I think all undergrad STEM programs should put A LOT MORE emphasis on mathematics and other fundamentals before bothering with heavy specializations.
The Arnold book is great, but it presumes a level of mathematical sophistication that isn't practical to achieve (at least in the US) until well into graduate school, and realistically?, only for Physics theory students or some Math students that are motivated to dive into Physics.
There are major theorems in the famous "Calculus on Manifolds" by Spivak that are exercises (and not end-of-chapter or starred exercises either) in Arnold.
The Arnold book is great, but it presumes a level of mathematical sophistication that isn't practical to achieve (at least in the US) until well into graduate school, and realistically?, only for Physics theory students or some Math students that are motivated to dive into Physics.