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3. Add gridlines to plot in sage. Franco Saliola improved *a lot* my initial patch by adding many options to make it work like in Matematica. See [http://trac.sagemath.org/sage_trac/ticket/3825 Ticket #3825] 
Sage days 9 Student Projects
Please add your project to this list. Follow the examples that are already there.
Mclean Edwards, Scott Zhou: BFGS Iterates. Plotting iterates, in an interactive manner, of the celebrated BFGS method for the minimization of nonconvex and convex functions. Comparison of sage, jyscript/piscript, and our own pythonbased solutions.
Jakub Marecek: Toy Integer Programming Solver. A very limited integer programming solver for instances with 3 variables, but complete with several primal heuristics in use today, and visualising the workings nicely. (Java & vtkHull?)
Further ideas: SVG and PDF Output for JyScript. A quick hack using Apache Batik (http://xmlgraphics.apache.org/batik/). TeX and PS and PDF Output for SAGE. A quick hack using Sketch (http://www.frontiernet.net/~eugene.ressler/).
Aurel Meyer: Symmetry groups of polytopes. Graphics to illustrate that all symmetry groups of regular polytopes are finite Coxeter groups.
Yair Go1dberg: 3D Graphing in PiScript. Plotting 3 dimensional functions in PiScript.
Steve Kieffer: Algebra sketches. Tools with which to produce sketches of a kind often drawn on blackboards to illustrate algebraic structures.
Michael Lamoureux: EasyBalls. A 2D animation of colliding balls, maybe with gravity, maybe with E&M if I can get the 3D in there.
Ryan Hoban: Hyperbolic Geometry. Using sage to draw geometric structures in the Hyperbolic plane.
Sébastien Labbé: Combinatorics on words.
 Use colors and @interact of sage to study equations on words.
[http://wiki.sagemath.org/Days9Projects?action=AttachFile&do=get&target=Equations_on_words_with_color.sws Equations_on_words_with_color.sws] (Next version of [http://code.google.com/p/sagewords/ sagewords package] needed to run it!!)
 Use jyscript and jython to create a java applet to illustrate Christoffel words
Add gridlines to plot in sage. Franco Saliola improved *a lot* my initial patch by adding many options to make it work like in Matematica. See [http://trac.sagemath.org/sage_trac/ticket/3825 Ticket #3825]
 Use colors and @interact of sage to study equations on words.
Arnaud Bergeron: Better adaptive plotting in Sage. At William's request, I am working on better adaptive refinement for Sage's plot() command.