In 2008 NPS commissioned a peer
comparison study from CES Consultants to evaluate the overall institution
against a carefully selected group of peer institutions. The intent of the peer
analysis was to provide quantitative information on the range and magnitude of
a number of key performance indicators to help NPS identify strengths and
weaknesses, and specific areas for improvement. Fifteen specific peer
institutions (CES peers) were selected for comparison:
California Institute of Technology
Carnegie Mellon University
Claremont Graduate University
Duke University
Georgia Institute of Technology
Illinois Institute of Technology
Massachusetts Institute of
Technology
North Carolina State University
Rensselaer Polytechnic Institute
Rice University
Stanford University
Stevens Institute of Technology
University of California, Santa
Barbara
University of Illinois,
Urbana-Champaign
University of Southern California
A wide variety of specific data
was collected for all of the institutions, and then averages and rankings in
various categories were computed. The final report was issued in January 2009, and we shall
refer to the results of the CES peer comparison in various parts of this
self-study for purposes of assessment.
In 2010, NPS commissioned another
study from Academic Analytics, LLC. The purpose of this study, which we shall
refer to as AA2010, was to generate quantitative measures of faculty scholarly
productivity at NPS.
The mission of the Department of
Applied Mathematics is to provide an exceptional mathematical education focused
on the unique needs of our students, to engage in relevant research, and to
provide quality service to the community. We are deeply committed to
maintenance of a well-designed curriculum and a supportive environment for our
students.
Because mathematics is the
language of science, it is fundamental to every quantitative science and
technology curriculum on campus. The primary role of the department is one of
service to the various technical curricula at NPS. This includes a very high
proportion of remedial undergraduate level coursework that is necessary for
students who are transitioning to graduate study after a long period away from
university. The Department of Applied Mathematics strives to provide
a solid mathematical foundation for all students as they make the transition
into graduate curricula. We provide high-quality instruction in all courses,
giving emphasis to relevant and modern mathematical techniques in our advanced
courses. And we encourage students to develop and utilize skills in analysis,
reasoning, creativity, and exposition as they acquire knowledge of mathematics
and its applications. We regularly engage with our client curricula to ensure
that our service courses remain up to date and meet their needs.
There are also a very small
number of students who are seeking degrees in Applied Mathematics. The primary
sponsor for students seeking a degree in Applied Mathematics is the Department
of Mathematics at the United States Military Academy (USMA). These students
come here for graduate study as preparation for an assignment to teach
mathematics at USMA. Prior to the cancellation of the 380 curriculum in early
2001, we also had a contingent of Naval officers who were preparing to teach
mathematics at the United States Naval Academy (USNA) as well as one or two
Marine Corps officers (to be similarly detailed). We also support a number of
students who decide to pursue a dual degree program while at NPS. We have found
this to be an excellent way to enhance our interdisciplinary activities across
the campus.
In
addition, we maintain active research programs, making a special effort to
respond to the needs of the NPS, DoN and DoD communities. By adhering to the
most stringent standards of scholarship, we ensure that the department
continues to hold the respect of the community of scholars worldwide. We serve
our profession, not only through scholarship, but also by our involvement in
professional organizations and by our editorial and administrative
contributions to the growing body of mathematical knowledge. We also serve the
NPS community with our active role in the governance of the School.
The Department of Applied
Mathematics has the longest history of any department at the Naval Postgraduate
School and traces its origins to the appointment of Ensign Guy K. Calhoun as
Professor of Mathematics in 1910. He would
later become the first faculty member assigned to the Postgraduate Department
that was created at Annapolis in 1912 to function as a preparatory school whose
students would complete their graduate studies at a civilian institution after
a year of study at Annapolis. The department was headed by a single officer
with a small office staff and the assistance of a single civilian engineer. At
its inception, the department had no regular faculty but relied on the
cooperation of civilian institutions as well as regular faculty from the
academic departments at USNA. Prof. Ralph E. Root, who had originally joined
the faculty in the Mathematics Department at Annapolis in 1913, quickly became
involved in the fledgling Postgraduate Department, and in 1914 he became the
first civilian faculty member of the new department when he was appointed as
its Professor of Mathematics and Mechanics. He had earned his Ph.D. at the
University of Chicago in 1911 under the direction of the illustrious Prof. E.H.
Moore whose list of doctoral students includes such notables as George
Birkhoff, Leonard Dickson, Theophil Hildebrandt, R.L. Moore, and Oswald Veblen.
Indeed, Root’s dissertation work was so fundamental to the early development of
the concept of ‘neighborhood’ that it encompasses an entire section in Aull and
Lowen’s Handbook of the History of General Topology.
By 1931 the Postgraduate
Department had evolved into a Postgraduate School that had fifteen faculty –
four in Mathematics and Mechanics (C.C. Bramble, W.R. Church, C.H. Rawlins, and
R.E. Root), three in Mechanical Engineering, three in Electrical Engineering,
two in Metallurgy and Chemistry, one in Physics, one in Radio, and one in
Modern Languages.
In 1946 Captain Herman A.
Spanagel (appointed Head of the Postgraduate School in April, 1944) instituted
a major reorganization of the school that created, for the first time,
traditional academic departments. The Department of Mathematics and Mechanics
was one of the seven original academic departments created in this
reorganization, and Prof. W.R. Church was appointed as chairman. Professor
Church, who had spent the war years on active duty in the Navy, was a keen
student of new developments in applied mathematics. The applications of statistics to strategy in
anti-submarine warfare had led to many other applications in the analysis of naval
operations. As this new area of science
continued to grow after the end of the war, Professor Church and the Department
of Mathematics and Mechanics were leaders in the development of the new
curriculum in operations analysis, which began in 1951-52. Professors Torrance from Mathematics and
Cunningham from Physics taught the initial courses in this discipline. They were soon assisted by Professor Tom
Oberbeck, who joined the Mathematics faculty in 1951. After a period of growth and development, during
which several statisticians were added to the faculty to handle the gradual
shift in emphasis from physical science to statistical analysis as the
curriculum adjusted to the needs of the Navy, the School created the Department
of Operations Research with Oberbeck as Chairman in 1962. He was succeeded,
three years later, by Jack Borsting, who was also from the Department of
Mathematics and Mechanics.
In 1966, the separation of
Operations Research from Mathematics was completed with the transfer of statistics
to the Department of Operations Research along with five of the professors who
covered this subject. At this time the
offspring to which Mathematics had given birth had nineteen professors and was
still growing. This is the same year that the Department of Mathematics and
Mechanics changed its name to the Department of Mathematics and R.E. Gaskell
took over as chairman following twenty years of impeccable leadership by W.R.
Church.
Professor Church was also keenly
interested in the development of the computer world, started in the war years
by the Harvard Mark I and by the University of Pennsylvania Moore School
Computer. Indeed, the Department of Mathematics and Mechanics had already
played a pivotal role in the history of computing by that point, as it was our
own Prof. C.C. Bramble who had recommended the development of the Harvard Mark
II for the Naval Proving Ground at Dahlgren. Howard Aiken, computer pioneer and
developer of the Mark II, recalls it this way in an interview in February, 1973:
“Mark
II was built for the Naval Proving Ground at Dahlgren on the recommendation of
Professor Clinton Bramble of the United States Naval Academy, who was a
mathematician and who was on duty as a Naval Officer. And Bramble was able to
foresee that they had to quit this hand stuff in the making of range tables.
That's why we built the computer. And Albert Worthheimer found the money for it
and signed the contract.
In
November of 1944, the Bureau of Ordnance requested the Computation Laboratory,
then operating as a naval activity, undertake the design and construction of an
automatic digital calculator for installation at the Naval Proving
Ground."
It is interesting to note the
Prof. Bramble’s first contacts with Dahlgren were in 1924. He notes in a January 1977 interview that:
“In
those days, there was no bridge across the Potomac. I used to call up, and
they'd send a boat over to Morgantown, Maryland, for me. When I came down, it
was just for general interest in ordnance problems while I was teaching
ordnance courses at the Naval Postgraduate School. The courses included
ballistics and gun design, both exterior and interior ballistics.
Naturally
I was interested in the current problems in those areas, so periodically I
would get in touch with Dr. Thompson, who was at that time the Senior Scientist
at Dahlgren. It was a very informal contact, but that was my way of maintaining
a live interest in current ordnance problems and the research that was going
on. I also did the same sort of thing with the Army Proving Ground at Aberdeen.
When
the national emergency [World War II] came on and the decision was made to move
the ballistics work out of Washington from the Bureau of Ordnance to Dahlgren,
the Postgraduate School was requested to transfer me to Dahlgren, but the Head
of the Postgraduate School wouldn't agree, so they compromised by sending me to
Dahlgren 4 days a week. That was the beginning of the ballistic work and the
beginning of the Computation Laboratory because, at that time, there were only
two mathematicians employed at Dahlgren. They were at about a GS-7 or GS-9
level. That was back about 1942, and there were also a couple of women at the
GS-5 level.”
Although he split his time
between the Postgraduate School and Dahlgren for several years at that point,
Prof. Bramble eventually moved to Dahlgren full-time in 1947 when he was
appointed Head of the Computation and Ballistics Department. In 1951 he was
selected as Dahlgren’s first Director of Research, a position he held until his
retirement in January 1954.
Although Professor W. E. Bleick,
1946, and B. J. Lockhart, 1948, had also been involved with these computer
developments before coming to the Department of Mathematics, it was Professor
Church who led the movement to obtain the first electronic automatic digital
computer. And so it was that in 1953, an NCR 102A, was hoisted by a crane
through a second floor window in Root Hall and installed in the Mathematics
Department. This precursor machine, as well as the development of its use in
instruction and research, resulted in the acquisition in 1960 of the world’s
first all solid-state computer – the CDC 1604 Model 1, Serial No. 1 – which was
designed, built, and personally certified in the lobby of Spanagel Hall by the
legendary Seymour Cray. This was the first of ten such machines, ordered by the
Navy’s Bureau of Ships for its Operational Control Centers. The installation of
the CDC 1604 coincided with the formation of the School’s Computer Center, now
named in honor of Professor Church.
Computer courses quickly became
standard in almost every curriculum in the School, and the use of the computer
in research work increased rapidly at the School. However, it was not until 1967 that the
school established the Computer Science courses and began adding faculty in
this area to the Department of Mathematics.
Two years later, Gary Kildall joined the department as an instructor of
mathematics to fulfill his draft obligation to the US Navy. His pioneering work
during his years as part of the department fundamentally changed the nature of
computing, particularly his creation of PL/M (the first high-level language developed for
microprocessors) and CP/M (the first
operating system for microcomputers).
Eventually, the existence of a
group of computing specialists within the Department of Mathematics and their
interaction with faculty in other departments (chiefly electrical engineering)
who worked with computers led to formation of the Computer Science Group in
1973; however, the professors involved maintained their status in the
Department of Mathematics until 1976 when the Department of Computer Science was
formed. At that time, five faculty
members moved from Mathematics to the new department.
Thus, in about thirty years, the
Department of Mathematics had seen two sub-disciplines emerge and develop into
thriving departments, each with its own cadre of graduate students, student
thesis effort, and sponsored research.
Following the separation of
Computer Science from Mathematics, the department saw a ten year period where
it was functioning once again almost exclusively as a service department. The Mathematics curriculum (380), which had
been established in 1956, was officially disestablished in 1976. The department
maintained its degree granting authority, but without an official curriculum,
only a handful of students received the MS in Mathematics between 1976 and
1987; most of these were dual majors with Operations Research.
The 380 curriculum was
reestablished in 1987, and this initiated a period of growth in the department.
More than half of the current faculty were recruited in the seven year period
following the reestablishment of the curriculum. Throughout the 1990s, the
department graduated an average of roughly six students per year with a steady
mix of inputs from the Navy, Army, and Marine Corps.
In early 2001 the superintendent,
RADM Ellison, officially closed the 380 curriculum ,ostensibly due to low Navy
enrollments. Although the department maintained its degree granting authority, RADM
Ellison did not allow other services to matriculate students in Applied
Mathematics during the remainder of term, and this led to the loss of student
inputs from the Army and Marine Corps. Upon his departure, the new
superintendent, RADM Wells, officially changed the enrollment policy and
allowed other services to matriculate in Applied Mathematics. Unfortunately, he
was not able to get the 380 curriculum officially reinstated, and hence Navy
students are still unable to enroll in the curriculum. In spite of this, the
department has been able to somewhat rebuild our program, and in the last two
years we have started to produce a small but steady stream of graduates.
·
1957-8:
Prof. William Edmund Milne
·
1981-2:
Prof. Garret Birkhoff
Although there were no official
academic departments at NPS prior to 1946, Ralph Root is generally considered
to be our first chairman as his original appointment to NPS was as head of
mathematics and mechanics. Having held
that post from 1914 until his retirement in 1946 we honor him by placing him
first in our historical list of the chairmen of the department.
·
1914-1945:
Ralph E. Root
·
1946-1965:
W. Randolph Church
·
1966-1971:
Robert E. Gaskell
·
1972-1973:
W. Max Woods
·
1974-1975:
Ladis D. Kovach
·
1976-1983:
Carroll O. Wilde
·
1984-1986:
Gordon E. Latta
·
1986-1992:
Harold M. Fredricksen
·
1993-1996: Richard
H. Franke
·
1996:
Guillermo Owen
·
1997-1998:
W. Max Woods
·
1999-2002:
Michael A. Morgan
·
2003-2008:
Clyde L. Scandrett
·
2009-Present:
Carlos F. Borges
At the present time the
department has sixteen tenured and tenure-track faculty, one of whom has been
on an extended leave of absence since 2006. This number of faculty actually
matches the number onboard back in 2001, although there have been four new
hires in that period to replace retiring faculty members. There is good
diversity among the tenure track faculty represented by three females and three
Hispanics. This distribution of 19% in each category is well above the NPS
averages (from the peer comparison study) of 16% and 11% respectively. And although
we are under the peer institution median of 30% female, we are well above the
peer institution median of 13% for underrepresented minorities. Indeed, we clearly have the most diverse
faculty of any department in the School of Engineering and Applied Sciences.
The chart below shows the age and years of service distribution for the
tenure-track faculty.
A complete listing of the faculty
as well as links to brief vitae and personal web pages can be found in Appendix
A. Several major school wide research and teaching awards have been won by our
current tenure-track faculty, including three Menneken Awards and one
Schieffelin Award. A summary of major awards and prizes won by our faculty is
available in Appendix B.
The department currently has two
non-tenure track research faculty members. Distinguished Visiting Professor Art
Krener has been resident with us since 2005. In 2009 Professor Margaret Cheney
joined us as a Research Professor. Although her primary focus is her regular
appointment as Professor of Mathematical Sciences at the Rensselaer Polytechnic Institute, she has
ongoing interdisciplinary collaborations here at NPS, and her appointment is
facilitating further collaborations both inside and outside of the department.
The department employs two
lecturers and one senior lecturer. Although their main focus is teaching the
remedial undergraduate mathematics courses that are essential to the transition
of NPS students to the various science and technology curricula, all of them
have a range of abilities well beyond that (one routinely teaches a graduate level
dynamics class for the Meteorology department). The quality of teaching from
this group of faculty is uniformly excellent and, indeed, one of them is a
Schiefellin Award winner. All three are retired O-5 military officers (one each
from the Army, Navy, and Air Force) and, as a result, are much attuned to the
particular needs of our students.
In addition to classroom
teaching, many are involved in curriculum reform efforts (course development,
review sessions, textbook and lab-manual writing etc.).
The departmental policy on
instructional workload follows the fact that NPS is obligated, by contract, to
pay all tenure-track faculty for ten months each year. Since the school
operates year-round and there are four academic quarters, each tenure-track
faculty member has one quarter each year (called their inter-sessional quarter)
during which they are paid only one month of direct salary and must either find
external funding or take leave without pay for the other two months. During the
three quarters in which they are on a full-time pay status, each faculty member
is required to teach a total of five sections as assigned by the chair.
Beginning in academic year 2009,
the school offered another option for faculty. In particular, a faculty member
who asks for only nine months of direct funding from the school is required to
teach only four sections during that time. Faculty exercising this nine-month
option are expected to secure external funding or take leave without pay for
the entire three months of their inter-sessional quarter.
Faculty choosing the nine-month
option may ‘buy out’ of additional teaching duties by securing more external
funding. In particular, a faculty member may, with the permission of the chair,
buy out of one additional class (reducing his/her annual load to three) by
securing thirty-three days of additional external funding within the nine month
window.
Lecturers are expected to teach
at least two sections in each quarter that they are being paid from direct
funds. There is no guarantee of employment in any quarter, and the number of
days they are paid in any quarter may vary depending on workload.
Faculty who engage in certain
paid administrative duties have reduced teaching loads (e.g., the chair does
not have a teaching obligation while serving as chair).
The department has a formal
mentoring process for assistant professors to help them on their academic
journey. Upon arrival at NPS and after a brief settling in period, the Chair
assigns each assistant professor a two-person mentoring team. The mentoring
team always has at least one full professor as the senior member. The mentoring
team is tasked with helping the mentee develop the basic framework for a rich
and rewarding academic career. This includes helping them:
·
Adapt to the
unique teaching demands of the school
·
Develop a
strong and relevant research program
·
Understand
the role of NPS in the Navy and DoD
·
Balance the
three pillars of teaching, scholarship, and service
The mentor team generates a
mentor report each year after the mentee has submitted his or her faculty
activity report. The mentor report summarizes the progress that the candidate
is making toward promotion and tenure and is used by the Chair and the
department as part of the annual renewal review.
The Graduate Program in Applied
Mathematics is designed to meet the needs of the Department of Defense for
graduates who are skilled in applying concepts from advanced mathematics to
real world military problems. A typical follow on assignment for graduates is
to be an instructor in mathematics at the U.S. Naval Academy at Annapolis or
the U.S. Military Academy at West Point. Program requirements are based on the
premise that graduate students should have broad exposure to graduate level
mathematics combined with hands-on experience, either through research
activities conducted within the department or through coordinated experiences
with other departments and other partners in industry, government labs, and
national research institutes. To achieve this goal, we offer a spectrum of
courses aimed at providing breadth of training, in addition to a depth of
knowledge in one of the areas of specialization represented within our research
ranks.
In addition to the Master of Science and
Doctor of Philosophy programs in Applied Mathematics, the department offers
individually tailored minor programs for many of the school's doctoral
students.
In order to enter a program leading to the
degree Master of Science in Applied Mathematics, the prospective student is
strongly advised to possess either a bachelor’s degree with a major in
mathematics or a bachelor’s degree in another discipline with a strong
mathematical orientation.
Any program that leads to the degree
Master of Science in Applied Mathematics for a student who has met the entrance
criteria must contain a minimum of 32 quarter-hours of graduate-level
(3000-4000 numbered) courses with a minimum QPR of 3.0. The program
specifications must be approved by both the department Chairman and the
Academic Associate. The program is subject to the general conditions specified
in the Academic Council Policy Manual as well as the following:
A
student must complete or validate the four course 1000 level calculus sequence
and the introductory courses in linear algebra and discrete mathematics.
The
program must include at least 16 hours in 3000-level mathematics courses and 16
hours of approved 4000-level mathematics courses.
Courses
in Ordinary Differential Equations, Real Analysis, and upper division Discrete
Mathematics are specifically required, and those at the 3000 level or above may
be applied toward the requirement above.
|
An acceptable thesis is required. The Department of
Applied Mathematics permits any student pursuing a dual degree to write a
single thesis meeting the requirements of both departments, subject to the
approval of the Chairmen and Academic Associates of both departments. |
The Department of Applied Mathematics
offers the degree Doctor of Philosophy in Applied Mathematics. Areas of
specialization will be determined by the department on a case by case basis.
Requirements for the degree include course work followed by an examination in
both major and minor fields of study, and research culminating in an approved
dissertation. It may be possible for the dissertation research to be conducted
off-campus in the candidate's sponsoring organization.
Entrance into the program will ordinarily
require a master’s degree, although exceptionally well-prepared students with a
bachelor’s degree in mathematics may be admitted. A preliminary examination may
be required to show evidence of acceptability as a doctoral student.
Prospective students are directed to contact the Chairman of the Applied
Mathematics Department or the Academic Associate for further guidance.
Certificate Programs
In recent years the department
has created two certificate programs wherein students can earn a certificate by
completing a prescribed program of coursework. The first of these was the Mathematics of Secure Communications
Certificate (curriculum
280) which was created in 2003. This certificate program has become very
popular with students from a variety of curricula. Second was the Scientific Computation Certificate (curriculum 283) which was launched in 2009.
We are currently moving our first cohort of students through this program and
have high hopes for its future success, particularly as a coherent minor
program for doctoral students in the various engineering programs on campus.
Student Body Profile
Our production of graduates has
been severely impacted by the official elimination of the 380 curriculum in
2001. Although the curriculum is still officially inactive for Navy students,
we reopened the master’s degree program for student inputs in 2006 at the
direction of then President RADM Wells. This allowed us to begin admitting Army
students and since that time our output has increased dramatically and we have
graduated an average of more than seven students per year (master’s, dual master’s,
and doctorate) since 2007.
A detailed list of graduates for
the past five years along with their thesis titles appears in Appendix D.
The department currently enrolls
more than 1,200 students in roughly 80 sections of mathematics courses per
year. Less than two percent of these enrollments are math graduate students.
Thus the magnitude of our service role to the university is huge and we take
our service mission very seriously. Technical majors, either engineering or science,
usually take four or more mathematics classes. In sum, we support 30 separate
curricula at NPS:
·
356 -
Information Systems & Operations
·
360 -
Operations Analysis
·
361 - Joint
Operational Logistics
·
362 - Human
Systems Integration
·
363 -
Systems Analysis (DL)
·
365 - Joint
Cmd, Cntrl, Comm, Comp/Intel (C4I) Sys
·
366 - Space
Systems Operations
·
368 -
Computer Science
·
370 -
Information Systems & Technology
·
372 -
Meteorology
·
373 -
Meteorology and Oceanography (METOC)
·
380 -
Applied Mathematics
·
399 -
Modeling, Virtual Environments & Simulation
·
525 -
Undersea Warfare
·
533 - Combat
Systems Sciences & Technology
·
570 -
Naval/Mechanical Engineering
·
580 -
Systems Engineering
·
590 -
Electronic Systems Engineering
·
591 - Space
Systems Engineering
·
595 -
Information Warfare
·
596 -
Electronic Warfare Systems International
·
814 -
Transportation Management
·
815 -
Acquisitions & Contract Management
·
816 -
Systems Acquisition Management
·
819 - Supply
Chain Management
·
820 -
Resource Planning/Mgmt for International Defense
·
827 -
Material Logistics Support Management
·
837 -
Financial Management
·
870 -
Information Systems Management MBA
·
999 - Staff
(Non-Degree)
Our core teaching load can
roughly be split into three tracks:
Calculus
Refresher Track – This consists of four classes
(MA1113, MA1114, MA1115, and MA1116) covering single-variable, multi-variable,
and vector calculus (although there are some variations). These classes are
generally taught in a highly accelerated mode so that they can be completed in
the first two quarters. This track is taken by students in most technical
curricula (i.e., a significant proportion of all students from GSEAS and GSOIS)
although those with sufficiently strong backgrounds may validate some or all of
these classes. Annual enrollments in this group during 2009 were 550 as
compared with 622 in 2006. This decrease of more than 10% is very significant
and reflects the large decrease in enrollments in the Engineering school over
the past three years.
Core
Analysis Track - This
consists of the core undergraduate analysis classes that are essential in
physical sciences and engineering. The basic courses are Ordinary Differential Equations
(MA2121), Partial Differential Equations (MA3132 or MA3139), Linear Algebra
(MA2043 and MA3046), and Numerical Analysis (MA3232). Courses from this track
are generally taken by students from GSEAS. Enrollments in this track are
highly variable and in decline due to collapsing enrollments in GSEAS
curricula.
Core
Discrete Mathematics Track – This
consists of core classes in mathematics essential in computer science and
operations research. The courses in this
track are Discrete Mathematics (MA1025, MA2025, and MA3025) and Linear Algebra
(MA3042). Courses in this track are generally pursued by students from GSOIS.
Enrollments in this track have been relatively stable.
The nature of the teaching effort
within the department is significantly different than that of other technical
departments on campus both within GSEAS and GSOIS. To better understand this,
consider the following table which summarizes the distribution of resident sections
by course content level for the 2009 academic year. The table is separated into
two parts, the GSEAS departments and then the GSOIS departments (which include
OR and CS, both of which were at one time part of MA).
|
Level |
EC |
MA |
MAE |
MR |
OC |
PH |
SE |
CS |
DA |
IS |
OR |
|
4000 |
42 |
7 |
30 |
13 |
12 |
24 |
14 |
64 |
42 |
36 |
56 |
|
3000 |
39 |
24 |
32 |
17 |
15 |
30 |
21 |
63 |
47 |
29 |
59 |
|
2000 |
30 |
10 |
15 |
2 |
2 |
13 |
2 |
7 |
7 |
1 |
8 |
|
1000 |
4 |
36 |
1 |
|
|
11 |
2 |
|
|
|
2 |
|
Total |
115 |
77 |
78 |
32 |
29 |
78 |
39 |
136 |
96 |
66 |
125 |
It is very clear from the data
that the teaching experience for faculty in Applied Mathematics is very
different than it is in other technical departments. A few things bear special
mention. First of all, we teach a tremendous number of sections at the first
year undergraduate level. Indeed, we taught 36 of 56 total such sections on
campus in 2009, nearly 65% of all sections at that level. Second, no technical department
on the entire campus teaches fewer sections of graduate level material. Indeed,
every other technical department taught a minimum of 35% of their sections at
the 4000 level, compared to just 9% in Mathematics. Even departments teaching
half as many total sections as we do, still teach nearly twice as many sections
at the 4000 level. The following bar graph summarizes this by showing the
percentage distribution of teaching efforts at the graduate (4000),
upper-division undergraduate (3000), and lower-division undergraduate (1000 and
2000) levels.
Another important factor which
impacts the teaching profile is the size of class sections. Consider the
following bar chart which summarizes the distribution of resident class section
sizes for all GSEAS departments for 2009.
This chart shows how very different
the teaching loads are in the department. We teach many more large classes
which is extremely demanding in an institution where there are no teaching
assistants, homework graders, etc. To get another perspective on this issue we
can examine teaching in AY2009 by weighted teaching credit (WTC). Weighted
teaching credit is computed by multiplying the number of students in a section
by the number of lecture hours and then summing over all sections. The
following chart summarizes teaching in AY2009 by weighted teaching credit for
resident sections only across all seven GSEAS departments.
The number to the right of each
department indicates the number of tenure-track faculty in that department for
AY2009. The much higher real teaching loads in mathematics are readily
apparent. Indeed, we teach nearly twice as much as MAE with the same number of
tenure-track faculty.
The chart below shows the combined effect of large class sizes and
low class level. It summarizes the distribution of teaching by weighted
teaching credit at the various levels.
The contrast in teaching profiles is both clear and critical. The
Department of Applied Mathematics is unique in that we do more than 70% of our
teaching at the first and second year undergraduate levels (1000 and 2000). This
impacts faculty careers in several ways. First, the extremely limited graduate
level teaching makes it far more difficult to develop and maintain active
research programs. Second, the incredible demands of fast-paced remedial
undergraduate level teaching makes classroom excellence a far more critical
issue in promotion and tenure decisions than in other departments. Third, the
time demands of teaching large sections of remedial mathematics to students
just returning to university studies leaves little time to pursue research
during teaching quarters (it is common
for tenure-track faculty in mathematics to log more weighted teaching credit in
a single quarter than tenure-track faculty in other departments log in an
entire year). All of these issues are amplified by the widely varying levels
of preparation of incoming students (including, direct entry students who often
come straight into multi-variable calculus without a refresher quarter in which
to relearn basic single variable calculus).
One final note is that none of the preceding includes any counting
or consideration of reading classes. This is another burden on the faculty
since the department generally offers six to ten such classes each year and
they are not accounted for in any way (i.e. no funding or other credit is
given).
The core campus process for evaluating instruction is the Student
Opinion Form (SOF). This is a Likert scale survey instrument that is
administered at the end of every quarter in every class section. The survey is
administered electronically and the data is centrally collected for use in a
wide variety of evaluation and assessment processes. Although there are sixteen
questions on the survey, two are of particular importance. Question twelve
(Q12) asks “Overall, I would rate this instructor:” and allows for a rating
from one to five with one indicating “Lowest 10%” and five indicating “Top 10%”.
Question thirteen (Q13) asks “Overall, I would rate this course:” with the same
rating scale.
One method of evaluating the department’s instructional
performance is to examine the results from these two questions in comparison
with the rest of the school. Because the data is a bit noisy, one gets a
clearer picture by considering a moving average. The tables below show
three-year moving averages of the data comparing the median performance of the
department to the school-wide median performance.
Not only is our median rating uniformly far above the campus-wide
median, it is nearly always comfortably above the campus-wide first quartile.
This reflects the strong emphasis placed on individual instructional
performance within the department. What makes this even more noteworthy is the
fact that it is done while teaching a high proportion of large, accelerated
pace, remedial undergraduate classes.
This graph also shows excellent performance by MA. We have made a
concerted effort in the last several years to tighten up our syllabi and
improve our offerings. The table above clearly shows that those efforts have
paid off in increased ratings of our courses. One should note that NPS as a
whole has remained relatively stagnant in this measure for about eight years.
We maintain an ongoing dialogue
with other client departments to make sure our courses continue to serve their
needs. In addition, the Mathematics Department is heavily involved with the
accrediting process for Engineering through ABET (the Accrediting Board for
Engineering Technologies). This process involves examining our course syllabi,
textbooks, and sample exams in our engineering mathematics courses.
Mathematics faculty are also
heavily involved as advisors and co-advisors for master’s and Ph.D. students
all across campus. This further strengthens our relationships with these
departments and has even led to several joint appointments over the years.
The department's research efforts
can be grouped into three broad areas, as delineated below. These areas have
considerable overlap and several faculty consider themselves associated with
more than one group. Beyond the areas listed below, a number of researchers
from the department have major interdisciplinary connections to researchers
from other departments across the campus. Indeed there are very prominent
collaborations with the departments of Computer Science, Defense Analysis,
Electrical and Computer Engineering, Mechanical and Aerospace Engineering,
Meteorology, Oceanography, Operations Research, and Physics.
Applied analysis is concerned with the
interface between fundamental mathematical structures which rely on continuity
and their use in the physical and social sciences. This research group has diverse interests
that include asymptotic analysis, control theory, mechanics (fluid and
orbital), and game theory. There are significant overlaps with the research
group in Numerical Analysis/Scientific Computing.
Regular
Faculty Members in the Applied Analysis Group
·
Don
Danielson
·
Chris
Frenzen
·
Wei Kang
·
Art Krener
·
Guillermo
Owen
·
Clyde
Scandrett
Current
Postdoctoral Members in the Applied Analysis Group
·
Cesar
Aguilar
Numerical
Analysis/Scientific Computing is the study of theories, computational methods,
numerical algorithms, and other tools required to practically solve
mathematical models of problems from science and engineering in a fast,
accurate, and efficient manner. The primary goal is the development of novel
techniques and approaches to approximation and efficient computation that are
at the heart of modern science. This research group is primarily focused on the
numerical solution of partial and ordinary differential equations, numerical
linear algebra, and approximation theory. There are very significant overlaps
with the research group in Applied Analysis.
Regular
Faculty Members in the Numerical Analysis / Scientific Computing Group
·
Carlos
Borges
·
Fariba
Fahroo
·
Frank
Giraldo
·
Bill Gragg
·
Beny Neta
·
Hong Zhou
Current
Postdoctoral Members in the Numerical Analysis / Scientific Computing Group
·
Jim Kelly
·
Shiva
Gopalakrishnan
·
Eric Choate
Discrete mathematics, sometimes called
finite mathematics, is the study of mathematical structures that are
fundamentally discrete, in the sense of not supporting or requiring the notion
of continuity. Discrete mathematics is extensively used in a variety of
critical applications such as cryptography, coding theory, combinatorics,
network analysis, and search algorithms for the internet.
Regular
Faculty Members in the Discrete Mathematics Group
·
David
Canright
·
Hal
Fredricksen
·
Ralucca Gera
·
Craig
Rasmussen
·
Pante
Stanica
Department research output in terms of peer-reviewed publications
is excellent. A comprehensive list of our peer-reviewed publications for the
years 2005 to 2009 can be found in Appendix C. The table below summarizes the total annual
output of peer-reviewed publications by our tenure-track faculty over the same
period.
We can paint a more useful overall picture of published research
output by looking at data from the recent peer comparison studies. Of
particular note in the CES study is the fact that NPS, as a school, ranked dead
last in terms of the number of journal articles produced, which indicates low aggregate
productivity in this regard. However, when one breaks out the results of the AA2010
peer comparison study to the departmental level, we see that the Department of
Applied Mathematics fares rather well against its peers. Note that there are
generally two comparisons, first against all similar sized departments (same
number of faculty ±5) from a database of over 300 other institutions, and then
against the fifteen CES peers. The tables below show the most salient features
in regards to publications and citations. Note that this data is collected by
looking at publications from a selected set of sources over the three year
period 2006-2008, and, hence, the total number of publications listed for each
department is generally undercounted. On the other hand, the metric is
consistent from institution to institution; hence, the comparisons are on the
whole valid measures of the relative publication statistics. First of all we
look at the percentage of faculty with a publication during the comparison
period.
One can more readily compare by looking at the ratio of the NPS
percentage to the CES and similar sized peer percentages as shown in this
chart.
In light of the substantial teaching loads our relative
performance in this category is quite good, particularly in comparison with
other NPS technical departments. The only two GSEAS departments that outperform
us are small, have minimal teaching loads, and have large numbers of research
faculty. Next we look at publications per author from the same study.
In this critical category we are ranked higher than any other
department on campus- both in absolute terms and in comparison to our peers.
This can be seen more readily by examining the relative publication rate (ratio
of NPS average to peer group average) which is displayed below.
Finally, it is noteworthy
that the work of math faculty is well cited in comparison to our peers. This
can be seen in the two charts that follow. The first displays ratio between the
percentage of our faculty with a citation and the same percentage for the peer
groups.
Note that we are clearly in the first tier of technical
departments in this regard. The second chart shows the ratio of the number of
citations per cited author between NPS and the peer groups. In some sense, the
citation rate indicates the impact of a particular author’s work and hence this
is a critical measure of the importance of our work to the wider community of
scientists.
Once again, in this critical area we are far stronger than the
other technical departments on campus.
Collectively, the departmental
research expenditures in 2009 total roughly $550,000 from external research
funding, most of which comes from ONR and AFOSR, with lesser amounts from other
DoN/DoD sources. Approximately one-third of the tenured and tenure-track
faculty have direct federally funded grant support. This is slightly above
average for mathematics faculty as documented in the Science and
Engineering Indicators: 2010 (Table 5.12), which notes that only 29.7% of
full-time mathematics faculty having doctoral degrees for at least four years
received federal research support in 2009. Although this average is much lower
than most other fields of science, it has been relatively stable in the field
of mathematics for many years. It is also worth noting that several additional
faculty are involved in externally funded research projects with principal
investigators from other NPS departments. External funding expended by these
faculty is not listed in the table below.
Unfortunately, efforts to attract
external research funding are hampered by the lack of a sustainable graduate
program and the effects of the high load of remedial undergraduate-level
teaching.
The department maintains an
active post-doctoral program. We currently have four National Research Council
post-docs residing in the department. Two are working with Prof. Giraldo in the
area of Scientific Computing, one is working with Prof. Krener in the area of
Applied Analysis, and one is working with Prof. Zhou in the area of Scientific
Computing.
The departmental policy on
scholarly activity has been crafted to support the mission of the Naval
Postgraduate School, and in view of that supportive posture, our approach
differs substantially from that of most civilian research universities. More
specifically we view research and scholarship as a means rather than as an end
in itself. In light of that, it is our policy that all tenure-track faculty
shall be engaged in meaningful scholarly activity as part of their regular
duties, and, furthermore, that such activity shall in some way support the
mission of the school. As a department, we recognize that the unique nature of
the Naval Postgraduate School carries with it very unique forms of meaningful
scholarly activity and we acknowledge that this can be very difficult to
assess. Moreover, we acknowledge that choosing simplistic numerical metrics
would hinder our ability to contribute and could adversely affect the quality
of our work. We strongly agree with the position of the American Mathematical
Society and their published 2006 statement regarding this issue – “When judging the work of most mathematicians, the key measure of value
for a research program is the quality of publications rather than the rate.”
The department places a high
premium on collegiality, and this is reflected in our internal structure and
governance. The Chair is elected by the department faculty and serves for a
term of three years after being appointed by the school’s President upon the
recommendation of the Provost. The department is strongly committed to a system
of shared collegial governance. There are several standing committees, as
outlined below, which recommend policies and actions on issues such as the
curriculum, hiring, and admissions. All critical strategic decisions are made
with the full participation of the faculty after study and recommendation by
the appropriate committee (or a specially appointed committee if the issue does
not naturally fall in the purview of one of the standing committees).
Significant effort is made to constitute committees that are representative of
the various groupings within the department (professorial rank, research area,
etc.). Once major strategic decisions have been made by the department, the
Chair is responsible for implementing them.
In addition to committee input,
the Chair convenes general faculty meetings once or twice per quarter as necessary,
and meets with individual committees on an as-needed basis.
·
Chair. Carlos Borges – The Chair plans and
administers the educational, personnel, and financial activities of the
department. The responsibilities of the Chair include:
o
Organizing
and supervising the department to carry out the educational policies of the
school and to accomplish the objectives of the various curricula
o
Planning and
supervising research programs in the departments to support the mission of the
school.
o
Planning the
academic program for the department
o
Representing
the department in academic and administrative matters, including the annual
Promotion and Tenure (P&T) activities
o
Recruiting
qualified academic personnel for the department, within authorized allowances,
and recommending their appointment
o
Recommending
faculty for promotion, tenure, and merit pay raises
o
Providing
professional evaluation of academic personnel and performance ratings of civil
service personnel assigned to the department
o
Maintaining
familiarity with related activities at civilian educational institutions and
technical and industrial organizations, so that curricula and courses are kept abreast
of educational and technical advances
o
Managing the
departmental budget, and representing the department in school-wide budgeting
processes
o
Overseeing
the mentoring program for faculty.
o
Designating
and supervising Associate Chairs to assist with departmental administrative
duties
o
Working with
the Program Officers in maintaining liaison with sponsors, developing new
programs, and in the sponsor evaluation and modification of programs
·
Associate
Chair for Instruction. Bard
Mansager - Appointed by and reports to the Chair; Primary responsibilities
include:
o
Serves as
Academic Associate
o
Oversees
student admissions
o
Designs and
oversees the course matrices of all Math majors
o
Oversees the
department's teaching mission, including interface with client disciplines
o
Focal point
for curriculum reform efforts of the department
·
Associate
Chair for Research. Frank
Giraldo - Appointed by and reports to the Chair; Primary responsibilities
include:
o
Oversees the
department’s research programs
o
Represents
the department to the Campus Research Board
o
Coordinates
research activities within the department
·
Associate
Chair for Computing. David
Canright - Appointed by and reports to the Chair; Primary responsibilities
include:
o
Oversees the
department’s computing facilities
o
Represents
the department on the Campus Computing Advisory Board
o
Coordinates
and oversees software licenses and other related issues
·
Colloquium
Coordinator. Art Krener – Appointed
by the Chair
o
Oversees the
departmental colloquium series
·
Library
Liaison. Hong Zhou – Appointed by the
Chair
o
Serves as a
liaison between the department and the
Dudley Knox Library
·
Webmaster. Ralucca Gera – Appointed by the Chair
o
Oversees the
maintenance of the department web pages
·
Planning
Committee. Makes
recommendations on long-range planning issues such as hiring, coordinated
research efforts, and new initiatives. Responsible for creating and updating
the department’s strategic plan. The Associate Chair for Research is an ex officio member. Reports to the Chair.
·
Course and
Curriculum Committee. Assigns
course coordinators to individual courses. Reviews class syllabi, curriculum
materials, and other issues related to the department’s teaching mission.
Coordinates with client curricula to ensure that our course offerings continue
to satisfy their requirements. Reports to the Associate Chair for Instruction.
·
Computing
Committee. Oversees
computing issues within the department including the selection of instructional
software. Reports to the Associate Chair for Computing.
·
Doctoral
Committee. Oversees
all aspects of the doctorate program to include admissions, curriculum,
selection of dissertation committees, and administration of qualifying
examinations. Reports to the Chair.
There are currently 2 staff
members:
·
Administrative
Support Assistant (ASA): Bea
Champaco - supervises office staff and is in charge of the department's
financial operations.
·
Office
Automation Assistant (OA): Stephanie
Muntean - assists department ASA with departmental operations and provides
support to faculty.
The Department of Mathematics
computing infrastructure is consists primarily of individual Windows machines
in faculty and graduate student offices. These are all connected to the campus
ITACS infrastructure and they provide nearly all of our software and hardware
support. The department replaces individual PCs on a three to four year cycle,
although funding for this requirement is a continuing problem.
Below is a summary of the
workstations and servers that comprise the department's computing
infrastructure.
·
Approximately 30 PCs ranging from new to four years old
·
Approximately 6 laptop computers
·
One LCD projector
·
One faculty member, Frank Giraldo, has a 4 Node, 32 Core
Apple XServe cluster.
·
High Performance Computing
Center.
This group promotes scientific computing at NPS by providing support to
researchers and departments who wish to engage in scientific computing, and
aims to establish NPS as a nationally recognized HPC "Center of Excellence."
The group’s high-performance computing facility provides a powerful baseline of
computation and storage infrastructure, including scientific workstations,
supercomputer systems, high speed networks, special purpose and experimental
systems, the new generation of large scale parallel systems, and application
and systems software with all components well integrated and linked over a high
speed network.
·
ITACS. The
Information Technology and Communications Services (ITACS) name reflects the
incorporation of all communication services, telephone support, and network
support into the core computing functions that have been provided by the Naval
Postgraduate School since 1953.
All faculty and staff are
evaluated annually for purposes of determining merit raises and to maintain an
ongoing dialogue regarding their personal goals and their role in the
development of the department. In addition, our curriculum, certificates, and
courses are overseen by the appropriate committee and/or administrative member
of the department. Below is a summary of how the faculty, staff, and programs
are evaluated and assessed.
Each faculty member is required
to submit quarterly workload forms outlining their planned activities at the
beginning of each quarter. At the end of the calendar year each faculty member
compiles and submits an annual Faculty Activity Report (FAR) which summarizes
their accomplishments in the prior year. The Chair is in charge of evaluating
the faculty on the basis of the quarterly workload forms, the annual Faculty Activity
Reports, and other information that may be pertinent for the year (e.g. student
opinion form data). These evaluations take into consideration the contributions
made to teaching, research, and service. Teaching evaluation includes classroom
performance, as well as the impact of any course development or reform efforts
(either within the department or elsewhere). The effectiveness of classroom
performance is largely determined by reviewing data from the student opinion
form although classroom visits by the Chair or other faculty (e.g. members of
the mentoring team for Assistant Professors) may also be used. For research,
the emphasis is on determining the impact of the faculty member's work,
measured using the guidelines and principles set forth in the Marto Report and the Powers Report. Although this approach is far more
demanding than simply counting papers or adding up grants, it is essential due
to the very non-traditional nature of the Naval Postgraduate School. Service
includes departmental committee work, as well as service to the school (e.g.
faculty council), service to the profession (e.g. conference organization), and
service to the community (e.g. outreach activities). Certain activities overlap
multiple criteria. For example, the directing and mentoring of graduate
students contributes to both the teaching and research missions of the
department. As another example, conference organization is a service to the
profession, but it also enhances and facilitates the organizer's research
program.
Each tenured or tenure-track
faculty member is rated on a scale of Meritorious or Unsatisfactory in
accordance with the school’s human resources office (HRO) procedure. There are
no fixed percentage weights on the contributions of research, teaching, and
service. In addition, junior faculty, are not expected to perform much service
(though many are involved in conference organization and outreach activities).
Each faculty member discusses his or her evaluation with the Chair annually.
Lecturers and senior lecturers
are also evaluated by the Chair. The evaluation criteria include classroom
teaching, the impact of course and curriculum development (e.g. developing
militarily relevant example problems or demonstrations), and service (e.g.
course coordination, review sessions, help-session coordination).
In early 2010, the current chair
created a new internal review process by which the faculty evaluate the chair.
This process is in its infancy, but uses an anonymous web based survey tool
that is implemented using Google documents (a dummy copy is viewable here). There are
a number of statements which are ranked on a Likert scale (strongly disagree to
strongly agree) as well as questions which allow anonymous written responses
and suggestions. Although this process needs additional refinement, initial
faculty reaction has been quite positive.
Each year at the end of the
campus promotion and tenure cycle, the Chair has individual meetings with all
potential promotion and tenure candidates inside the department. For untenured
tenure-track faculty, the meeting is focused on the candidate’s timeline and
generally includes a discussion of the mentor report for that year, the level
of progress in the case, and specific actions to be taken in any areas that are
deficient or worthy of specific attention. For tenured associate professors,
the discussion is meant to determine the candidate’s progress toward promotion
to full professor and the candidate’s interest in putting his or her case
forward in the next P&T cycle.
Following these discussions, if
there are any cases to be considered for the next cycle, the Chair tasks the
candidate with generating a draft of their promotion package and convenes a
meeting of the appropriate faculty (e.g. tenured full professors to consider
promotion to full cases) to consider whether the case is at a level that merits
further consideration. Once a set of promotion candidates has been determined,
the chair appoints an individual department evaluation committee (DEC) for each
candidate consisting of three faculty (two from within the department and one
outside member) to prepare the case for formal consideration. The candidate
then prepares a complete documentation package, and the DEC then prepares a
report evaluating the candidate and making a positive or negative
recommendation to the department. After the DEC report and the documentation
are complete, this is made available to the appropriate group of faculty - the
tenured faculty (in the case of promotion candidates to associate professor) or
the professors (in the case of promotion candidates to Professor). The
appropriate faculty meet to consider the case. The meeting opens with a straw
vote (by secret ballot) which is tallied and announced to those present. This
is followed by a detailed discussion of the case generally led by the DEC chair
and ends with a final vote, also by secret ballot (the Chair tallies but does
not participate in the voting). After the final vote, the Chair writes a report
noting the outcome of the faculty vote and formulating his or her
recommendation on the case. The full documentation package, the DEC report, and
the Chair report are then forwarded to the campus-wide Faculty Promotion
Council for consideration by the full school.
The University's Human Resources
Office (HRO) oversees the review process of all university staff. HRO mandates
that each staff member be given a written annual review along with a face-to-face
meeting with his or her supervisor.
Teaching evaluation within the
department is two-pronged. The primary source of information is the Student
Opinion Form (SOF) which is administered campus wide by the Registrar. This
instructor/course evaluation instrument incorporates a set of sixteen questions
presented, as noted above, on a Likert scale, as well as an area for written
commentary by the students. The SOF is administered electronically and must be
submitted by the students to the Registrar prior to the release of course
grades (a student’s grade cannot be released until the SOF is submitted, so
compliance is 100%). After the submission of course grades the numerical SOF
data is summarized (max, min, average, and standard deviation) and distributed
to the individual faculty and to their respective department chairs. The
written comments are returned only to the individual faculty. In addition to
the SOF, the Chair (and mentors in the case of junior faculty) will informally
visit classes from time to time to aid in the assessment of teaching. The
visits of mentors are generally recorded in the annual mentor reports so that
they can be used in the faculty evaluation and promotion process.
As mentioned in the section on
departmental operations, we have a standing course and curriculum committee to
review and oversee our courses and curriculum, as well as coordinate our
offerings with our various client curricula around the school. In addition,
each course in the catalog has an official course coordinator who is charged
with day-to-day monitoring of content, deciding on textbooks, handling course
validation requests, etc.
The chair currently conducts an exit briefing with each and every student receiving a degree in Applied Mathematics. This is done in a face-to-face meeting where the students are asked to give specific input on our graduate programs and their experience in them. Although the discussion is started using generic questions such as “What is your general impression of the program?” it also involves more specific questions like “What specific changes could we make that would improve the program?” The chair summarizes the responses and uses them as one tool for assessing the program.
First and foremost, it is
critical to understand that NPS allocates department budgets in a manner very
far removed from the models used in most universities. The process underwent a
very large change in 2009 with the adoption of the “nine month model,” but is
still fundamentally one of ‘steering by the wake’ in that the current year’s
direct teaching (DT) budget allocation is primarily based on the number of
eligible sections taught in the previous year (an eligible section is one in
which there were 7 or more enrolled students). From our perspective the process
of determining the DT budget is basically:
1.
There is a
base allocation that covers each tenure track faculty member for 9 months and
the Chair for 12 months
2.
Count the
number of eligible sections (S) taught in the previous year
3.
Determine
the base capacity (C) of the department by multiplying the number of
tenure-track faculty (not counting the Chair) by 4 (the nominal teaching load)
4.
The
exceptional sections E = S – C is divided by 8 and that many years of
additional salary is added to the base budget
Because of the small enrollments,
many required sections fall below the eligible threshold, and hence, even
though they must be taught to meet requirements, they are not accounted for in
the budget allocation. This generally leads to serious budget shortfalls in the
summer quarter that are particularly difficult in the Department of Applied
Mathematics, since this is one of our heaviest teaching quarters. The table
below shows the history of initial faculty labor budget allocations versus
actual end of year expenditures exclusive of extramural research funding. It is
important to note two things. First, over the course of every year there are
additional transfers for various reasons (e.g. one of our faculty teaches a
class for another department). Second, the funding model underwent a
fundamental change in 2009 that made it far more realistic, although there are
still serious problems.
|
Year |
Initial |
Expended |
|
2005 |
$1,581,875 |
$1,641,824 |
|
2006 |
$1,587,218 |
$2,064,705 |
|
2007 |
$1,365,424 |
$2,203,826 |
|
2008 |
$1,506,174 |
$2,778,515 |
|
2009 |
$2,423,897 |
$2,992,863 |
To expand on the current budget
picture, we can analyze the situation in 2009 in more detail since this is the
only year for which we have data under the new funding model. The initial
allocation left out two important and known issues for the year – funding a
full-year sabbatical for the previous chair and funding the work of one senior
lecturer in managing an NPS program with Singapore. Even though both of these
requirements were well understood by the academic planning office before the
initial allocation, many hours had to be spent by the chair to get budget
transfers to fund these external mandates, and, indeed, the full funding for
these two issues did not arrive until August 21, 2009, just weeks before the
close of the fiscal year. Had these properly been included in the initial
allocation, we would have started the year with $2,673,897. Over the course of
the year, there were additional transfers in and out for various reasons, and
the department ended the year with a faculty labor shortfall of roughly
$27,000. This shortfall is orders of magnitude less than in previous years
where it was not uncommon to run nearly $1,000,000 in the red.
The most serious issue regarding
faculty labor budgeting is the failure to properly fund essential teaching
requirements that fall below the 7 student enrollment threshold. This
introduces significant problems, as many required classes operate very near the
threshold and enrollment variability basically leads to ‘unfunded mandates’ in
that the department has to teach required core classes for which it has not
been funded. What is more disturbing is the unwillingness of the administration
to provide additional funding in light of the high degree of efficiency of our
operations. Consider the following chart which shows the cost of resident
teaching in six of the GSEAS departments (systems engineering is excluded
because a high percentage of their teaching is distance learning and the
budgeting process for that is very different). The chart shows two measures of
cost. The first is computed by dividing the mission-funded teaching budget for
each department by the total enrollments. The second is computed by dividing
the mission-funded teaching budget for each department by the total number of
four-unit weighted teaching credits (4-WTC). The four-unit weighted teaching
credit is computed by dividing the weighted teaching credits by four. This
measure is highly comparable to enrollments but compensates for some of the
practices in other departments (e.g. splitting a 4-unit class into two 2-unit
classes) that create the illusion of more teaching by proliferating sections.
It is very clear from the data
that our costs are roughly half of those for the other GSEAS departments.
Indeed, we are unquestionably the most efficient technical department at NPS.
In light of this fact, it is difficult to understand the difficulty we have had
trying to convince the administration to fund some of the smaller
graduate-level sections we need to teach for our students and in order to
maintain the professional competence of our faculty.
Staff labor budgets are such a
continual problem that we simply operate with an expectation of running a
deficit which will eventually be paid from campus funds. The department is
authorized staff support of an Administrative Support Assistant and an Office
Automation Assistant; this authorization provides barely sufficient staffing
for a department of this size. The full cost of these positions is well-known
in advance, but the initial allocation is consistently less than 60% of the
known cost.
The department receives an annual
operations (OPTAR) budget of roughly $40,000. This is used to pay virtually all
operating costs, including office supplies, electronic equipment (printers,
office computers, etc.), software licenses, department travel, honoraria, etc.
The department has made
significant improvements since the last external review in 1985. It is worth
noting that the 1985 self
study
notes seven issues from the previous
review in 1979 and follows up with their status in 1985. Before proceeding it
is worth revisiting those issues one more time. The first five issues have all
been solved in the intervening years, they are:
The lack of a unified research
effort is regarded as a weakness by members of the department – The 1985 report remarks that no progress
had been made since 1979. Happily, in 2010 we have made great progress on this
issue. The department has focused in a few key areas (applied analysis,
scientific computation / numerical analysis, and discrete mathematics) and we
have good collaborative efforts within the department as well as fruitful
interdisciplinary collaborations.
Average to indifferent
performance by faculty on loan from other departments – The 1985 report remarks that there had
been progress as the department had been allowed to recruit faculty. It is a
pleasure to note that this is no longer an issue, as we rarely use faculty from
other departments to teach classes in mathematics. However, it bears mention
that even in recent years, when we have used faculty from other departments,
the quality of instruction has been consistently unacceptable. Moreover, there
have been recent discussions of forcing the department to use faculty from
other departments to teach calculus. This is a grave concern.
The department lacks expertise in
applied algebra and discrete mathematical structures – This problem had been solved in 1985 and
remains solved to this day as we have a very strong group of faculty in these
areas.
The department has a need for
increased expertise in numerical analysis, numerical methods for differential
equations, and computation – The 1985
report notes that they had begun to address the problem, but had not yet done
so. Happily, in 2010 this is no longer a problem. Indeed these areas are
particular strengths for the department at the current time and, in fact, account
for the majority of our external grant funding.
The department needs “new blood” – Although there is a history of long gaps in
recruiting, it is not a major issue at the current time as we have recruited
four new faculty in the last six years.
The remaining two issues are
still very serious concerns:
Lack of graduate students in
mathematics – The 1985
report notes that this was still a significant problem in 1985. Soon after that
report, the 380 curriculum was reinstated and there followed a period of growth
that showed real promise from 1990 to 2001, graduating an average of 6 students
per year. By 2005 the closure of the 380 curriculum had brought the department
back to 1985 levels, and we have struggled, with some success, to recover from
there.
The lack of means to combat the
teaching of mathematics courses in other departments – The 1985 report notes that this remains a
problem and, sadly, the situation remains unchanged to this day. There is
substantial course poaching and duplication across the campus, and repeated
attempts to eliminate this needless duplication of effort have borne no fruit.
This problem had been documented as early as 1947, and without intervention
from the school administration, there is little hope that this practice will
abate in the future.
These two issues are very closely
related to the two very specific recommendations made in the external
review from 1985. They are:
Encourage and support the growth
of a mathematics degree program- The
history here has been mixed. Indeed the school did reinstate the 380 curriculum
following the 1985 review, and there was a solid period of support which led to
the growth of a small but high quality program. Unfortunately, the ill-advised
cancellation of the 380 curriculum in 2001 has done tremendous damage to the
program from which we still have not recovered.
The Naval Postgraduate School
should at least double its support for the teaching of advanced mathematics
courses – It was specifically noted that
the 15 units of graduate level math being offered in 1985 was far from
sufficient. Since that time there has not been a significant increase in the
support for teaching of advanced mathematics courses. Although the department
has taught more than 30 units on numerous occasions, some of these sections
have fewer than 7 students, and the department has to teach them “out of hide.”
In sum, this issue has not been addressed and remains a very serious one.
Having now reviewed past issues,
we point out our main goals and issues moving forward. Many if not all of them
are related to the issues from the last two reviews (1979 and 1985) as seen
above. Indeed, all of them relate to the fact that the teaching profile in the
department is excessively weighted toward classes at the 1000 and 2000 level; there are
few opportunities to teach at the 4000 level. This issue was discussed above in
the section on our instructional program where we noted a clear and critical contrast
between our teaching profile and that in other comparable departments at NPS.
The Department of Applied Mathematics is unique in that we do nearly 70% of our
teaching at the first and second year undergraduate levels (1000 and 2000). This
impacts faculty careers in several negative ways. First, the extremely limited
graduate level teaching makes it far more difficult to develop and maintain
active research programs. Second, the incredible demands of fast-paced remedial
undergraduate level teaching makes classroom excellence a far more critical
issue in promotion and tenure decisions than it is in other departments. Third,
the time demands of teaching large sections of remedial mathematics to students
just returning to university studies leaves little time to pursue research
during teaching quarters. All of these issues are amplified by the widely
varying levels of preparation of incoming students (including direct entry students
who often come straight into multi-variable calculus without a refresher
quarter in which to relearn basic single variable calculus).
There are three primary causes for this state of affairs –a lack
of campus support for graduate level mathematics courses, a small graduate
program, and course poaching -and we must address each of them in order to
improve the situation.
We believe that a regular and
reliable offering of graduate level mathematics would lead to increased
enrollments in these very classes. There are increasing numbers of doctoral
students in many technical curricula who would be eager to pursue a minor in
mathematics, but often shy away from the option because they cannot be certain
that classes they need for the minor will be offered. We have taken a first
step with the creation of two certificate programs which attract both master’s
and Ph.D. students from other curricula. But even these are difficult to
coordinate since we generally need to secure a full cohort (at least seven
students) before we begin. If, on the other hand, students and program officers
knew in advance that certain classes would be offered on a regular basis
(annually or biannually), then we believe we could fill the seats with students
seeking certificates, as well as those Ph.D. students in need of a minor. An
administration commitment to fund just twelve sections per year at the 4000
level would likely be enough to put us on a path to self-sufficiency.
The Department of Applied
Mathematics is currently the only department without a Navy-sponsored master’s
degree program. While we have been able to rebuild a steady, although small,
input of students from the Army and complement this with a few dual master’s,
the numbers are simply not sufficient to maintain a high-quality graduate level
department. Although faculty are generally engaged in thesis advising both
inside and outside the department, a larger group of math graduate students
would materially improve our opportunities to teach graduate level mathematics
as well as maintain active and relevant research programs. We need to convince
the Navy to officially reinstate the 380 curriculum and to begin sending
students. We believe there is a real need for a core group of officers with
graduate math degrees to teach at the US Naval Academy. Moreover, we believe
the Navy would benefit by having more members of the officer corps with
advanced degrees in mathematics.
There is a significant and
ongoing problem with course poaching and duplication by other departments. This
was clearly noted in the 1985 review and continues to this day. It is worth
special mention that this is a long-standing problem at NPS. Indeed, in 1947
the Heald Report (Report on
the Educational Program of the United States Naval Postgraduate School. By an
Advisory Committee to the American Council on Education, Henry T. Heald,
Chairman. New York: American Council on Education, June 27, 1947) made special mention of this problem. The
report noted that the school’s failure to use standard individual courses as
building blocks resulted in a “complicated array” of very similar courses. And
furthermore, that this led to small, uneconomical classes and related
inefficiencies. This practice continues to have a serious negative impact both
on the department and the school in several ways.
Above all, it is an inefficient
use of school resources since this practice results in multiple versions of
essentially the same material being taught in very small sections by a variety
of people in a variety of departments. This practice is particularly prevalent within
GSEAS where, for example, nearly half of the departments offer their own course
in ocean acoustics, and nearly every department offers its own version of a
numerical methods course. This practice also hurts the students since they are
often taking classes that have been watered down or lack academic rigor
precisely because they are being taught outside of the department in which they
should be legitimately housed.
More troubling for us is the fact
that most of the poaching and duplication occurs at the 3000 and 4000 level, so
it is a major contributor to the unhealthy teaching profile in the department. For
example, consider PH3991 – Theoretical Physics. The textbook for this course is
Mathematical Methods in the Physical
Sciences by Mary Boas, and the course is essentially one on methods of
applied mathematics. This class is generally offered twice a year with a dozen
or more students each time. There are many more examples similar to this one
all over campus. For a detailed description of course poaching and duplication
issues currently affecting the department see Appendix E.
|
|
Carlos Borges (vita): Professor
and Department Chair, PhD. UC Davis (Home
Page) Research Interests: Numerical Analysis, Numerical
Linear Algebra, Applied Approximation Theory, Orthogonal Polynomials,
Floating-point Computation. |
|
David Canright (vita): Associate Professor and Associate Chair for Computing , PhD. UC
Berkeley (Home Page) |
|
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Les Carr (vita): Lecturer, PhD. Naval Postgraduate School |
|
Margaret
Cheney (vita) : Research Professor, Ph.D. Indiana University (Home Page) |
|
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Don Danielson (vita): Professor, PhD. Harvard University (Home Page) |
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Doyle Daughtry (vita): Lecturer, MA. East Carolina University |
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Fariba Fahroo (vita): Professor, PhD. Brown University |
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Hal Fredricksen (vita): Professor, PhD. University of Southern California (Home Page) |
|
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Chris Frenzen (vita): Associate Professor, PhD. University of Washington (Home Page) |
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Ralucca Gera (vita): Assistant Professor, PhD. Western Michigan University (Home Page) |
|
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Frank Giraldo (vita): Professor and Associate Chair for Research, PhD. University of
Virginia (Home Page) |
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Bill Gragg (vita): Professor, PhD. UCLA (Home Page) |
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Wei Kang (vita): Professor, PhD. UC Davis (Home Page) |
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Arthur J. Krener (vita): Distinguished Visiting Professor, PhD. UC Berkeley (Home Page) |
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Bard Mansager (vita): Senior Lecturer and Associate Chair for Instruction, MA. UC San
Diego |
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Beny Neta (vita): Professor, PhD. Carnegie-Mellon University (Home Page) |
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Guillermo Owen (vita): Distinguished Professor, PhD. Princeton University |
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Craig Rasmussen (vita): Associate Professor, PhD. University of Colorado (Home Page) |
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Clyde Scandrett (vita): Professor, PhD. Northwestern University |
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Pantelimon Stanica (vita): Professor, PhD. SUNY Buffalo (Home Page) |
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Hong Zhou (vita): Associate Professor, PhD. UC Berkeley (Home Page) |
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The Menneken Faculty Award for Excellence in Scientific Research:
- Frank Giraldo
- Wei Kang
The Sigma Xi Carl E. Menneken Research Award:
- Bill Gragg
The Rear Admiral John Jay Schieffelin Award for Excellence in Teaching:
- Carlos Borges
- Gordon Latta (Emeritus)
- Bard Mansager
- Arthur Schoenstadt (Emeritus)
- Maurice Weir (Emeritus)
- Carroll Wilde (Emeritus)
AIAA Fellows:
- Fariba Fahroo (Associate Fellow)
- Beny Neta (Associate Fellow)
ICA Fellows:
- Ralucca Gera (Associate Fellow)
- Craig Rasmussen
- Pante Stanica (Associate Fellow)
IEEE Fellows:
- Wei Kang
- Art Krener
SIAM Fellows:
- Art Krener
Guillermo Owen holds the title of Distinguished Professor and is a member of the following:
- Colombian Academy of Exact and Physical
Sciences
- Royal Academy of Sciences and Arts of Catalonia
- Third World Academy of
Sciences
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Ross, I.M. 2009, "Zero-propellant maneuver guidance", IEEE Control
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approach to separable nonlinear least squares problems and its application to
discrete least squares rational approximation", Electronic Transactions
on Numerical Analysis, vol. 35, pp. 57-68.
Borm, P., Van den Brink, R., Hendrickx, R.
& Owen, G. 2009, "The VL control measure for symmetric networks",
Social Networks, , pp. 85-91.
Chartrand, G., Okamoto, F., Rasmussen, C.W.
& Zhang, P. 2009, "The set chromatic number of a graph", Discussiones
Mathematicae Graph Theory, vol. 29, pp. 545-561.
Chun, C., Bae, H.J. & Neta, B. 2009,
"New families of nonlinear third-order solvers for finding multiple
roots", Computers & Mathematics with Applications, vol. 57, no.
9, pp. 1574-1582.
Chun, C. & Neta, B. 2009, "A
third-order modification of Newton's method for multiple roots", Applied
Mathematics and Computation, vol. 211, no. 2, pp. 474-479.
Chun, C. & Neta, B. 2009, "Certain
improvements of Newton's method with fourth-order convergence", Applied
Mathematics and Computation, vol. 215, pp. 821-828.
Cusick, T.W.,
Li, Y. & Stanica, P. 2009, "On a conjecture of balanced symmetric Boolean
functions", J. Mathematical Cryptology, vol. 3, no. 4, pp. 273--290.
Cusick, T.W. & Stanica, P. 2009, Cryptographic
Boolean Functions and Applications, Academic Press.
Cusick, T.W. & Stanica, P. 2009,
"Sums of the Thue-Morse sequence over arithmetic progressions", Advances
and Applications in Discrete Mathematics, vol. 4, no. 2, pp. 127-135.
Dartyge, C., Luca, F. & Stanica, P. 2009,
"On digit sums of multiples of an integer", J. Number Theory., vol.
129, no. 11, pp. 2820-2830.
Dea, J.R., Giraldo, F.X. & Neta, B. 2009,
"High-order non-reflecting boundary conditions for the linearized 2-D
Euler equations: No mean flow case", Wave Motion, vol. 46, no. 3,
pp. 210-220.
Gera, R., Hattingh, J.H., Jafari Rad, N.,
Joubert, E.J. & van der Merwe, L. 2009, "Vertex and edge critical
total restrained domination in graphs", The Bulletin of the Institute
of Combinatorics and its Applications, vol. 57, pp. 107-117.
Haegel, N.M., Mills, T.J., Talmadge, M.,
Scandrett, C.L., Frenzen, C.L., Yoon, H., Fetzer, C.M. & King, R.R. 2009,
"Direct imaging of anisotropic minority-carrier diffusion in ordered
GaInP", Journal of Applied Physics, , pp. 023711 (5 pp.).
Jangveladze, T., Kiguradze, Z. & Neta, B.
2009, "Large time behavior of solutions to a nonlinear
integro-differential system", Journal of Mathematical Analysis and
Applications, vol. 351, no. 1, pp. 382-391.
Jangveladze, T., Kiguradze, Z. & Neta, B.
2009, "Large time behavior of solutions and finite difference scheme to a
nonlinear integro-differential equation", Computers & Mathematics
with Applications, vol. 57, no. 5, pp. 799-811.
Jangveladze, T., Kiguradze, Z. & Neta, B.
2009, "Finite difference approximation of a nonlinear integro-differential
system", Applied Mathematics and Computation, vol. 215, pp.
615-628.
Kang, W., Ross, I.M., Pham, K. & Gong, Q.
2009, "Autonomous observability of networked multi-satellite systems",
AIAA J. of Guidance, Control, & Dynamics, vol. 32, no. 3, pp.
869-877.
Kilic, E. & Stanica, P. 2009,
"Generating matrices for weighted sums of second order linear
recurrences", J. Integer Seq., vol. 12, no. 2, pp. Article 09.2.7,
11.
Kilic, E. & Stanica, P. 2009, "Factorizations and
representations of second order linear recurrences with indices in arithmetic
progressions", Bulletin Mex. Math. Soc., vol. 15, pp. 23-36.
Konyagin, S.V., Luca, F. & Stanica, P.
2009, "Sum of divisors of Fibonacci numbers", Unif. Distrib.
Theory, vol. 4, no. 1, pp. 1--8.
Luca, F. & Stanica, P. 2009,
"Fibonacci numbers of the form pa ± pb" in Proceedings of
International Conference on Fibonacci Numbers Congressus Numerantium, , pp.
177-183.
Luca, F. & Stanica, P. 2009, "On
Machin's formula with powers of the golden section", International
Journal of Number Theory, vol. 5, no. 6, pp. 973-979.
Maitra, S., Subba Rao, Y.V., Stanica, P.
& Gangopadhyay, S. 2009, "Nontrivial solutions to the cubic sieve
congruence problem x3=y2 z \pmod p", Special
Issue on Applied Cryptography & Data Security in Journal of ``Computacion y
Sistemas'' (eds. F. Rodriguez-Henriquez, D. Chakraborty), vol. 12, no. 3,
pp. 253--266.
McCormick, G.H. & Owen, G. 2009,
"Terrorists and their sponsors: An inquiry into trust and
double-crossing" in Mathematical Methods in Counterterrorism, ed.
J. Farley,.
Owen, G. 2009, "Endogenous Formation of
Coalitions", International Game Theory Review, , pp. 461-470.
Petrakos, N., Dinolt, G., Michael, B. &
Stanica, P. 2009, "Cube-type algebraic attacks on wireless encryption
protocols", IEEE Computer, , pp. 106-108.
Rasmussen, C.W. & Okamoto, F. 2009,
"Set vertex colorings and joins of graphs", Czechoslovak
Mathematical Journal, vol. 59, no. 4, pp. 929-941.
Restelli, M. & Giraldo, F.X. 2009,
"A conservative semi-implicit discontinuous Galerkin method for the
Navier-Stokes equations in non-hydrodynamic mesoscale modeling", Siam
Journal on Scientific and Statistical Computing, vol. 31, pp. 2231-2257.
Wang, H.Y., Zhou, H. & Forest, M.G. 2009,
"Sheared Nematic Liquid Crystal Polymer Monolayers", Discrete and
Continuous Dynamical Systems-Series B, vol. 11, no. 2, pp. 497-517.
Canright, D.R.
& Batina, L. 2008, "A Very Compact "Perfectly Masked" S-box
for AES", Applied Cryptography and Network Security - ACNS 2008. 6th
International Conference. Proceedings (Lecture Notes in Computer Science Vol.
5037), , pp. 446-459.
Chun, C. &
Neta, B. 2008, "Some modification of Newton's method by the method of
undetermined coefficients", Computers & Mathematics with
Applications, vol. 56, no. 10, pp. 2528-2538.
Cusick, T.W.,
Li, Y. & Stanica, P. 2008, "Balanced symmetric functions over GF(p)", IEEE Trans. Inform.
Theory, vol. 54, no. 3, pp. 1304--1307.
Demetriou, M.A.
& Fahroo, F. 2008, "Natural observers for a class of second order
bilinear infinite dimensional systems", Proceedings of the 46th IEEE
Conference on Decision and Control, , pp. 4155-60.
Eroh, L. &
Gera, R. 2008, "Global alliance partition in trees", Journal of
Combinatorial Mathematics and Combinatorial Computing, , no. 66, pp. 161-9.
Fahroo, F.
& Ross, I.M. 2008, "Pseudospectral methods for infinite-horizon
optimal control problems", Journal of Guidance Control and Dynamics, vol.
31, no. 4, pp. 927-936.
Fahroo, F.
& Ross, I.M. 2008, "Convergence of the costates does not imply
convergence of the control", Journal of Guidance Control and Dynamics, vol.
31, no. 5, pp. 1492-1497.
Filaseta, M.,
Luca, F., Stanica, P. & Underwood, R.G. 2008, "Galois groups of
polynomials arising from circulant matrices", J. Number Theory, vol.
128, no. 1, pp. 59--70.
Fredricksen,
H.M., Ionascu, E.J., Luca, F. & Stanica, P. 2008, "Minimal Niven numbers",
Acta Arith., vol. 132, no. 2, pp. 135-159.
Gera, R. &
Shen, J. 2008, "Extension of strongly regular graphs", Electronic
Journal of Combinatorics, vol. 15, no. 1.
Giraldo, F.X.
& Restelli, M. 2008, "A study of spectral element and discontinuous
Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale
atmospheric modeling: Equation sets and test cases", Journal of
Computational Physics, vol. 227, no. 8, pp. 3849-3877.
Giraldo, F.X.
& Warburton, T. 2008, "A high-order triangular discontinuous Galerkin
oceanic shallow water model", International Journal for Numerical
Methods in Fluids, vol. 56, no. 7, pp. 899-925.
Gomez, D.,
Gonzalez-Aranguena, E., Manuel, C. & Owen, G. 2008, "A value for
generalized probabilistic communication situations", European Journal
of Operational Research, vol. 190, no. 2, pp. 539-556.
Gomez, D.,
Gonzalez-Aranguena, E., Manuel, C., Owen, G., del Pozo, M. & Saboya, M.
2008, "The cohesiveness of subgroups in social networks: A view from game
theory", Annals of Operations Research, vol. 158, no. 1, pp. 33-46.
Gong, Q.,
Fahroo, F. & Ross, I.M. 2008, "Spectral algorithm for pseudospectral
methods in optimal control", Journal of Guidance Control and Dynamics, vol.
31, no. 3, pp. 460-471.
Gong, Q., Ross,
I.M., Kang, W., Fahroo, F. & Mao, J. 2008, "Connections Between the
Covector Mapping Theorem and Convergence of Pseudospectral Methods for Optimal
Control", J. Computational Optimization and Applications, vol. 41,
no. 3, pp. 307-335.
Kang, W., Ross,
I.M. & Gong, Q. 2008, Pseudospectral Optimal Control and Its Convergence
Theorems, Springer.
Kim, Y.J.,
Giraldo, F.X., Flatau, M., Liou, C.S. & Peng, M.S. 2008, "A
sensitivity study of the Kelvin wave and the Madden-Julian Oscillation in
aquaplanet simulations by the Naval Research Laboratory Spectral Element
Atmospheric Model", Journal of Geophysical Research-Atmospheres, vol.
113, no. D20.
Koster, M.,
Lindelauf, R., Lindner, I. & Owen, G. 2008, "Mass-mobilization with
noisy conditional beliefs", Mathematical Social Sciences, vol. 55,
no. 1, pp. 55-77.
Lauter, M.,
Giraldo, F.X., Handorf, D. & Dethloff, K. 2008, "A discontinuous
Galerkin method for the shallow water equations in spherical triangular
coordinates", Journal of Computational Physics, vol. 227, no. 24,
pp. 10226-10242.
Lindner, I.,
Grofman, B. & Owen, G. 2008, "Modified power indices for indirect
voting" in Power, Freedom, and Voting, eds. M. Braham & F.
Steffen, Springer Verlag, , pp. 119-138.
Mao, J. & Kang, W. 2008, "A three tier cooperative
control architecture for multi-step semiconductor manufacturing process", Journal
of Process Control, vol. 18, pp. 954-960.
Neta, B. 2008,
"On Popovski's method for nonlinear equations", Applied
Mathematics and Computation, vol. 201, no. 1-2, pp. 710-715.
Neta, B. 2008,
"New third order nonlinear solvers for multiple roots", Applied
Mathematics and Computation, vol. 202, no. 1, pp. 162-170.
Neta, B. &
Johnson, A.N. 2008, "High-order nonlinear solver for multiple roots",
Computers & Mathematics with Applications, vol. 55, no. 9, pp.
2012-2017.
Neta, B. &
Johnson, A.N. 2008, "High order nonlinear solver", J. Comput.
Methods Sci. Eng., vol. 8, no. 4-6, pp. 245--250.
Neta, B., van
Joolen, V.J., Dea, J.R. & Givoli, D. 2008, "Application of high-order
Higdon non-reflecting boundary conditions to linear shallow water models",
Communications in Numerical Methods in Engineering, vol. 24, no. 11, pp.
1459-1466.
Owen, G. 2008,
"Endogenous formation of coalitions", Int. Game Theory Rev., vol.
10, no. 4, pp. 461--470.
Owen, G. &
McCormick, G.H. 2008, "Finding a moving fugitive. A game theoretic
representation of search", Computers & Operations Research, vol.
35, no. 6, pp. 1944-1962.
Stanica, P.
2008, "On the nonexistence of bent rotation symmetric Boolean functions of
degree greater than two" in Proceedings of NATO Advanced Studies
Institute (Boolean Functions in Cryptology and Information Security - Nato
Science for Peace and Security) Ed. O.A. Logachev, Berlin, pp. 214--218.
Stanica, P.
& Maitra, S. 2008, "Rotation symmetric Boolean functions---count and
cryptographic properties", Discrete Appl. Math., vol. 156, no. 10,
pp. 1567--1580.
Van den Brink,
R., Borm, P., Hendrickx, R. & Owen, G. 2008, "Characterizations of the
β - and the degree network power measure", Theory and Decision, vol.
64, no. 4, pp. 519-536.
Wang, H. &
Zhou, H. 2008, "Extendability of Equilibria of Nematic Polymers", Abstract
and Applied Analysis, .
Wang, H.Y.
& Zhou, H. 2008, "Stokes efficiency of molecular motor-cargo
systems", Abstract and Applied Analysis, .
Wang, H.Y.
& Zhou, H. 2008, "Multiple branches of ordered states of polymer
ensembles with the Onsager excluded volume potential", Physics Letters
A, vol. 372, no. 19, pp. 3423-3428.
Wang, H. &
Zhou, H. 2008, "Exact solution of a constrained optimization problem in
thermoelectric cooling", Applied Mathematical Sciences, vol. 2, no.
4, pp. 177-186.
Wilson, L.,
Zhou, H., Kang, W. & Wang, H. 2008, "Controllability of non-Newtonian
fluids under homogeneous extensional flow", Appl. Math. Sci. (Ruse), vol.
2, no. 41-44, pp. 2145--2156.
Zhou, H., Kang,
W., Krener, A.J. & Wang, H. 2008, Homogeneous flow field effect on the
control of Maxwell materials.
Alonso-Meijide,
J.M., Carreras, F., Fiestras-Janeiro, M.G. & Owen, G. 2007, "A
comparative axiomatic characterization of the Banzhaf-Owen coalitional
value", Decision Support Systems, , pp. 701-712.
Cusick, T.W.,
Fredricksen, H.M., Ionascu, E.J. & Stanica, P. 2007, "Remarks on a
sequence of minimal Niven numbers" in Proceedings of SEQUENCES, ed.
S.W. Golomb, Springer-Verlag, , pp. 162-168.
Cusick, T.W.,
Fredricksen, H.M. & Stanica, P. 2007, "On the delta sequence of the
Thue-Morse sequence", Australas. J. Combin., vol. 39, pp. 293-300.
Filaseta, M.,
Luca, F., Stanica, P. & Underwood, R.G. 2007, "Two Diophantine
approaches to the irreducibility of certain trinomials", Acta Arith., vol.
128, no. 2, pp. 149--156.
Frenzen, C.L.,
Ionascu, E.J. & Stanica, P. 2007, "A proof of two conjectures related
to the Erdos-Debrunner inequality", JIPAM. J. Inequal. Pure Appl.
Math., vol. 8, no. 3, pp. Article 68, 13.
Gera, R. 2007,
"On dominator colorings in graphs", Graph Theory Notes N. Y., vol.
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Ping, Z. 2007, "Stratified domination in oriented graphs", Journal
of Combinatorial Mathematics and Combinatorial Computing, vol. 60, pp.
105-25.
Gong, Q., Ross,
I.M. & Kang, W. 2007, "A pseudospectral observer for nonlinear
systems", Discrete Contin. Dyn. Syst. Ser. B, vol. 8, no. 3, pp.
589--611 (electronic).
Ionascu, E.J.,
Luca, F. & Stanica, P. 2007, "Heron triangles with two fixed
sides", J. Number Theory, vol. 126, no. 1, pp. 52--67.
Ionascu, E.J.
& Stanica, P. 2007, "Extreme values for the area of rectangles with
vertices on concentrical circles", Elem. Math., vol. 62, no. 1, pp.
30--39.
Ji, G.H., Wang,
Q., Zhang, P.W., Wang, H.Y. & Zhou, H. 2007, "Steady states and their
stability of homogeneous, rigid, extended nematic polymers under imposed
magnetic fields", Communications in Mathematical Sciences, vol. 5,
no. 4, pp. 917-950.
Kang, W., Gong,
Q. & Ross, I.M. 2007, "On the Convergence of Nonlinear Optimal Control
using Pseudospectral Methods for Feedback Linearizable Systems", International
Journal of Robust and Nonlinear Control, vol. 17, pp. 1251-1277.
Luca, F. &
Stanica, P. 2007, "Linear equations with the Euler totient function",
Acta Arith., vol. 128, no. 2, pp. 135--147.
Mao, J. &
Kang, W. 2007, "Benchmark study of run-to-run controllers for the
lithographic control of the critical dimension", Journal of
Micro/Nanolithography, MEMS, and MOEMS, vol. 6, no. 2.
Neta, B. 2007,
"P-stable high-order super-implicit and Obrechkoff methods for periodic
initial value problems", Computers & Mathematics with Applications,
vol. 54, pp. 117-126.
Owen, G. &
Lindner, I. 2007, "Cases where the Penrose limit theorem does not
hold", Mathematical Social Sciences, vol. 53, no. 3, pp. 232-8.
Rasmussen, C.W.
2007, "On Efficient Construction of Minimum-Sum Vertex Covers", Graph
Theory Notes of New York LII, , pp. 45-54.
Stanica, P.
2007, "Graph eigenvalues and Walsh spectrum of Boolean functions" in Combinatorial
number theory de Gruyter, Berlin, pp. 431--442.
Wang, H.Y.
& Zhou, H. 2007, "Monotonicity of a key function arised in studies of
nematic liquid crystal polymers", Abstract and Applied Analysis, .
Zhou, H. &
Forest, M.G. 2007, "Nematic liquids in weak capillary Poiseuille flow:
structure scaling laws and effective conductivity implications", International
Journal of Numerical Analysis and Modeling, vol. 4, no. 3-4, pp. 460-477.
Zhou, H.,
Forest, M.G. & Wang, Q. 2007, "Anchoring-induced texture & shear
banding of nematic polymers in shear cells", Discrete and Continuous
Dynamical Systems-Series B, vol. 8, no. 3, pp. 707-733.
Zhou, H. &
Wang, H.Y. 2007, "Elongational perturbations on nematic liquid crystal
polymers under a weak shear", Physics of Fluids, vol. 19.
Zhou, H. &
Wang, H.Y. 2007, "Steady states and dynamics of 2-D nematic polymers
driven by an imposed weak shear", Communications in Mathematical
Sciences, vol. 5, pp. 113-132.
Zhou, H., Wang,
H.Y. & Wang, Q. 2007, "Nonparallel solutions of extended nematic
polymers under an external field", Discrete and Continuous Dynamical
Systems-Series B, vol. 7, pp. 907-929.
Zhou, H., Wang,
H.Y., Wang, Q. & Forest, M.G. 2007, "Characterization of stable
kinetic equilibria of rigid, dipolar rod ensembles for coupled dipole-dipole
and Maier-Saupe potentials", Nonlinearity, vol. 20, no. 2, pp.
277-297.
Zhou, H. &
Wang, H. 2007, "Asymptotic study on the extendability of equilibria of
nematic polymers", International Journal of Contemporary Mathematical
Sciences, vol. 2, no. 21, pp. 1009-1023.
Zhou, H.,
Wilson, L. & Wang, H.Y. 2007, "On the equilibria of the extended
nematic polymers under elongational flow", Abstract and Applied
Analysis.
Cui, Z.L.,
Forest, M.G., Wang, Q. & Zhou, H. 2006, "On weak plane Couette and
Poiseuille flows of rigid rod and platelet ensembles", Siam Journal on
Applied Mathematics, vol. 66, no. 4, pp. 1227-1260.
Demetriou, M.A.
& Fahroo, F. 2006, "Model reference adaptive control of structurally
perturbed second-order distributed parameter systems", International
Journal of Robust and Nonlinear Control, vol. 16, no. 16, pp. 773-799.
Fahroo, F.
& Ito, K. 2006, "Optimal absorption design for damped elastic
systems", 2006 American Control Conference (IEEE Cat. No. 06CH37776C), ,
pp. 5 pp.|CD-ROM.
Fahroo, F.
& Ito, K. 2006, "Optimal absorption design and sensitivity of
eigenvalues", Proceedings of the 45th IEEE Conference on Decision and
Control (IEEE Cat. No. 06CH37770), , pp. 6 pp.|CD-ROM.
Gera, R. &
Ping, Z. 2006, "On stratification and domination in graphs", Discussiones
Mathematicae Graph Theory, vol. 26, no. 2, pp. 249-72.
Gera, R.,
Rasmussen, C.W. & Horton, S. 2006, "Dominator colorings and safe
clique partitions", Proceedings of the Thirty-Seventh Southeastern
International Conference on Combinatorics, Graph Theory and Computing, vol.
181, pp. 19--32.
Gera, R.,
Rasmussen, C.W., Stanica, P. & Horton, S. 2006, "Results on the
min-sum vertex cover problem", Congressus Numerantium, vol. 178,
pp. 161--172.
Giraldo, F.X.
2006, "High-order triangle-based discontinuous Galerkin methods for
hyperbolic equations on a rotating sphere", Journal of Computational
Physics, vol. 214, no. 2, pp. 447-465.
Giraldo, F.X.
2006, "Hybrid Eulerian-Lagrangian semi-implicit time-integrators", Computers
& Mathematics with Applications, vol. 52, no. 8-9, pp. 1325-1342.
Giraldo, F.X.
& Taylor, M.A. 2006, "A diagonal-mass-matrix
triangular-spectral-element method based on cubature points", Journal
of Engineering Mathematics, vol. 56, no. 3, pp. 307-322.
Gong, Q., Kang,
W. & Ross, I.M. 2006, "A pseudospectral method for the optimal control
of constrained feedback linearizable systems", IEEE Trans. Automat.
Control, vol. 51, no. 7, pp. 1115--1129.
Hamzi, B.,
Krener, A.J. & Kang, W. 2006, "The controlled center dynamics of discrete
time control bifurcations", Systems Control Lett., vol. 55, no. 7,
pp. 585--596.
Ji, G.H., Wang,
Q., Zhang, P.W. & Zhou, H. 2006, "Study of phase transition in
homogeneous, rigid extended nematics and magnetic suspensions using an
order-reduction method", Physics of Fluids, vol. 18, no. 12.
Kang, W. 2006,
"Moving horizon numerical observers of nonlinear control systems", IEEE
Trans. Automat. Control, vol. 51, no. 2, pp. 344--350.
Kang, W. &
Krener, A.J. 2006, "Normal forms of nonlinear control systems" in Chaos
in automatic control CRC Press, Boca Raton, FL, pp. 345--376.
Luca, F. &
Stanica, P. 2006, "$F1F2F3F4F5F6F8F10F12=11!",
Port. Math. (N.S.), vol. 63, no. 3, pp. 251--260.
McCormick, G.H.
& Owen, G. 2006, "A game model of counterproliferation, with multiple
entrants", Int. Game Theory Rev., vol. 8, no. 3, pp. 339--353.
Melman, A.
& Gragg, W.B. 2006, "An optimization framework for polynomial
zerofinders", Amer. Math. Monthly, vol. 113, no. 9, pp. 794--804.
Neta, B. 2006,
"Variational data assimilation and optimal control - Preface", Computers
& Mathematics with Applications, vol. 52, no. 8-9, pp. XIII-XV.
Neta, B. 2006,
"Professor Ionel Michael Navon - Dedication", Computers &
Mathematics with Applications, vol. 52, no. 8-9, pp. XVII-XXI.
Owen, G. &
Grofman, B. 2006, "Two-stage electoral competition in two-party contests:
persistent divergence of party positions", Social Choice and Welfare, vol.
26, no. 3, pp. 547-569.
Owen, G.,
Lindner, I., Feld, S.L., Grofman, B. & Ray, L. 2006, "A simple
"market value" bargaining model for weighted voting games:
characterization and limit theorems", International Journal of Game
Theory, vol. 35, no. 1, pp. 111-128.
Ross, I.M.
& Fahroo, F. 2006, "Issues in the real-time computation of optimal
control", Mathematical and Computer Modelling, vol. 43, no. 9-10,
pp. 1172-1188.
Zhou, H. &
Forest, M.G. 2006, "Anchoring distortions coupled with plane Couette &
Poiseuille flows of nematic polymers in viscous solvents: Morphology in
molecular orientation, stress & flow", Discrete and Continuous
Dynamical Systems-Series B, vol. 6, no. 2, pp. 407-425.
Ammar, G.S.,
Gragg, W.B. & He, C. 2005, "An efficient QR algorithm for a Hessenberg
submatrix of a unitary matrix" in New Directions and Applications in
Control Theory Springer, Berlin, pp. 1--14.
Banks, W.D.,
Luca, F., Saidak, F. & Stanica, P. 2005, "Compositions with the Euler
and Carmichael functions", Abh. Math. Sem. Univ. Hamburg, vol. 75,
pp. 215--244.
Canright, D.R.
2005, "A Very Compact S-box for AES", Cryptographic Hardware and
Embedded Systems - CHES 2005. 7th International Workshop. Proceedings (Lecture
Notes in Computer Science Vol. 3659), , pp. 441-455.
Foguel, T.
& Stanica, P. 2005, "Almost Hamiltonian groups", Results
Math., vol. 48, no. 1-2, pp. 44--49.
Georgescu, C.,
Joia, C., Nowell, W.O. & Stanica, P. 2005, "Chaotic dynamics of some
rational maps", Discrete Contin. Dyn. Syst., vol. 12, no. 2, pp.
363--375.
Gera, R. &
Zhang, P. 2005, "On stratified domination in oriented graphs", Congr.
Numer., vol. 173, pp. 175--192.
Gera, R. &
Zhang, P. 2005, "Realizable triples for stratified domination in
graphs", Math. Bohem., vol. 130, no. 2, pp. 185--202.
Giraldo, F.X.
2005, "Semi-implicit time-integrators for a scalable spectral element
atmospheric model", Quarterly Journal of the Royal Meteorological
Society, vol. 131, no. 610, pp. 2431-2454.
Giraldo, F.X.
& Warburton, T. 2005, "A nodal triangle-based spectral element method
for the shallow water equations on the sphere", Journal of
Computational Physics, vol. 207, no. 1, pp. 129-150.
Hamzi, B.,
Kang, W. & Krener, A.J. 2005, "The controlled center dynamics", Multiscale
Model. Simul., vol. 3, no. 4, pp. 838--852 (electronic).
Kang, W., Song, M. & Xi, N. 2005, "Bifurcation control,
manufacturing planning, and formation control", Acta Automatica Sinica,
vol. 31, no. 1, pp. 84--91.
Kang, W., Xi,
N., Tan, J., Zhao, Y. & Wang, Y. 2005, "Coordinated formation control
of multiple nonlinear systems", J. Control Theory Appl., vol. 3,
no. 1, pp. 1--19.
Krener, A.J.,
Kang, W., Hamzi, B. & Tall, I. 2005, "Low codimension control
singularities for single input nonlinear systems" in New Directions and
Applications in Control Theory Springer, Berlin, pp. 181--192.
Limaye, N.B.,
Sarvate, D.G., Stanica, P. & Young, P.T. 2005, "Regular and strongly
regular planar graphs", J. Combin. Math. Combin. Comput., vol. 54,
pp. 111--127.
Luca, F. &
Stanica, P. 2005, "Prime divisors of Lucas sequences and a conjecture of
Ska\l ba", Int. J. Number Theory, vol. 1, no. 4, pp. 583--591.
Luca, F. &
Stanica, P. 2005, "On a conjecture of Ma", Results Math., vol.
48, no. 1-2, pp. 109--123.
Luca, F. &
Stanica, P. 2005, "Fibonacci numbers that are not sums of two prime
powers", Proc. Amer. Math. Soc., vol. 133, no. 7, pp. 1887--1890
(electronic).
Neta, B. 2005,
"P-stable symmetric super-implicit methods for periodic initial value
problems", Computers & Mathematics with Applications, vol. 50,
no. 5-6, pp. 701-705.
Saboya, M.,
Flam, S. & Owen, G. 2005, "The not-quite non-atomic game:
Non-emptiness of the core in large production games", Mathematical
Social Sciences, vol. 50, no. 3, pp. 279-97.
Stanica, P.
2005, "Cholesky factorizations of matrices associated with r-order recurrent sequences", Integers,
vol. 5, no. 2, pp. A16, 11 pp. (electronic).
Umstattd, R.J.,
Carr, C.G., Frenzen, C.L., Luginsland, J.W. & Lau, Y.Y. 2005, "A
simple physical derivation of Child-Langmuir space-charge-limited emission
using vacuum capacitance", American Journal of Physics, vol. 73,
pp. 160-163.
van Joolen,
V.J., Neta, B. & Givoli, D. 2005, "High-order Higdon-like boundary
conditions for exterior transient wave problems", International Journal
for Numerical Methods in Engineering, vol. 63, no. 7, pp. 1041-1068.
Wang, Q.,
Sircar, S. & Zhou, H. 2005, "Steady state solutions of the
Smoluchowski equation for rigid nematic polymers under imposed fields", Communications
in Mathematical Sciences, vol. 3, no. 4, pp. 605-620.
Zhou, H. &
Forest, M.G. 2005, "A numerical study of unsteady, thermal, glass fiber
drawing processes", Communications in Mathematical Sciences, vol.
3, no. 1, pp. 27-45.
Zhou, H.,
Forest, M.G., Zheng, X.Y., Wang, Q. & Lipton, R. 2005,
"Extension-enhanced conductivity of liquid crystalline polymer
nano-composites", Times of Polymers (Macromolecular Symposia Vol.228), ,
pp. 81-9|313.
Zhou, H., Wang,
H.Y., Forest, M.G. & Wang, Q. 2005, "A new proof on axisymmetric
equilibria of a three-dimensional Smoluchowski equation", Nonlinearity,
vol. 18, no. 6, pp. 2815-2825.
Dea, J.R. (2008), High-order
non-reflecting boundary conditions for the linearized Euler equations
[electronic resource], Naval Postgraduate School, Monterey, Calif.
Phillips, D.D. (2008), Mathematical
modeling and optimal control of battlefield information flow [electronic
resource], Naval Postgraduate School, Monterey, Calif.
2009
Alevras, D., Simulating tsunamis in the
Indian Ocean with real bathymetry by using a high-order triangular
discontinuous Galerkin oceanic shallow water model [electronic resource],
Naval Postgraduate School, Monterey, Calif.
Bernotavicius, C.S., Modeling a 400 Hz
signal transmission through the South China Sea basin [electronic resource],
Naval Postgraduate School, Monterey, Calif.
Geary, A.C., Analysis of a
man-in-the-middle attack on the Diffie-Hellman key exchange protocol
[electronic resource], Naval Postgraduate School, Monterey, California.
Gibbons, S.L., Impacts of sigma
coordinates on the Euler and Navier-Stokes equations using continuous Galerkin
methods [electronic resource], Naval Postgraduate School, Monterey, Calif.
Kim, A.M., Simulating full-waveform LIDAR
[electronic resource], Naval Postgraduate School, Monterey, California.
Mantzouris, P., Computational algebraic
attacks on the Advanced Encryption Standard (AES) [electronic resource],
Naval Postgraduate School, Monterey, California.
McNabb, M.E., Optimizing the routher
configurations within a nominal Air Force base [electronic resource], Naval
Postgraduate School, Monterey, California.
Petrakos, N., Cube-type algebraic attacks
on wireless encryption protocols [electronic resource], Naval Postgraduate School,
Monterey, California.
Smith, W.T., A game theoretic approach to
convoy routing [electronic resource], Naval Postgraduate School, Monterey,
Calif.
2008
Damalas, K.A., Analysis of analytic models
for the effect of Insurgency, Naval Postgraduate School, Monterey, Calif.
Fernandez, C.K., Pascal polynomials over
GF(2) [electronic resource], Naval Postgraduate School, Monterey, Calif.
Florkowski, S.F., Spectral graph theory of
the Hypercube [electronic resource], Naval Postgraduate School, Monterey, Calif.
Giannoulis, G., Efficient implementation
of filtering and resampling operations on Field Programmable Gate Arrays
(FPGAs) for Software Defined Radio (SDR) [electronic resource], Naval
Postgraduate School, Monterey, Calif.
Pollatos, S., Solving the maximum clique
problems on a class of network graphs, with applications to social networks
[electronic resource], Naval Postgraduate School, Monterey, Calif.
Shankar, A., Optimal jammer placement to
interdict wireless network services [electronic resource], Naval
Postgraduate School, Monterey, Calif.
2007
De Luca, T.J., Performance of Hybrid
Eulerian-Lagrangian Semi-Implicit time integrators for nonhydrostatic mesoscale
atmospheric modeling [electronic resource], Naval Postgraduate School,
Monterey, Calif.
Fletcher, D.M., Realizable triples in
dominator colorings [electronic resource], Naval Postgraduate School,
Monterey, Calif.
Karczewski, N.J., Optimal aircraft routing
in a constrained path-dependent environment [electronic resource], Naval
Postgraduate School, Monterey, Calif.
Martinsen, T., Refinement composition
using doubly labeled transition graphs [electronic resource], Naval
Postgraduate School, Monterey, Calif.
Spence, L.J., On the calculation of
particle trajectories from sea surface current measurements and their use in
satellite sea surface products off the Central California Coast [electronic
resource], Naval Postgraduate School, Monterey, Calif.
Wilson, L.M.Z., Controllability of
Non-Newtonian fluids under homogeneous flows [electronic resource], Naval
Postgraduate School, Monterey, Calif.
2006
Sopko, J.J., Modeling fluid flow by
exploring different flow geometries and effect of weak compressibility
[electronic resource], Naval Postgraduate School; Available from National
Technical Information Service, Monterey, Calif; Springfield, Va.
2005
House, J.B. , Optimizing the Army's base
realignment and closure implementation while transforming and at war
[electronic resource], Naval Postgraduate School, Monterey, Calif.
Course poaching and duplication are serious issues at NPS.
The problem is longstanding and was noted as early as 1947 in the Heald Report (Report
on the Educational Program of the United States Naval Postgraduate School.
By an Advisory Committee to the American Council on Education, Henry T. Heald,
Chairman. New York: American Council on Education, June 27, 1947). The
report noted that the school’s failure to use standard individual courses as
building blocks resulted in a “complicated array” of very similar courses. And
furthermore, that this led to small, uneconomical classes and related
inefficiencies. This practice continues to have a serious negative impact both
on the department and the school.
We now outline the most serious issues
of poaching and duplication currently plaguing the department.
PH3991 Theoretical Physics (4-1) Spring/Fall
Discussion of heat flow, electromagnetic waves, elastic waves, and
quantum-mechanical waves; applications of orthogonal functions to
electromagnetic multipoles, angular momentum in quantum mechanics, and to
normal modes on acoustic and electromagnetic systems. Applications of complex
analysis to Green Function in quantum mechanics and
electromagnetism. Application of Fourier series and transforms to resonant
systems. Applications of partial differential equation techniques to equation
of physics. Prerequisites: Basic physics, multivariable calculus, vector
analysis, Fourier series, complex numbers, and ordinary differential equations.
Comments: This is essentially a mathematics class and is taught using a mathematics textbook “Mathematical Methods in the Physical Sciences” by Mary L. Boas. We do not currently teach a version of this class but this is a prime example of course poaching. The fact that this 3000 level class has been poached means that the math department has fewer opportunities to teach at that level. PH3991 is offered twice per year (every spring and fall) to about 15 students each time.
MN2039 Basic Quantitative Methods in
Management
(4-0) Fall/Spring
This course introduces the mathematical basis required for advanced management
and cost-benefit analysis. Math topics include algebra, graphs, differential
calculus, including both single and multiple variable functions, and indefinite
and definite integrals. Management concepts include cost-benefit and
cost-effectiveness analysis, marginal analysis, unconstrained and constrained
optimization, and welfare analysis. Prerequisite: College algebra or consent of
instructor.
Comments: This class is a direct duplication of:
MA2300 Mathematics for
Management
(5-0) Winter/Spring/Summer
Mathematical basis for modern managerial tools and techniques. Elements of
functions and algebra; differential calculus of single- and multi-variable
functions; integration (antidifferentiation) of single-variable functions.
Applications of the derivative to rates of change, curve sketching, and
optimization, including the method of Lagrange multipliers. Prerequisite: College
algebra.
It uses the same textbook (Brief Calculus and Its Applications – Goldstein, Lay, and Schneider) and the syllabus was adapted from the syllabus for MA2300. The students who used to take MA2300 now take MN2039 instead (MA2300 has not been taught since 2001 as a result of this outright theft of a class). MN2039 is offered once per year (every fall) to about 30 students.
ME3440 Engineering Analysis (4-0) As Required
Rigorous formulation of engineering problems arising in a variety of
disciplines. Approximate methods of solution. Finite difference methods.
Introduction to finite element methods. Prerequisites: ME2201, ME2502 or ME2503, and ME3611.
ME3450 Computational Methods in
Mechanical Engineering (3-2) Fall/Spring
The course introduces students to the basic methods of numerical modeling for
typical physical problems encountered in solid mechanics and the thermal/fluid
sciences. Problems that can be solved analytically will be chosen initially and
solutions will be obtained by appropriate discrete methods. Basic concepts in
numerical methods, such as convergence, stability and accuracy, will be
introduced. Various computational tools will then be applied to more complex
problems, with emphasis on finite element and finite difference methods, finite
volume techniques, boundary element methods and gridless Lagrangian methods.
Methods of modeling convective non-linearities, such as upwind differencing and
the Simpler method, will be introduced. Discussion and structural mechanics,
internal and external fluid flows, and conduction and convection heat transfer.
Steady state, transient and eigenvalue problems will be addressed.
Prerequisites: ME3150, ME3201, ME3611.
MR4323 Numerical Air and Ocean
Modeling
(4-2) Spring/Fall
Numerical models of atmospheric and oceanic phenomena. Finite difference
techniques for solving hyperbolic, parabolic and elliptic equations, linear and
nonlinear computational instability. Spectral and finite element models.
Filtered and primitive equation prediction models. Sigma coordinates. Objective
analysis and initialization. Moisture and heating as time permits.
Prerequisites: MR4322, OC4211, partial differential equation, MA3232 desirable.
OC4323 Numerical Air and Ocean
Modeling
(4-2) As Required
Numerical models of atmospheric and oceanic phenomena. Finite difference
techniques for solving elliptic and hyperbolic equations, linear and non-linear
computational instability. Spectral and finite element models. Filtered and
primitive equation prediction models. Sigma coordinates. Objective analysis and
initialization. Moisture and heating as time permits. Prerequisites: MR4322 or OC4211, partial differential equations; numerical analysis
desirable.
PC2911 Introduction to Computational
Physics
(3-2) As Required
An introduction to the role of computation in physics, with emphasis on the
programming of current nonlinear physics problems. Assumes no prior programming
experience. Includes a tutorial on the C programming language and Matlab, as
well as an introduction to numerical integration methods. Computer graphics are
used to present the results of physics simulations. Prerequisites: None.
SE3030 Quantitative Methods of
Systems Engineering (3-2)
This course discusses advanced mathematical and computational techniques that
find common application in systems engineering. It also provides an
introduction to MATLAB, a computational tool useful in obtaining quantitative
answers to engineering problems. Among the topics addressed in this course are
vector analysis, complex analysis, integral transforms, special functions,
numerical solution of differential equations, and numerical analysis.
Prerequisites: SE1002, SE3100 or consent of instructor.
Comments:
This collection of classes all duplicate material from
MA3232 Numerical
Analysis
(4-0) Spring/Summer/Fall/Winter
Provides the basic numerical tools for understanding more advanced numerical
methods. Topics for the course include: Sources and Analysis of Computational
Error, Solution of Nonlinear Equations, Interpolation and Other Techniques for
Approximating Functions, Numerical Integration and Differentiation, Numerical
Solution of Initial and Boundary Value Problems in Ordinary Differential
Equations, and Influences of Hardware and Software. Prerequisites: MA1115, MA2121 and ability to program in MATLAB and MAPLE.
MA3243 Numerical
Methods for Partial Differential Equations (4-1) Winter
Course designed to familiarize the student with analytical techniques as well
as classical finite difference techniques in the numerical solution of partial
differential equations. In addition to learning applicable algorithms, the
student will be required to do programming. Topics covered include: Implicit,
Explicit, and Semi-Implicit methods in the solution of Elliptic and Parabolic
PDE's, iterative methods for solving Elliptic PDEs (SOR, Gauss-Seidel, Jacobi),
the Lax-Wendroff and Explicit methods in the solution of 1st and 2nd order
Hyperbolic PDEs. Prerequisites: MA3132 and the ability to program in a high
level language such as Fortran, C, or MATLAB.
Several of the classes, particularly MR4323 and OC4323, appear to be poor alternatives to a proper class in numerical analysis such as MA3232 or MA3243. Some of the classes are taught regularly and others are not. In particular:
· ME3440 has not been taught since 1998.
· ME3450 is taught every fall and spring to about a dozen students.
· MR4323 is taught every year in the spring to roughly 8-10 students.
· OC4323 is taught every year in the fall usually to fewer than 6 students.
· PC2911 is taught sporadically, roughly once a year in either winter or summer with about a dozen students.
·
SE3030 appears to never have been taught.
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