Does a girl's education and her mixed work in the university and laboratory contradict Islamic Sharia?

A woman's residence in a dwelling without a mahram is permissible if temptation (fitna) is averted and suspicion is dispelled, for the presence of a mahram is only required during travel. As for studies that necessitate forbidden mixing with men, they are impermissible. A woman's desire to benefit people and serve knowledge does not justify such studies. A woman can benefit people through other means that do not involve forbidden mixing.