Advice on REU application for math

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When writing a personal statement, focus on your passion for math, specific areas of interest, and relevant experiences that demonstrate your capabilities as a researcher. It's beneficial to articulate why you enjoy math and how it relates to your academic and career goals. Including details about specific projects at the institution you're applying to can strengthen your statement by showing alignment with their offerings. While discussing the broader impact of math on society can add depth, it should not overshadow your personal connection to the subject. Seeking feedback from professors can provide valuable insights to enhance your statement.
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I'm just wondering if anyone has any advice on writing personal statements. Is there anything I should absolutely say or anything I should absolutely not say? What should the focus be?

Should it go something like: why I like math, what kind of math I like, any relevant experiences with math I have, and why I think I would be a good researcher? Should I talk about why I like math? Should I talk about the specific projects at that school and how that fits in with my interests (so like a statement of interest in my personal statement)?

Also, I was talking to a classmate and she said when she applied for an REU she talked about math on a nonpersonal level, as well, as in how she believes math is beneficial to the entire world. Is this something I should go into great detail about?

I am planning to speak to at least one of my professors about this, but any feedback would be appreciated. Thank you.
 
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http://alumnus.caltech.edu/~natalia/studyinus/guide/statement/link4.htm
 
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