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Re: Request for Collective Wisdom...

W_Craig Carter wrote:

> (*Below is a request for suggestions for "hints for beginners. The
> preface is a bit long-winded" *)
> I am working on an applied math for physical scientists undergraduate
> text---I am using Mathematica as the engine to learn and solve
> problems quickly.
> I have an appendix that I have been creating (empirically) for  a
> couple years: "Common Mathematica Beginners' Errors." This wasn't
> difficult.
> I am now considering how to write another Appendix: "Mathematica Usage
> Paradigms for Beginners."  This one is not as straightforward because
> it will be a list of short sequences of Mathematica code. The size of
> the list should be a compromise between length, completeness, and
> "orthogonality."
> Some topics are obvious to (subjective) me: work symbolically and with
> exact representations; scale to remove units when possible; visualize
> often and when in doubt evaluate as a number; pure functions are
> power; avoid the outdoors unless you have applied the documentation,
> lists are your friends...
> Nota bene, this is a book for undergraduates who have just received
> the "physics, chemistry, and multivariable calculus" catechism, and
> (typically) don't appreciate that there are common themes in their
> education (think back...).
> (* Punchline: *)
> I would sincerely appreciate thoughtful (bullet-type) suggestions for
> paradigms.  (off-line or on- as you please).
> PS: Implicit in this is what a dear friend called "The Homotopy
> Conjecture."  Give me a small working example, and it can deformed
> into a complicated one for my own purposes.
> PPS: I expect a small fraction of snarky answers---I won't respond.

Hi Graig,

I would suggest the following to be added to your list:

1. Learn to see Mathematica expressions in FullForm (it is incredible 
how many "bugs" or "weird" behaviors or "unexpected" results can be 
avoided or explained just by looking at the FullForm of the incriminated 

2. Everything is an expression (at least in Mathematica :-)

3. Do not trust blindly, check the results (differentiate back an 
integral, check the limits on both sides, plug the solution to an 
equation into the original equation).

4. Everything is an expression (reloaded :-)

Best regards,
-- Jean-Marc

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