This section has been written for undergraduates who might want to consider advanced study in the mathematical and computer sciences. It may raise more questions than it answers. Please contact an advisor or a faculty member if you need further information or advice.
An undergraduate degree in computer science prepares you for many good jobs: applications programmers, systems analysts, etc. An undergraduate degree in mathematics might have fewer clear career paths (e.g., actuary, teacher). But there are many jobs that require advanced degrees: university professor, head of an industrial research division, etc. And there are many others that are difficult to attain without an advanced degree. Many graduate students report that they returned to school because they quickly reached a ceiling in industry above which they could not climb; project managers were almost always people with M.S. or Ph.D. degrees.
Research teams in the top industry think-tanks (IBM research centers, Xerox PARC, etc.) and government labs (USA: Argonne, Los Alamos, NASA, NSA, Sandia, etc.) consist primarily of people holding masters or doctorate degrees. For better or for worse, the people who have the most flexibility in their choice of projects and methods, whether in industry or academics, are usually those with the highest degrees.
One of the goals of education is to make people aware of how little they know. An undergraduate major acquires a great deal of knowledge, but there are many (fun!) things that you do not have time to explore. The excitement of exploring the cutting edge of knowledge, and the thrill of your first research result, something you have discovered that no one else in the world knows, are worth savoring.
Very few graduate students in the mathematical and computer sciences pay tuition. Because of this, even the most expensive private schools are accessible to most students who meet admission requirements.
Some students are supported by fellowships (i.e., scholarships). These fellowships are based on scholastic aptitude rather than on need. Some are awarded in nationwide competition by government (USA: DOE, NSF) or private foundations. Some are awarded by the individual schools.
Some students are supported by their employers and given full or part release time to complete their degree requirements. Often the student is required to stay with the company for a minimum time after completion of the degree.
The majority of graduate students work their way through school on assistantships, serving as teaching or research assistants. The typical work load is 20 hours per week, and the experience can be a valuable preparation for a career.
Teaching assistants may grade papers, teach laboratory or recitation sections, or be responsible for lecturing to a small section of a course. These assistants work under more or less close supervision by a faculty member, and usually attend training sessions before their first semester as a teaching assistant.
The jobs of research assistants may be less structured. They are responsible for learning about the general orientation of their professor's research and may assist that professor by developing or maintaining software or hardware, writing reports, supervising other students, and presenting research results at meetings.
Students on assistantships have these extra duties, but they also have office space and tend to feel more at home in the department. Students with fellowships or outside support need to make extra efforts to interact with faculty members and network with fellow students.
Typical stipends for fellowships and assistantships include tuition, benefits such as health insurance, and a modest salary. Graduate students don't get rich, but they don't starve.
Think back to the transition you made from high school to college. Your first semester may have been a time of great upheaval as you adjusted to additional freedom and additional responsibilities. Most students find college much less structured than high school, and they need greater discipline to budget their time and complete long-range projects.
Graduate students have much the same reaction as they make the transition from undergraduate life. A typical full-time course load is 9 hours. This means less time spent in class, but the demands of a graduate course are much greater than those of an undergraduate one, and students might spend three or four hours of preparation for every hour in class. Standards are higher: a ``C'' is often not a passing grade for a graduate student, even in an undergraduate-level course. There are fewer ``checkpoints'' (exams and due dates), and it is easier to yield to an urge to procrastinate.
A masters student typically completes a specified set of courses in the first year or so, and then spends time working on a research project with an individual faculty member. The completed project is written up as a thesis, and then the candidate gives a talk to a group of three or four faculty members and ``defends'' the work. The entire process may take two years, perhaps three. Some schools allow a written exam plus a scholarly paper to substitute for the research project.
The Ph.D. student follows a similar track, perhaps taking some required courses and a written exam. Before research is begun, however, there is usually an oral ``candidacy'' exam during which the candidate presents the research idea and is questioned on the necessary background knowledge. The student then completes the thesis research, writes it up, and has an oral defense. The entire process may take five years of graduate study (three beyond the masters degree), possibly as few as three years or as many as seven years.
The matchmaking of students to thesis advisors is a rather informal process. The student needs some initiative in order to seek out an advisor with compatible ideas and working style.
The thesis writing period is a particularly unstructured one with no exam or homework deadlines to meet. Again, extra discipline is required to keep the work progressing.
If you are a mathematical or computer sciences major in a top-20 department, typically get A's and B's, have a good deal of self discipline, and are MOTIVATED, then you are a competitive applicant for the best graduate schools in the country. If your department is not top-20, then in addition to the top schools, you might want to apply to some lower-ranked departments as well. If your ultimate aim is a top-ranked school, then a masters degree from a mid-range school, coupled with supportive letters from your professors, can be a stepping stone toward this goal.
There are several things you can do (beginning in your freshman year!) that will make admission to graduate school and future success easier. Luckily, they are also good preparation for the business world, so you do not need to sacrifice any of your options.
Start working on the application process early in Fall for admission the following Fall.
Some students go on to graduate school directly after completing their undergraduate degrees; others gain some work experience before returning to school. There are arguments for and against each choice, but if your motivation is high, generally sooner is better, especially if your goal is a Ph.D.
Don't sell yourself short: if you are a high-achieving undergraduate, then you have the potential to be a very successful graduate student. Be prepared to work hard, but don't be afraid to accept the challenge.