #26

Earlier quoted context omitted.

I'm a software developer. I need to understand computer science papers to get my work done. I've studied enough. High school and several courses in college. Enough that I should be able to take it from here and learn on my own.

So let me get this straight...You are mainly a software developer who has an issue with math notation that is meant for mathematicians? Could it perhaps be that you haven't taken enough math to become in tune with how it's done/studied/read? I come from the other direction. I studied math first. And yes, at first I had an issue with the long variable/function names. But soon enough I realized that programming is done…

I agree. As someone who has done mathematics research, and studied on the purest end of the math spectrum, it's so aggravating to hear engineers who "took BOTH differential equations classes" explain how math should be when they clearly don't know what they're talking about.

Re: Programming as a Way of Thinking

#115

Post by markc »

ccleve wrote: post #22

This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong. In the software business we learned a long time ago to name our variables properly, name our functions logically, and to control complexity by breaking ideas into modules and then hiding the details inside. If you can't name something, then you don't know what it is, and that tells you that you should rethin…

Short variable names as "doing it wrong" depends on context. There are good reasons in math and in programming to use short names. See for example:

Descriptive Variable Names: A Code Smell. http://degoes.net/articles/insufficiently-polymorphic

Re: Programming as a Way of Thinking

#117

Post by neves »

neves wrote: post #116

BTW, the article author, Allen B. Downey, has a marvelous collection of free technical books: http://greenteapress.com/wp/

And in his books, he does what he prays: teach you complex topics using computer programs. I don't know if it is a good approach of the general population, but for us programmers, it certainly is.

Re: Programming as a Way of Thinking

#118

Post by tarlinian »

dragandj wrote: post #92
gbrown wrote: post #53

Earlier quoted context omitted.

Languages like Julia allow you to use greek letters. Just saying.

Doesn't any language that support Unicode allow that? Java for example. But, it's rather impractical to use, since greek letters are not that easy to type with English keyboard.

Julia's REPL allows for LaTeX like notation (e.g,. you can type \alpha to get the matching Greek letter), which makes it quite natural to use the Greek letters in places that make sense.

Re: Programming as a Way of Thinking

#119

Post by mtempm »

shubhamjain wrote: post #5

> With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later. This is exactly how I understood it. Three years back, WebAudio API was a new addition in browsers and I decided I should make something with it. I settled on building a Whistle Detector using a ci…

That's a very interesting comment to me because I may be perhaps the opposite. I got a slow and frustrating start learning application development--I wasnt getting it. I felt I was following instructions on how to write esoteric insutructions and not understanding how it worked. I found the book Code by Petzold and read it. Then I discussed some of this with other developers and realized they were even more clueless than I was.

It seems some people love theory/understanding while some love building something practical/useful.

Re: Programming as a Way of Thinking

#120

Post by mtempm »

misingnoglic wrote: post #108
mathgladiator wrote: post #20

Earlier quoted context omitted.

I've had thoughts like this, using sci-py to teach kids how to hack math. Our education system is kind of sad face.

It was definitely cool - he had us writing python functions to estimate the area under a curve (and then visualize it), and other things I don't quite remember at this moment. Once he made us define math functions just based on there being a 0, and a successor function, which happens to be what I'm doing in a graduate Math Logic course at my university.

That's really incredible.

It's sad to see educators like this get pushed out of their field. I had some incredible teachers as well, but also some awful ones. There needs to be greater competitive components added to the education system, such as statistically significant pupil success in education and career outcomes.

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