[Blindmath] Accessible display format for matrices

Thu Nov 17 15:20:20 UTC 2011

Thanks. It's been a little too long since I worked linear algebra as a 
sighted reader... I'm mostly having fun reading the discussion because 
I'm suddenly figuring out how to conceptualize matrices nonvisuallyfor 
myself. Breakthrough for me.

Tami

On 11/17/2011 02:42 AM, Michael Whapples wrote:
> As memory goes, 0 has a different meaning here and would be wrong to use.
>
> Michael Whapples
> On 16/11/11 23:21, Tami Kinney wrote:
>> What about using "NULL" to indicate that the blank cell represents a
>> null value? Or "0" which, I suppose in this context would mean pretty
>> much the same thing... Depending.
>>
>> Just a thought. /smile/
>>
>> I am loving this discussion!
>>
>> Tami
>>
>> On 11/16/2011 12:45 PM, Birkir R. Gunnarsson wrote:
>>> My worry is that I am not sure that screen readers all necessarily
>>> announce black cells, they may simply skipover them to the next
>>> non-blank cell. If this isn't the case for any screen reader, there is
>>> no worry. If there is, this is a huge problem, when you need to be
>>> absolutely sure which cells in a matrix are blank.
>>> Also I thought that entering, say a "--" would look visually appealing
>>> enough, thogh I don't know this.
>>> That is the source of my point. If I am working with a 4 by 4 matrix
>>> with blanks in it, I want to be sure that it is a 4 by 4 set of cells
>>> and I can identify the contents of each, even if it is blank.
>>>
>>>
>>> On 11/16/11, Michael Whapples<mwhapples at aim.com> wrote:
>>>> I think the main point missed here is that NVDA can do cell
>>>> navigation, OK
>>>> may be not quite as nice (in some peoples' minds) but still perfectly
>>>> accessible. I am sure if it became such an issue someone would feel
>>>> pushed
>>>> enough to add it to opensource products like NVDA and then that
>>>> might push
>>>> the commercial offerings to catch up as they would be lacking.
>>>>
>>>> Michael Whapples
>>>> ----- Original Message -----
>>>> From: "Sina Bahram"<sbahram at nc.rr.com>
>>>> To:<john.gardner at orst.edu>; "'Blind Math list for those interested in
>>>> mathematics'"<blindmath at nfbnet.org>
>>>> Sent: Tuesday, November 15, 2011 11:41 PM
>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>
>>>>
>>>>> That's cell navigation, no? in other words, that read 2, 5, 8 if
>>>>> you were
>>>>> navigating down a keypad, instead of reading, 1,2,3:
>>>>> 4,5,6: 7,8,9.
>>>>>
>>>>> Take care,
>>>>> Sina
>>>>>
>>>>> -----Original Message-----
>>>>> From: blindmath-bounces at nfbnet.org
>>>>> [mailto:blindmath-bounces at nfbnet.org]
>>>>> On Behalf Of John Gardner
>>>>> Sent: Tuesday, November 15, 2011 5:39 PM
>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>
>>>>> Hmmm, it is news to me. I use CTRL-ALT arrows to navigate html tables
>>>>> with
>>>>> NVDA all the time. I know the NVDA folks are developing richer table
>>>>> navigation, but this row/column navigation method works perfectly
>>>>> well. I
>>>>> actually prefer NVDA for this purpose and lots of other web tasks,
>>>>> particularly filling out forms. It is really stable compared to the
>>>>> other
>>>>> screen readers.
>>>>>
>>>>> John
>>>>>
>>>>>
>>>>> -----Original Message-----
>>>>> From: blindmath-bounces at nfbnet.org
>>>>> [mailto:blindmath-bounces at nfbnet.org]
>>>>> On
>>>>> Behalf Of Sina Bahram
>>>>> Sent: Tuesday, November 15, 2011 1:51 PM
>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>
>>>>> I just confirmed this. NVDA does not currently have row/column
>>>>> reading,
>>>>> but
>>>>> I'll be requesting this, today.
>>>>>
>>>>> I'm discussing the matter with some folks on twitter. *glances at
>>>>> previous
>>>>> statement, and shakes head* never thought I'd say that,
>>>>> before.
>>>>>
>>>>> Ken, thanks again for the heads up.
>>>>>
>>>>> Take care,
>>>>> Sina
>>>>>
>>>>>
>>>>>
>>>>> -----Original Message-----
>>>>> From: blindmath-bounces at nfbnet.org
>>>>> [mailto:blindmath-bounces at nfbnet.org]
>>>>> On
>>>>> Behalf Of Ken Perry
>>>>> Sent: Tuesday, November 15, 2011 4:40 PM
>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>
>>>>>
>>>>> No what I mean is a way to read the entire row for example 7 8 9 NVDA
>>>>> doesn't seem to have that feature as of yet. In jaws they use
>>>>> Microsoft
>>>>> key , for rows and Microsoft key . for columns It is just an easy
>>>>> way to
>>>>> read the whole set of numbers and. The cell navigation is a good as
>>>>> well
>>>>> which it seems all the screen readers handle that.
>>>>>
>>>>> Ken
>>>>>
>>>>> -----Original Message-----
>>>>> From: blindmath-bounces at nfbnet.org
>>>>> [mailto:blindmath-bounces at nfbnet.org]
>>>>> On
>>>>> Behalf Of Michael Whapples
>>>>> Sent: Tuesday, November 15, 2011 3:30 PM
>>>>> To: Blind Math list for those interested in mathematics
>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>
>>>>> I am not sure what keys you mean.
>>>>>
>>>>> To navigate by cells in NVDA you use ctrl+alt+<cursors> to move
>>>>> around the
>>>>> table. Also users of the Mac and voiceover have this sort of
>>>>> navigation.
>>>>>
>>>>> If you mean a way of defining which order NVDA reads through a
>>>>> table when
>>>>> doing continuous reading, then there is no option for that. However I
>>>>> would
>>>>> imagine such a feature would be fairly simple to be added for those
>>>>> who
>>>>> are
>>>>> familiar with NVDA code.
>>>>>
>>>>> Michael Whapples
>>>>> On 15 Nov 2011, at 19:03, Ken Perry wrote:
>>>>>
>>>>>> I agree with you in essence but when your designing something for a
>>>>>> class it would be nice if the students who can not afford jaws can
>>>>>> still get good access like I said I hope I am missing the keys for
>>>>>> NVDA but I haven't found them yet.
>>>>>>
>>>>>> Ken
>>>>>> -----Original Message-----
>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>> [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Sina Bahram
>>>>>> Sent: Tuesday, November 15, 2011 1:35 PM
>>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>
>>>>>> Wait a minute, NVDA doesn't have row/column reading?
>>>>>>
>>>>>> First off, let's not code to the lowest common denominator: we have
>>>>>> enough of that in this field.
>>>>>>
>>>>>> I can't speak to system access, but I will start contacting NVDA guys
>>>>>> right now about this issue.
>>>>>>
>>>>>> Ken, thanks for the heads up. I just assumed they had something so
>>>>>> basic.
>>>>>>
>>>>>> Take care,
>>>>>> Sina
>>>>>>
>>>>>>
>>>>>> -----Original Message-----
>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>> [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Ken Perry
>>>>>> Sent: Tuesday, November 15, 2011 1:23 PM
>>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>
>>>>>>
>>>>>> I agree except for one problem. With jaws you can use windows , and
>>>>>> windows . to read the row or column in order but I have yet to find a
>>>>>> way to do that with either system access or nvda. My first method
>>>>>> allows you to read a whole row no matter the screen reader so I guess
>>>>>> it depends if you need to be able to read a whole row of the numbers.
>>>>>> Maybe you could add this feature fast enough to NVDA though, if it is
>>>>>> not there and I just have not found it.
>>>>>>
>>>>>> OH all the screen readers seem to read the table version of the
>>>>>> matrix
>>>>>> fine by cells its just the row and column reading that I like with
>>>>>> Jaws if you have to use tables.
>>>>>>
>>>>>>
>>>>>> -----Original Message-----
>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>> [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Sina Bahram
>>>>>> Sent: Tuesday, November 15, 2011 1:05 PM
>>>>>> To: 'Blind Math list for those interested in mathematics'
>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>
>>>>>> Where as a simple html table would be ideal for both.
>>>>>>
>>>>>>
>>>>>> -----Original Message-----
>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>> [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Richard Baldwin
>>>>>> Sent: Tuesday, November 15, 2011 12:50 PM
>>>>>> To: Blind Math list for those interested in mathematics
>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>
>>>>>> I am assuming that the blind student can scroll up and down through
>>>>>> the rows using the up and down arrow keys, encountering only three
>>>>>> values with each press of the arrow key.
>>>>>>
>>>>>> Another alternative would be to put all nine values for a 3x3 matrix
>>>>>> on the same line with some sort of delimiter to indicate that each
>>>>>> group of 3 values represents a row.
>>>>>>
>>>>>> However, there is a problem with this also. Despite the need to
>>>>>> accommodate blind students in the course, I must also make certain
>>>>>> that I accommodate the needs of sighted students. Sighted students
>>>>>> are
>>>>>> accustomed to seeing matrices written in rows and columns and all of
>>>>>> the textbooks present matrices in that format. I must use a format
>>>>>> that works for both the blind students and the sighted students,
>>>>>> which
>>>>>> is one of the reasons that I like this approach. It should work for
>>>>>> blind students and it looks nominally correct for sighted
>>>>>> students. Not
>>>>> ideal for either but adequate for both.
>>>>>>
>>>>>> Dick Baldwin
>>>>>>
>>>>>> On Tue, Nov 15, 2011 at 11:29 AM, Ken Perry<kperry at blinksoft.com>
>>>>>> wrote:
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> The good part is if you have it in this kind of form and the student
>>>>>>> has another form he or she likes better its not hard to reparse
>>>>>>> this.
>>>>>>>
>>>>>>> Ken
>>>>>>>
>>>>>>> -----Original Message-----
>>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>>> [mailto:blindmath-bounces at nfbnet.org]
>>>>>>> On
>>>>>>> Behalf Of Richard Baldwin
>>>>>>> Sent: Tuesday, November 15, 2011 12:21 PM
>>>>>>> To: Blind Math list for those interested in mathematics
>>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>>
>>>>>>> Great! This makes it work. Now when I tab into the first row of the
>>>>>>> matrix, I hear three bar nine bar eight. Given an announcement
>>>>>>> that a
>>>>>>> matrix follows, a blind student should be able to mentally separate
>>>>>>> the columns and the rows without having to space through the
>>>>>>> characters individually.
>>>>>>>
>>>>>>> This scheme, or something very similar is what I will probably use.
>>>>>>>
>>>>>>> Thanks,
>>>>>>> Dick Baldwin
>>>>>>>
>>>>>>> On Tue, Nov 15, 2011 at 9:26 AM, Icewolf<icewolf2011 at gtwebdesign.us>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> Hello,
>>>>>>>> I don't have my copy of NVDA up at the moment. To change the
>>>>>>>> punctuation
>>>>>>>> level:
>>>>>>>> 1. From the desktop press NVDA(insert key) plus n. This will get
>>>>>>>> you into NVDA's settings.
>>>>>>>> 2. Arrow down to preferences, then arrow right into the menu.
>>>>>>>> 3. Arrow down till you hear, or see, the voice settings option and
>>>>>>>> then press enter.
>>>>>>>> 4. Once in this dialog box tab around till you see or hear the
>>>>>>>> punctuation option. This will be a combo box.
>>>>>>>> 5. Arrow up and down through the choices. I believe they are none,
>>>>>>>> some, most, and all.
>>>>>>>> 6. Choose all then tab to ok and press enter.
>>>>>>>> There might be a way to do this on the fly without having to go
>>>>>>>> into
>>>>>>>> the preferences menu, but I am still a novice at NVDA and don't
>>>>>>>> know
>>>>>>>> it
>>>>>>> yet.
>>>>>>>> Hope this helps,
>>>>>>>> Greg W.
>>>>>>>>
>>>>>>>> Yesterday is forever gone, tomorrow may never come, today is the
>>>>>>>> day
>>>>>>>> of all days.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On 11/15/2011 9:47 AM, Richard Baldwin wrote:
>>>>>>>>
>>>>>>>>> Ken,
>>>>>>>>>
>>>>>>>>> You wrote: "Did you turn punctuation to all before trying this?"
>>>>>>>>>
>>>>>>>>> I'm a novice at using NVDA.
>>>>>>>>>
>>>>>>>>> How do I make that setting?
>>>>>>>>>
>>>>>>>>> Thanks,
>>>>>>>>> Dick Baldwin
>>>>>>>>>
>>>>>>>>> On Tue, Nov 15, 2011 at 8:35 AM, Ken Perry<kperry at blinksoft.com>
>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> Did you turn punctuation to all before trying this?
>>>>>>>>>>
>>>>>>>>>> ken
>>>>>>>>>>
>>>>>>>>>> -----Original Message-----
>>>>>>>>>> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces@**
>>>>>>>>>> nfbnet.org<blindmath-bounces at nfbnet.org>] On Behalf Of Richard
>>>>>>>>>> Baldwin
>>>>>>>>>> Sent: Tuesday, November 15, 2011 9:26 AM
>>>>>>>>>> To: Blind Math list for those interested in mathematics
>>>>>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>>>>>
>>>>>>>>>> This approach works pretty well with NVDA as long as there is an
>>>>>>>>>> announcement immediately before the matrix that a matrix follows.
>>>>>>>>>> This is needed so the student will know to use the right and left
>>>>>>>>>> arrow keys to step through the matrix elements. When the down
>>>>>>>>>> arrow is used to enter the matrix, NVDA simply speaks 398 with no
>>>>>>>>>> acknowledgement of the bars (or semicolons either);
>>>>>>>>>>
>>>>>>>>>> Dick Baldwin
>>>>>>>>>>
>>>>>>>>>> On Tue, Nov 15, 2011 at 7:14 AM, Ken Perry<kperry at blinksoft.com>
>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>> I know everyone on here will cringe but in truth this is how I
>>>>>>>>>> would
>>>>>>>>>>> want it but again I like using just a text editor and this way
>>>>>>>>>>> seems to work great with jaws for me. This is just a simple page
>>>>>>>>>>> with a 3 by
>>>>>>>>>>> 3 matrix. It has the bars because<pre> elements don't get
>>>>>> converted.
>>>>>>>>>>>
>>>>>>>>>>> <html>
>>>>>>>>>>> <body>
>>>>>>>>>>> <H1>A Matrix</h1>
>>>>>>>>>>> <pre>
>>>>>>>>>>> 3 | 9 | 8
>>>>>>>>>>> 4 | 6 | 5
>>>>>>>>>>> 6 | 4 | 8
>>>>>>>>>>> </pre>
>>>>>>>>>>> </body>
>>>>>>>>>>> </html
>>>>>>>>>>>
>>>>>>>>>>> -----Original Message-----
>>>>>>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>>>>>>> [mailto:blindmath-bounces@**nfbnet.org
>>>>>>>>>>> <blindmath-bounces at nfbnet.org>] On Behalf Of Richard Baldwin
>>>>>>>>>>> Sent: Tuesday, November 15, 2011 8:03 AM
>>>>>>>>>>> To: Blind Math list for those interested in mathematics
>>>>>>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>>>>>>
>>>>>>>>>>> Thanks Ken,
>>>>>>>>>>>
>>>>>>>>>>> So far, that seems to be the most accessible option. I suppose I
>>>>>>>>>>> could style the matrices as<pre>xx</pre> and put them in XHTML
>>>>>>>>>>> tables. That should make them accessible to a screen reader and
>>>>>>>>>>> also make them look reasonable for the sighted students in the
>>>>>>>>>>> course. Maybe there is a unicode character that could be used to
>>>>>>>>>>> create the vertical bars that typically appear on printed
>>>>>>>>>>> matrices.
>>>>>>>>>>> If so, I wonder how a screen reader would treat those
>>>>>>>>>>> characters.
>>>>>>>>>>>
>>>>>>>>>>> Other suggestions are welcome.
>>>>>>>>>>>
>>>>>>>>>>> Thanks,
>>>>>>>>>>> Dick Baldwin
>>>>>>>>>>>
>>>>>>>>>>> On Tue, Nov 15, 2011 at 6:47 AM, Ken Perry<kperry at blinksoft.com>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>> When I did my matrix class back in the early 90's I used a text
>>>>>>>>>>>> editor and an old laptop calculator called Xplore. The
>>>>>>>>>>>> calculator still exists but the newest version is not that
>>>>>>>>>>>> accessible. I would just type the matrix out in a text editor
>>>>>>>>>>>> and space the
>>>>>>> columns.
>>>>>>>>>>>> That way when I wanted two add two rows I would block one row
>>>>>>>>>>>> and put it under the other and move things around. I know that
>>>>>>>>>>>> is not pretty but it gave me a good feel of how the sighted
>>>>>>>>>>>> folks
>>>>>> did it.
>>>>>>>>>>>> I got to the point where I could do up to 2 4 by 4 matrixes in
>>>>>>>>>>>> my head only writing down values as I multiplied them or if I
>>>>>>>>>>>> was trying to solve them. It would take a bit of work to get
>>>>>>>>>>>> back to that point now but all I am saying is don't give up on
>>>>>>>>>>>> the simple text editor it sometimes is nice to be able to
>>>>>>>>>>>> easily see all the
>>>>>>>>>>>>
>>>>>>>>>>> numbers in a row at a time.
>>>>>>>>>>
>>>>>>>>>>> Ken
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> -----Original Message-----
>>>>>>>>>>>> From: blindmath-bounces at nfbnet.org
>>>>>>>>>>>> [mailto:blindmath-bounces@**nfbnet.org
>>>>>>>>>>>> <blindmath-bounces at nfbnet.org>] On Behalf Of Richard Baldwin
>>>>>>>>>>>> Sent: Tuesday, November 15, 2011 6:53 AM
>>>>>>>>>>>> To: Blind Math list for those interested in mathematics
>>>>>>>>>>>> Subject: Re: [Blindmath] Accessible display format for matrices
>>>>>>>>>>>>
>>>>>>>>>>>> Hi Pranav,
>>>>>>>>>>>>
>>>>>>>>>>>> Thanks for the input. I understand how a spreadsheet can be
>>>>>>>>>>>> used
>>>>>>>>>>>> for doing matrix computations. The main thing that I am looking
>>>>>>>>>>>> for is the most accessible display format. For example, MathML
>>>>>>>>>>>> can be used to create beautiful matrix equations in an HTML
>>>>>>>>>>>> page.
>>>>>>>>>>>> Beautiful, that is, for sighted students. However, NVDA becomes
>>>>>>>>>>>> silent when it encounters MathML in a web page. I don't have a
>>>>>>>>>>>> copy of Jaws, so I don't know how it reacts to MathML in a web
>>>>>>>>>>>> page.
>>>>>>>>>>>>
>>>>>>>>>>>> Most normal equations can be handled in an accessible manner by
>>>>>>>>>>>> writing them on a single line using programming format. Matrix
>>>>>>>>>>>> equations, on the other hand typically require three or four
>>>>>>>>>>>> lines.
>>>>>>>>>>>> I wondering how to configure those three or four lines in
>>>>>>>>>>>> such a
>>>>>>>>>>>> way that a blind student can make sense of them.
>>>>>>>>>>>>
>>>>>>>>>>>> Thanks,
>>>>>>>>>>>> Dick Baldwin
>>>>>>>>>>>>
>>>>>>>>>>>> On Tue, Nov 15, 2011 at 4:11 AM, Pranav
>>>>>>>>>>>> Lal<pranav.lal at gmail.com>
>>>>>>>>>>>>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Hi Richard,
>>>>>>>>>>>>>
>>>>>>>>>>>>> I have worked a bit with matrices. At the time I did, a
>>>>>>>>>>>>> spreadsheet was the solution I chose. I could add rows and
>>>>>>>>>>>>> columns without a fuss and they were accessible. Excel is the
>>>>>>>>>>>>> tool to go for in windows. No special tool is required.
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 11/15/11, Richard
>>>>>>>>>>>>> Baldwin<baldwin at dickbaldwin.**com<baldwin at dickbaldwin.com>>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> I will be teaching the following course for the first time in
>>>>>>>>>>>>>> the Spring
>>>>>>>>>>>>>> 2012 semester.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> GAME 2302 - Mathematical Applications for Game Development
>>>>>>>>>>>>>> (3-3-1) Presents applications of mathematics and science in
>>>>>>>>>>>>>> game and simulation programming. Includes the utilization of
>>>>>>>>>>>>>> matrix and vector operations, kinematics, and Newtonian
>>>>>>>>>>>>>> principles in games and simulations. Also
>>>>>>>>>>>>>>
>>>>>>>>>>>>> covers
>>>>>>>>>>>>>
>>>>>>>>>>>>>> code optimization.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The course must be accessible for blind and VI students. Even
>>>>>>>>>>>>>> if there
>>>>>>>>>>>>>>
>>>>>>>>>>>>> are
>>>>>>>>>>>>>
>>>>>>>>>>>>>> accessible textbooks at the college level covering these
>>>>>>>>>>>>>> topics (which I
>>>>>>>>>>>>>> doubt) it is far too late to adopt a new textbook for the
>>>>>>>>>>>>>> course.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I really need suggestions from those who teach mathematics
>>>>>>>>>>>>>> and
>>>>>>>>>>>>>> blind students who study mathematics regarding the most
>>>>>>>>>>>>>> accessible formats for presenting matrix equations.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If special reader software is required (beyond a standard
>>>>>>>>>>>>>> screen
>>>>>>>>>>>>>>
>>>>>>>>>>>>> reader), I
>>>>>>>>>>>>>
>>>>>>>>>>>>>> need to know that also.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks in advance.
>>>>>>>>>>>>>> Dick Baldwin
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> Richard G. Baldwin (Dick Baldwin) Home of Baldwin's on-line
>>>>>>>>>>>>>> Java Tutorials http://www.DickBaldwin.com
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Professor of Computer Information Technology Austin Community
>>>>>>>>>>>>>> College
>>>>>>>>>>>>>> (512) 223-4758
>>>>>>>>>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>>>>>>>>>> http://www.austincc.edu/**baldwin/<http://www.austincc.edu/bal
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> dw in/> ______________________________**_________________
>>>>>>>>>>>>>> Blindmath mailing list
>>>>>>>>>>>>>> Blindmath at nfbnet.org
>>>>>>>>>>>>>> http://nfbnet.org/mailman/**listinfo/blindmath_nfbnet.org<http
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>>>>>>>>>>>>> pranav.lal%
>>>>>>>>>>>>> 40
>>>>>>>>>>>>> gm
>>>>>>>>>>>>> ail.com
>>>>>>>>>>>>> ______________________________**_________________
>>>>>>>>>>>>> Blindmath mailing list
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>>>>>>>>>>>>>
>>>>>>>>>>>>> or
>>>>>>>>>>>>> g/baldwin%40d>
>>>>>>>>>>>>> ic
>>>>>>>>>>>>> kb
>>>>>>>>>>>>> aldwin.com
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>> Richard G. Baldwin (Dick Baldwin) Home of Baldwin's on-line
>>>>>>>>>>>> Java
>>>>>>>>>>>> Tutorials http://www.DickBaldwin.com
>>>>>>>>>>>>
>>>>>>>>>>>> Professor of Computer Information Technology Austin Community
>>>>>>>>>>>> College
>>>>>>>>>>>> (512) 223-4758
>>>>>>>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>>>>>>>> http://www.austincc.edu/**baldwin/
>>>>>>>>>>>> <http://www.austincc.edu/baldwin/>
>>>>>>>>>>>> ______________________________**_________________
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>>>>>>>>>>>>
>>>>>>>>>>>> .o
>>>>>>>>>>>> rg/kperry%40blin>
>>>>>>>>>>>> ks
>>>>>>>>>>>> oft.co
>>>>>>>>>>>> m
>>>>>>>>>>>>
>>>>>>>>>>>>
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>>>>>>>>>>>>
>>>>>>>>>>>> .o
>>>>>>>>>>>> rg/baldwin%40dic>
>>>>>>>>>>>> kb
>>>>>>>>>>>> aldwin.com
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> Richard G. Baldwin (Dick Baldwin) Home of Baldwin's on-line Java
>>>>>>>>>>> Tutorials http://www.DickBaldwin.com
>>>>>>>>>>>
>>>>>>>>>>> Professor of Computer Information Technology Austin Community
>>>>>>>>>>> College
>>>>>>>>>>> (512) 223-4758
>>>>>>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>>>>>>> http://www.austincc.edu/**baldwin/
>>>>>>>>>>> <http://www.austincc.edu/baldwin/>
>>>>>>>>>>> ______________________________**_________________
>>>>>>>>>>> Blindmath mailing list
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>>>>>>>>>>>
>>>>>>>>>>> org/kperry%40blinks>
>>>>>>>>>>> oft.co
>>>>>>>>>>> m
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> ______________________________**_________________
>>>>>>>>>>> Blindmath mailing list
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>>>>>>>>>>>
>>>>>>>>>>> org/baldwin%40dickb>
>>>>>>>>>>> aldwin.com
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> Richard G. Baldwin (Dick Baldwin)
>>>>>>>>>> Home of Baldwin's on-line Java Tutorials
>>>>>>>>>> http://www.DickBaldwin.com
>>>>>>>>>>
>>>>>>>>>> Professor of Computer Information Technology Austin Community
>>>>>>>>>> College
>>>>>>>>>> (512) 223-4758
>>>>>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>>>>>> http://www.austincc.edu/**baldwin/
>>>>>>>>>> <http://www.austincc.edu/baldwin/>
>>>>>>>>>> ______________________________**_________________
>>>>>>>>>> Blindmath mailing list
>>>>>>>>>> Blindmath at nfbnet.org
>>>>>>>>>> http://nfbnet.org/mailman/**listinfo/blindmath_nfbnet.org<http://n
>>>>>>>>>>
>>>>>>>>>> fb net.org/mailman/listinfo/blindmath_nfbnet.org>
>>>>>>>>>> To unsubscribe, change your list options or get your account info
>>>>>>>>>> for
>>>>>>>>>> Blindmath:
>>>>>>>>>>
>>>>>>>>>> http://nfbnet.org/mailman/**options/blindmath_nfbnet.org/**
>>>>>>>>>> kperry%40blinksoft.co<http://nfbnet.org/mailman/options/blindmath_
>>>>>>>>>>
>>>>>>>>>> nf
>>>>>>>>>> bnet.org/kperry%40blinksoft.co>
>>>>>>>>>> m
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> ______________________________**_________________
>>>>>>>>>> Blindmath mailing list
>>>>>>>>>> Blindmath at nfbnet.org
>>>>>>>>>> http://nfbnet.org/mailman/**listinfo/blindmath_nfbnet.org<http://n
>>>>>>>>>>
>>>>>>>>>> fb net.org/mailman/listinfo/blindmath_nfbnet.org>
>>>>>>>>>> To unsubscribe, change your list options or get your account info
>>>>>>>>>> for
>>>>>>>>>> Blindmath:
>>>>>>>>>>
>>>>>>>>>> http://nfbnet.org/mailman/**options/blindmath_nfbnet.org/**
>>>>>>>>>> baldwin%40dickbaldwin.com<http://nfbnet.org/mailman/options/blindm
>>>>>>>>>>
>>>>>>>>>> at h_nfbnet.org/baldwin%40dickbaldwin.com>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>> ______________________________**_________________
>>>>>>>> Blindmath mailing list
>>>>>>>> Blindmath at nfbnet.org
>>>>>>>> http://nfbnet.org/mailman/**listinfo/blindmath_nfbnet.org<http://nfb
>>>>>>>>
>>>>>>>> ne t.org/mailman/listinfo/blindmath_nfbnet.org>
>>>>>>>> To unsubscribe, change your list options or get your account info
>>>>>>>> for
>>>>>>>> Blindmath:
>>>>>>>> http://nfbnet.org/mailman/**options/blindmath_nfbnet.org/**
>>>>>>>> baldwin%40dickbaldwin.com<http://nfbnet.org/mailman/options/blindmat
>>>>>>>>
>>>>>>>> h_ nfbnet.org/baldwin%40dickbaldwin.com>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> Richard G. Baldwin (Dick Baldwin)
>>>>>>> Home of Baldwin's on-line Java Tutorials http://www.DickBaldwin.com
>>>>>>>
>>>>>>> Professor of Computer Information Technology Austin Community
>>>>>>> College
>>>>>>> (512) 223-4758
>>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>>> http://www.austincc.edu/baldwin/
>>>>>>> _______________________________________________
>>>>>>> Blindmath mailing list
>>>>>>> Blindmath at nfbnet.org
>>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>>> To unsubscribe, change your list options or get your account info
>>>>>>> for
>>>>>>> Blindmath:
>>>>>>>
>>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/kperry%40blink
>>>>>>>
>>>>>>> s
>>>>>>> oft.co
>>>>>>> m
>>>>>>>
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> Blindmath mailing list
>>>>>>> Blindmath at nfbnet.org
>>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>>> To unsubscribe, change your list options or get your account info
>>>>>>> for
>>>>>>> Blindmath:
>>>>>>>
>>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/baldwin%40dick
>>>>>>>
>>>>>>> b
>>>>>>> aldwin.com
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> Richard G. Baldwin (Dick Baldwin)
>>>>>> Home of Baldwin's on-line Java Tutorials http://www.DickBaldwin.com
>>>>>>
>>>>>> Professor of Computer Information Technology Austin Community College
>>>>>> (512) 223-4758
>>>>>> mailto:Baldwin at DickBaldwin.com
>>>>>> http://www.austincc.edu/baldwin/
>>>>>> _______________________________________________
>>>>>> Blindmath mailing list
>>>>>> Blindmath at nfbnet.org
>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>> To unsubscribe, change your list options or get your account info for
>>>>>> Blindmath:
>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/sbahram%40nc.rr
>>>>>>
>>>>>> .com
>>>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> Blindmath mailing list
>>>>>> Blindmath at nfbnet.org
>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>> To unsubscribe, change your list options or get your account info for
>>>>>> Blindmath:
>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/kperry%40blinks
>>>>>>
>>>>>> oft.co
>>>>>> m
>>>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> Blindmath mailing list
>>>>>> Blindmath at nfbnet.org
>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>> To unsubscribe, change your list options or get your account info for
>>>>>> Blindmath:
>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/sbahram%40nc.rr
>>>>>>
>>>>>> .com
>>>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> Blindmath mailing list
>>>>>> Blindmath at nfbnet.org
>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>> To unsubscribe, change your list options or get your account info for
>>>>>> Blindmath:
>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/kperry%40blinks
>>>>>>
>>>>>> oft.co
>>>>>> m
>>>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> Blindmath mailing list
>>>>>> Blindmath at nfbnet.org
>>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/mwhapples%40aim
>>>>>>
>>>>>> .com
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Blindmath mailing list
>>>>> Blindmath at nfbnet.org
>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/kperry%40blinksoft.co
>>>>>
>>>>> m
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Blindmath mailing list
>>>>> Blindmath at nfbnet.org
>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/sbahram%40nc.rr.com
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Blindmath mailing list
>>>>> Blindmath at nfbnet.org
>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/john.gardner%40orst.e
>>>>>
>>>>> du
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Blindmath mailing list
>>>>> Blindmath at nfbnet.org
>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/sbahram%40nc.rr.com
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Blindmath mailing list
>>>>> Blindmath at nfbnet.org
>>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>> To unsubscribe, change your list options or get your account info for
>>>>> Blindmath:
>>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/mwhapples%40aim.com
>>>>>
>>>>>
>>>>>
>>>>> __________ Information from ESET NOD32 Antivirus, version of virus
>>>>> signature database 6636 (20111116) __________
>>>>>
>>>>> The message was checked by ESET NOD32 Antivirus.
>>>>>
>>>>> http://www.eset.com
>>>>>
>>>>>
>>>>>
>>>>
>>>>
>>>> __________ Information from ESET NOD32 Antivirus, version of virus
>>>> signature
>>>> database 6636 (20111116) __________
>>>>
>>>> The message was checked by ESET NOD32 Antivirus.
>>>>
>>>> http://www.eset.com
>>>>
>>>>
>>>>
>>>>
>>>> _______________________________________________
>>>> Blindmath mailing list
>>>> Blindmath at nfbnet.org
>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>> To unsubscribe, change your list options or get your account info for
>>>> Blindmath:
>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/birkir.gunnarsson%40gmail.com
>>>>
>>>>
>>>
>>> _______________________________________________
>>> Blindmath mailing list
>>> Blindmath at nfbnet.org
>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>> To unsubscribe, change your list options or get your account info for
>>> Blindmath:
>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/tamara.8024%40comcast.net
>>>
>>>
>>
>> _______________________________________________
>> Blindmath mailing list
>> Blindmath at nfbnet.org
>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>> To unsubscribe, change your list options or get your account info for
>> Blindmath:
>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/mwhapples%40aim.com
>>
>
>
> _______________________________________________
> Blindmath mailing list
> Blindmath at nfbnet.org
> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
> To unsubscribe, change your list options or get your account info for
> Blindmath:
> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/tamara.8024%40comcast.net
>
>