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

[Albretch Müller]

Mathematicians, Physicists and Engineers don't really need to learn
about computers since to them it becomes like second nature and CS folks
have their own "funky" ways to see and use Mathematics/Logic (let's not
get into their self-aggrandizing, self-serving AI philosophy nonsense
;-)). Apparently, this creates a vacuum, as I have noticed while trying
to motivate my 14 year old nephew to learn Math more "seriously".

I have searched deep and wide for such an introductory book in which
high school Math would be foremost and computer programming (preferably
C, C++ or Java) would just be introduced as examples and exercises to
keep students "motivated", something like:

* number sense <-> primitive data types (a little bit of how
processors internally do Math)
* (computable) function <-> algorithms
* algebraic like terms <-> SQL records <-> objects created based on
the same class definition (the addition operation for those objects
would not be naturally defined, but the addition of their quantifiable
attributes certainly can, as well as the stratification of the
non-quantifiable ones)
* sets (of elements/objects basically sharing their "belongingness")
would be like objects belonging to abstract classes
...

Do you have any suggestions about such books or terminological
glossaries attempting to map Mathematical and CS concepts?

lbrtchx

[Jorgen Grahn]

Are you sure that's the best way to trick your nephew into serious maths?

Maths and computer science are both about reasoning within set systems,
but I don't think programming ever helped my interest in maths.

Two ideas though:

- I really liked Douglas Hofstadter's "Godel, Escher, Bach" at that
age. It plays interesting games with small systems; I think it
introduces lambda calculus, amongst other things. You could buy that
one.

- Functional programming (languages like Haskell) are really more
beloved by mathematicians than C and C++. You may have more luck
searching there.

Randall Munroe's book "What if?" is also fun and useful, but it uses
maths as an engineer would.

/Jorgen

--
// Jorgen Grahn <grahn@ Oo o. . .
\X/ snipabacken.se> O o .

[Chris M. Thomasson]

Fwiw, imvho, fractals and games have always seemed like a fairly nice
way to introduce both programming and math to youngsters. A kid says
they do not like math and will never end up using a lot of it anyway.
Well, show them a wild fractal animation and/or a cool game, and ask if
they like it. If the answer is anything close to yes: Try to explain to
them how math and programming made it possible. Sometimes, it can create
a lasting spark, so to speak...

[Jorgen Grahn]

Yes. But it sounded to me he was going for things like algebra, and
the parts of mathematics that are more about proving things. I may be
wrong, but the connection between that aspect of maths and programming
seems a bit weak.

[Albretch Müller]

On 10/21/2017 05:44 PM, Jorgen Grahn wrote:
>>> Maths and computer science are both about reasoning within set systems,
>>> but I don't think programming ever helped my interest in maths.
>>
>> Fwiw, imvho, fractals and games have always seemed like a fairly nice
>> way to introduce both programming and math to youngsters. A kid says
>> they do not like math and will never end up using a lot of it anyway.
>> Well, show them a wild fractal animation and/or a cool game, and ask if
>> they like it. If the answer is anything close to yes: Try to explain to
>> them how math and programming made it possible. Sometimes, it can create
>> a lasting spark, so to speak...
>
> Yes. But it sounded to me he was going for things like algebra, and
> the parts of mathematics that are more about proving things. I may be
> wrong, but the connection between that aspect of maths and programming
> seems a bit weak.

and I am. what I have in mind is kind of mapping the high school Math
curriculum to an introduction to coding one. I am not so sure my nephew
(most kids) would be impressed, but maybe some other kid will and I
would be fine with that.

Do you know of attempts at mapping Math at CS concepts in any way?

lbrtchx

[Manfred]

I am skeptical too about similarities between maths and computer science.
I would say they both need a similar mindset, i.e. being comfortable
with dealing with strict logic, in that they both are exact sciences.
But their respective subjects are quite different, I think.
The math domain ranges e.g. from (numerical) space topology to
functional analysis, space transformations, calculus and so son.
Computer science ranges e.g. from resource management to modeling,
complexity management, networking/communications, and so on.
(obviously not exhaustive listings, but I think they give the idea)

In my line of work I deal with calculation software for the applied
domain we work in, but even in this context only a fraction of my code
is actual computation, most of it is about UI, modeling, I/O,
interfacing, data storage, etc.