Overview of Mathematica

I attended the virtual overview of Mathematica today (at 10 am EST).
Mathematica is among the most powerful computer programs for doing mathematics, and now has many other applications.  I think the presenter, with his great enthusiasm, bit off more than his audience could chew in a one hour session.  Mathematica has some very nice abilities for the teaching of calculus.  It is very handy with making slides – the presenter whipped off a set of integration slides in literally a few seconds.  It also has a tool that makes it easy to create homework assignments, and even easier to grade them.  This feature, however, was not presented since time ran out just as the presenter was getting to it.  What was presented were some of the basics, like syntax, and then a wealth of information that mainly had to do with advanced uses of Mathematica in various fields of research.

We learned, very quickly how to:
Solve systems of equations, do regression and interpolation
How to do integrals with Mathematica
How to use a palette to enter commands as if in longhand
How to do 3D plots, presenter made a nice upside down cone
That Mathematica does very difficult integrals such as Integral[(sqrt( tan x))] or the Integral[sin x/ e ^{-x}]
How to solve a system of partial differential equations.  How to plot 3-D parametric equations.  He plotted a beautiful 3-D butterfly pattern
In 3d plots – how to choose x and y range, color, restrict domain etc..
How to do stream density plot as in plotting an electric or magnetic field.
Visualization of graphs in Mathematica is excellent.
Lots of data is available for manipulation and plotting; plotted finance data for Google and weather data for Sacramento high temps with single commands.  27500 proteins available on data with detailed 3-D rendering
There is a tool that can construct a food chain diagram intuitively
Generate a complicated random walk with one line of code
Three methods of Programming in mathematica
Procedural program which has loops like in C, Pascal or Fortran
Functional programming :  makes use of built in Mathematica functions: for example, you can use Norm or Euclideandistance to find distance.
Rule based approach: This finds a pattern and replaces it everywhere with a calculation
Pattern matching  (genome data) using rule based program to find substrings in a gene
Parallel computation – If you have access to a network or multiprocessor, Mathematica can do
heavy calculations in parallel, which makes them run faster.
Advanced image processing
Lots of external connectivity — to data bases e.g.
Tools for making slide shows
Generating and correcting homework assignments
Mathematica Community:  Math group for posting questions, Web Group

Mathematica is probably too powerful and costly for high school use.  However, it does have many awesome tools for solving math problems, doing graphics, and creating lecture slides.  If I were teaching at a college, I would be excited about using it.

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