OT Math rant, was Re: [sdiy] DSP book recommendation wanted

Fri Sep 25 13:33:17 CEST 2009

I certainly agree with Cheater that Mathworld is not a place to learn  
new stuff. I've tried, and it's like trying to learn from a  
dictionary. A Polish dictionary.

Lots of math sites make everything *far* more complicated than it  
needs to be and spend a lot of time baffling you with long words,  
techniques you don't know named after dead mathematicians you've  
never heard of, and write the whole thing with obscure symbols that  
only mathematician's browsers will display.

I actually love math, but in recent years I've become extremely  
frustrated by the apparent inability or unwillingness of the academic  
math world to explain things or let anyone else into their little  
game. I'm beginning to suspect that they don't want us to know and  
would rather we all thought it was complicated and impenetrable. I  
can't forgive that kind of attitude in any field (and I see it a lot  
in computing, which is my own field).

One example; I've been baffled for a long time by the e^jø stuff that  
I keep seeing in filter theory and whathaveyou. Yesterday I found an  
explanation on the dspguide.com. It turns out that it's a alternative  
way of writing a complex number as a vector (e.g. an angle and a  
magnitude, rather than a x,y coord).
WELL, WHY THE HELL DIDN'T YOU JUST *SAY* SO??!!!
The actual explanation and math behind the conversion from one form  
to the other is very simple and can easily be described in half a  
page. However, having read no end of stuff on the topic, I'd *never*  
come across such an explanation until yesterday. I doubt you'll find  
it quickly and easily on mathworld.

Ok, rant over.

T.

On 25 Sep 2009, at 09:39, cheater cheater wrote:

> Sorry if you felt hurt, Dave!
>
> The first point is that reference books are made with being a closed
> source of information, i.e. any topic mentioned in a book like that
> can be fully explained by that book, to some specific level.
>
> The second point is that references are mostly ordered in a logical
> order, which makes them great for learning. If you open a reference
> book at the topic 'sequence', then the next topic will be either
> 'series' or 'arithmetic progression' or something else that is what
> you should learn next in order to maximize your learning input.
>
> Now if you go here:
> http://mathworld.wolfram.com/Sequence.html
> you don't get that benefit. Sure, the 'Series' topic is referred to,
> but find it in that list:
>
> 196-Algorithm, A-Sequence, Alcuin's Sequence, Appell Cross Sequence,
> Appell Sequence, B2-Sequence, Basic Polynomial Sequence, Beatty
> Sequence, Binomial-Type Sequence, Carmichael Sequence, Cauchy
> Sequence, Convergent Sequence, Cross Sequence, Decreasing Sequence,
> Degree Sequence, Fractal Sequence, Giuga Sequence, Increasing
> Sequence, Infinitive Sequence, Integer Sequence, Iteration Sequence,
> List, Nonaveraging Sequence, Polynomial Sequence, Primitive Sequence,
> Reverse-Then-Add Sequence, Score Sequence, Sequence Density, Series,
> Sheffer Sequence, Signature Sequence, Sort-Then-Add Sequence,
> Steffensen Sequence, Ulam Sequence
>
> How is someone supposed to learn from that?
>
> For this reason authors write themed reference books, for example a
> reference for students, or a reference for abstract algebra, or
> topology. Mathworld has everything kludged together in order to be
> 3-in-1 like head&shoulders.
>
> Furthermore, I find that mathworld often has long definition chains.
> That is, in order to understand definition A you need to understand B,
> to understand B you need C and D, and to understand each you need E,
> F, G, H and I and J. This is very often excessive.
>
> Reference books are usually written so that those definition chains  
> are minimal.
>
> Yet another point is that often the definitions in Mathworld just have
> way to much in them. For example, imagine I don't know what an
> integral is, and I want to learn about it as I would learn from a
> reference book. I would go here:
>
> http://mathworld.wolfram.com/Integral.html
>
> Now I would have not only been confused by this, since my teacher told
> me to read about integrals, not 'Riemann integrals', but I'll have
> also been indoctrinated by 1988 'New Math' quotes, and will have
> learned nothing.
>
> Now let's read on. In a few short lines, they jump from (5) which is
> usually the first formula that you see in a course on integrals right
> into (8) which assumes the reader will have started multivariate
> calculus. This is almost never the case when learning about integrals.
>
> Oh, should I learn the identities too? Let's look at 11-16... that
> might be on the exam - oh boy - better learn em. Put some more garbage
> in my head that I won't use in the next 3 years or so.
>
> Mathworld is a handy reference, but it doesn't stand up compared to
> CRC in the way as I did, and that is to make it a learning tool. You
> *might* find Mathworld very useful when you are trying to remember
> something you've learnt once, but it's definitely not a thing to learn
> new ideas with.
>
> Another point where physical objects win with websites is that they
> are tangible and invariable. If you learn something, and then forget
> it, a hazy idea about how the page layout has looked could lead you to
> the definition. This is not an uncommon way of re-learning things with
> books. With mathworld, however, the layout will have almost certainly
> changed, since it depends on the window size, zoom level, browser, and
> the definition page may have been added to or removed from.
>
> Finally, books get worked on by typesetters while mathworld doesn't.
> It makes them much easier to read and learn from.
>
> D.
>
>
> On Fri, Sep 25, 2009 at 7:02 AM, Dave Manley <dlmanley at sonic.net>  
> wrote:
>> cheater cheater wrote:
>>>
>>> Mathworld doesn't beat CRC in that CRC is an ordered, closed work  
>>> and
>>> mathworld is neither.
>>
>> You say that like it is a bad thing.  Mathworld is ordered, is  
>> hyperlinked
>> to related topics and references and is searchable.  Are the  
>> editors of the
>> CRC references any better than those of Mathworld?  Doesn't  
>> Weisstein has
>> his own massive tome on mathematics published by CRC Press?  Is
>> http://www.amazon.com/CRC-Encyclopedia-Mathematics-Third-Set/dp/ 
>> 1420072218/
>>  somehow better at 4300 pages, 21 lbs, and $398?  Sometimes, I  
>> think you
>> just like to be contrary.  Or have I missed your point?
>>
>> -Dave
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