: Explaining a major-studies change I am an engineering student trying to write a statement of purpose for graduate school and I am having trouble properly introducing in writing why I'm applying

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I am a professor. Your challenge is difficult, if you haven't taken ANY courses in the subject, it would be hard to accept you over somebody that has proven some ability and interest by taking a course.

That said, an undergraduate that has published (in something besides a vanity journal that accepts anyone) is unusual, so you need to mention that. It would help if you show ability through your academic record, as well. I am more likely to consider somebody that aces all their courses (or at least all the courses relevant to the field), just because it proves they CAN learn whatever it takes to land in the top 10%.

Along the same lines, I compare the difficulty of the courses taken and even the difficulty of semesters taken: Given roughly equivalent GPA I am more impressed by a student that takes 15 or 18 hours per semester than one that takes 12; I am more impressed by a student that enrolls in summer sessions than one that does not. These show maturity to me.

I would say, gloss over the early engineering, or cast it differently.

Don't say you changed your mind (which is what you are saying if you wanted to follow the engineering path). Say you knew you wanted something that would develop and exercise the analytic and technical strengths you believed you had, and at the time an engineering curriculum seemed the best fit for doing that. You had success with this (including a publication), and it was that success that led you to discover [not stumble upon] what you now believe is your true calling, X, which is the career you now intend to pursue.

Because unlike engineering, the same analytic and technical skills applied to X have far more impact on you emotionally. Success in this field is more important, more satisfying, and you can see the ramifications can be life changing for others, even life saving. This inspires you, and you feel that while engineering was a good choice for building a problem-solving foundation, X is the path you must pursue moving forward.

As I said, this won't necessarily work, but I would rather have a graduate student I think is going to plant his butt in a chair and work every day, than I want a graduate student that is just going through the motions and meeting the minimum requirements. That difference is what you need to convey.

Your academic path so far may not get you into the final tier of potential candidates. If it does, then consider the academic issues settled: The final questions are sorting that final tier, to decide what makes me think candidate A will work harder at this than candidate B.

For my own first PhD program, I was later told by the department head that the reason he chose me was simple: I had taken two extra courses in the field, one as an elective and the other in my final semester as just 3 more hours than I needed to graduate. That was two more courses than anybody else in the final tier, and to him this proved I had passion for the subject and wasn't afraid to work.

Good luck!

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