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I am a Japanese undergraduate junior student who is thinking of applying to graduate programs in Mathematics in the U.S. and the biggest problem for me is the Letter of Recommendation. I am planning to ask a teacher of my English class for one of my LOR because my senior who went for a grad school(Engineering) in the U.S. did so. My intention is that she can prove that I have sufficient English skills to study in the U.S.

However, from what I have seen on the Internet, no one seemed to do so and all of LORs have to be from people in relevant fields. Is getting a LOR from an English teacher for Math Ph.D. program good or bad?

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    I don't have the experience to write an authoritative answer. That said, based on your question your English is quite good, and it can't hurt for a prospective thesis advisor to know that. If you're allowed multiple letters of recommendation one from your English teacher might be useful. Better still, write a literate cover letter. – Ethan Bolker Dec 4 '19 at 23:48
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    20 years ago, when I chaired my department's graduate admissions committee, we required applicants from non-English-speaking countries to provide a letter, from a native speaker of English, attesting to the applicant's ability to speak English. This letter was in addition to the usual letters of recommendation about the applicant's mathematical ability. (I don't see this requirement on the department's current web site; maybe the requirement has been dropped, or maybe the web site has been damaged by administrative beautification.) – Andreas Blass Dec 5 '19 at 2:57
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Knowledge of the English language is often a hit-or-miss requirement, i.e., either you have a recognized English qualification (TOEFL, IELTS...) and you can study there, or you do not have it and you cannot study there. In many institutions, this is checked by administrative personnel, independently of the selection committee.

Having better English knowledge than other applicants who also have the qualification will in most cases not give you any advantage over them. The selection committee (or the prospective PhD professor, depending on the location) will almost exclusively consider your qualifications in your research field when deciding whether to admit you.

I would recommend trying to obtain recommendation letters from people that can say good things about your skills in your field.

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    The assertions in this answer are not universally correct... – paul garrett Dec 4 '19 at 14:53
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    I agree with this answer. You only have a few letters of recommendation to give, use them on people who can speak to your mathematical abilities. You will have to document your English language abilities using your TOEFL anyway. – Wolfgang Bangerth Dec 4 '19 at 16:38
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    @paulgarrett they are not, that is why I tried to qualify every statement with "often", "in most cases", etc. My concluding recommendation still stands though. – wimi Dec 5 '19 at 9:20
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Ask the professors who know you very well and can speak of your ability to succeed in the program.

P.S. I got into the grad program I wanted. I had 2 LoR from the field and 1 from non-field. The strongest letter would come from my non-field professor who knows very well about my work ethic and passion, and what I can bring into the program.

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