(Much of this content applies to all undergraduate students, but in various places there is a slant toward students in the Department of Mathematics.)
During your years as a student, you will hear and read about what you must do to earn a degree. For example, there are courses that you have to take and graded work in those courses that must be completed. Your college may require you to do other activities as well.
Typically, information you read about your major/degree will specify the minimum necessary accomplishments. Yet, doing the minimum is not noble. Would you hire someone whose work-related performances consisted of just doing the minimum? When you are ready to graduate, and potential employers or graduate school admissions committees look at your accomplishments as a student, will your record convey that you do the least, or will it show that you always go beyond the minimum? Looking ahead to your future in a professional career, do you want to be known as the employee who can be counted on to do nothing but the least required?
Earning excellent grades in classes is important, but it should not be the end-all. There are plenty of additional things that you can and should be doing if you want a reputation that leads to impressive letters of recommendation from faculty members and accomplishments that positively grab the attention of others. Here are examples:
(1) Establish an excellent reputation for professionalism. Be punctual for appointments, class lectures/discussions, and all commitments in your life. Dress and act in a manner that is appropriate for each setting. When communicating with professionals (faculty members, advisors, administrators, and so on), address people by name, use complete sentences with proper spelling, punctuation, and grammar. Include your full name of record, UC San Diego PID, and major in all written communication with UC San Diego officials. Put the current date on documents that you create, fill-in, or sign. Your homework, reports, time cards, etc. should be legible and thoroughly completed.
Before rushing to say or write something unflattering, ask yourself whether you have all relevant facts and might be about to do something that you will later regret. There are times when displeasure is warranted; nonetheless, it may help to temporarily displace your thoughts from a situation before replying. Regardless of whether you are religious, consider the golden rule.
(2) Professionally get to know faculty members and help them get to know you. It should not be difficult to do this, and does not need to cost you nothing out of pocket, but it is your responsibility to make it happen.
Office hours are a forum where you can let a faculty member see what kind of student you are. If you go to ask questions about homework or concepts learned in class, make it evident that you have done your absolute best to think through the topic or problem first. Show that your objective is to learn the subject matter so that you can reason your way to solving future problems, not just get correct answers to current problems. Once you think you understand something that before was confusing, ask the professor to give you a problem to solve in his/her presence.
Office hours do not only need to be used to talk about class-related material. If you are interested in a professor’s research, ask about it. If you read something interesting related to the subject, but that is outside the scope of your classwork, feel free to bring it up to your professor. If you are curious about your professor’s experiences as an undergraduate and graduate student, ask about those. Of course, be respectful of a faculty member’s limited time and the possibility that other students might be waiting to see her/him.
(3) Make use of opportunities to work with faculty and staff members and graduate student teaching assistants. Every undergraduate student has access to the Dine-with-a-Professor and Coffee-with-a-Professor programs. Visit your college’s student affairs office for more information on these great (and free!) ways to meet directly with a faculty member or graduate student teaching assistant in a social setting.
Additionally, there are a plenitude of other opportunities (in your department, college, or elsewhere) to interact with faculty members, advisors, and other staff members. Let people see your character. Are you a person of your word who can be counted on for reliability, thoroughness, trustworthiness, excellence in all that you do, and who is always growing intellectually? You never know what opportunities may come your way.
(4) Research work and internships. Graduate school admissions committees and employers want candidates who are capable of handling the work they offer. They appreciate applications who have already demonstrated excellence in output and a sustained interest in the nature of the work.
If you have any intention of applying to graduate school in the future, you are wise to get involved in research work in the subject matter while you are an undergraduate student. (The Department of Mathematics Honors Program is excellent as a component of preparation for graduate school in mathematics.) If you hope to enter the working world directly upon earning your baccalaureate degree, you should be finding opportunities while an undergraduate student to work in the field. Internships are advertised through campus resources (such as Port Triton through the UC San Diego Career Center), but you can also find them on your own by going to the careers or jobs links at company websites. The UC San Diego Academic Internship Program (www.aip.ucsd.edu) is a way to complete an internship and get acknowledgement for it on your transcript. If you find an internship that is not already accepted by the AIP, you can ask its people whether it can be accepted for AIP credit.
(5) Conferences/conventions. Academic or professional conferences and conventions are places where you can learn more about a subject and meet important people who could be instrumental in your future. These occasions also allow you to more closely question your own interest. Realistically, do you see yourself spending your life studying/practicing in this field and being excited about it in the long-term? This is not easy to answer if you have not gotten to know professionals in the field and learned about their experiences.