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When applying for tenure-track positions in mathematics at SLACs, one typically includes one recommendation letter from the math advisor and another as a math teaching letter. However, for the third letter, which would be a better choice: (a) another math teaching letter or (b) a letter from a co-advisor from a different department (which is not STEM)? On one hand, mathematicians may not give as much weight to a letter from a non-mathematician. On the other hand, a co-advisor might be able to provide more personal insights about the applicant compared to a second teaching letter.

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I am a professor of mathematics at Denison University, a good liberal arts college in Ohio. I've been on around 10 hiring committees. Based on my experiences, my impression is that you would be better off with option (a) another math teaching letter.

To be clear: Denison wants to know that candidates who get hired here will be excellent teachers and will also have a strong scholarly program resulting in several peer reviewed publications in good journals, before tenure. The "non-STEM" comment made me worry that such a letter might be more harmful than helpful, if it somehow triggered the idea that the research program was not solid and serious. Now, if you had said the co-advisor was in STEM, then their letter could help a bit, for the reasons you wrote, but I still think it wouldn't help as much as a letter from another mathematician. Note that even teaching letters will generally comment a bit on your research skills, service activities, and collegiality. Furthermore, most letters from advisors are glowing and don't carry a ton of weight. That might be even more true of letters from non-STEM advisors, since we don't know their experience supervising math PhD students.

Lastly, I want to point out that you don't need to limit yourself to three letters. When I applied to liberal arts jobs in 2014, I had 5 letters. Some places might have restricted to allowing 4. I've certainly read hundreds of files with 4 letters. The key should be to pick people who really know you, know the kind of jobs you're looking for (i.e., can emphasize aspects of your file that make you a good candidate for a job at a liberal arts college), and can write convincingly. For sure, you should only include a teaching letter from someone who has observed you teach. Even better if you've had conversations with them about your goals and development as a teacher. Good luck!

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