To give you some idea of what professors do, here is a brief description of typical activities included in the areas of Research, Teaching, and Service.

### Research

- Doing mathematics research. Many laypeople mistakenly think that all mathematics is currently known. This could not be further from the truth! In fact, there is more mathematics research being done now than at any time in history. Math professors do a variety of things in their research, such as developing new mathematics to solve unanswered questions, using existing mathematics to model real-world phenomena, and applying mathematical techniques to assist with problems in the physical sciences, medicine, engineering, data analysis, or a variety of other fields.
- Writing up research results in papers and submitting these papers for publication.
- Writing textbooks or monographs that can be used by other researchers or in graduate courses.
- Submitting grant applications to support their research, and administering grants (e.g., working with budgets, submitting reports) that have been awarded.
- Traveling to conferences to give talks, share research results, and stay abreast of what is currently going on in their field of study.
- Traveling to other universities to give invited colloquium or seminar talks.
- Traveling to other universities or research centers to collaborate on projects with other researchers.
- Reading papers, journals, or books to keep updated on new advances in their area of research.
- Speaking with researchers who are visiting from other universities in order to learn about their work or collaborate on projects.
- Organizing, attending, and speaking in research seminars on the UH campus.
- Supervising a research project or group that may contain several postdocs and students.
- Doing university paperwork related to research (e.g., submitting travel requests, submitting reimbursement requests for travel or research purchases,
preparing and submitting reports on how grant or university money was used).

### Teaching

- Teaching classes at the undergraduate or graduate level. The typical math professor at UH will teach one or two classes each semester. Math professors usually teach a variety of courses, and may be asked to teach any math courses at the undergraduate level or beginning graduate level. In addition to to the time spent in the classroom, keep in mind that professors must prepare for classes, write lectures or create slides, hold office hours, create homework and exams, grade, and respond to student questions in person and through email. Depending on the number of students in the course, or the level of the material, these activities can be very time consuming.
- Writing letters of recommendation for students.
- Supervising Undergraduate Research Projects (Unlike in many of the physical sciences, such projects usually often do not help mathematics professors with their own research. They engage in such projects to help students learn and to train them to do research.)
- Supervising Independent Studies or Masters Theses for graduate students.
- Being a Ph.D advisor for a student (or multiple students) who are working on their doctorate degree. This involves guiding the students' research, helping them with their work, and teaching them to be research mathematicians.
- Designing new courses at the undergraduate or graduate levels, and updating the curriculum requirements for various degrees.
- Writing textbooks that can be used in undergraduate courses, either at UH or at other universities
- Running organizations for students or serving as faculty advisor for such organizations. For undergraduate students, this includes such organizations as the Pi Mu Epsilon-Math Club, the Putnam Team, the Undergraduate Colloquium. For Graduate Students, this includes such organizations as the Graduate AMS Chapter, the Graduate SIAM Chapter, and the Graduate AWM Chapter. .
- Bringing speakers to campus to tell students about job or research opportunities.
- Administering and grading Qualifying Exams for graduate students who wish to advance into the Ph.D. program.
- Creating new degree programs or options within degree programs, such as the
Mathematical Biology program or
mathematical finance option at the undergraduate levels, or the various
graduate degree programs.

### Service

- Serving on committees in the mathematics department.
- Serving on committees at the college level. (For Mathematics, this is the College of Natural Sciences and Mathematics).
- Serving on committees at the university level.
- Refereeing papers. (Journals send submitted papers to professors to ask them to read through the papers carefully and give their opinions on whether the paper should be published.)
- Writing reviews of published mathematics papers or books.
- Serving as an editor for a journal. This often involves accepting submissions to the journal and contacting referees for reports that will help decide whether the paper is published.
- Organizing research conferences. These are often national or international events that can involve participation and coordination of numerous researchers.
- Organizing and participating in mathematics outreach activities in the community. This can involve high school programs, math contests for high school and middle school students, or running Math Circles to give talks to local high school and middle school students.
- Serving on panels for the National Science Foundation, National Security Agency, or other institutions, in order to review grant applications and make suggestions on which applications should be funded.
- Serving professional societies, such as the American Mathematical Society, the
Mathematical Association of
America, or the Society of Industrial and Applied Mathematics.

Most professors work 60 hours per week or more to keep up with their responsibilities, and they also have to travel frequently. Many do all of this while trying to balance a family and home life. Although most professors love their jobs, many of them are overworked and at certain times they may be tired, stressed, or overwhelmed. Be aware of what they do, and how hard they work, and be considerate of their time when you deal with them.

Remember the above list of activities (which, mind you, is just a partial list) when you wonder why professors act so busy, or why they aren't always available, or why they are not free to meet with you if you stop by their office unannounced or outside of Office Hours.

When classes aren't in session (e.g., during summers or breaks) it doesn't mean professors aren't working. It means they are working on their other professional obligations --- often parts of their job that are difficult to do when teaching a class, or activities that require large, uninterrupted periods of time (such as large research or writing projects). These are very important parts of their job that sometimes have to be put on the back-burner while classes are in session.

If you ask professors to do extra work beyond what they are already doing for the class (e.g., create a practice exam, hold a review session, write up solutions to homework, post their lectures online), sometimes they have to say no. It's not that they don't want to help you. Sometimes it is the case they actually

If you want to get an idea of what activities a particular professor is involved with, take a look at their website. Most professors will often have a copy of their Curriculum Vitae (CV) on their website, which lists their publications and activities.

There is a Chinese Translation of this Article thank you to the translating efforts of Shouyue Zhang at the University at Albany.

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