what to do, for the mathematically-disabled people (only half-joking)

what to do, for the mathematically-disabled people (only half-joking)

[Mehdi Saada]

What would you advise, for a mathematically impaired person such as myself, who gets a headache trying to implement a simple vector fusion algorithm ?
And however I try, a few days, changes nothing to the outcome, shit doesn't get done, and I'm left furious at myself. And I know it well, at my age, when I, am the problem.
Are those algorithm books useful, can they really hammer the logic muscles in my brain ?
Basically, I cannot see in my head the (simple, I stress that out) program playing out.

Thanks,
Mehdi

Re: what to do, for the mathematically-disabled people (only half-joking)

[Mehdi Saada]

Algebra I Chrystal
A mathematical introduction to logic, Enderton
[Cormen-AL2011]Introduction_To_Algorithms-A3
Introduction to Computing, exploration in language, logic and machines 266p

Enderton was advised here once, but I don't know if "logic" really is my problem.

Re: what to do, for the mathematically-disabled people (only half-joking)

[Brian Drummond]

On Thu, 07 Jan 2021 13:46:06 -0800, Mehdi Saada wrote:

> What would you advise, for a mathematically impaired person such as
> myself, who gets a headache trying to implement a simple vector fusion
> algorithm ?
> And however I try, a few days, changes nothing to the outcome, shit
> doesn't get done, and I'm left furious at myself. And I know it well, at
> my age, when I, am the problem.
> Are those algorithm books useful, can they really hammer the logic
> muscles in my brain ?
> Basically, I cannot see in my head the (simple, I stress that out)
> program playing out.
> 
> Thanks,
> Mehdi

Sometimes, I find mocking it up in a spreadsheet helps!

Sounds dumb, but...

Say, I can think of a testcase and I know what the output should look 
like, start with a column of figures and more columns of (transformed by 
equation) figures, and ideally a column computing an error function.

Why is the error column 0 here, but not there? ... aaah...

For example I've designed pipelined versions of algorithms that way, 
before implementing in FPGA, and LUT-based quadratic interpolators to 
approximate reciprocal and square root, to get within 1 LSB error at 
single precision (multiplication/addition are cheap in FPGA, division/
sqrt not so much)

Also mocked up James Watt's link motion, a 5th order approximation to 
straight line using only rotary motion.

YMMV.

-- Brian

Re: what to do, for the mathematically-disabled people (only half-joking)

[Paul Rubin]

Mehdi Saada <00120260a@gmail.com> writes:
> What would you advise, for a mathematically impaired person such as
> myself, who gets a headache trying to implement a simple vector fusion
> algorithm ?

I don't quite understand the question: you want to get better at coding
algorithms?  You want to learn more math?  More about algorithms?

In any case, exercise will do you more good than reading.  Do you know
how quicksort works?  If yes, try coding it.  That will get you better
at getting all the details right when you implement something.

Enderton's book that you mention is about mathematical logic, a good
subject, but maybe not what you want.

For math in general, try a math textbook in a topic that interests you.
Logic, algebra, analysis, whatever.  Write out answers to the exercises
as if you were taking a class and doing the homework to hand in.  For
algorithms, I still like Knuth's TAOCP series, though it is considered
old fashioned these days.  It has lots of good exercises.

Re: what to do, for the mathematically-disabled people (only half-joking)

[Mehdi Saada]

> I don't quite understand the question: you want to get better at coding 
> algorithms? You want to learn more math? More about algorithms? 
Worst. I have literal head-ache half-way writing a simple algorithm. My brain won't get me far enough.
I got back at algebra exo, which some help, to go past some blockade. then I'll go further and further, since I always loved math. I have help in a talented friend, and good books.
I am, making progress, fortunately. At some point I'll use your books, or whatever seems useful.
> Knuth's TAOCP series, though it is considered old fashioned these days. It has lots of good exercises.
Got it. I love "old fashioned" in math, always better.

Re: what to do, for the mathematically-disabled people (only half-joking)

[Shark8]

On Friday, January 8, 2021 at 4:24:11 PM UTC-7, 0012... wrote:
> > I don't quite understand the question: you want to get better at coding 
> > algorithms? You want to learn more math? More about algorithms?
> Worst. I have literal head-ache half-way writing a simple algorithm. My brain won't get me far enough. 
> I got back at algebra exo, which some help, to go past some blockade. then I'll go further and further, since I always loved math. I have help in a talented friend, and good books. 
> I am, making progress, fortunately. At some point I'll use your books, or whatever seems useful.
> > Knuth's TAOCP series, though it is considered old fashioned these days. It has lots of good exercises.
> Got it. I love "old fashioned" in math, always better.
Another few suggestions:
(1) Try working "backwards", from the result to the input; like induction.
(2) For real-world analogs, use the analog! [Like using 3x5 cards as a stack.]
(3) For Algebra, remember that you have to keep both sides of the equal balanced; for calculus, always remember that it's about rates-of-change.
(4) There are a lot of 'tricks' that work because of identities, but sometimes you have to "go the long way" to arrive at the simple.

Though it doesn't touch identities, deriving the sum formula is a good example here; consider the problem of summation, given S(n) is there a formula?
S(n) = 1 + 2 + 3 + 4 + 5 [...] + n
but also
S(n) = (n) + (n-1) + (n-2) + (n-3) + [...] + n-(n-1)
Adding these
2S(n) = (n+1) + (n+1) + (n+1) + (n+1) + [...] + (n+1); n times n+1
So
2S(n) = n*(n+1)
which means we can divide both sides by 2.

S(n) = ( n*(n+1) ) / 2

So we end up with something that uses an addition, a multiplication, and a division (by 2) to replace something that would have been a loop and n additions.

Re: what to do, for the mathematically-disabled people (only half-joking)

[Mehdi Saada]

Le mardi 12 janvier 2021 à 01:14:23 UTC+1, Shark8 a écrit :
> (1) Try working "backwards", from the result to the input; like induction. 
That one was pretty enlightening ! Indeed, it is useful.

I am painstakingly going through algebra books. Slooooowly at first, since this part is meant to burn in my brain what is in effect, a symbolic manipulation software. But it feels great, finally being on the level of mental awareness that people had when computers weren't around.