Financial engineering is a multidisciplinary field involving financial theory, the methods of engineering, the tools of mathematics and the practice of programming. Quant (Qualitative Analyst) is a broad term that covers any person who uses math for practical purposes, including financial engineers.
The top schools offering the major are:
Mechanical Engineering (ME) involves designing and manufacturing everything from small individual parts and devices (e.g., microscale sensors and inkjet printer nozzles) to large systems (e.g., spacecraft and machine tools). 
The role of a mechanical engineer is to take a product from an idea to the marketplace. In order to accomplish this, a broad range of skills are needed including mathematics, physics, material science, thermal and mechanics, and manufacturing. the frontier of research includes Robotics, Micro Electro-mechanical Systems (MEMS), Mechatronics, Nanotechnology, Biomechanics, Acoustical engineering and etc. The industry includes health, environment, energy, security and electrical engineering.
The top university offering ME are :
Let's look at some ME projects: