Coursera course on CS linear algebra using Python

[kcrisman]

Just FYI, seems relevant.

https://www.coursera.org/course/matrix

If someone knows the instructor, they should tell him to use Sage :-)
though we aren't at Python 3 yet, which it sounds like is what he'll
use.

[William Stein]

It says " You will write small programs in the programming language
Python to implement basic matrix and vector functionality and
algorithms, and use these to process real-world data..." so I'm
guessing he views the lack-of-math-functionality in Python as an
advantage for his teaching style.

I personally disagree that it is an advantage. And processing real
world data using your own pure-path implementation of basic algorithms
seems painful. I'd at least use numpy/scipy.

William


>
> --
> You received this message because you are subscribed to the Google Groups "sage-edu" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to sage-edu+u...@googlegroups.com.
> To post to this group, send email to sage...@googlegroups.com.
> Visit this group at http://groups.google.com/group/sage-edu?hl=en.
> For more options, visit https://groups.google.com/groups/opt_out.
>
>



--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[kcrisman]

On Apr 10, 1:20 pm, William Stein <wst...@gmail.com> wrote:

> On Wed, Apr 10, 2013 at 10:16 AM, kcrisman <kcris...@gmail.com> wrote:
> > Just FYI, seems relevant.
>
> >https://www.coursera.org/course/matrix
>
> > If someone knows the instructor, they should tell him to use Sage :-)
> > though we aren't at Python 3 yet, which it sounds like is what he'll
> > use.
>
> It says " You will write small programs in the programming language
> Python to  implement basic matrix and vector functionality and
> algorithms, and use these to process real-world data..." so I'm
> guessing he views the lack-of-math-functionality in Python as an
> advantage for his teaching style.
>
> I personally disagree that it is an advantage.  And processing real
> world data using your own pure-path implementation of basic algorithms
> seems painful.  I'd at least use numpy/scipy.
>

Right. I guess as a "blended" course it is interesting, but I hardly
think that people who know *neither* LA *nor* any programming would be
a good candidate for this course's level of discourse. It's pretty
hard to teach two things at once.

[Gerald Smith]

Ah!  Linear Algebra!  This creates an itch I have to scratch, especially if you intend to emphasize its computer applications.

I firmly hold that modern approaches to teaching Linear Algebra  are deeply crippled by failing to go far enough in their concepts.  I am a huge fan of the Geometric Algebra of Dr. David Hestenes, Professor Emeritus of Mathematical physics at Arizona State University.   This is to be sure based on Clifford Algebra but in a way that is vastly more user friendly, something you find too rarely in mathematics nowadays.  think of defining "vector" so it is compatable with the traditional definition used in physics, an entity having direction and magnitude, representable by a string of REAL numbers. I should note that complex numbers are not permissible as components as  the equation" i^2 = -1" is not unambiguous in Geometric Algebra.  There are many possible entities whose square can equal -1  and they are best handled using a spinor algebra.   These fundamental spinor algebras play a big role in Geometric Akgebra, especially the sopinor algebra of E2 (complex numbers) and of E3 (quaterrnions).  The spinor algebra of E4 corresponds to the idea of Lorenz transformations but these are preferentially handled  by introducing non-trivial unipotent elements and doing it as a hyperbolic geometry.  Has anybody here ever played with hyperbolic numbers, those evil cousins of the complex numbers?  ^,..,^    Hint: (instead of "a+bi" you have "a+bu" such that u^2=1 and u <> 1,-1   You should find it trivial to show these numbers can be proper divisors of zero. It is  also easy to show that non-trivial idempotents exist too.)

To make up for restricting the definition of vector, geometric Algebra allows for multidimensional vectors "nvectors" and mixed forms of different dimensions called "multivectors".  The simplest familar example would be a classic complex number which combines a 0-vector (i.e., a scalar) with a 2 -vector (i) in an E2 vector space.  Geometric Algebra puts as much emphasis on the Outer Product of two vectors as on the Inner Product and in fact combines the two into a more general Geometric Product.   This results in an algebra on vectors that lets you define +, -, *, /  operations on vectors with the p[roviso that multiplication is not commutative but is associative and elements may violate the zero product property of real numbers, in a word an algebra mote or less equivalent to matrix algebra. The concept of the determinant of a square matrix cannot be given a simple intuitive explanation without using the concept of Outer Product  nor can you really make clear why Cramer's Rule without recourse to the concept of Outer Product of vectors. 

Geometric Algebra, or its extensions Geometric Calculus and Conformal Algebra or the hyperbolic Space-Time Algebra (used to provide a mathematical language for Special Relativity) are just some of the rich variety of topics that have been developed using Dr. Hestenes' concepts.  I a impressed by the number of computer oriented people who say that they never really understood Linear Algebra until after they had studied Geometric Algebra.  This was true for me too.  the problem with traditional approaches to teaching Linear Algebra is that it overwhelmingly emphasizes the algebraic component; this in a subject that has very rich geometric interpretations and applications.  As Dr. Hestenes puts it: "Geometry without Algebra is mute, but Algebra without geometry is blind!"  for a student of mathematics, connecting the linguistic/grammatical aspects of mathematics with the visual/geometric is absolutely essential to understanding the subjects.  Showing a bunch of Greek letters and arcane symbols dancing across a page does not adequately convey understanding.  I do not know if Geometric Algebra has been implemented in Sage Math yet, but it has been implemented on computers and I suspect that it may have been implemented in Python.  If anybody knows anything about this I would be delighted to know about it.

Cheers!  Math Bear    ^,..,^  

---

From: kcrisman <kcri...@gmail.com> a
To: sage-edu <sage...@googlegroups.com>
Sent: Wednesday, April 10, 2013 12:16 PM
Subject: [sage-edu] Coursera course on CS linear algebra using Python

--
You received this message because you are subscribed to the Google Groups "sage-edu" group.

To unsubscribe from this group and stop receiving emails from it, send an email to sage-edu+unsub...@googlegroups.com.