Has Anyone on Quora Given the Bachelors Interview for école Polytechnique?

While I cannot browse Quora directly, many users share their experiences regarding university interviews, including prestigious institutions like école Polytechnique. Here, I recount my experience after being accepted for a dual major in Physics and Mathematics.

Initial Interview Questions

The interview started with the interviewer asking me about my background and studies. He specifically delved into the topics of physics, particularly asking about the experiments I had conducted. After mentioning my recent studies on atomic and nuclear physics, he asked me to explain the concept to someone who was unfamiliar with it. He then quizzed me on various terms and concepts, like the distance of closest approach and gold foil in Rutherford's experiment, to test the depth of my understanding.

Adapting to Expert-Level Discussion

Initially, I had to explain the concept as if to a layperson. However, the interviewer gradually increased the complexity of the questions, asking me to re-explain the concept as if I was talking to an expert in the field. This was an interesting challenge, as I needed to differentiate between my layperson explanation and an advanced one quickly.

Mathematical Problem Solving

Following the discussion, the interviewer asked about the remaining time for math problems, indicating that the interview would take an additional 25 minutes out of the 50-minute schedule. He mentioned I could solve one or up to seven problems depending on my skill level. The first problem was:

Checking if ( x^1^{20} 2x - 1 ) is true for all real numbers. I took 20 seconds in silence before saying that this problem could be solved using the binomial theorem. The solution is as follows:

( x^{20} 2x - 1 ) is expanded using the binomial theorem, and it can be shown that the statement is always true.

Second Math Problem

The second problem involved finding all possible pairs ( (p, q) ) where ( p ) and ( q ) are prime numbers and the polynomial ( F(x) x^2 px q ) has integral roots. This problem required some trial and error, but with continuous suggestions from my interviewer, I was able to solve it.

The solution involves using the properties of prime numbers and the conditions for integral roots of the polynomial, leading to the identification of the pairs ( (p, q) ) that satisfy the given conditions.

Conclusion

This experience highlighted the importance of having a strong foundational understanding of both physics and mathematics. While last-minute preparation might not be necessary if you are passionate about your subject, regular engagement with the material is crucial. The interview demonstrated the depth of knowledge and adaptability required to succeed in institutions like école Polytechnique.

If you are aspiring to apply to école Polytechnique or any other prestigious institution, sharing your experiences and insights can be incredibly helpful for others. Do you have any questions about the interview or preparation tips for physics and mathematics?