Re: [math-fun] Symbolic Calculation
Actually, this is one book (actually _three_ books!) that you really want to buy. I marked up nearly every single page of all three volumes. I think I learned more math from Knuth than from all of the rest of my math courses combined. You can probably get the 3-volume set used if you look on EBay. Another keeper: Feynmann's Lectures on Physics. You can learn more physics from these volumes than from any six other physics or math courses. At 06:02 PM 5/6/2011, David Makin wrote:
Oh ! I guess |I'll have to read it properly at last (been meaning to for about 15 years). Previously I've just gleaned one or two gems from it but not read the whole thing - if I remember correctly the most useful item for me from it (in the past) was the max/med/min method to get the approx, 3D magnitude., though knowing my memory nowadays I could have got that from somewhere else entirely ;) Another visit to the library is in order.
On 6 May 2011, at 21:03, Henry Baker wrote:
Knuth's Art of Computer Programming, among others. I would hope that it is accessible to UK "A" levels!
At 12:37 PM 5/6/2011, David Makin wrote:
On 6 May 2011, at 19:53, Joerg Arndt wrote:
* Henry Baker <hbaker1@pipeline.com> [May 06. 2011 20:25]:
You know that the Casio performs an inverse lookup for sure?
As an aside, there is an interesting trend in symbolic algebra that's been going on for 35 years or so: doing less traditional algebra & more numerical calculations. E.g., instead of using bignums to compute the inverse of an integer determinant, compute the determinant mod p for enough p's; using "black box programs" to compute polynomials & computing the coefficients (if you really want them) by interpolating enough point values.
Note this method (compute mod enough coprime moduli, then CRT) is 1) exact 2) bloody fast
Where can I find details of (compute mod enough coprime moduli, then CRT) ? (that someone with only UK "A" level math can understand) (I mean for example - what's CRT here ?)
When I was 17, I enrolled at the University of Texas and started working at a small Tokamak there in order to pay my rent and tuition. A year later I got accepted at Berkeley and went there to study Math and Physics. The professor I worked for at UT gave me the Feynman Lectures as a going away present. I studied them when I was an undergrad, and still have them to this day. One day I hope to pass them on to my son. He's only 7 now, so I don't know what his future interests will be. But he is very good at integer computation and fractions, which I consider a good sign for a boy his age. On Fri, May 6, 2011 at 8:35 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Actually, this is one book (actually _three_ books!) that you really want to buy. I marked up nearly every single page of all three volumes.
I think I learned more math from Knuth than from all of the rest of my math courses combined.
You can probably get the 3-volume set used if you look on EBay.
Another keeper: Feynmann's Lectures on Physics. You can learn more physics from these volumes than from any six other physics or math courses.
At 06:02 PM 5/6/2011, David Makin wrote:
Oh ! I guess |I'll have to read it properly at last (been meaning to for about 15 years). Previously I've just gleaned one or two gems from it but not read the whole thing - if I remember correctly the most useful item for me from it (in the past) was the max/med/min method to get the approx, 3D magnitude., though knowing my memory nowadays I could have got that from somewhere else entirely ;) Another visit to the library is in order.
On 6 May 2011, at 21:03, Henry Baker wrote:
Knuth's Art of Computer Programming, among others. I would hope that it is accessible to UK "A" levels!
At 12:37 PM 5/6/2011, David Makin wrote:
On 6 May 2011, at 19:53, Joerg Arndt wrote:
* Henry Baker <hbaker1@pipeline.com> [May 06. 2011 20:25]:
You know that the Casio performs an inverse lookup for sure?
As an aside, there is an interesting trend in symbolic algebra that's been going on for 35 years or so: doing less traditional algebra & more numerical calculations. E.g., instead of using bignums to compute the inverse of an integer determinant, compute the determinant mod p for enough p's; using "black box programs" to compute polynomials & computing the coefficients (if you really want them) by interpolating enough point values.
Note this method (compute mod enough coprime moduli, then CRT) is 1) exact 2) bloody fast
Where can I find details of (compute mod enough coprime moduli, then CRT) ? (that someone with only UK "A" level math can understand) (I mean for example - what's CRT here ?)
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I hope you named your son William ;-) He's probably old enough now to learn about quaternions... In another year, you might have to teach him something non-associative! At 09:15 PM 5/6/2011, Rowan Hamilton wrote:
When I was 17, I enrolled at the University of Texas and started working at a small Tokamak there in order to pay my rent and tuition. A year later I got accepted at Berkeley and went there to study Math and Physics. The professor I worked for at UT gave me the Feynman Lectures as a going away present. I studied them when I was an undergrad, and still have them to this day. One day I hope to pass them on to my son. He's only 7 now, so I don't know what his future interests will be. But he is very good at integer computation and fractions, which I consider a good sign for a boy his age.
On Fri, May 6, 2011 at 8:35 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Actually, this is one book (actually _three_ books!) that you really want to buy. I marked up nearly every single page of all three volumes.
I think I learned more math from Knuth than from all of the rest of my math courses combined.
You can probably get the 3-volume set used if you look on EBay.
Another keeper: Feynmann's Lectures on Physics. You can learn more physics from these volumes than from any six other physics or math courses.
At 06:02 PM 5/6/2011, David Makin wrote:
Oh ! I guess |I'll have to read it properly at last (been meaning to for about 15 years). Previously I've just gleaned one or two gems from it but not read the whole thing - if I remember correctly the most useful item for me from it (in the past) was the max/med/min method to get the approx, 3D magnitude., though knowing my memory nowadays I could have got that from somewhere else entirely ;) Another visit to the library is in order.
On 6 May 2011, at 21:03, Henry Baker wrote:
Knuth's Art of Computer Programming, among others. I would hope that it is accessible to UK "A" levels!
At 12:37 PM 5/6/2011, David Makin wrote:
On 6 May 2011, at 19:53, Joerg Arndt wrote:
* Henry Baker <hbaker1@pipeline.com> [May 06. 2011 20:25]: > You know that the Casio performs an inverse lookup for sure? > > As an aside, there is an interesting trend in symbolic algebra > that's been going on for 35 years or so: doing less traditional > algebra & more numerical calculations. E.g., instead of using > bignums to compute the inverse of an integer determinant, compute > the determinant mod p for enough p's; using "black box programs" to > compute polynomials & computing the coefficients (if you really want > them) by interpolating enough point values.
Note this method (compute mod enough coprime moduli, then CRT) is 1) exact 2) bloody fast
Where can I find details of (compute mod enough coprime moduli, then CRT) ? (that someone with only UK "A" level math can understand) (I mean for example - what's CRT here ?)
My first name is actually William. My mom was a mathematician who specialized in algebra and really liked quaternions. I like math, but I am really a physicist. And it took me some time to realize the connection between quaternions and 19th century vector analysis (i.e. Maxwell). By then I was moving on to grad school, and things were getting much more complicated. Rowan. PS As far as I know, I have no family relation to WRH. But I am a direct descendant from the old Dukes of Hamilton in Scotland, so who knows? Then again, I am a Hamilton on my dad's side, and my mom's side is just a bunch of Norwegian farmers from Minnesota... On Fri, May 6, 2011 at 9:27 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I hope you named your son William ;-)
He's probably old enough now to learn about quaternions... In another year, you might have to teach him something non-associative!
At 09:15 PM 5/6/2011, Rowan Hamilton wrote:
When I was 17, I enrolled at the University of Texas and started working at a small Tokamak there in order to pay my rent and tuition. A year later I got accepted at Berkeley and went there to study Math and Physics. The professor I worked for at UT gave me the Feynman Lectures as a going away present. I studied them when I was an undergrad, and still have them to this day. One day I hope to pass them on to my son. He's only 7 now, so I don't know what his future interests will be. But he is very good at integer computation and fractions, which I consider a good sign for a boy his age.
On Fri, May 6, 2011 at 8:35 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Actually, this is one book (actually _three_ books!) that you really want to buy. I marked up nearly every single page of all three volumes.
I think I learned more math from Knuth than from all of the rest of my math courses combined.
You can probably get the 3-volume set used if you look on EBay.
Another keeper: Feynmann's Lectures on Physics. You can learn more physics from these volumes than from any six other physics or math courses.
At 06:02 PM 5/6/2011, David Makin wrote:
Oh ! I guess |I'll have to read it properly at last (been meaning to for about 15 years). Previously I've just gleaned one or two gems from it but not read the whole thing - if I remember correctly the most useful item for me from it (in the past) was the max/med/min method to get the approx, 3D magnitude., though knowing my memory nowadays I could have got that from somewhere else entirely ;) Another visit to the library is in order.
On 6 May 2011, at 21:03, Henry Baker wrote:
Knuth's Art of Computer Programming, among others. I would hope that it is accessible to UK "A" levels!
At 12:37 PM 5/6/2011, David Makin wrote:
On 6 May 2011, at 19:53, Joerg Arndt wrote:
> * Henry Baker <hbaker1@pipeline.com> [May 06. 2011 20:25]: >> You know that the Casio performs an inverse lookup for sure? >> >> As an aside, there is an interesting trend in symbolic algebra >> that's been going on for 35 years or so: doing less traditional >> algebra & more numerical calculations. E.g., instead of using >> bignums to compute the inverse of an integer determinant, compute >> the determinant mod p for enough p's; using "black box programs" to >> compute polynomials & computing the coefficients (if you really want >> them) by interpolating enough point values. > > Note this method (compute mod enough coprime moduli, then CRT) is > 1) exact > 2) bloody fast
Where can I find details of (compute mod enough coprime moduli, then CRT) ? (that someone with only UK "A" level math can understand) (I mean for example - what's CRT here ?)
participants (2)
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Henry Baker -
Rowan Hamilton