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That's great. A colleague asked me about iteration recently when I was trying the convince the dept that Geogebra is better than another graphing package. I can now give them a resource and learnt something new.

Appreciation by Dave (guest), 18 Oct 2009 18:23
cobwebs in GeoGebra 3.2 by Michael Borcherds (guest), 14 Jun 2009 19:21

One more thing… it might be nice to close with a discussion of how the existence of simple loops and non-simple loops in the diagrams relates to the generators of the coordinate ring. I know we talked about this briefly in DC and what I was thinking about didn't really work, but I think there's something there and if we can figure out something (anything really) to say about how they relate to the generators it might make a nice close to the paper… re-emphasizing the usefulness of the diagrammatic point-of-view and particularly the recurrences.

Okay, here's the latest version (also posted on the wiki). I have updated all files to the wiki as well. A couple of things that I still need to work on:

1) Better introduction to spin networks/trace diagrams. I don't really say what they are to begin with. I will try to keep this brief.
2) Need to add in a lot of references.

Finally, something for us to think about. Your rank 3 cf's are listed as X(a,b,c,d,i,j) and mine as X(a,b,c,d,e,f). I put in some comments about the relationship between the two forms, and I propose that we use subscripts to separate the two pieces… e.g. yours could be X_{a,b,c,d}^{i,j} since a,b,c,d represent Sym_*(V) but i,j just describe how to pick out some Sym_*(V). Then mine could be just X_{a,b,c,d,e,f} since they all represent explicit Sym_*(V). Let me know what you think. It would be detrimental I think to write everything in terms of your i,j because that is so unnatural for diagrams.

I'd like to give this a few days rest then will hit the whole thing again and figure out the introductory diagram material. I will likely copy/paste most of that so it shouldn't take too long.


My latest revisions by elishapetersonelishapeterson, 20 Jan 2009 19:43

I have finished going through my work to double-check to make sure I have not made any glaring errors. At this point I have checked and double-checked in multiple ways, and my results agree with those provided in your table of central functions (as listed in the paper). Yeah!!! Expect major updates to come your way soon.

Study hard, and have a Merry Christmas/Happy Holidays!

Good luck on the TEE by elishapetersonelishapeterson, 15 Dec 2008 17:10

The TEE is scheduled for Tuesday, 16-Dec from 0735-1105 in the following locations:

  • Section A1: Bartlett Hall 309
  • Section B1: Bartlett Hall 310

You are authorized 5 handwritten note sheets for the exam (front/back). Calculators are not permitted.

A review session will be held on Saturday, 13-Dec from 0830-1100 in Thayer Hall 342.

Here are the checklists from the first for blocks:

The lowest WPR score has been dropped in AMS. Some of you should see your grades go up quite a bit!

Remember that there are still roughly 1/3 of the course points to be assigned, between the Project and the TEE!

WPR Drop by elishapetersonelishapeterson, 04 Dec 2008 02:24

When/where: I'll be speaking on November 20, in Thayer Hall 344 from 1355-1450. See abstract below.

Dynamic Mathematics and Pursuit/Evasion Games
Dr. Elisha Peterson
Assistant Professor/Davies Fellow, USMA

Abstract: Pursuit/Evasion Games are simple games in which the primary objective is either to chase down the opposing team, or to avoid capture by the opposing team. These games are played out all around us. Think of football, ultimate frisbee, and capture-the-flag… and what would Hollywood do without car chases? Exact solutions can be found for simple versions of these games using differential equations. However, this talk focuses on visualizations of these games when there are two or more teams and lots of players involved. Several scenarios will be illustrated using a Java platform that automatically updates solutions whenever parameters are changed. This visual approach is one example showing how making mathematics "dynamic" can lead to additional insights into the underlying situation.

Optional Lecture by elishapetersonelishapeterson, 20 Nov 2008 13:02

When/where: This Friday we will have a guest lecture in Thayer Hall 144 during Dean's Hour. See abstract below.

Mathematics and the "Age of Biology"
Dr. Ben Cole
Technical Director of Research, NSA

Abstract: I will address what I feel will become the most significant new technical challenges that lie ahead of us - specifically the manner in which humans will join with the information network - thereby highlighting both the promise and the peril of human enhancement. I will attempt to show why computer science, engineering, physics and mathematics are the basic disciplines that will lead the way in forcing new biological understandings of what it means to be human. I will mention a new effort that has just begun at NSA to understand the place of neuroscience in computation and communication, then conclude with a look at some of the new things that you can get this Christmas which will allow you, yourself to become an actual "player" in the Age of Biology that is dawning.

Guest Lecture 4 by elishapetersonelishapeterson, 20 Nov 2008 12:58

The second project has been posted and is available at http://usmasvdzdeanext/departments/math/courses/ma153/Projects/Project%202/P2RoadRunner.pdf. The topics include material from the early part of chapter 16. As with the first project, this project will be completed in groups, and will be due the Thursday after Thanksgiving break.

The idea behind the first problem is reflected somewhat in the applet at… if you're struggling to figure out what's going on it may be worth checking out.

Project 2 by elishapetersonelishapeterson, 12 Nov 2008 11:43

When/where: This Friday we will have a guest lecture in the Mahan Hall Auditorium during Dean's Hour. See abstract below.

Recommender Systems for Fun and Profit
Dr. Chris Volinsky
Director of Statistics Research, AT&T Research, Florham Park, NJ

Abstract: In October 2006, Netflix released 100 million movie ratings as part of a $1M prize for any team that could improve their movie recommendation system by more than 10%. This landmark data set generated intense interest from the statistics and machine learning communities, and attracted entries from over 3000 teams from academia and industry. In this talk, I will review AT&T's experience analyzing this data using collaborative filtering techniques, leading to our winning a $50,000 progress prize, as well as a subsequent project applying the methodology to television viewing data.

Here's a fun pic from the Kenyon College math department website:


Does your birthday appear in pi??? Check out to see.

Pi in the Ski by elishapetersonelishapeterson, 05 Nov 2008 18:23

Another chance for bonus points and some fun: POTW is here. Have a good weekend!

POTW #8 by elishapetersonelishapeterson, 01 Nov 2008 11:10

I have posted an applet for visualizing 2D vector fields at This has some advantages over mathematica… you can adjust the boundaries of the plot with the mouse and also play around with the flowlines.

2D Vector Fields Applet by elishapetersonelishapeterson, 29 Oct 2008 15:19

Both WPR III and Project I are now graded. You should be able to see your project grades, but the WPR grades will not be available until later. The projects will be returned tomorrow (Wednesday), and the WPR's either Wednesday or Thursday.

Project Grading Done by elishapetersonelishapeterson, 28 Oct 2008 17:09
  1. For some more help visualizing the regions in problem 15.6.34, I've posted a notebook (courses:ma153/15-6-34.nb).
  2. The next problem of the week is here! Have fun!
POTW #7 and 15.6.34 by elishapetersonelishapeterson, 24 Oct 2008 14:32

See this notebook for some tricks for visualizing volumes of integrations. (Right-click to save to your computer.)

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