algebra on SWiK

- hmatrix

Thu, 14 Aug 2008 17:08:55 -0700

dansmath.com

Thu, 14 Aug 2008 11:05:18 -0700

A Neighborhood of Infinity: Geometric Algebra for Free!

Sun, 10 Aug 2008 15:08:08 -0700

A Neighborhood of Infinity: More Low Cost Geometric Algebra

Sun, 10 Aug 2008 15:08:08 -0700

User:bermsek

Fri, 08 Aug 2008 13:21:01 -0700

Teach Yourself the Entire Course in 24 Hours

Sign up for the Web’s first and still the only newsletters for students on biology, chemistry, physics, and math. Get your winning edge with the insider’s study tips and tutorials in learning all branches of science and math. Build your intuition and discover the rapid path to rapid learning.

Algebra II - Math for Morons Like Us

Mon, 28 Jul 2008 15:23:57 -0700

On this and the following pages, we’ll try to clear up some common problems people have with intermediate algebra (Algebra II) and trigonometry (which ought …

http://library.thinkquest.org/20991/alg2/index.html

Intermediate Algebra-TOC

Mon, 28 Jul 2008 15:22:14 -0700

MathNotes currently offers two new resources to help you strengthen your understanding of the mathematics you are studying: InterAct Math software tutorials …

http://www.mathnotes.com/aw_intermediate.html

Teach Yourself Intermediate Algebra Visually in 24 hours

Mon, 28 Jul 2008 15:19:55 -0700

This rapid learning course is one of the pre-college math courses to prepare for the pre-requisite to college level math. The 24 chapters will enable you to master the algebra needed for college level courses, such as college algebra, college calculus etc.

http://www.rapidlearningcenter.com/mathematics/intermediate-algebra/intermediate-algebra.html

User:denismanson

Fri, 25 Jul 2008 15:01:15 -0700

Elementary Algebra Visually in 24 Hours

http://www.rapidlearningcenter.com/mathematics/elementary-algebra/elementary-algebra.html

This college prep course is the first of pre-college math sequence. Elementary Algebra (i.e. Introductory Algebra), along with the next course Intermediate Algebra, are the two prerequisite math courses, prior to College Algebra.

Screenshots // Maxima CAS

Wed, 23 Jul 2008 10:49:59 -0700

StartingPoints - MathEclipse

Sun, 20 Jul 2008 14:45:43 -0700

Monads from Algebra and the the Gray Code from Groups

Sat, 19 Jul 2008 06:45:08 -0700

User:alberdarko

Thu, 17 Jul 2008 09:08:25 -0700

Prepare your exam powerfully with rapid learning 3-step process (1) Master the core concepts with rich-media videos; (2) Sharpen your problem solving skill with interactive drills. (3) Super review with condensed cheat sheets.

GeoGebra

Wed, 16 Jul 2008 10:51:40 -0700

GeoGebra is a dynamic mathematics software for schools that joins geometry, algebra and calculus. It is an interactive geometry system.

PostScript and PDF files for "An Invitation to General Algebra ..."

Wed, 09 Jul 2008 09:48:59 -0700

Recursion Schemes: A Field Guide

Fri, 04 Jul 2008 02:47:25 -0700

Macaulay 2 home page

Tue, 24 Jun 2008 01:00:21 -0700

Macaulay 2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.

GAP System for Computational Discrete Algebra

Tue, 10 Jun 2008 15:13:19 -0700

GeoGebra

Fri, 06 Jun 2008 18:54:58 -0700

REASC

Wed, 04 Jun 2008 22:51:41 -0700

Jean-Jacques Dubray (now with SAP) has posted an interesting SOA pattern on his blog. REASC: a pattern for constructing Composite Applications.

This pattern seems to assume a fairly simple event algebra - each event refers to a state-change of a single resource. This appears to restrict the pattern to atomic events.

How can the pattern be extended to support compound events? For example, in building an SOA to support the real-time business, I may want to create BI services that generate compound events. For example, an event may be triggered when the frequency of some transaction exceeds some threshold, or when some new pattern is detected in the data. These compound events might possibly be composed from atomic events, but this may not be the best way to specify them. In any case, I do not want to be forced to define compound (aggregate) resources that correspond to these compound events.

It is possible that JJ intends this kind of event algebra to be contained within the Coordinator. But I should prefer to elaborate the event itself to allow for event composition. This would also allow for amplification and attenuation (as found in Stafford Beer).

I am also interested in exploring the use of the REASC pattern for the service-based business, where resource perhaps equates to business asset. How might we interpret the Coordinator function in service-based B2B collaborations?

Technorati Tags: SOA service-oriented

Doubting Events

Wed, 04 Jun 2008 22:51:40 -0700

In my previous post on Cancelling Events, I pointed out that new information sometimes causes us to revise our opinion as to whether a given event had occurred. Marco Seiriö wants to handle my example by adding probability into an event model. According to Marco, you would require that each part of the system can deal with these probabilities.

I can see that probabilistic events could be useful sometimes. However, I am not convinced we need to propagate these probabilities (and the accompanying complexity) throughout the system. I'd prefer to find a way of containing the complexity, so that some parts of the system are presented with a simple binary event statement (either it happened or it didn't) while other parts of the system may be presented with a more complex probabilistic event statement (it might have happened, with probability X%). This is a form of attenuation. - it can be regarded as an application of the need-to-know principle.

This attenuation could be managed architecturally by layering - for example we might separate a process coordination layer (which knows about the probabilities) from a process execution layer (which doesn't).

There is another problem with probabilities - which is that they may change continuously. If a promised action does not appear, the probability that the other person has forgotten increases with time. In the car accident example, if the driver fails to respond under certain conditions, it becomes increasingly likely (but still not certain) that the driver is dead or unconscious. The emergency response parts of the system may need to respond in real-time or near-real-time to this continously shifting probability, but we want to decouple this from other parts of the system that do not have this requirement.

More fundamentally, probability introduces some algebraic challenges that can be solved for relatively simple examples (and perhaps the car accident example is relatively simple) but don't scale for more complex examples (I guess I'll have to construct one).

Scilab Home Page

Fri, 30 May 2008 09:45:30 -0700

multitude - Google Code

Sun, 11 May 2008 02:19:07 -0700

Information Algebra

Mon, 17 Mar 2008 16:50:07 -0700

I get more information from two newspapers than from one - but not twice as much information. So how much more, exactly? That depends how much difference there is between the two newspapers.

Even if two newspapers report the same general facts, they typically report different details, and they may have different sources. To the extent that there are differences in style and detail between the two newspapers, this typically reinforces my confidence in the overall story because it indicates that the journalists are not merely reusing a common source (such as a company press release).

In the real world, we are accustomed to the fact that information and intelligence needs double-checking and corroboration. And yet in the computer world, there is a widespread belief that it is always a good thing to have a single source of information - that repeated messages are not only unnecessary but wasteful. Data cleansing wipes out difference in the name of consistency and standardization, leaving the resulting information flat and attenuated. A single source of information ("single source of truth") sometimes means a single source of failure - never a good idea in an open distributed system.

Writing about this in an SOA context - when three heads are better than one - Steve Jones describes this as redundancy, and points out the potential value of redundancy to increase reliability. He quotes Lewis Carroll (as Andrew Clarke points out, it was actually the Bellman): "What I tell you three times is true."

The same quote can be found at the head of Chapter 3 of Gregory Bateson's Mind and Nature, available online as Multiple Versions of the World. This expands on Bateson's earlier slogan "Two descriptions are better than one".

Bateson himself used the word "redundancy", but it is not a simple redundancy that can be plucked out without a second thought. Thinking about the consequences of adding and subtracting redundancy is a hard problem - Paulo Rocchi calls it calculus, but I prefer to call it algebra.

GeoGebra- Math software

Tue, 26 Feb 2008 11:44:36 -0800

Geometry, Algebra, Calculus freeware

Colloquium Detail

Sat, 02 Feb 2008 19:41:08 -0800

Talk on the SAGE open source computer algebra project.

SAGE: Open Source Mathematics Software

Sat, 02 Feb 2008 19:41:08 -0800

Home page for SAGE open source computer algebra (and more) package

SAGE: Open Source Mathematics Software

Sat, 02 Feb 2008 19:40:17 -0800

Home page for SAGE open source computer algebra (and more) package

SAGE: Open Source Mathematics Software

Fri, 25 Jan 2008 01:03:52 -0800

SAGE: Open Source Mathematics Software

Mon, 21 Jan 2008 11:00:20 -0800