Wondering if someone can tell me how to convert the old flow chart style Matrix systems to the "new" 3rd edition Matrix systems that just use ACIFS. I'm thinking of just taking the rating of the IC and rolling randomly to increase the various stats, based on the security rating of the system. Anybody have anything more scientific?

A bit of background.
I'm running a long (hopefully) campaign starting in 2050 and going through as many of the modules as I can fit into the campaign plot. I wanted to run something I was familiar with but something that wasn't so old fashioned and clunky. I had played 3rd edition but not ran it before but I had run 2nd ed. quite a bit. Everything is going pretty well but my Matrix-fu isn't up to the task. I don't want to have to recreate every Matrix run in the modules. I remember in 2nd edition there was a chapter in the back with conversions for various books, anything like that for 2nd or 1st to 3rd?

Honestly, almost nothing. You still have the same map for the character to navigate. Make up ACIFS based on the average difficulty of the tasks listed in the network map. Remove some of the extra defenses, since they're replaced with the security tally, but some of the programs will still be tied to a particular node or item.

You still use the map? I didn't get that from the book and the First Run adventure.

You don't need the exact same map really, as the VR2/3E 'nodes' aren't strictly regulated to purpose like 1E/2E (SPU, Data Store, I/O etc), but multiple nodes still exists, for the chokepoint security scheme, honeypots, etc etc.

Like Bigity said.

(But I do generally use a map. Honestly, it's easier to grok, and to make an interesting series of engagements. SR3 is just too abstract to be any good for an adventure.

Depends on if you want to do it the long way or the short way. The short way is "Look at the difficulty listed and use Plastic Warrior's Random Matrix Generator to make a new host". That's what I usually end up doing.

However, if you want to actually put a few hours of work into it, what you need to do is really analyze what the pre-VR2 system is trying to do compared to a VR2/SR3 node system. In some cases, it's obvious. SPUs are set up specifically to be treated the same way as nodes on a PLTG. You can see the chokepoints and other features that have pretty direct SR3 translations.

However, many of them aren't so easy to figure out. In that case, I'd suggest figuring out what the writer was trying to do with the system and create something that's similar. Try running through the old school version (without dice rolling or anything else, just assume you succeed but note the difficulty). If it looks like the only way to get to the datastore the adventure requires is to go through a SAN that's Red to a Green SPU to an Orange SPU with grey IC or the CPU with black IC and finally to the datastore, that means you can set it up pretty easily as a tiered network with three hosts. First one's a Red Average (bottleneck) to a much more laid back one (say Green Average or Orange Easy) with lots of Probes/Scouts to up their tally and thus get them to the higher levels of the sheaf (hitting the grey and possibly even the black IC) and - here's where that Orange Easy suddenly turns evil - carries that tally over to the final Orange Hard or or so host with all the juicy R&D files...and the tight sheaf that nails them almost immediately. That way, you get a very similar experience to the original intent without having to fret over why the hell there's 8 SPUs on here, one of them only having control over all the vending machines and copiers in the building.

For the record, I'm rusty on system design terms for SR3 and pre-VR2 Matrix, so please forgive me if I misused something or misremembered a rule. I'm sure someone will correct me. I'm much better at cracking systems than I am building them