The Reasoning: In this campaign wizard magic and alchemist magic is exactly the same, just different amounts. So why should an alchemist who wants to expand their wizard training have to start again at level 1? However, you don't want to make them TOO powerful or what's the point in being a wizard
My solution: Examine the spell chart for the level the alchemist is, and take the greatest spell level, say 3. Take and look on the wizard chart and find the first time a wizard gets a corresponding level of that type, or "5" in the example above. "Set" the alchemist at that level. DO NOT retroactively give the alchem/wiz any spells. When the alchem wizard gains a level, add the spells they would get as if they had rose to the next level of wizard, in the above example 1 2nd 1 3rd (I believe)
Is this balanced? Please take a look at the charts and let me know.
edit: The alchemist uses spells chosen from the sorc/wiz list, but uses the bard spell progression to balance out their other abilities.