Is it permissible to study at the College of Engineering with the intention of graduating to gain social status?

It is permissible to study in engineering colleges and the like for the purpose of social status, but it is better for a Muslim to intend to benefit Muslims. A Muslim is permitted to seek worldly gain through worldly knowledge like engineering and mechanics, by learning it to earn a salary or wage, and there is no harm in that. However, if he intended to benefit Muslims through what he learned, such as learning engineering to make Muslims self-sufficient and avoid bringing in disbelieving engineers, or to meet the needs of Muslims in mechanics, that would be better for him, and he would be rewarded for it, thereby gaining both this world and the religion. If he only desires this world, there is no sin upon him, just like someone who buys and sells to increase wealth.