Our graduate program emphasizes both pure and applied mathematics, and we have strong research groups in topology, geometry, partial differential equations, analysis, number theory and algebra. Our program also places an emphasis on mathematics education, since the vast majority of PhDs from our program take their first jobs in an academic environment, typically in four-year colleges and universities.
Here is an overall description of the PhD program: Before embarking on research, the entering PhD student completes three of four breadth requirements in algebra, analysis, applied math and geometry/topology. Each of these requirements consists of completing a basic full-year graduate level sequence and a comprehensive exam on undergraduate material within the area. After this, the student typically finds an advisor who helps him/her form a committee and devises an oral exam based upon more advanced material. Upon passing this exam, the student advances to candidacy and begins work on his/her PhD dissertation.
To carry out this program, well-prepared students begin by taking basic graduate courses. Basic graduate courses which are offered every year include
201ABC. Real analysis.
In addition, we usually offer basic sequences in complex variables, differential geometry, numerical analysis, partial differential equations and ordinary differential equations.
More advanced courses on offered on topics which vary from year to year. These usually reflect current research interests of the faculty. Seminars in algebra, applied mathematics, arithmetic and geometry, differential geometry, functional analysis, operator algebras and topology treat more advanced topics and current research. During the academic year 1998-99, the Mathematics Department sponsored, among other things, a workshop on automorphic forms and a Southern California Analysis and PDE Meeting. During the summer of 1999, the differential geometry group has scheduled a Summer Conference in Geometry which will coordinate with a workshop on geometry and physics being run by the Institute of Theoretical Physics. These and similar activities provide opportunities for graduate students to become aware of current research trends.
The specialties offered by the graduate program reflect the interests of the faculty members. The Department has made an attempt to modernize its offerings by making new recruitment in needed areas. In recent years, new appointments have been made in algebraic geometry, differential geometry, number theory, operator algebras, complex variables and numerical analysis.
In addition to the PhD, the Department offers MA degrees which can be completed by either taking a comprehensive exam or writing a masters thesis.
The applicant pool
During the period 1993-98, the PRP data shows that we received 435 applications for admission into graduate school. Of these, 321 were accepted (73.8%) and 86 matriculated (19.8%). Although the overall rate of acceptance is high, most students find it financially difficult to attend unless they are offered financial assistance. This is particularly crucial for foreign applicants. Mathematics is attractive as a specialty for foreign students, but lack of an adequate supply of tuition fellowships has made it impossible for many of these students to enter our program.
A perusal of recent admission data bases reveals that students who apply to our graduate program have a wide range of preparation, ranging from applicants who have 99 percentile scores on the GRE's, for example, to those whose scores are lower than the 50 percentile ranking. One trend we notice is that foreign applicants tend to be better prepared than domestic ones.
Although we have not systematically tracked students via ethnic group, we can report the following statistics regarding gender in the applicant pool:
1995-96 34.1% women
1996-97 28.8% women
1997-98 41.9% women
1998-99 39.8% women
1999-2000 40.4% women
Here is some additional information relevant to our most recent admissions cycle (1999-2000): Of 32 offers, 16 went to women. We made 3 offers to foreign students, 15 to California residents, and 14 to out of state people. 7 out of 8 fellowship offers went to women. Our perception is that over time the percentage of applicants who are women is increasing. The same can be said of the percentage of new PhD degrees which are given to women.
We advertise the basic information regarding our program at our website. Upon request, we send prospective graduate students a graduate student brochure, which gives an overview of mathematics at UCSB, and a Graduate Student Handbook, which describes the mechanics of going through our program. We also advertise in the AMS publication "Assistantships and Graduate Fellowships in the Mathematical Sciences."
Members of the Graduate Committee review applications for admissions under the overall direction of the committee chair. The primary criteria used are grades in previous courses, performance on the Graduate Record Exam, letters of recommendation and research interests as described in a Statement of Purpose. In the case of foreign students, satisfactory performance on a test of proficiency in english (TOEFL) is mandatory, particularly if they are to be supported as Teaching Assistants.
To ensure reasonable standards, we very rarely admit students with GPAs under 3.0. (We may rarely admit a person with GPA under 3.0 who has successfully done graduate work at a Cal-State University.)
We have tried to make our graduate program more comfortable for ethnic minorities and all genders by making sure we have adequate representation on the faculty. Recent faculty recruitments have increased the number of women on our faculty, and several ethnic groups are now well represented. We believe our faculty to be relatively diverse, as far as mathematics departments go.
Assessment of Graduate Performance
Up until advancement to candidacy, the quality of student work in the graduate program is assessed by grades in graduate courses and by performance on the qualifying exams. In determining whether a student has passed the area requirements at the PhD or MA level, the graduate committee considers not only the performance on the exam itself, but also the grades in the basic sequences, in consultation with the faculty who have taught the basic courses. Students who fail to pass the area exams often leave the program with an MA degree.
Instructors have fairly wide leeway as to what standards will correspond to what grades. For this reason, the Graduate Committee is just as concerned with comments that faculty make about the level of students within their courses as with the grades themselves. The Department is small enough that instructors get to know the individual students quite well.
After advancement to candidacy, performance is for the most part assessed by the student's PhD advisor, in consultation with the PhD committee. The final requirement for obtaining a PhD is successful defense of the thesis.
From the most recent statistics obtained by PRP we estimate that 38.3% of PhD students are able to successfully complete a PhD degree. This is slightly lower than the campus average success rate of 40.8%.
The higher than average rate of attrition in the Mathematics Department is partially explained by the fact that we admit almost all entering students into the MA/PhD program, including many students who are not well prepared for graduate work. Other departments would admit many of these students into the MA program only. Our policy does provide high-risk students with the opportunity to determine if they can in fact succeed at graduate work. However, the student survey suggests that some students are disappointed when two years of hard work results in only an MA degree.
Although we do not typically admit students with GPA's below 3.0, it is our perception that inadequate undergraduate preparation (often indicated by lower GPA's) is one of the major causes of attrition in our program. A more serious problem is that domestic undergraduate programs do not always prepare students adequately for graduate work. This is evidenced by the fact that many new graduate students must take some undergraduate courses before embarking on the basic graduate courses. This delay can be a source of discouragement.
We have not kept data on differences in attrition/success related to ethnicity, although it is clear that students from China have done unusually well in UCSB's mathematics program, just as at many other universities throughout the US. One could speculate that cultural heritage and values have an effect on choice of mathematics as a career.
As far as gender goes, we note that in the five-year period 1995-99, 5 out of 23 new PhD's (or 21.7%) went to women. These figures are in line with the percentage of new PhD's nationwide that went to women, as reported in the departmental self-assessment. Over the same five-year period, the percentage of math graduate students who are women has varied between 19% and 26%. We do not discern a significant difference between success rates of women versus men.
Graduate Student Support
Financial support for graduate students is typically in the form of Teaching Assistantships, although some students receive fellowships or are supported through research grants. Decisions regarding financial support are made by the Graduate Committee at the same time as it reviews applications for admission into the graduate program. Most entering graduate students who are fluent in English are offered Teaching Assistantships, which can be renewed for a period of up to six years, if they make adequate academic progress and are successful within the classroom.
The typical duties of a Teaching Assistant include running discussion sections for four to six hours per week, holding office hours and helping instructors grade exams. More advanced graduate students, who already hold masters degrees, are sometimes supported as Teaching Associates and given the responsibility for running an entire course on their own.
A Teaching Assistantship currently pays $13,329 for nine months. From this, residents of California must pay $646.70 per quarter in fees. Nonresidents must pay an additional $3128 per quarter in nonresident tuition fees, making graduate study financially impossible for most nonresidents unless they receive tuition fellowships. During the 1998-99 year, the Department had a fund of $82,000 which it could give out in the form of tuition fellowships. Domestic students who are not California residents can usually apply for residency at the end of one year, but this possibility is not open to foreign students.
It is important to note that the Teaching Assistant program not only supports graduate students but prepares them for careers in teaching. Therefore the Department runs an intensive TA training class for new TAs which begins intensively about two weeks prior to the beginning of the fall quarter and continues lightly on into the quarter. This class gives new TAs practice in running discussion sections and making up quizzes. This course also includes videotaping of discussion sections as well as classroom visits of the TA training instructor.
Academic Advising and Progress Toward Degrees
There are two graduate advisors, one in pure mathematics and one in applied mathematics. They help each student design his/her program and monitor progress towards a degree up until the point at which the student chooses a PhD advisor. After this, the PhD advisor is the primary source of guidance for the student.
Students are expected to complete an MA degree within two years and a PhD within five years. Students who take longer than five years to obtain a PhD are given a much lower priority for support after the fifth year. The statistics from PRP indicate that the actual median time to PhD is significantly lower than in many other disciplines at UCSB.
Student progress is monitored by the Graduate Committee, which decides every spring which students will be given support for the following year. Each student is given a written evaluation at that time. Graduate Advisors go over student grades each quarter and talk with those having problems. Also the Graduate Advisors get informal information from faculty teaching graduate courses during the quarter, and meet with students as soon as possible to try to resolve difficulties.
Facilities and Overall Climate for Graduate Work
Office space in the graduate tower is available for graduate students who have teaching assistant appointments. Graduate students also have access to computers and the internet through a Computer Lab. We have recently acquired additional space which has been designated a "grad quiet room" and dedicated as a study area for graduate students.
We believe that the climate for graduate study at UCSB is excellent. Comments from the graduate student survey on this question were mostly positive. Most of the instructors are willing to talk for long hours with individual graduate students on topics not just restricted to mathematics. Every afternoon, there is a departmental tea, in which faculty and students
are encouraged to interact. Students are encouraged to organize their own seminars and study groups to make learning more enjoyable. For example, the graduate students have organized their own seminars in topology and algebra, independent of the current research seminars organized by faculty members.
Once every two years the department hosts a "career fair" which typically features a panel of representatives from academia and industries, such as computer software and computer gaming. Aside from this, job placement for new PhD's is primarily the responsibility of the student's thesis advisor. The Graduate Secretary assists with gathering letters of recommendation that are sent to prospective employers.
The vast majority of our new PhD's take their first jobs within academia, although at least three graduates during the most recent five-year period found jobs within the computer industry.
The Graduate Student Survey
Statistics from the graduate student survey show that the graduate students are more satisfied with the quality of graduate instruction in mathematics than in the average department at UCSB. Students praise the quality, dedication and approachability of the faculty. Of course, there are some negative comments as well. But the overall tone of the comments is quite positive, considering the fact that graduate students on the campus as a whole were considering a strike at the time to gain union recognition.
Explicit negative comments from graduate students indicate dissatisfaction with computing facilities, the copying machines and office space. The Department has made efforts to address these problems by purchasing two new copiers and new computers for the Computer Lab, which is dedicated to serve the computing needs of the graduate students. Noise continues to be a problem in the admittedly small office cubicles in the graduate tower, but as mentioned above, we have allocated space for a "quiet room" in which graduate students can study.
Another complaint is that the calculus curriculum changes too frequently. In fact, the Department has shifted modes of instruction in the past several years, first to Harvard calculus, then back to a more traditional philosophy. We believe that this process is converging to a more stable curriculum.