Like everyone has said, the 1 caliber rule is the best way to design a cannon. Something to keep in mind though, such rules are devised to ensure a reasonable factor of safety in the design. If you were to calculate the minimum necessary wall thickness to withstand a blast, you may be surprised at how thin it is (obviously, depending on material). Math can certainly give us all the answers we want, but because of the many variables involved, it can be hard to account for everything. Even then, you'd want to use a factor of safety that would give you a reason to believe that when you ignite a charge you don't get blown up, or worse...blow up someone else. By sticking with tested and established rules for design, we don't have to "reengineer the wheel," just size it appropriately, using any number of safe materials according to that rule, and then we can have fun knowing we are doing it safely.
Wanting to run the numbers for academic research is great. It will give you an idea of what the factor of safety on your design is, which is always nice to know. On a cannon, I want it pretty high.
Math is a friend of an engineer, but established design rules can be even nicer, so long as you utilize them according to their conditions.