On November 16, the University of Rochester administration announced its decision to terminate the graduate program in mathematics immediately, and to reduce the full time mathematics faculty from 21 to 10 "over time". There was absolutely no attempt to obtain outside evaluations of our program. The Mathematics Department was informed of this decision one hour before the formal public announcement. The story had already been "preplanted" with the *New York Times*.

This document is a detailed report on the current situation of the Mathematics Department at the University of Rochester. The purpose of this report is to address the specific charges for this decision which were stated in the Dean's "Rationale for the restructuring plan" and which is quoted in Appendix A8.

This department has a solid core of distinguished senior faculty together with a group of young people who are contributing to the strength and prestige of the department. Some of the evidence for this is as follows: Approximately 60% of the faculty receive some form of Federal grant support. Four have received Sloan Fellowships. Two have given invited talks at the International Congress of Mathematicians. Two others have given invited addresses at the Annual National Meeting of the American Mathematical Society. Short biographical sketches for all current faculty of the department are included in Appendix A7. We list (1) fields of interest, (2) selected publications, (3) grant support, and (4) invited addresses. We feel that these biographies paint a strong picture of research quality.

Undergraduate teaching is taken seriously. Two-thirds of the calculus courses are taught by the faculty. The other third is taught by our graduate students. These students are selected carefully and have performed well. The summary of student evaluations given in section 3 corroborates this claim. ( We stress this point because some of the harshest criticism of the administration is directed at our calculus teaching.)

During the last 6 years, our graduate program had a student body varying from 31 to 40. We produced 37 Ph.D.s during this period. More details are included in section 4. The quality of the applicants has been steadily increasing. In addition, we have tried to exercise the highest feasible mathematical standards for admission of our graduate students.

One of the justifications given by the Dean for the severity of the suggested cuts is the NRC ranking for the Mathematics Department. Although we have serious concerns about the validity of the NRC rankings of mathematics departments, upon closer inspection they give evidence of the strength for our department. The NRC ranked 139 departments as follows: (i) "distinguished" means 4.01 to 5 points, (ii) "strong" means 3.01 to 4 points, and (iii) "good" means 2.51 to 3.00 points. The precise NRC ranking for the University of Rochester Mathematics Department is 2.9. It is stated explicitly in the NRC report that there is a strong positive correlation coefficient (of .5) between size of department and ranking; namely larger sized departments tend to do better in these rankings. There is an admitted statistical error in these rankings. In addition, there are ONLY 27 departments in the top half of the NRC rankings which receive Federal support at a rate greater than the 60% rate here.

**Table of Contents**

Section 1. Introduction

Section 2. Fact Sheet

Section 3. Some aspects of undergraduate teaching

Section 4. Some aspects of the graduate program

Section 5. The NRC data

**Appendicies**

A1. Brief report on graduate recruitment 1994, 1995

A2. Retention of students in the calculus sequence

A3. Mathematics being taught by engineering at Rochester

A4. Summary of some teaching innovations

A5. Report on linkages

A6. Tables

A7. Short Biographies

A8. The Dean's "Rationale for the restructuring plan"

Number of faculty: 22 ( 1 untenured ) Number of graduate students: presently 31 Average number of undergraduate mathematics degrees: 32 per year for the last 5 years. Number of students in mathematics courses: Fall '95: 1,271 students, 4,936 credit hours (almost all of those are in 4 credit courses) Spring '95: 976 students, 3,920 credit hours (almost all in 4 credit courses)

Graduate students: From 1989 to 1995,37 Ph.D. degrees in mathematics were granted. Of these 37 students, 29 found employment at academic institutions, 6 found employment in the private or public sector, and 2 are yet to be employed. Of those who found academic employment, 21 are at research universities and 8 are at colleges which concentrate entirely on teaching.

Total grant income budget:

6/91.....$768,714

5/92.....$916,414

6/93...$1,151,635

6/94...$1,203,136

6/95...$1,475,671

Thirteen members of the department currently have grants. Overhead charged by the university for National Science Foundation Grants was negotiated at 57%. The overhead charged for the academic year ending on June 1995 was $206,889.

Cost of the stipends for the graduate program in the academic year ending June 1995: $182,844

Remarks: Every member of the department teaches four courses per year with the exception of one member who teaches three.

Every member of the department holds a Ph.D. in mathematics and every member of the department has a respectable publication record.

**Section 3. Some Aspects of Undergraduate Teaching**

The Mathematics Department makes a strong effort to maintain quality in the teaching of undergraduates. Performance in this area is monitored by two kinds of teaching evaluations. Those who teach a course or sections of a course are evaluated by students using a form designed and compiled by the University Administration.

Graduate students (and the very few undergraduates) who are teaching assistants are evaluated by students using a TA evaluation designed and compiled by the Mathematics Department. It is our view that the statistics so collected confirm that we have maintained a high level of quality in undergraduate teaching.

The data collected by the university allows for two categories of evaluation, student satisfaction with the instructor and student satisfaction with the course. Since this information is collected over the whole College, comparisons can be made between the evaluations of the Mathematics Department and the evaluations of the entire Natural Sciences Division. (In the Spring of 1994 the classification of departments was changed and mathematics fits into what is now called Formal Reasoning which includes Mathematics, Statistics, and Computer Science.) The data indicates that, in the period from Fall 1992 to Spring 1995, there is no significant difference between the student evaluations of teaching in the Mathematics Department and the student evaluations of teaching in Formal Reasoning (1995) and in the Natural Sciences Division.

For example, the ratings for Spring 1995 are stated with 5 being the highest possible rating. In smaller courses with no more than 20 students, instructor approval was rated 4.43 for mathematics and 4.33 for Formal Reasoning. The corresponding numbers for course approval were 4.15 for mathematics and 4.15 for Formal Reasoning as a whole. In middle sized courses between 21 and 40 students, instructor approval was 3.70 for mathematics and 4.14 for Formal Reasoning while corresponding course approval was 3.56 for mathematics and 3.71 for Formal Reasoning. In the largest courses with 41 to 100 students, instructor approval was 4.49 for mathematics and 4.23 for Formal Reasoning, while course approval was 3.79 for mathematics and 3.66 for Formal Reasoning.

We find the following particularly instructive: During the years >of 1992 to 1995, the category of courses with 41 to 100 students (which includes first and second year calculus courses), the student evaluation of mathematics instruction and mathematics courses has been consistently higher than the average for Natural Sciences or Formal Reasoning as a whole.

In middle sized and smaller courses, the comparative ratings of mathematics and natural sciences (or Formal Reasoning) oscillate from year to year. Sometimes, mathematics is rated higher and sometimes it is the other way around.

Each semester approximately one third of our calculus courses are taught by graduate students. Their performance has been outstanding. Seventy five percent of them were rated better than the average rating in Formal Reasoning as a whole. We pick these graduate students carefully on the basis of their previous performance as TA's.

The TA's who teach recitations are evaluated via an evaluation form which is scaled from a low of 1 to a high of 5. The data indicates that there is a high level of student satisfaction with the performance of these graduate students. For example, in Spring 1995 and Fall 1994, 11 out of 16 received an overall evaluation of at least 4. In Spring 1994, 7 out of 15 received an evaluation of at least 4, and in Fall 1993, 12 out of 15 received an evaluation of at least 4. During this entire period precisely one evaluation was below 3.

Three other undergraduate activities supported by the Mathematics Department should be mentioned. The first is an undergraduate mathematics society. The second was the development of a summer mathematics camp for the Pew Midwest Science Cluster. Members of the Mathematics Department conducted this summer math camp. Finally, each year, members of the department help students to prepare for the Putnam Mathematical Competition.

**Section 4: Some Aspects of the Graduate Program**

From 1989 to 1995, the University of Rochester granted 37 Ph.D. degrees in Mathematics, an average of roughly 6 per year. Upon the completion of their degrees, 29 found employment at academic institutions, 6 found employment in the private or public sector, and 2 are yet to be employed. Of those who found academic employment, 21 are at research universities and 8 are at colleges which concentrate entirely on teaching.

We feel that our students from this period have done well. Among the schools which employ them are Duke University, Northwestern University, Queens College, University of Lille, University of Minnesota, University of Georgia, Centro de Investigacion del I.P.N., and Berea College. Among the private companies which employ them are Xerox and I.T.T..

Students from earlier periods are presently on the faculty of Dartmouth and Notre Dame.

The quality of the applicants to the graduate program has been steadily increasing. Although some of the admitted students chose to go elsewhere (e.g. Princeton, MIT, and Berkeley) , there are currently three students who have used fellowships which could be used anywhere.

The following information can be extracted from the National Research Council evaluation of graduate programs.

(1) Is the level of grant support in the University of Rochester Mathematics Department "minimal," as described by the Dean in his "Rationale for restructuring" ?

No, in fact the level of outside grant support here has been very strong when compared with departments which have similar rankings, and is respectable even when compared with departments in the first quartile.

The NRC figures state that 60% of our faculty (of 25 at the time) had federal support at some time between 1986 and 1992, and this agrees with our own numbers.

Of the 33 mathematics departments in the top quartile in the NRC ratings,18 have less than or equal to this level of support. Of the 34 departments (excluding us) in the second quarter, 25 have less than or equal to this level of support. Of the 13 departments which are tied with us or which are immediately ahead of us in the rankings ( namely, those places with numerical ratings of 2.9 to 3.06 ), 10 of them have less than or equal to this level of support. The 60% support figure for the Mathematics Department indicates the high level of respect which our faculty commands nationally.

(2) How is the U of R math department doing, given its modest size?

The NRC report notes, on p.3, that there is a sizable correlation between rankings and departmental size. In departments of mathematics the correlation coefficient is .5 (as noted in the table on p.453). The size of the U of R Mathematics Department's was 25 at the time of the NRC survey. ( The size is currently 21 regular and one temporary faculty.) This puts it substantially below the mean for departments in the first and second quartiles, which are 46 and 34 faculty, respectively. The thirteen departments with which it is tied or which are immediately ahead of it in the rankings have a mean size of 32.

Thus, the U of R Mathematics Department is doing well for its size.

Furthermore, there is a smaller, but significant, positive correlation between faculty size and percent of faculty with federal grant support; for mathematics departments, this is .18. Again, given the relatively small size of the Mathematics Department here, the level of support is very good.

(3) How good can a research university be without a doctoral program in mathematics? We can look at the success that other such universities have had.

Notice that 29 of the top 30 research universities cited in the US News and World Report have doctoral programs in mathematics. Also, 27 of them are ranked by the NRC; Emory and Tufts have unranked programs. The only one without a doctoral program in mathematics is Georgetown University, which has a graduate program in chemistry, but not in engineering or in other physical sciences.

The following information is taken from the 1995 NRC report. We looked at disciplines (other than mathematics) in the physical sciences, engineering, and some social sciences in which U of R currently has doctoral programs. Consider 10 such fields, namely

CHEMICAL ENGINEERING (93 schools ranked)

CHEMISTRY (168 schools ranked)

COMPUTER SCIENCE (44 schools ranked)

EARTH SCIENCES (100 schools ranked)

ECONOMICS(107 schools ranked)

ELECTRICAL ENGINEERING (126 schools ranked)

MATERIALS SCIENCE (65 schools ranked)

MECHANICAL ENGINEERING (110 schools ranked)

PHYSICS (147 schools ranked)

POLITICAL SCIENCE (97 schools ranked)

In each field one can look for the schools ranked in the top half which do NOT have doctoral programs in mathematics. We found only five schools that fit this description. Three of them (UC San Francisco, Oregon Graduate Inst. Sci & Tech, and Rockefeller U) do not have undergraduate programs of any kind, and the other two ( U of Kansas, and U of Akron) have doctoral mathematics programs (according to their WWW pages) not ranked by the NRC.

The conclusion is that **there is no competing university ranked in the top half of any of these 10 disciplines which does not have a doctoral program in mathematics.**

**A1. Brief report on Graduate Recruitment 1994, 1995**

For the Fall class of 1994, we successfully recruited our two top candidates with two Sproull Fellowships. The yield with the remaining candidates was not good. One feature is that we offered a stipend of $8,500 which was very low compared to other institutions.

Here are some examples which were taken from the AMS publication "Assistantships and Graduate Fellowships in the Mathematical Sciences". These appear to be typical amounts for departments at our level.

Berkeley.........................$10,818

Cornell..........................$10,212

MIT................... ..........$12,510

Northwestern University..........$10,530

University of Minnesota..........$10,800

The stipend offered here was far from competitive.

In 1995 we saw the continuance of a trend toward higher quality applicants to the mathematics department. Our goal was to recruit six new graduate students. We typically overbook by double that amount. Our yield was five. Two of our candidates won Sproull Fellowships in a university wide competition.That is two years in a row for which candidates from the Mathematics Department won Sproull fellowships. This fact gives more substance to the view that the quality of our applicants is improving.

In addition, we offered a higher stipend of $12,500 to six of our candidates. These candidates were identified as having potential for both excellent scholarship and teaching. One of these six offers was accepted. The other 5 went elsewhere: MIT, Cornell, UC San Diego, and two to Berkeley.

**A2. Retention of Students in the Calculus Sequence**

Since the undergraduate tuition revenue stream is enhanced by higher retention rates, it is a legitimate concern that students finish taking the calculus which they set out to learn.

Although we have not seen the data, it has been asserted that one third of those who start calculus do not finish it. While we do not have precise statistics on the rate at which students fail a calculus course, we believe that this rate is not very high and is, in fact, lower than corresponding rates at comparable insitutions.

We assume that it has been taken into account that many students drop from the faster paced Math161-162 sequence to the slower paced Math141-142-143 sequence. If these "drops" have not been accounted for, the figures regarding drop-outs and failures are misleading.

The claim that 1/3 of the students who start a course do not complete it with a passing grade is not supported by our enrollment data. We have the raw data from the registrar giving the enrollment figures for the beginning and the end of a term. The figures below are a sample for the academic year 94/95 and are typical for the last 5 years. See Table 3 in Appendix A6.

These figures are presented in the following format:

Course 141 142 143 (Fall,Sept/Jan) 254/243 99/91 41/38 Course 161 162 163 164 (Fall,Sept/Jan) 313/293 150/130 119/105 74/64 Course 141 142 143 (Sprng,Jan/June)124/115 170/179 22/20 Course 161 162 163 164 (Sprng,Jan/June)47/35 272/233 115/95 81/68

For example, 254 students enrolled in Math 141 at the beginning of the Fall term and 243 were enrolled in January at the end of the Fall term.

Freshman calculus is taught in 2 sequences, 141-143, and 161-162. Students switch between the sequences. Sophomore courses are Differential Equations ( Math 163) and Multi-variable calculus ( Math 164).

There is another source of error in interpreting the completion rate for the calculus sequence, namely, the fact that many majors do not require or evenly strongly encourage their students to complete an entire calculus sequence. Frequently, one course suffices.

Here is a summary of minimum mathematics requirements for B.A. programs with any mathematics requirements at all. The first four programs are among the most popular in the college and none of them require or even strongly encourage a full sequence of calculus.

Biology requires 161-162 or 141-142 ( not including 143) with the B.S. requiring in addition 163 or Statistics 201, 212, or a computer science course.

Economics requires 141 and recommends additional mathematics.

Environmental Studies requires 161 or 141-142.

Certificate in Management Studies requires 141.

Chemistry requires 161-162 ( or 141-143) with the B.S. requiring in addition 163 plus one additional course in mathematics, computer science, or statistics.

**A3. Mathematics Being Taught by Engineering at Rochester**

The Mechanical Engineering Department teaches four courses which are essentially equivalent to courses taught by the Mathematics Department.These courses and their history ( as recalled by Segal and Pizer ) are as follows:

1. Differential Equations ( Math 163 and ME 163 ). The ME department taught this for a short time in the 1970's. They stopped teaching it prior to 1975. They began teaching it again about 5 years ago.

2. Vector Calculus (Math 164 and ME 164). ME taught this for a while in the 1970's. They stopped teaching it in 1978. They began teaching it again about 5 years ago.

3. Boundary Value Problems ( Math 281 and ME 202). ME started teaching this about 10 years ago.

Note:

(i) At the time ME started teaching these courses, ME was in a school of engineering was separate from the school of arts and sciences in which mathematics resided. Each school had a separate dean.

(ii) ME began teaching ME 201 and 202 because ( as they admitted at the time or at least some of their faculty did) that they were losing students and they wished to "capture" them. Their students were not quitting because of mathematics courses rather they were quitting because they were interested in different subjects.

(iii) Nationally, enrollments in engineering are cyclical. Also it seems that nationally that the interests of engineering departments in teaching mathematics courses is also cyclical. These cycles may not be unrelated.

**A4. Summary of Some Teaching Innovations**

(1) Numerical analysis: Math 280, (1987-1990)

Over several years the Mathematics Department developed this course from a cookbook survey of algorithms to a course centered around a small number of principles for developing algorithms and analyzing errors. In particular, the use of Peano's theorem as a basis for analyzing "theoretical" errors is emphasized. Among the myriad of elementary textbooks with "numerical analysis" titles, very few share this philosophy--we are now using a book by Kincaid and Cheney which is reasonably attuned to this philosphy. Even though this is a computationally intensive course, it has seemed useful to keep the technology from overwhelming the content of the course--we have used in succession Xgraph ( developed, then abandoned at the U of R ), graphing calculators, and this next term we will use the freeware programs Xfunctions and mathPAd in the classroom. Students are encouraged to use any calculating tools with which they are comfortable in doing the homework.

The Mathematics Department used Hypercard for advising student majors in mathematics. This project began in 1990, was greatly improved in 1992, and recently converted to world wide web ( seehttp://www.math.rochester.edu for the current incarnation.)

The Mathematics Department also uses the Academic File Server to distribute some homework answers, practice tests, etc.. This has been expanded to include delivery via world wide web.

(2) Concrete mathematics: Math 220, (1993)

This course was converted from the standard smorgasbord-like discrete mathematics course (a little logic, a little set theory, some combinatorics, and proof by induction) to a more focused study of recursive relations and sums using Knuth's book Concrete Mathematics. The new course MTH 200 (Transition to higher mathematics) covers some of the original smorgasbord topics for those interested. (3) Qualitative ODE: Math 173 (1994)

The department experimented with Math 171-174 by teaching the differential equations section emphasizing nonlinear techniques. While this has been considered more advanced material in the past, Hubbard and West's book on the subject and the existence of computer programs for doing phase plane analysis now makes it possible to successfully include this information in the initial introduction to differential equations. The resulting emphasis on qualitative behavior is both more interesting, and in these days of symbolic differential equation solvers, more useful, than the traditional approach.

(4) Using Xfunctions and mathPad in Math 163: (Spring 1991 and following)

These freeware programs are smaller and less obtrusive than Mathematica or Maple, but allow cover us to cover what were previously considered "advanced" topics such as phase plane analysis and in the general geometric aspects of differential equations. This benefits non-majors as much as or more than majors. Mechanical Engineering also adopted the use of Xfunctions.

(5) Using Xfunctions in Math 141: ( Spring 1993)

This is very useful in the early weeks of the course.

(6) Using Mathematica in Differential Geometry: (Fall 1994)

Mathematica turned out to be very effective in the differential geometry course even though it was only used in a few classes. Several student questionnaires suggested (without prompting) ways in which its use could be expanded in future classes. Next time attempts will be made to use computer displays even more during the course.

(7) Geometer's sketchpad in Projective Geometry (Spring 1994)

Geometer's sketchpad software was used to good advantage in the first part of the course. This gives a great visual feel for the material which is usually lacking in this course. Some of the material was tied to applications in computer graphics in addition to the usual theoretical results.

(8) Physics 121/ Math161Q(1995)

This pair of courses loosely couples the first semester of physics with the first semester of differential calculus. Several experiments are taking place at once: (i) Coordination of material between math and physics, (ii) development of more substantial problems,and (iii) use of computers in delivering and grading homework.

(9) Math 141-143, Math 161-164 (1994)

After extensive meetings with a Math Task Force consisting of the Dean of Undergraduates, with members of the Mathematics, Engineering, and Physics Departments, the Mathematics Department revised the pace of the calculus sequence. This pace was slowed down so as to allow for more time to discuss applications, to practice technique, and to explain ideas. (10) Math 200

A new course was introduced, Transition to Higher mathematics, to ease the passage of majors from calculus to more abstract courses.

(11) Math 325

This course was in Problem Solving, designed for majors at the Junior and Senior level. This course also drew students from Mathematics Education.

(12) Math 238

The course in Combinatorial Analysis was modernized to include some design theory and some coding theory.

(13) Math 285

In Spring 1996, a new course, Methods in Applied Mathematics is being introduced.

(14) Math 215, Fractals and Computer Graphics (cross listed with Computer Science)

This course was introduced in 1992 and is offered on a yearly basis. Topics include the Mandelbrot set, Julia sets, dynamical sytems, and iterated functions systems. The fractal utility program Fractint is used to illustrate (with the help of an overhead luminator) many examples. The coursework consists of various programming projects and experiments with fractals.

Since the issue of linkages has been raised by the administration, we have prepared this report for the AMS fact finding delegation. It is based on a questionnaire sent to the members of the Mathematics faculty.

To the extent that the term linkage, as used by the administration, makes any sense to us, we have identified the following activities that can be so construed. Before presenting our summary, we raise the question whether this novel parameter of linkage is an appropriate measure of the legitimate activity of any Mathematics Department.

I. Transfer of information

------There have been at least five collaborations with faculty in other departments resulting in joint papers or successful grant applications.

------There have been at least ten instances of consultations resulting in acknowledgements in published papers.

------Most of us have answered technical questions raised by faculty and graduate students from other departments. It is our view that the average adjunct, expert in calculus pedagogy, would not have been very helpful for providing answers.

II. Institutional linkages

------Bridging Fellowships

Three of our faculty have bridged to Electrical Engineering, Chemical Engineering, and Computer Science. In each case, these bridges have led to further collaboration or consultations. In contrast to the three successful applications there was a distressing failed application. One faculty proposed to bridge to computer science with the aim of a substantial upgrade of of the course in discrete mathematics, especially under the impact of Mathematica, and Maple. It was turned down by the Dean as lacking intellectual content. How does this auger for the future of undergraduate instruction in mathematics at Rochester ?

------Cross-listed courses with Statistics--there are 5. In the past, there were cross-listings with Computer Science, but these have been dropped in the current catalog.

-----Math Physics Seminar, presently dormant for lack of funds. It has been operating for over twenty years.

III. Instructional Linkages

-----Upper level mathematics courses are prerequisites or strongly recommended for other undergraduate degree programs, e.g. Computer Science, Economics, all 4 Engineering programs, Chemistry, Physics, Statistics. These include Math 201, 220,235,280,281, and 282.

-----Three of our faculty have served as contributing outside members of Ph.D. theses committees.

-----All the respondents to the questionnaire have taught courses attended by graduate students or faculty from other departments: Economics, Physics, Computer Science, Business, Biology, Statistics, Chemical Engineering, Mechanical Engineering, Optics, and the Medical School. Some faculty have given reading courses tailored to the individual requirements of the non-mathematics students taking the course.

Table Number 1

**Summary Of The Mathematics Department Teaching Evaluations**

Comparison of the Mathematics Department's means with means for the division of natural science (Fall 1990-Spring 1994) and with means for the division of formal reasoning (Fall 1994-Spring 1995)

**Overall Student Rating of Instructor and Course**

Class Size =* * <= 20 21 <= * <=40 41 <= * Math Div Math Div Math Div Sp 95 Inst 4.43 4.33 3.70 4.14 4.49 4.23 Crse 4.15 4.15 3.56 3.71 3.79 3.66 Fl 94 Inst 4.00 4.21 4.20 4.14 3.67 3.50 Crse 3.71 3.87 3.61 3.60 3.45 3.37 Sp 94 Inst 4.17 4.09 4.10 4.08 2.93 3.94 Crse 3.95 3.93 3.66 3.85 3.19 3.78 Class Size =* * <= 20 21 <= * <=40 41 <= * Fl 93 Inst 3.9 4.1 3.7 3.8 4.2 3.7 Crse 3.7 4.0 3.5 3.7 4.1 3.6 Sp 93 Inst 4.0 4.1 4.1 4.0 4.1 3.9 Crse 3.8 4.0 3.6 3.8 3.7 3.7 Fl 92 Inst 3.9 4.2 3.6 3.9 4.0 4.0 Crse 3.7 4.1 3.5 3.8 3.4 3.8 Sp 92 Inst 4.0 4.1 4.0 3.9 4.0 3.7 Crse 3.7 4.0 3.6 3.7 3.5 3.5 Fl 91 DATA NOT AVAILABLE Sp 91 Inst 4.1 4.1 3.9 3.8 4.0 3.9 Crse 3.9 4.0 3.7 3.7 3.7 3.7 Fl 90 Inst 4.3 4.2 3.6 3.7 4.0 3.9 Crse 4.0 4.0 3.6 3.7 3.7 3.7 CUMMULATIVE MEANS Inst 4.08 4.16 3.88 3.94 3.93 3.75 Crse 3.84 3.98 3.60 3.70 3.61 3.58

Table Number 2

**Summary of Mathematics Department Teaching Evaulations for Calculus Courses, MTH 141-164**

Spring 1994- Spring 1995

Comparison of the Mathematics Department's means with means for the division of natural science (Spring 1994) and with means for the division of formal reasoning (Fall 1994-Spring 1995)

**Overall Student Rating of Instructor and Course**

Class Size =* * <= 20 21 <= * <=40 41 <= * Math Div Math Div Math Div Sp 95 Inst 4.22 4.33 4.04 4.14 4.28 4.23 Crse 3.80 4.15 3.69 3.71 3.71 3.66 Fl 94 Inst 2.96 4.21 4.18 4.14 3.63 3.50 Crse 2.66 3.87 3.58 3.60 3.65 3.37 Sp 94 Inst 4.55 4.09 3.79 4.08 3.20 3.94 Crse 4.18 3.93 3.45 3.85 3.12 3.78

Table 3

**Math Course Enrollments**

COURSE Fall 94 Fall 93 Fall 92 Fall 91 Fall 90 NUM Spr 95 Spr 94 Spr 93 Spr 92 Spr 91 MTH 141 Sep/Jan 297/310 287/243 274/264 340/320 319/320 Jan/Jun 124/115 91/126 132/128 117/96 115/91 MTH 142 Sep/Jan 78/78 91/76 82/50 57/41 69/61 Jan/Jun 230/220 170/175 170/173 230/209 221/219 MTH 143 Sep/Jan 39/37 38/34 35/28 87/70 93/69 Jan/Jun 22/20 7/21 19/15 24/15 56/54 MTH 161 Sep/Jan 334/320 371/293 398/317 428/323 383/280 Jan/Jun 34/31 37/49 40/32 n/o n/o MTH 162 Sep/Jan 150/130 141/130 134/133 120/104 122/97 Jan/Jun 242/233 272/233 274/238 280/220 204/184 MTH 163 Sep/Jan 119/105 128/103 178/142 170/128 181/143 Jan/Jun 126/128 115/95 133/122 128/115 142/121 MTH 164 Sep/Jan 62/60 69/74 92/75 111/85 83/62 Jan/Jun 55/40 90/64 131/118 138/130 143/119

Sep/Jan and Jan/Jun are the dates of the enrollment figures gathered. The numbers e.g. 297/310 are the figures reported by the registrar when classes began and when classes ended.

n/o: course not offered

1. Carol Bezuidenhout: Ph.D. 1985, University of Minnesota

Field: probability

Articles: 7 research articles including [The critical contact process dies out (with G. Grimmett), Annals of Probability, 18(1990), 1462-1482].

Other activities: Van Vleck Assistant

Professor, University of Wisconsin, Madison, 1985-1987.

2. Frederick R. Cohen: Ph.D. 1972, University of Chicago

Field: algebraic topology

Articles: Over 60 research articles including (1) [Torsion in homotopy theory, Annals of Math., 109(1979), 121-168 ( with J. C. Moore and J. A. Neisendorfer)], and (2) [The homology of Cn-spaces , Springer-Verlag Lecture Notes in Math., v. 533, 208-353]. Grant support: (1) Alfred P. Sloan Fellowship 1979-1983, (2) NSF 1975-present, (3) Member, Insitute for Advanced Study, 1975-77 Other activities: (1) Editorial board of Proceeding of the AMS 1987-1991, (2) editorial board of Forum Mathematicum, DeGruyter (1987-present...), (3) invited address at the International Congress of Mathematicians (1983), and (4) Journees de topologie of the Swiss Mathematical Society,Lausanne, June 1996.

Student theses: five currently supervising two

3. Michael Cranston: Ph.D. 1980, University of Minnesota

Field: probability

Articles: 35 research articles including (1) [The strong law of large numbers for a Brownian polymer, (with T.S. Mountford), Ann. of Probability, to appear], and (2) [Gradient estimates on manifolds using coupling, Journal of Functional Analysis, v99, no.1,110-124, 1991]. Grant support: National Security Agency, National Science Foundation (1985-88, 90-present), and Army Research Office MRI at Cornell (1990-1994). Other activities:(1)Invited scholar ETH ( Zurich, June 1994), (2) Universite de Paris VI, ( June 1990), and (3) Hour invited address at American Math. Soc. Central Section , Kansas, March 1994, and (4) Co-organizer AMS Summer Research Insitute, July 1993.

Student theses: two

4. Michael E. Gage: Ph.D. 1978, Stanford Unversity

Field: differential geometry, nonlinear differential equations, integral geometry

Articles: 15 research articles including (1) [Curve shortening on surfaces, Annales Scientifiques de l'Ecole Normal Superieur 2(1990), 229-256], and (2)[A proof of Gehring's linked sphere conjecture, Duke Math J., v. 47, No3, (1980), 615-620]. Grant support: (1) NSF grants: 1986-1990 NSF, and (2) Visiting professor, Institute des Hautes Etudes Scientifiques, Paris, France, Fall 1986 Other activities: (1) Invited hour address Conference on Motion by Mean curvature and Its Applications -- Levico, Italy, June,1994, (2) Micro-program in Riemannian Geometry, Fields Institute, August, 1993, and (3) Invited to speak at Cleveland Symposium (1995) of TMS--The Minerals, Metals & Materials Society.

Student theses: three and one currently finishing

5. Samuel Gitler: Ph.D. 1960, Princeton University

Field: algebraic topology

Articles: Over 40 articles together with 7 monographs, books, and edited conference proceedings including [A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra ( with E.H. Brown Jr.), Topology 12(1973)]. Grant support: (1) Rockefeller Foundation,1957-1959, (2) Institute for Advanced Study 1964-1965 and 1985-1986, and (3) National Science Foundation 1989-present.

Other activities: Invited hour address at the annual AMS meeting 1972, member of the Colegio Nacional from Mexico, recipient of the National Prize in Science from Mexico in 1976.

Students: two in Rochester

6. Steven Gonek: Ph.D. 1982, University of Michigan

Field: Analytic number theory, theory of the zeta function

Articles: 20 articles including (1) [Mean values of the Riemann zeta-function and its derivatives, Inventiones. Math. 75(1984), 123-141], and (2) [ Simple zeroes of the zeta function of a quadratic number field II ( with B. Conrey and A. Ghosh), Analytic Number Theory and Diophantine Problems, Proceedings of a Conference at Oklahoma State Univ., Birkhauser, Basel, 1987]. Grant support: NSF 1985-86, 1988-90 Other activities: Invited lectures at (i) International conference on Analytic Number Theory, Kyoto, Japan, May 1996, and (ii) University of Toronto, October 1994.

Student theses: currently supervising four

7. Allan Greenleaf : Ph.D. 1981, Princeton University

Field: Harmonic analysis

Articles: 12 articles including (1)[ Determining singularities of a potential from the singularities of back scattering ( with G. Uhlmann), Comm. in Mathematical Physics, 1993] and (2) [Non-local inversion formulas for the x-ray transform (with G. Uhlmann), Duke J. Math. 1989] Grant support: (1) Alfred P. Sloan Fellowship 1990-1992, (2) NSF support for 9 out of the last 10 years

Other activities: Review 2-3 NSF proposals per year and member of NSF Review Panel

Student theses: five currently supervising one

8. Martin A. Guest: Ph.D. 1981, Oxford University

Field: geometry and topology

Articles: 27 research articles including (1) [Group actions and deformations for harmonic maps (with Y. Ohnita), Jour. Math. Soc. Japan 45 (1993) 671-704], and (2) [Configuration spaces and the space of rational curves on a toric variety, BAMS 31 (1994), 191-196] Grant support: (1) NSF grants (1984-86, 1991-93), (2) MSRI Fellowship 1984, (3) Humboldt Fellowship (Max Planck Inst., Bonn, 1986-87), (4) NSF/JSPS Fellowship to visit Tokyo Metropolitan University, 1989/90, and (5) NSF/CGP Fellowship to visit Tokyo Institute of Technology, 1994. Other activities: Hour Invited address, Mathematical Society of Japan meeting, Kobe, Japan, 4/1994.

Student theses: two currently supervising two

9. John R. Harper: Ph.D. 1967, University of Chicago

Field: algebraic topology

Articles: 34 articles including (1) [Co-H-maps to spheres, Israel J. Math., 66(1989)223-237], (2) [H-spaces with torsion, Memoirs AMS, 22(223) 1979]

Grant support: NSF support 1970-1987

Other activities: Two books: (1) Algebraic Topology: A first Course, Addison-Wesley / Benjamin -Cummings (1981), (2) Secondary Cohomology Operations ( book in preparation), and (3) Midwest Topology Seminar invited speaker,

Student theses: five currently supervising one

10. Naomi Jochnowitz: Ph.D. 1976, Harvard University

Field: Algebraic number theory, modular forms

Articles: Eight including (1) [Congruences between modular forms of half integral weights and implications for class numbers and elliptic curves, Inventiones. Math, 126 pages, to appear], and (2) [A p-adic conjecture about derivatives attached to modular forms", Proceedings of the Boston conference on p-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, (Barry Mazur and Glenn Stevens, editors), Contemporary Mathematics, 165. Grant support: NSF 1991-1995

Other activities:(1)Lady Davis Postdoctoral Fellowship (1976-1977), (2) Science Scholar of the Mary Ingraham Bunting Institute of Radcliffe College (1983-1985), (2) Tamarkin Assistant Professor of Mathematics, Brown University, 1979-1982, (3) Mathematical Sciences Research Institute, Spring 1995, and (4) New Vistas in Automorphic Forms, Harvard, 1995, invited talk, and (5) invited talk in the conference on p-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture that was jointly sponsored by Harvard and Boston University.

Student theses: one

11. Richard B. Lavine: Ph.D. 1965, MIT

Field: Mathematical physics, Schrodinger operators

Most influential work: Introduced commutators into quantum scattering theory [ See Reed &Simon, Methods of Modern Mathematical Physics IV, p.p 157-163]

Main research goal: Understand resonances ( without asymptotics) [Comm. Math. Phys. 128(1990), 263-284] Articles:24 including [On the inverse scattering transform for the n-dimensional Schrodinger operator, Topics in Soliton Theory and Exactly Solvable Non-linear equations, World Scientific ( with A. Nachman ), 1987].

Student theses: eight

12. Yi Li : Ph.D. 1988, University of Minnesota

Field: Non-linear partial differential equations Articles: 28 articles including [Travelling fronts in cylinders, preprint (with C. Li )]

Grant support: NSF grants 1988-present

Other activities: (1) L.E. Dickson Instructor, University of Chicago, and (2) Excellent Ph.D. Thesis Award, May 26, 1988 , School of Mathematics, University of Minnesota

13.Saul Lubkin: Ph.D. 1963, Harvard University

Field: algebraic geometry and homological algebra

Articles: 13 articles including [ A p-adic proof of Weil's Conjecture, Ann. of Math., 97(1968), 105-255] and [On a Conjecture of Andre Weil, Amer. J. of Math., 89 (1967), 443-458].

Grant support: (1) Alfred Sloan fellowship 1968-1970, (2) NSF Postdoctoral Fellow, Oxford (64-65) and Stanford (65-66), and (3) NSF grants.

Other activities: (1) Invited Colloquia at Harvard, IAS, Princeton, Berkeley, Toronto, Oxford, Oslo, Copenhagen, (2) Senior Visiting Fellow of the Science Research Council of the U.K., (3) a principal speaker at the Barsotti Memorial Symposium, University of Padua, Abano Terme, Italy, June 24-27, 1991, (4) Book, Cohomology of completions, North Holland (1971) (5)Book, Lifted p-Adic Cohomology, contracted, being proofread. (6)Sole Editor, Mathematical Studies series of books, Elsevier Press, the Netherlands, 1994-present.

Students: four currently supervising one

14. Carl Mueller: Ph.D. 1979, University of California at Berkeley

Field: probability

Articles: 29 articles including (1) [Coupling and invariant measures for the heat equation with a noise term, Annals of Probability, 21(1993), 2189-2199], and (2) [On the extinction of measure-valued critical branching Brownian motion, Annals of Probability 17, (1989)].

Grant support: NSF (1982-88, 1991-95), and NSA (1991-95, 1995-98).

Students: one

15. Adrian Nachman: Ph.D. 1980, Princeton University

Field: Inverse scattering problems

Articles: 20 including [Reconstructions from boundary measurements, Ann. of Math. 128(1988), 531-576], and (2)[Global uniqueness for a two dimensional inverse boundary value problem, Annals of Math., to appear]

Grant support: (1) 1990-1997 ONR Nonlinear Aspects of Multidimensional Inverse Scattering Problems, P.I., (2)1986-1989 NSF Inverse Problems in Potential Scattering, Co-principal Investigator with R. Lavine (3)1994-1996 U.S. Army New Methods for Quantitative, High Resolution Ultrasonic Imaging of the Breast, Co-investigator with R. C. Waag, P.I., and (4) 1992-1996 NIH Ultrasound Imaging and Tissue Characterization, Co-investigator, with R. C. Waag, P.I. Other activities: (1) Keynote speaker at the AMS/SIAM Conference on Impedance Tomography, University of Washington, 1995,, and (2) Editorial Board of Inverse Problems, 1991-1994. Collaborators: Emil Wolf ( optics), Martin Feinberg ( engineering), Robert Waag ( electrical engineering and radiodology)

Students: one

16. Joseph A. Neisendorfer: Ph.D. 1972, Princeton University

Field: algebraic topology

Articles: 29 papers, 1 Memoir [Primary homotopy theory, Memoirs of the AMS, 232] including (1) [The double suspension and exponents of the homotopy groups of spheres, Ann. of Math., 110(1979), 549-565], and (2) [On the homotopy groups of a finite dimensional space, Comm. Math. Helv., 59(1984), 253-257].

Grant support: NSF grant support 1979-present.

Other activities: (1) Invited hour address, American Mathematical Society, Annual Meeting, 1983, and (2) Finalist teacher of the year award 1989

Students: four

17. Arnold K. Pizer: Ph.D. 1971, Yale University

Field: algebraic number theory

Articles: 22 articles including (1) [Ramanujan Graphs and Hecke Operators, Bulletin of AMS (New Series) 23 (1990), 127-137], and (2) [Orders in Quaternion Algebras (with H. Hijikata and T. Shemanske), J. Reine angew. Math. 394 (1989), 59-106].

Grant support: (1) NSF Grant (1972-83, 1991-1996), and (2)NSF SCREMS (1993-1996) (co-PI with D. Ravenel)

Other activities: (1) "Ramanujan Graphs" at Computational Perspectives on Number Theory, A Conference in Honor of A.O.L. Atkin, September 14-16, 1995 Chicago, Ill., and (2) Member of the 1988 NSF panel for evaluating curriculum development in Mathematics/Calculus in the 21-st century

Students: four

18: David Prill: Ph.D. 1965, Princeton University

Field: Several complex variables

Outside support: (1) University of Munich, Verwalter einer Assistentenstelle, 1966-67, (2) Eidgenossische Technische Hochschule, Zurich Switzerland, 1970-71, and (3) University of Bonn, Germany, under aegis of SFB 40, 1977-78.

Articles: 7 including [The fundamental Group of the Complement of an Algebraic Curve, Manuscipta Math. 14(1974), 163-172].

Ph. D. Students: Five

19. Douglas C. Ravenel: Ph.D. 1972, Brandeis University

Field: algebraic topology

Articles: 50 articles including (1) [Localization with respect to certain periodic homology theories, Amer. J. Math., 106(1984), 351-414], and (2) [The nilpotence and periodicity theorems in stable homotopy theory, Seminaire Bourbaki, Expose' 728, Asterisque 189-190(1990), 399-428]

Grant support:(1) NSF 1972- present, (2) Alfred Sloan Foundation fellowship 1977-81, and (3)Troisieme Siecle(Switzerland), 1980

Other activities: (1) invited address, International Congress of Mathematicians, 1978, (2) Seminaire Bourbaki, Paris, 1990, (3) Holiday Symposium, New Mexico State Univ. 1989. Books: (4) Complex cobordism and stable homotopy grpups of spheres, Academic Press, 1986, and (5) Nilpotence and Periodicity in Stable Homotopy Theory, Ann. of Math. Studies, 128, Princeton, 1992

Students: two here and four while at the University of Washington

20. Sanford Segal : Ph.D. 1963, University of Colorado

Field: complex variables, history of science, and math education

Articles: 45 articles including [Iterative characterization of powers and exponentials, Aequationes Mathematicae, 37(1989), 201-218]

Grant support: Alexander von Humboldt Foundation (Germany), Spring 1988

Other activities: (1) member, Advisory Board for NSF grant (PMSA) to Rochester City School District, and (2) Nine Introductions in Complex Analysis, North Holland, 1981

Students: five

21. Barbara Shipman: Ph.D. 1995, Arizona

Field: Geometry, moment mappings, representations of Lie algebras, and their applications to integrable systems

Articles: On the geometry of certain isospectral sets in the full Konstant-Toda lattice, to appear

Other activities: A series of talks in the geometry seminar of the University of Rochester.

22. Norman Stein: Ph.D. 1957, Cornell University

Field: algebraic topology

Articles: 9 including [Secondary characteristic classes, Ann. of Math., 76(1962), 510-523, (with F.P.Peterson)]

Grants: Various grants over the years ( NSF and Air Force)

Students: five

**The Dean's Rationale for the Restructuring Plan**

"Effective teaching of calculus is an essential ingredient of a quality undergraduate educational experience at Rochester, particularly given the large proportion (over 70%) of first year students who enroll in the calculus sequences. Although arguments could be made that graduate students in Math play a key role in calculus instruction, much like the role that graduate students in English play in basic-level writing courses, the dwindling numbers of Math graduate students undercut one rationale for retaining a Ph.D. program in Math. There are other ways to service our need for calculus instruction, including the hiring of non-research (adjunct) faculty and/or the redirection of other qualified faculty from other disciplines. "Coupled with these concerns is a Ph.D. program in Math that is of modest distinction (though certain subgroups of faculty are nationally prominent). Its NRC ranking is 58.5 (42 percentile). As shown in Table B, 25 of the top 30 institutions have higher ranked Math graduate programs, 3 do not offer a Ph.D. in Math, and only 1 has a poorer ranked graduate program. Despite good intentions by several faculty in Math, undergraduate instruction is less than optimal, the best graduate students are going to other programs, and no reasonable investment in the department would push our ranking to a level commensurate with the overall institution.

"For these reasons, we do not believe that continuation of the Ph.D. program in Math is justified. Linkages with other departments and programs are minimal, as is grant income (generally true of Math departments). We believe that a refocused department that emphasizes quality calculus instruction (to a smaller undergraduate student body), attention to majors and minors, and individual research excellence, will best serve the overall needs of the College. A reduction in steady-state faculty size over time from 21 to 10 FTEs, with additional non-tenure-track teaching faculty who staff much of the elementary calculus sequences, can achieve these goals."