For elementary math, I’d recommend AoPS Volume 1 and Volume 2. Once you get thru them properly you can get <A3 if it’s elementary. Also try easier HS Olympiad Problems (think Canada or Mexico). For calculus and beyond, probably coursework is helpful. Maybe try Spivak Calculus to be able to do say, A2 from this year. For Linear Algebra, I like linear algebra done wrong (treil). It’s probably not worth going thru like Artin for algebra just to solve algebra problems on the putnam. That is, for stuff beyond calc and linear algebra, just take classes at ur college.

and of course, practice. i think mit has their putnam coursework online if you find it useful. also, just do old problems.