What advice will you give to an IIT graduate in Mechanical/Civil Engineering, who strongly wants to pursue a research career in computer science/mathematics, and has completed the basic courses of CS in coursera?

1. Take courses in your department that involve significant use of computational and mathematical tools -- e.g., those related to CFD, finite element analysis, robotics, parallel computation. 2. Take some coursework in CS department to strengthen your claim of knowing about CS -- data structures, algorithms, automata theory. 3. Take some more advanced coursework in math department to increase your math maturity. 4. Participate in open source projects online. Try getting involved in some Google Summer of Code projects. 5. Try doing some short, limited-scope projects with faculty from your department, and from CS, math departments.