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Re: Series[log[x], {x, 0, 3}]

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  Re: Series[log[x], {x, 0, 3}] Murray Eisenberg <murray@math.umass.edu> - 2011-05-27 10:13 +0000
    Re: Series[log[x], {x, 0, 3}] Helen Read <readhpr@gmail.com> - 2011-05-28 11:18 +0000

#2744 — Re: Series[log[x], {x, 0, 3}]

Then how would you state in symbols the fact, say, that the standard 
matrix of the composite of two linear transformations is their matrix 
product? Or that the derivative of the composite f@g is (f'@g)*g' ?
Do you always write such things either in words or symbolically but with 
explicit arguments?

On 5/25/2011 7:31 PM, Helen Read wrote:
> It's definitely a matter of taste. I almost never use the circle
> notation for function composition, and I dislike the @ notation for
> similar reasons.
>
> HPR
>
> On 5/25/2011 5:55 AM, Murray Eisenberg wrote:
>> I agree that in many instances, using something of the form f@x may seem
>> at odds with traditional mathematical notation. (Although it's still
>> useful in avoiding the eye-nuisance of nested brackets in a construction
>> such as g[f[x]].)
>>
>> But something of the form g@f[x] is very natural from the viewpoint of
>> traditional mathematical notation: the "@" is reminiscent of the circle
>> operator denoting functional composition.
>>
>> Usually, using @ seems to be a matter of either stressing a particular
>> meaning or else making an expression easier to read. (Making an
>> expression easier to type is hardly ever the reason I, at least, would
>> use @.)
>>
>> On 5/24/2011 5:59 AM, Helen Read wrote:
>>> On 5/23/2011 6:24 AM, Bill Rowe wrote:
>>>> On 5/22/11 at 6:55 AM, hszhao.cn@gmail.com (Hongsheng Zhao) wrote:
>>>>
>>>> While I cannot speak for DrMajorBob, my reason for using the
>>>> notation f@x rather than f[x] is primarily readability. Constrast
>>>>
>>>> Sqrt[Abs[Sin[x]]]
>>>>
>>>> with Sqrt[Abs@Sin@x]
>>>>
>>>> Both do the same, but for me, it is easier to see what the
>>>> second form does than the first. Deeply nested brackets are more
>>>> difficult for me to read. And there is the additional factor of
>>>> less typing required for the second form.
>>>
>>> Each to his/her own. Personally I far prefer the nested brackets, which
>>> to me is more readable -- it's closer to familiar written mathematical
>>> notation, and it's clear where each function ends.
>>>
>>> And I don't see how the @ sign results in any less typing.
>>>
>>> @  requires pressing two keys simultaneously, Shift+2
>>>
>>> [ ] requires two keys (one at a time), the [ and ]
>>> or two keys simultaneously Alt+]  to get matched brackets
>>>
>>>
>>
>
>
>
>

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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#2754

This is getting way off topic, but I don't generally have occasion to 
write such things, and I didn't say that I never use the circle 
notation, rather, *almost* never.

HPR

On 5/27/2011 6:13 AM, Murray Eisenberg wrote:
> Then how would you state in symbols the fact, say, that the standard
> matrix of the composite of two linear transformations is their matrix
> product? Or that the derivative of the composite f@g is (f'@g)*g' ?
> Do you always write such things either in words or symbolically but with
> explicit arguments?
>
> On 5/25/2011 7:31 PM, Helen Read wrote:
>> It's definitely a matter of taste. I almost never use the circle
>> notation for function composition, and I dislike the @ notation for
>> similar reasons.
>>
>> HPR
>>
>> On 5/25/2011 5:55 AM, Murray Eisenberg wrote:
>>> I agree that in many instances, using something of the form f@x may seem
>>> at odds with traditional mathematical notation. (Although it's still
>>> useful in avoiding the eye-nuisance of nested brackets in a construction
>>> such as g[f[x]].)
>>>
>>> But something of the form g@f[x] is very natural from the viewpoint of
>>> traditional mathematical notation: the "@" is reminiscent of the circle
>>> operator denoting functional composition.
>>>
>>> Usually, using @ seems to be a matter of either stressing a particular
>>> meaning or else making an expression easier to read. (Making an
>>> expression easier to type is hardly ever the reason I, at least, would
>>> use @.)
>>>
>>> On 5/24/2011 5:59 AM, Helen Read wrote:
>>>> On 5/23/2011 6:24 AM, Bill Rowe wrote:
>>>>> On 5/22/11 at 6:55 AM, hszhao.cn@gmail.com (Hongsheng Zhao) wrote:
>>>>>
>>>>> While I cannot speak for DrMajorBob, my reason for using the
>>>>> notation f@x rather than f[x] is primarily readability. Constrast
>>>>>
>>>>> Sqrt[Abs[Sin[x]]]
>>>>>
>>>>> with Sqrt[Abs@Sin@x]
>>>>>
>>>>> Both do the same, but for me, it is easier to see what the
>>>>> second form does than the first. Deeply nested brackets are more
>>>>> difficult for me to read. And there is the additional factor of
>>>>> less typing required for the second form.
>>>>
>>>> Each to his/her own. Personally I far prefer the nested brackets, which
>>>> to me is more readable -- it's closer to familiar written mathematical
>>>> notation, and it's clear where each function ends.
>>>>
>>>> And I don't see how the @ sign results in any less typing.
>>>>
>>>> @  requires pressing two keys simultaneously, Shift+2
>>>>
>>>> [ ] requires two keys (one at a time), the [ and ]
>>>> or two keys simultaneously Alt+]  to get matched brackets
>>>>
>>>>
>>>
>>
>>
>>
>>
>

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