I. Ph.D. in Mathematics

A Ph.D. in Mathematics generally requires from three to six years of graduate work beyond the bachelor's level. The first years are spent in coursework, while the later years are spent primarily doing original research culminating in a dissertation. Most graduate students in mathematics can get financial support for their study - both tuition and a stipend for living expenses. In return for this support the student often performs some service for the department, most commonly teaching lower level courses.

The majority of Ph.D.'s get employment at academic institutitions, either at research universities such as Duke or at colleges devoted primarily to undergraduate teaching. At research universities most faculty members spend only part time teaching while devoting time to research in mathematics. The employment situation for Ph.D.'s in mathematics for academic positions is currently very tight but is likely to get better in the future. There are also many opportunities for non-academic employment of Ph.D.'s, especially in the more applied areas of mathematics.

The core courses for a student interested in graduate school in mathematics (either pure or applied) are the sequences 200-201, 203-204, and 205-206. At least two of the sequences should be taken. It is suggested that at least one of these sequences be taken no later than the junior year. In addition to the core courses, students are encouraged to take electives based on their interests. Students interested in applied mathematics should consider: 131, 135-136, 160 (or 221), 196S and 240. Advanced students should consider taking standard graduate level courses (numbered 250 and above) in their senior and occasionally in their junior years.

The choice of graduate school and the area of graduate study may make a significant difference in future job prospects. Students considering graduate school in mathematics are urged to consult with their instructors and with the Director of Graduate Studies.

II. Statistics

Students who intend to pursue graduate work in statistics should follow the program above and should include some of the following electives: 135, 136, 241, as well as CPS 6 or 8 (or the equivalent). A strong background in mathematics (especially analysis and linear algebra) and computing is the best basis for graduate work in statistics.

Students who do not intend to pursue graduate work should elect Math 135, 136, 241, CPS 6 or 8 as well as some of the following courses: Math 242, 240, 196S, 160 (or 221), STA 242, 203S, CPS 100.

At present, job prospects are good at all degree levels for those who have a strong background in statistics and some computer programming experience. Statistics students at all levels are encouraged to include computer programming courses in their study. For further information, see Professor Donald Burdick, Institute of Statistics and Decision Sciences, in 223B Old Chemistry.

III. Applications of Mathematics

Many students major in mathematics with a primary interest in some other discipline (often a double major). Graduate and professional schools in many areas consider an undergraduate major in mathematics to be a desirable background.

Most students with applied interests will wish to include 131, 135, 136 in their program. Other electives depend on the particular interest:

Students planning to go to professional school (medicine, law, business) can choose a program based mainly on interest. Those intending to go to graduate school in another department of arts and sciences or engineering should plan their program in consultation with that department as well as the mathematics department.

IV. Actuarial Science

Yesterday perceived primarily as an insurance mathematician, today's actuary is more likely to be a manager or consultant applying his quantitative training to the solving of business problems of all types. Actuaries earn professional status by developing a high degree of insurance and financial expertise, both on the job and by passing examinations administered by the Society of Actuaries or the Casualty Actuarial Society.

While successful actuaries have come from diverse college majors, the obvious candidates are those possessing strong math, verbal and leadership skills. Unlike cut and dried math problems, the problems an actuary is likely to face contain additional business, social, and political considerations. There will often be more than one solution, or there may be no practical solution at all. Insurance companies actively recruit Duke Math majors-several each year accept positions with such firms.

You should start on the actuarial examinations while you are still an undergraduate. Sophomore or junior year is the optimal time to take the first exam (Calculus and Linear Algebra). Strive to pass the first two examinations before college graduation, else employment opportunities will be greatly diminished. (These examinations are formidable; the passing percentages in May 1990 were only 40.6%and 37.6%.) To help you decide if you're suited to an actuarial career, try to find a summer internship with an insurance company or consulting firm. (Summer openings are limited and are often filled by January or February. You'll improve your chances if you've passed the first exam.)

Some of the topics of the earlier examinations and recommended Duke courses are:

Other useful courses are accounting, finance, economics, and computer science.

UNC-Chapel Hill's Curriculum in Mathematical Sciences has developed an Actuarial Science option through which students may take specialized courses in actuarial mathematics during the spring semester. Under a reciprocal agreement between the two universities, students at Duke may enroll concurrently in courses offered by UNC-Chapel Hill. Inquiries about these courses or actuarial science in general may be made to Charles W. Dunn, a former Duke graduate and Fellow of the Society of Actuaries. His office is in the First Federal Building at Five Points (phone 688-8913).

More information about the exams can be obtained from the Director of Undergraduate Studies.

V. Teaching Mathematics

For teaching certification, most states require competence in the four areas: analysis, algebra, geometry, probability and statistics.

Note that STA 112 fulfills the state requirement, but does not count toward the major.

Mathematics majors with teaching certification are greatly needed in the field of secondary education (and are vigorously recruited at Duke). Since many people with degrees in mathematics find more lucrative employment elsewhere and may not be interested in teaching, school systems are often forced to employ as teachers of mathematics people for whom mathematics is, at best, a strong related field. There are several paths which you might pursue to major in Math and also to be certified to teach:

1. Complete the teaching block (the required education courses for certification and teaching practice) in undergraduate school and go directly into secondary school (grades 9-12) teaching.

2. Complete this block and go back to graduate school later to obtain a Master's or Doctor's degree. This could qualify you for any number of occupations. Some examples are: (1) teacher in secondary school with higher pay scale, (2) teacher in a junior college or community college, (3) supervisor of mathematics teachers in secondary schools, (4) director of mathematics curriculum in public or private schools. It should be noted that some experience in teaching at the secondary school level is usually required for consideration for these positions. Many states require teachers to continue their education and renew their certification. It is thus possible to acquire the Master's degree in many universities while continuing to teach at the secondary level.

3. Complete the undergraduate degree in Mathematics and continue straight into graduate school to obtain an MAT or MA in Mathematics education. This would prepare you for a teaching position with advanced pay scales in many secondary schools. Also some junior colleges employ teachers who hold these degrees. Duke now has an MAT program.

4. Complete the undergraduate degree in Mathematics and prepare to teach in a private school. This does not require extensive certification, but EDU 246 should be taken.

For further information, see Professors David Malone, Program in Education, 213 West Duke Building, East Campus, or Jack Bookman, 211 Physics Building.