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（独立的）加上副词后缀 -ly 构成的副词，表示"独立地、不依赖他人地"。 worse 是形容词 bad 的比较级形式，表示"更糟糕的"，在这里用于强调前文提到的情况已经不好，而后面提到的情况更加严重。