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Re: Thorough Mathematical intro to "computer 'science'" ...

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On 10/23/2017 01:31 AM, Stefan Ram wrote:
 >>  Mathematicians, Physicists and Engineers don't really need to learn
 >> about computers since to them it becomes like second nature
 >
 >   Just ask a mathematician, a physicist or an engineer about
 >   the pumping lemma or ask them to write a recursive descent
 >   parser for Java and see what happens to that "second nature"
 >   when you test it.

  Second nature does not relate to "magic". They will certainly get what 
it is about and implement it effortlessly. I don't even see what would 
be the big deal about a recursive descent parser.

 >>      Apparently, this creates a vacuum, as I have noticed while trying
 >> to motivate my 14 year old nephew to learn Math more "seriously".
 >
 >   I wonder if it is possible or necessary to do this.

  Any specifics about what makes you wonder about it?

 >   Many very successful people hate and despise math.

  The way I would put it is "very successful people" also have the 
psychological need to "hate" some things. In order to talk and even 
think about their daily lives, people use lots of Math. I show to my 
students how even animals understand Algebra. At some point they see and 
feel how neurotically stupid those "I hate Math" reactions sound. Would 
you 'hate', say, pencils?

 >>  Do you have any suggestions about such books or terminological
 >> glossaries attempting to map Mathematical and CS concepts?
 >
 >   They only map superficially, they do not map directly. An
 >   algorithm might implement a function, but one also might say
 >   that an array or a java.util.Map implements a function.

  Well, yes, but how superficially and/or directly goes into the land of 
interpretations/opinions.

  For example, I have had PhDs (in "humanities" (those subjects of 
studies based on gossiping ;-))) tell me "they never understood 
fractions" and after a few minutes of going through the "you can only 
add mangoes to ..." routine they have told me "you make things seem 
easier than they are" ;-) Most people who say "they don't understand 
fractions", don't even realize what they are talking about and you 
notice it when they tell you about "the number on the top and the number 
on the bottom" (as if numbers were having sex or something ;-)). I ask 
them: "where is the number on which bottom?" (visual people tend to have 
shaky minds). Then I proceed to explain to them that the word 
"denominator" comes from the Latin verb "denominare" which means "to 
name", so "fifths" and "halves" would be like "mangoes", "oranges", 
"books", "flower petals", ... and you can only add ... to? ...

  Then I use the intrinsic algebraic aspect of fractions to 
"darüberhinausgehend" introduce algebraic ones. Again little resistance 
when they see those dreaded Xs "..., but what is the 'meaning' of the 
X?" then I explain to them that the beauty of Algebra is exactly that it 
doesn't effing matter and I ask them: "what is the 'meaning' of one 
dollar?" ...

  I also tell my students if they use cell phones they can certainly 
understand what (computable) functions are:

  https://ergosumus.wordpress.com/2017/10/23/functions/

 >   Infinity and limits, on the other hand, often are important
 >   parts of mathematical concepts (there is an infinite number
 >   of real numbers, most of them with infinitively many digits
 >   in their decimal expansion) that often cannot be implemented
 >   directly in a computer representation of theese concepts.
 >   (There is only a finite amount of double values in Java.)

  Hmm! What is it exactly you can't implement with a computer? Who cares 
about the infinite numbers, say, a quadratic function describes when all 
you need is the three coefficients describing it or their generating 
formulas (which you could also use in vectorial ways)?

  I have found very few things that are not easily implementable with 
algorithms, but, yes, when you use binary based arithmetic you can only 
do approximate Arithmetic division and multiplication with any number 
that is not a power of two, but no one and nothing would stop you from 
doing Math in a totally algebraic way, using prime numbers as the basis 
of a numeric system. In fact, I tell my students that the use of numbers 
in Math was a relatively late adoption in the "Western culture", that 
Egyptians didn't know about "numbers", nor did they care to keep their 
society running just fine for centuries based on ropes and walks (the 
regular floods of the Nile, the sun, stars, ... their  sweat, ...).

 >   (I wrote more about this topic in my other answers to your
 >   question in other programming newsgroups.)

  Thank you,
  lbrtchx

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Thread

Thorough Mathematical intro to "computer 'science'" ... Albretch Müller <tekmonk2005@yahoo.com> - 2017-10-22 19:28 -0400
  Re: Thorough Mathematical intro to "computer 'science'" ... Albretch Müller <tekmonk2005@yahoo.com> - 2017-10-23 14:49 -0400
    Re: Thorough Mathematical intro to "computer 'science'" ... Joerg Meier <joergmmeier@arcor.de> - 2017-10-27 09:33 +0200
      Re: Thorough Mathematical intro to "computer 'science'" ... Arne Vajhøj <arne@vajhoej.dk> - 2017-10-27 10:37 -0400
        Re: Thorough Mathematical intro to "computer 'science'" ... Martin Gregorie <martin@address-in-sig.invalid> - 2017-10-29 01:40 +0000
      Re: Thorough Mathematical intro to "computer 'science'" ... Martin Gregorie <martin@address-in-sig.invalid> - 2017-10-27 17:25 +0000
        Re: Thorough Mathematical intro to "computer 'science'" ... Joerg Meier <joergmmeier@arcor.de> - 2017-10-28 23:30 +0200

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