Could you please correct the sentences for me
I hope to embrace challenges in a new environment and work with people from different cultures. Moreover, I would like to continue to enhance my skills in materials science and gain experience in order to work independently on scientific problems in sufficient depth and breadth. With my academic experience, I think that I am competent enough to study this program; and I believe that by doing this program at XXX, I will be able to pursue the advanced knowledge of materials science that I am interested in and apply it to solve real industrial problems.
<ul><li>"expect" is for what you think a situation will be like. "hope" seems better for what you think you will be like.</li><li>"experience" is usually singular when talking about practical knowledge, e.g. "I have a lot of experience", "You need more experience"</li><li>"profound" does mean "deep" but usually in the sense of philosophy, spirituality, wisdom, etc.</li></ul>