When there are answers this might be suitable for Math Learning Materials My untrusty HP48GX graphic scientific calculator conked out two or three years ago and since then for my limited needs (e.g graphs on this forum) in that time I used odd little programmes I found around for graphics and a few computings of 1st order d.e.'s. and other odd graphs. Now I need to get back into some scientific computing. There is quite a difference between a handheld device like my old one and sitting at a computer. Like you just do more with a handheld than with a machine you, as it were, make an appointment with. But the handheld math calculator seems now to me a dated concept and surely I can do all I did before better now on the iPad with its more serious graphics etc. with apps? I wonder what you can recommend for my requirements and criteria. My needs Now: right now I want to calculate out curve families for algebraic etc. functions that may involve equations solving Including functions given by programmes And right now just 1st-order nonlinear ode's aka phase plane plots. More demanding I want symbolic manipulation. I find chains of algebraic substitutions, expansions, cancellations etc. not only boring but I am very error-prone. The old HP was quite limited, and some calculations could take even hours with cycles of expanding and collecting for instance without knowing too much what it was doing, yet when it did in its stupid fashion work, end results were error-free and so saved me time. So I need something like that, only better, I also want it to handle determinants and matrices etc., but symbolically not just numerically. Later: Higher order d.e.s, and PDE's in 1, 2, 3 D so maybe pretty usual stuff for many of you. Possibly more special, I shall probably be wanting to do algebraic calculations with hundreds of terms, not really doable at all by hand. As far as possible I want one app, or not too many different things. Maybe expandable. I find you can spend a lot of time finding your way around each new app if you don't use the same one, plus could paying for things not used much. Perhaps the only thing for later on is Mathematica? I did try it about ten years ago and I think I can still find it on an old disk. I didn't do much: I have a couple of manuals, but at the time, not being a very computer person, they appeared to me a lot of words from which I was unable to extract any operational meaning (what to do) or any at all. I see it has come down in price since then and there is a home version. At £200 I would wait for a bit. I couldn't make out if you can use it on or with the iPad. OTOH free apps don't usually seem to amount to much - I've seen some I wouldn't put in the hands of an early secondary school student, they are so absurdly limited. I should say I am now outside of any academic institution and this is for work I'll do at home. What strategy and products would you advise for someone like me to get an act together? (Never in professional math as such but got into mathy stuff via biology).