There is this book: Fast Introduction for Programmers:

http://www.wolfram.com/language/fast-introduction-for-programmers/en

but I am not sure if this is what you want.

Thank you, everyone. I did not realize that DelayedSet gets literally substituted (like a define in C). Back to reading about basics...

My bad about those rules: this UI is quite different from what I got used to (on typical forum) and confused me quite a bit -- I don't remember running across them.

See what happens if you use a different variable, for instance k, instead of n in the definition of M, leaving everything else the same:

Clear[F, G, M];
F[x_] := UnitStep[x]*UnitStep[10 - x]*1/10
G[x_] := DiscreteConvolve[F[n], F[n], n, x]
M[x_] := DiscreteConvolve[G[k], F[k], k, x]
DiscretePlot[{F[x], G[x], M[x]}, {x, 0, 30}]

In your definition of M[x_] you call G[n], which translates to

DiscreteConvolve[F[n], F[n], n, n]

which is trouble, because the summation index is the same as the parameter. Look at the difference between G[m] and

G[n] // PiecewiseExpand

The problem goes away with immediate definition = instead of your delayed definition :=

Unfortunately DiscretePlot does no check on the variables it is fed.

Hi First, your code is highly inefficient, since you do not really compute the discrete convolution until you call the graphics, and then for each value of the horizontal axis you repeat the convolutions. This happens since you used := (SetDelayed) in place of = (a simple Set). So,

F[x_] = UnitStep[x]*UnitStep[10 - x]*1/10;
DiscretePlot[F[n], {n, -5, 15}]
G[x_] = DiscreteConvolve[F[n], F[n], n, x];
DiscretePlot[G[n], {n, -5, 22}, PlotRange -> All]
M[x_] = DiscreteConvolve[G[n], F[n], n, x];
DiscretePlot[{F[x], G[x], M[x]}, {x, 0, 30}]

F is defined for a support range between 0 and 10 therefore G has a support range of 20. Changing the support range to 1 (in place of 0) shows the expected results HTH yehuda