What students should understand is the existence of links among apparently different subjects and the impossibility of studying them independently or, worse, studying one and neglecting the others.

independently 是形容词 independent 的副词形式，由前缀 in-（表示"不"）和 dependent（"依赖的"）组成，字面意思是"不依赖地"。这里指"不依靠其他事物地、单独地"学习各门学科。