The Department of Mathematics
University of Colorado, Colorado Springs
A Self-study for the Academic Program Review AY 2012-2013
Greg Morrow, Chair. Contributions by Gene Abrams, Bob Carlson, Radu Cascaval, Sarbarish
Chakravarty, Zachary Mesyan, Shannon Michaux, Greg Oman, James Parmenter, Barbara
Prinari, George Rus, Rinaldo Schinazi, and Yu Zhang.
Summary of the Self-study.
1. The Mathematics Department is one of the largest department on the UCCS campus in
terms of the number of Student Credit Hours taught, including Extended Studies credit
hours.
2. The Mathematics Department offers the B.S. and B.A. in Mathematics, an M.S. in
Applied Mathematics, a Master of Sciences (M.Sc) with Mathematics Emphasis, and the
Mathematics track of the Applied Science Ph.D.
3. Faculty size:
Tenured or tenure-track full time: 10
Instructors (NTTF): 2.75
Lecturers: 12 (Fall 2012)
Graduate Teaching Fellows: 4 (Fall 2012)
4. The Mathematics Department has a healthy and vibrant undergraduate program
highlighted by active student research projects, contest participation, placement of
graduates as teachers in secondary schools, and placement of graduates in doctoral
programs.
5. The Mathematics Department offers service courses in support of diverse UCCS
programs, including engineering, computer science, business, education, biology,
chemistry, physics and psychology.
6. There are three active centers of research in the Mathematics Department: Algebra,
Differential Equations and Applied Math, and Probability and Stochastic Processes. The
Department has a vigorous research program that is funded by several national funding
agency grants.
7. The Department has established a strong student retention program whose elements
include the Mathematics Center, the Student Supplementary Instruction program, the
Math Placement Test requirement, and diagnostic processes and advising efforts for atrisk students.
8. The Department delivers college level programs for high school students and reaches out
to the community more generally through its interactions with educational institutions at
several levels.
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Summary of Program Planning Initiatives.
1. Increase enrollments and graduates in the degree programs supported by the Mathematics
Department.
2. Increase the number of tenure track faculty to improve education by (a) reducing the extent
of the Department’s reliance on lecturers, (b) allowing for smaller sections of various
courses, and (c) increasing the range of expertise in the Mathematics Department.
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3. Create a Math Computing Lab and incorporate more use of computers and computing in the
undergraduate curriculum.
4. Offer a BS/MS degree.
5. Establish a multi-purpose seminar room for Mathematics.
6. Improve the resources for graduate students of the Department, including office space and
graduate course availability.
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Table of Contents
I. PROGRAM/UNIT HISTORY.............................................................
1
II. CURRENT STATUS OF PROGRAM................................................. 2
1. Goals and Objectives ............................................................................. 2
Follow Up On The Recommendations Made By The 2006 Reviewers..… 4
2. Teaching ................................................................................................ 7
The BA and BS Majors.............................................................................. 7
The MS and MSc Graduate Programs ....................................................... 7
The Mathematics Track Of The Applied Science PhD………………..… 8
Student Support ........................................................................................ 8
Retention Strategies.................................................................................... 8
Undergraduate Student Research, Conferences, and Math Contests.......... 9
MathOnline, Math 90/99, and CU Succeed.............................................. 10
Computing Technology In The Curriculum…………………………….. 10
Minors In Mathematics and Statistics........................................................ 10
Service Courses ......................................................................................... 10
Student Advising ....................................................................................... 11
Teaching/Curriculum Development ........................................................... 11
3. Research/Creative Work ......................................................................... 11
4. University/Community Service................................................................ 12
5. Available Resources ................................................................................. 12
6. Diversity and Inclusiveness....................................................................... 13
III. STUDENT OUTCOME ASSESSMENT............................................... 13
The Student Learning Outcomes ................................................................. 14
Assessment Tools ........................................................................................ 14
Assessment Process……………………………………………………….. 14
IV. PROGRAM/UNIT PLANNING............................................................. 14
Appendices
I.
Faculty Curriculum Vitae
II.
Mathematics Retention, Promotion, and Tenure (RPT) Criteria
III.
College Comparative Data
IV.
Student Data Including Survey Data
V.
Library Information
VI.
Mathematics Assessment Report
VII. Fall 2011 Pass Rates In Lower Division Math Courses
VIII-a. Math Enrollment History
VIII-b. Math Degrees Conferred
VIII-c. Student Credit Hours By Program
VIII-d. Mathematics Student Credit Hours By Faculty Type, Fall 2012
VIII-e. Structural Comparisons By Department
IX.
Mathematics Track of the Applied Science PhD Core Syllabi
X.
Mathematics Outreach Activities
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I.
PROGRAM/UNIT HISTORY
The Department of Mathematics at the University of Colorado, Colorado Springs (UCCS) was last
reviewed during the Academic Year 2005-2006. Since then the Department personnel has changed
considerably.
Professor Jeremy Haefner (former Dean of the Engineering College) and Professor Jim Henderson
(former Vice-Chancellor for Student Success) had formally been part of the Math faculty as of July 1,
2006. Henderson joined the teaching faculty during AY 2007-2008 after stepping down from the ViceChancellor of Student Success position, and then left the University in July, 2008. Haefner also left the
University in about the same time frame. Professor Keith Phillips and Kulumani Rangaswamy were both
teaching half-time under phased retirement agreements until July, 2007, at which time they both retired.
Not counting Haefner and Henderson, the Math department had 11 active full-time tenure track faculty
and one half-time instructor in AY 2003-2004. Dr. Barbara Prinari and Dr. George Rus were both hired
to start in Fall, 2009—Prinari was hired in an Assistant Professor position that replaced one of the two
retired faculty lines mentioned above; Rus was hired in a full Instructor position. Professor James Daly
retired on July 1, 2009. The replacement of Daly’s position was delayed one year until Dr. Zachary
Mesyan came to the Department as an Assistant Professor in Fall, 2010. Dr. Seung Son left the
Department after being denied tenure. Dr. Gregory Oman came to Math as an Assistant Professor in
Fall, 2011. Finally James Parmenter, MS, was hired as a full time Instructor starting Fall, 2012. The
following promotions occurred (reverse chronological order): Dr. Barbara Prinari to Associate Professor
with tenure (2012); Dr. Radu Cascaval to Associate Professor with tenure (2010); Shannon Michaux to
Senior Instructor (2009); Dr. Sarbarish Chakravarty to Professor (2007); Dr. Greg Morrow to Professor
(2006). Finally in 2012, the LAS College Dean, Dr. Peter Braza, was tenured as a Professor of
Mathematics.
The faculty consists of the following members:
Instructors:
Senior Instructor Shannon Michaux (3/4-time), James Parmenter (full-time),
George Rus (full-time)
Assistant Professors: Zachary Mesyan, Gregory Oman
Associate Professors: Radu Cascaval, Barbara Prinari
Professors:
Gene Abrams, Peter Braza, Robert Carlson, Sarbarish Chakravarty, Greg Morrow,
Rinaldo Schinazi, Yu Zhang.
Professors Emeriti:
James Daly, Keith Phillips, Kulumani Rangaswamy.
The Director of the Mathematics Center, Dr. Jenny Dorrington, is an Assistant Professor Attendant of
Mathematics, teaching 2 courses per semester in Mathematics.
Faculty expertise is as follows:
Algebra (Abrams, Mesyan, Oman)
Differential Equations and Applied Math (Carlson, Cascaval, Chakravarty, Prinari)
Probability and Stochastic Processes (Morrow, Schinazi, Zhang)
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II.
CURRENT STATUS OF PROGRAM (for past three years)
1. Goals and objectives
The Department of Mathematics strives for excellence in its teaching, research, and service missions.
Towards those ends, the following goals for the Mathematics Department have been identified.
a) To provide a strong, coherent curriculum for undergraduate and graduate majors in
mathematics.
These Mathematics degrees are designed to serve the needs of the students as well as the employers in
government, industry, and educational fields. The programs are revised as needed to maintain high
standards and enhance the mathematics educational experience. For example, recently the BA
Secondary Teaching option was significantly revised in cooperation between the LAS College and the
College of Education into a four-year degree plan from the previous five-year plan. A streamlined
curriculum based on the nationally recognized UTeach model for preparing Math and Science secondary
school teachers, initiated at the University of Texas, Austin, has been implemented at UCCS. There are
currently 26 math majors enrolled in the UCCS Teach program. A new course, Math 3480, Functions &
Modeling, is being taught by the Department for this program. Another recent development has been the
introduction of the Computational Math course, Math 2650 (offered each academic semester since
Spring 2011), to satisfy the requirement for the Modeling capstone courses (Math 4480 and Math 4850).
Also very recently a Math Honors Track was created within the Math BA/BS degrees.
At the graduate level, several key groupings of graduate courses were organized and revised, and in a
few cases new courses were introduced to form four core areas for the Mathematics track of the Applied
Science PhD.
b) To provide service courses for engineering, computer science, physics, and other such diverse
fields as business, biology, education and economics.
Mathematics has a strong series of service courses due in part to its longstanding association with the
engineering school. Math is also reaching out to Biology and Chemistry with the recently inaugurated
course Calculus for the Life Sciences (Math 1330). Math helps support the use of the computing
software Matlab by integrating this software package in its curriculum, including the capstone
curriculum.
c) To become an active and robust center of research in selected areas of mathematics.
As a small research department, the Department’s objective is to reach for excellence in selected areas
of mathematics that are outgrowths of existing natural strengths of the department. Past Departmental
hiring practices have reflected this philosophy. For example recently the Algebra group was restored to
its former 3 member status with the last two tenure track hires. Specifically, Math currently maintains,
and continues to support, the growth of excellence in areas of algebra, applied math, and probability
theory. This strategy is consistent with the high quality research goals of the UCCS campus.
(d) To provide quality teaching in each course that is offered by the Mathematics Department.
The Department has a number of faculty who have either been nominated or achieved teaching awards
from the LAS College, the UCCS campus, and the CU system. Recently Shannon Michaux received the
Campus Outstanding Instructor Award (2011); Michaux also won the LAS College Outstanding Part#"
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time Instructor Award (2010). Gene Abrams became a President’s Teaching Scholar in 1996. An active
mentoring program exists for all new teachers in the Department. This includes tenure track faculty
paired as mentors with Graduate Teaching Fellows. There is a feeling in the Department to expand this
mentoring process.
(e) To maximize student success.
The Department offers a wide variety of services, in particular, the Supplemental Instruction program,
diagnostic quizzes in lower division courses, and the Math Placement Test, which are designed to
maximize student success. The Department continues to maintain these programs, including for example
ongoing analysis and revision of the placement test.
(f) To implement innovative methods in the teaching of mathematics.
Innovative teaching methods are to be encouraged in order to prepare students to succeed in our rapidly
changing world. The Mathematics Department advocates and implements this goal through the
Supplemental Instruction Program, group learning, and the use of computing and technology. The
Department has distinguished itself with an innovative use of the internet for distance learning.
(g) To establish strong connections between the Mathematics Department and regional
educational institutions.
Through the coordinated grant activities of the Mathematics Department, the UCCS College of
Education, and mathematics teachers from the Pikes Peak area, the Department seeks to coordinate the
transition for students shifting from high school to college. Associated outreach programs supported by
the Department include (see Appendix X):
• The Pikes Peak Math Teachers' Circle: A Problem Solving Professional Development
Community.
• The UCCS MathOnline program.
• CU Succeed in Mathematics.
• Sky Sox Math Youth Days.
The Department also has a strong network of relationships with regional higher education institutions.
For example an NSF grant entitled “Collaborative research: CCLI Phase, Colorado Momentum: Oral
Assessment in the Mathematical Sciences Classroom” involved Gene Abrams together with
investigators from CU-Boulder Applied Math.
(h) To establish opportunities for students to be placed in further education or workplace
positions.
Mathematics education provides important learning and critical thinking skills valued by many
employers and institutions. The Department seeks to advise students on job and educational
opportunities, and to generally support students in attaining their aspirations for new work and learning
environments. The Department organizes events with the Math Club and other groups wherein a math
faculty (especially Bob Carlson) leads a discussion on career opportunities. There is an upcoming plan
to utilize Pi day (3/14) as an opportunity to recruit for the BA Secondary Teaching option program.
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Follow up on the recommendations made by the 2006 reviewers.
i.
Enrollments and graduation rates.
Over the past 3 years the Mathematics student credit hours (SCH) have been growing at the same rate as
the College of Letters Arts and Sciences (Appendix VIII-c), between 4% and 5% per year (shown by
multi-year average changes). The number of mathematics majors is increasing similarly (Appendix VIIIa). Yet the number of conferred undergraduate degrees has not grown appreciably from the period 20002005 to 2006-2011 (six fiscal years in each case, Appendix VIII-b). The average number of
undergraduate degrees conferred was exactly the same for the two intervals: 16.0 degrees per year. The
recent introduction of the UCCS Teach program will reduce the time required to achieve teaching
certification. This should enhance enrollment in the BA Secondary Teaching program. Due to a timely
graduation process in UCCS Teach, this program is expected to help boost graduation rates in Math.
The graduate program has diversified over the past six years (Appendix VIII-b), but has also slimmed
down (Appendix VIII-a). A backlog of Master of Science (MSc) with Math emphasis students have now
graduated, and there are not large numbers of students coming to fill their places. The Department has
had success in recruiting graduate students from the UCCS student population: 9 of 19 students
currently in the math graduate programs earned degrees at UCCS.
ii.
Part-time instruction and new faculty positions.
Since the last review the Department lost one tenure track faculty line overall and gained two
instructors. The strong dependence on honorarium instruction continues: almost one-half of the
mathematics Student Credit hours are being taught by non-permanent faculty in Fall 2012 (where
instructors are counted as permanent faculty, Appendix VIII-d). The 2006 external reviewers warned
against the strategy of hiring instructors instead of tenure-track faculty. The Math Department still has
very few instructors in its non-tenure track teaching force as compared to other departments with large
service components in LAS (see Structural Comparisons by Department, Appendix VIII-e). While the
Mathematics Department strongly feels the need to recover a tenure track faculty line lost in the move
from Engineering to LAS in 2006 (indeed to expand the number of tenure track faculty lines), the
department at the same time recognizes the value and versatility of its non-tenure track faculty.
iii.
Articulation of expectations.
The standard expectation in LAS is a 3-2 teaching load for tenure track faculty. Full-time Instructors
teach 4-4. Tenure track faculty “&'()"*+,(-().,)/0"1'2/-(3"45)-*/.("-,"5.6.5..7"8+'5,4/(9"4,7"&'()"34:."
4"('()4-,.7"4,7"4*)-:."*+&&-)&.,)")+"1'2/-*4)-+,;< (Ref. Math RPT document, Sect 3.3, Appendix II).
NSF and NSA grants do not provide faculty with funds to buy out an offload. Therefore, practically the
only funded research offloads available in Mathematics are from internal scholarly works (CRCW)
grants, primarily aimed at junior faculty.
iv.
Ph.D.
The Mathematics track of the Applied Science PhD was officially approved in 2009. The Department is
committed to offering PhD core sequences (Appendix IX) each year and to expanding its Graduate
Teaching Fellow program to qualified PhD students. Yet the program has some start-up wobbles. No
official extra-departmental funding has yet been garnered for that program. So far the Mathematics track
of this PhD program is slowly developing student-wise. There is a shortage of overall teaching capacity
for a redesigned set of PhD core courses, some of them new (see Appendix IX). In the long run, given
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the 3-2 teaching load, there is concern among some faculty about how much teaching credit a tenure
track faculty will earn for taking on PhD level thesis guidance.
As one proposed solution to the funding issue, Math realizes well the need to interact with industry to
gain support for the program, for example by means of a tuition assistance arrangement for a PhD
seeking employee.
v.
Recruiting and support of graduate students.
MS Applied Mathematics students who are awarded a fellowship to teach two courses and take at least
two courses per academic semester are designated Graduate Teaching Fellows. These students are now
supported in the range of $16,600 - $19,200 per academic year (depending on the exact teaching loadbetween 12 and 14 hours per academic year- and whether the MS level Comprehensive Exam has been
passed). During the summer, additional teaching is available for pay at the honorarium rate. No tuition
waiver is available. The local military and industry (especially USAFA) support graduate students with
partial or full scholarships as well.
vi.
Faculty work load.
The tenure track faculty workload is heavy given the research expectations of the department. To
alleviate this problem somewhat, the Dean offers initial offloads for new tenure track hires. Math
follows up with some departmental offloads for junior faculty, with an expectation that external grant
proposals or research projects with students would develop. While external grants will not generally
continue to provide academic year offloads, they will at least provide summer support and extra travel.
Student research projects have a combined teaching and research value, and in the case of undergraduate
research may also lead to internal funding for both the student and the faculty mentor.
vii.
Math Center.
The Math Center has flourished under the direction of Dr. Jenny Dorrington. The Center supports 1000
and 2000 level Math courses with individual and group tutoring, Supplemental Instruction (SI) sessions,
and general math advising for a large range of students. The tutoring community of course includes
some math majors, so the Math Center is one place a few of the math majors can gather together outside
of classes and still feel supported by the Department. The Department also hires certain math majors to
be Supplemental Instructors. Thus the Math Center and Math Department collaborate on providing SI
sessions for a broad array of math courses, including 3000 level math service courses.
viii. Communication with other departments/colleges.
Math supports a process of prerequisite enforcement for lower division service courses. After working
for more than a decade without an effective system, the Department recently collaborated with the
Office of Student Success to establish enforced prerequisites via the computerized registration system
for those courses, coming on line with the Spring 2013 registration. Once it became apparent about four
years ago that there would be an updated student information system, Math moved forward with a two
step procedure.
The first step was to build an online Math Placement Test that first-time freshmen taking math courses
are required to take. Fortunately the Department was assisted by a PhD level lecturer who had
experience in the design and analysis of placement tests and who was hired as one member of a team to
develop a home-grown test. Note that the Math department refused to use ACT scores as a placement
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tool. Shannon Michaux, Mathematics coordinator of lower division instruction, was instrumental in
organizing the Math Placement Test development process and also in working with Student Success to
integrate the test into the freshmen orientation package, and to standardize the online format and access
for students.
In the second step, since the hoped for enforcement itself did not come automatically with the new
student information system, Math undertook to introduce an ad hoc process of prerequisite checking by
utilizing both faculty and staff in a collaborative effort with Student Success to identify students who did
not meet the prerequisites in certain targeted lower division math courses. It has finally become a
priority of the campus to implement a requisite package of the new Student Information system (ISIS).
In fact now, with relative ease, an enforcement protocol has been established in the registration system
for lower division math courses.
In the process leading up to this automatic enforcement there were discussions with the College of
Business associate dean and advising staff to emphasize the need for honoring the placement process in
the College Algebra and Business Calculus sequence.
Along a related but different line the MATH 1330 Calculus for Life Sciences course was developed as a
“terminal” math course for Biology majors. A significant amount of energy was spent working with the
Biology and Chemistry departments in working out how this course could best fit into their programs.
Besides the basic relationship that has arisen with Biology with respect to the delivery of calculus,
Chemistry has also benefited from these developments. Indeed Chemistry recently joined its Innovation
track students to the population served by MATH 1330.
ix.
Faculty salaries and honorarium pay.
After accounting for the 2% to 2.5% delayed raise in the 2011-2012 reported compensation figures,
salaries in the full professor category at UCCS Math are still 8% to 10% below the median for
departments of Mathematics of Group M (Master’s granting) institutions reporting in the AMS 20112012 salary study. Salaries for associate professors are still below the median level, but less so
percentage-wise than the full professor group, and salaries at the assistant professor level match the
median salary of these group M mathematics departments. (All comparisons are based on 2011-2012
data.)
Honorarium (lecturer) pay has increased only as there have been increases to faculty salaries overall.
Lecturer pay is currently $802/cr. hr. (increased from $763/cr. hr. two years ago). Lecturers are limited
to 7 hours of teaching per semester of the academic year. Instructor salary is currently $36,300 for the
academic year 2012-2013. Instructors who have a specified number of exceeding expectations ratings in
annual merit reviews may apply for promotion to Senior Instructor after 5 years of teaching service. Pay
for summer teaching is comparable to AY pay for instructors.
It suffices to say that lecturer pay is still very low. Since Math depends heavily on its honorarium
instructors (as shown in point ii above) especially as compared with other departments with a large
service component, an acknowledgment of a senior lecturer status and pay scale would seem
appropriate.
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2. Teaching
The Department of Mathematics offers over 50 sections of courses during each of the Fall and Spring
semesters, and supports a full slate of nearly a dozen core courses during the summer semester. In
addition Math organizes several sections of pre-collegiate math courses each semester (5 sections in
Fall, 2012) taught by Pikes Peak Community College (PPCC) instructors through an Interagency
agreement between UCCS and PPCC. In all, over 12,000 credit hours in mathematics are taken by
students from the main campus throughout an academic year. Another 1,500 credit hours are taken
through the Extended Studies campus each year (Appendix VIII-c). Besides a viable, well-rounded, and
high quality curriculum for its majors, the Department offers many in-depth service courses for students
in various science, engineering, and business-related disciplines. The Department supports a minor in
mathematics (currently pursued by 80 students; 78 math minor, 2 stats minor) which is quite popular
among science and engineering majors.
The mathematics major continues to grow in the same way that the campus has been steadily growing
over the last few years (See Appendix VIII-a for enrollment figures of all Math degrees). As of census
date in Fall 2012 there were 96 Math majors. As yet there seems to be a lag in numbers of BA/BS
degrees conferred, and Math would like to help undergraduate students graduate in a timely manner. It is
not known exactly why there is a lag, but some faculty suspect that it is due to the fact that some
students take extra time to pass a capstone course like Modern Analysis I, MATH 4310. This course in
particular is currently offered only once per academic year. The UCCS Teach program in the BA
Mathematics Secondary Teaching option is a bright spot that promises to help boost and stabilize
graduation rates. Timely graduation in this option is expected due to the fact that there is extra support
for student advising from both Education and Math.
The Mathematics Department degree programs are as follows: B.A. Mathematics, B.S. Mathematics,
M.S. in Applied Mathematics, Master in Sciences (M.Sc) with Mathematics Emphasis, and a
Mathematics track of the Applied Science Ph.D.
The BA and BS Majors: The course offerings in mathematics are structured in such a way that major
courses double as service courses throughout the 3000 level with the exception of Number Theory
(Math 3110), which is strongly recommended for Modern Algebra I (Math 4140), and Estimation
Convergence and Approximation (Math 3410), which is strongly recommended for Modern Analysis I
(Math 4310). The standard sequence for engineering, mathematics and physical science students
consists of three calculus courses (Math 1350, 1360, and 2350; each 4 credit hours) together with
Differential Equations (Math 3400) and Linear Algebra (Math 3130). The other required courses for a
BA mathematics major are Discrete Math (Math 2150), Probability and Statistics (Math 3810) or
Statistics (Math 3100), Modern Algebra I (Math 4140), Modern Analysis I (Math 4310) and
Mathematical Modeling (Math 4480) or Stochastic Modeling (Math 4850). The Department offers a
wide range of 4000 level elective courses, almost all of which are double listed as 5000 level courses.
The BS major has the same required number of hours (42 hrs.) in mathematics but differs from the BA
as follows. In place of the Modern Algebra I (Math 44140), the BS degree requires the student to take a
two-course sequence at the 4000 level in either Statistics or Applied Math. Finally, on the one hand the
BA Secondary Teaching option students are required to take Number Theory (3110), Functions &
Modeling (3480), and Higher Geometry (4210). On the other hand the BS students must complete a
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secondary area and take either Numerical Analysis (4650) or Numerical Computing (CS 4600).
The MS and MSc graduate programs:
The MS degree in Applied Mathematics offers the student an opportunity to study specific areas of
applied mathematics including statistics, probability, differential equations, applied analysis, modeling,
algebra, and coding theory. The students must take all their course-work for the degree at the 5000 level
(and must take Math 4140 and 4310 in addition if these are not already in hand). All students must
complete Linear Algebra I (Math 5130) and Modern Analysis II (Math 5320). Students must pass a
comprehensive exam in analysis, and are required to make an oral presentation regarding some aspect of
advanced mathematics. There are two MS Applied Math graduates currently in doctoral programs of
study (Univ. Arizona Applied Math and CU-Denver Applied Math). Last year Barbara Prinari (Math)
and Marek Grabowski (Physics) jointly guided an MS Applied Math thesis.
The Department supports the Master of Science with Math Emphasis (MSc) students in a slightly
different way than the MS Applied Math students. The MSc program makes a convenient option for
students wanting to change into a Math graduate degree starting from, say, a minor in math. The MSc
students must complete the Modern Algebra I and Modern Analysis I courses at the 4000 level and may
credit these toward the degree. In addition to a minimum of 15 credit hours of mathematics at the 5000
level, students are required to take at least one course from a discipline other than mathematics but
related to their mathematics study. The MSc students are paired with a faculty advisor to help guide the
student to completion of a culminating mathematics paper.
The Mathematics track of the Applied Science PhD: This recently developed program has been designed
around the following core subject areas: Complex Analysis, Applied Differential Equations, Probability,
Functional and Real Analysis, and Ring Theory. See http://www.uccs.edu/math/phd-appliedscience/general-information.html for an outline of the program. Bob Carlson has prepared a student
handbook style document (with recent additions in Algebra by Zak Mesyan) for this program (Appendix
IX).
Student Support: Courses taught in the Department are supported in a number of ways. First, the
Mathematics Center offers drop-in tutoring service to all students enrolled in 1000 and 2000 level
mathematics courses, and to some extent the 3000 level mathematics service courses. The Math Center
is staffed by graduate students enrolled in the MS Applied Mathematics program and by mathematically
competent undergraduate students. A number of the Department’s courses, both lower division and
upper division, are supported by the Supplemental Instruction (SI) Program. The SI Program was
instituted over 15 years ago to take advantage of the positive effects of group collaborative work among
mathematics students. The program works as follows. Students (typically junior or senior math or
science majors, but math graduate students for the upper division courses) are designated as the SI
Leader for a given course. This leader organizes supplemental instruction sessions (typically two
sessions per week for at least one hour per session). The leader is charged with engendering discussion
amongst the students in response to questions that any student might ask. Students have responded to
such sessions quite enthusiastically as borne out by the end of semester surveys. In addition, the SI
leaders gain hands-on experience with the pedagogical process, experience which will be valuable for
BA mathematics majors, many of whom will pursue careers in teaching.
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Retention strategies: A major concern of this department is to increase retention of students.
Mathematics courses are a major hurdle for many students. For instance, about 45% of students on
average fail or withdraw (are assigned grades D, W, or F) from Calculus I and II, and indeed this rate
persists in other lower division courses as well (see Appendix VII). Several approaches have been taken
to alleviate this problem, one of them being to offer different approaches to calculus. Thus about five
years ago the Department introduced Math 1310-1320, Calculus with Refresher Precalculus, a six credit
hour two-semester sequence, equivalent in content to Calculus I. Gene Abrams received NSF support to
design this sequence that includes oral assessment sessions. The Department recently also introduced
Math 1330, Calculus for Life Sciences, again equivalent to Calculus I when taken as a terminal math
course.
Another retention strategy has been to make sure students have the prerequisite material, for example
algebra and trigonometry in the case of Calculus I. Hence, for the last several years, every calculus
instructor starts the course with an algebra and trigonometry review followed by a “diagnostic” quiz at
the beginning of the second week of class. Students who fail the quiz are encouraged to drop the class
and enroll in Precalculus (Math 1050) or Math 1310, Calculus with Refresher Precalculus (during Fall
semesters). To help reinforce this process there has been a drive in Mathematics to institute prerequisite
enforcement in lower division math courses. There is some disagreement among math faculty about
preparedness of students for these courses. Nevertheless we expect success rates in lower division math
courses to improve with the implementation of mandated prerequisites for these courses via the
computerized registration system, where a passing math placement test score counts as a prerequisite.
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A retention strategy on the horizon is coordination of Math 1350. One possibility is to introduce
common exams across sections, test it a few years and reevaluate. Common exams can also be used in
Math 1050, Precalculus, where some coordination already takes place. In further retention strategies, all
instructors of math courses numbered 1350 and below are encouraged to make use of the online Early
Alert system managed by the Office of First Year Experience (Barbara Gaddis, Director). The students
who are at risk for failing their course as evidenced by a diagnostic quiz and first exam are contacted by
a math retention specialist who will mention the instructor’s office hours, the Math Center, the
Supplemental Instruction program, study habits workshops, and other interventions. In summary the
Department’s approach to retention is a combined strategy, with continuing efforts to track the data at
hand, to enforce prerequisites, to provide guidance to students by means of diagnostic quizzes and
advising, to introduce course coordination, and to offer reasonable class sizes no larger than 45.
Undergraduate Student Research, Conferences, and Math contests: Over the past 5 years there has been
more attention given by the Department to undergraduates in pursuit of graduate school placement
including placement in mathematics PhD programs. We are aware of five undergraduate math students
who have gone on to PhD programs over the past five years; the first of these just graduated at CUBoulder, Applied Math. The other institutions at which these students are studying toward a PhD are as
follows: Florida State, SUNY Binghamton, North Carolina State, and Arizona State. Some
undergraduate research papers have been coming out over the last few years, something that hadn’t
really been happening consistently until faculty with NSF RUI grants began to attract student interest.
Associated with this rise in organized undergraduate research activity was the recent appearance of the
first ever Putnam competition team at UCCS. The Math Incline weekly free seminar hosted by math
faculty now supports the Putnam team in studying challenging math problems. For over ten years
Mathematics has consistently sponsored teams for the Mathematical Contest in Modeling (MCM); some
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of those teams have earned meritorious ratings. In addition each year there is a series of regional
undergraduate math conferences for students to attend and present their own research, often written in
collaboration with a math faculty. In 2009 the annual Pikes Peak Regional Undergraduate Math
Conference was hosted at UCCS. Every year there is a SIAM student conference in Denver with
participation by groups of faculty and students from UCCS Math.
MathOnline: This is an Extended Studies program for students to take college level mathematics courses
at a distance. A majority of MathOnline students are mathematically advanced high school students. The
instructor delivers what is essentially a 'standard' lecture to a main campus section of the same course,
but uses a computer, graphics tablet, and wireless microphone, which allows the lectures to be broadcast
synchronously via the internet. Both the live classroom sessions as well as the recorded sessions of these
classes are presented to the MathOnline students. One advantage to this system is that the archived
lectures are commonly utilized by the main campus students. Office hours are handled via email or via
the internet using audio and a live graphics tablet. Instructors are paid for the extra work of these
students according to the number enrolled in the Extended Studies section. The courses offered under
the MathOnline program are: Calculus 1, Calculus 2, Calculus 3, Discrete Math (2150), Number Theory
(3110), Linear Algebra (3130), and Differential Equations (3400).
Math 90/99: Math 90, Algebra I, and Math 99, Algebra II (Intermediate Algebra) are offered as a
sequence in Extended Studies leading up to College Algebra (Math 1040). These classes are limited to
30 student section sizes, and are taught by Pikes Peak Community College (PPCC) instructors under an
Inter-agency agreement between PPCC and UCCS.
CU Succeed: This is a partnership between the UCCS Math Department and Colorado high schools to
provide college credit for selected high school mathematics courses. The Department identifies high
school teachers who are qualified to serve as honoraria and who agree to teach their courses in
accordance with the University's standards. The courses are established in our system and taught in the
high schools. Students enrolled in one of these courses have the opportunity to earn college credit for
successful completion of the course. Math offers CU Succeed courses for Precalculus, Calculus 1, and
AP Statistics.
Computing Technology in the Curriculum: Some of the Department’s upper level undergraduate courses
support curricula that require students to use mathematical software such as Maple and Matlab in order
to complete homework, long-term projects, and various group assignments. One example is Numerical
Analysis (Math 4650/5650), a popular course for undergraduates and graduates alike. Another is the
Mathematical Statistics I & II sequence (Math 4810, 4820). The Mathematical Modeling course (Math
4480), one of two capstone modeling courses for all math majors, is another key example. It provides
students hands-on learning experience about the use of computer algebra systems (mainly Matlab) in
solving mathematical and real world problems. In-class presentations and frequent Matlab tutor visits
help students get acquainted with the specifics of the software. Math 2650, Computational Math, was
recently made a prerequisite for both Mathematical Modeling and Stochastic Modeling (Math 4850).
Minors in Mathematics and Statistics: The minor in mathematics requires 24 hours of courses given by
the Department with at least nine of those hours numbered above 3020. One of the courses must
maintain a certain level of abstraction; here Discrete Math (Math 2150) is a possibility to fill this
requirement. The minor in statistics requires 21 hours in approved math courses given by the
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Department, and must include at least one 4000 level statistics course as well as both Math 3100,
Statistics for the Sciences, and the calculus-based Math 3810, Probability and Statistics.
Service Courses: Many departments on campus (including psychology and nursing) require the mastery
of the content from College Algebra (Math 1040). In the case of the Business College, mastery of both
College Algebra and Calculus for Business and Economics (Math 1120) are required. Calculus for Life
Sciences (Math 1330) or Calculus I (Math 1350) is required of Biology students. The calculus sequence
(Math 1350, 1360, and 2350) is required of a number of engineering and physics majors. Discrete
Mathematics (Math 2150) is a required course of computer science majors. Math 3010 and 3020
(Mathematics for Elementary Teachers I & II) serves the needs of the College of Education. Linear
Algebra (Math 3130), Differential Equations (Math 3400), and Probability and Statistics (Math 3810)
are required of Mechanical Engineering majors. There are many other examples of service by the
Department to majors other than math.
Student Advising: After taking a five year hiatus from required advising for all math students every
year, the Mathematics Department has re-introduced required undergraduate advising for newly declared
majors (See http://www.uccs.edu/math/student-resources/advising.html). Graduate students are required
to meet with the graduate faculty advisor to approve a plan of study. Students opting for the thesis
option of the MS degree work with their thesis advisor throughout their second year of studies.
Teaching/Curriculum Development: Since the last Department of Mathematics Review in 2006, three
new undergraduate courses have been developed. These are:
• Math 1330, Calculus for the Life Sciences, a 4 cr. hr. course that is a terminal calculus 1 course,
designed primarily for Biology majors (offered each Fall and Spring).
• Math 2650, Computational Math, a 1 cr. hr. course on an introduction to Matlab, including
writing programs in Matlab.
• Math 3480, Functions and Modeling, an inquiry based course in mathematics for the BA
Secondary Teaching option.
The Computational Math course has been introduced to prepare students for the capstone course option:
Math Modeling (Math 4480) or Stochastic Modeling (Math 4850). Math 2650 is now required for these
modeling courses. The Functions & Modeling course is one of three 3000 level courses that the BA
Math Secondary Teaching option students must take in the UCCS Teach LAS Core, the others being
UTLS 3020, Research Methods, and UTLS 3030, Perspectives on Science & Mathematics.
3. Research/Creative Work
The overwhelming majority of the tenured and tenure-track faculty members are very active in research,
publish papers that have been judged to have significant impact on the scientific communities of interest,
and are invited to national and international conferences. There is an active group of faculty regularly
applying for and obtaining external funding. Currently there are three active national funding agency
grants in Mathematics (Chakravarty, Prinari, Schinazi), and one five-year travel grant from the Simons
Foundation (Abrams). In 2012, five faculty (Abrams, Mesyan, Prinari, Schinazi, and Zhang) have
submitted grant proposals to national research funding agencies. Recently Bob Carlson was awarded a
Biofrontiers (internal) grant that provides a teaching offload as well as travel. This grant activity overall
is really remarkable, given the teaching load, the size of the department, and the commitment of its
members to maintaining high quality in their teaching. Note that that the department currently has one of
the strongest groups in ring theory nationwide (including Professor Emeritus Rangaswamy). This group
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organizes regular seminars that reach out to neighboring institutions, like Colorado College. Note that
these research strengths bode well for the fledgling Mathematics track of the Applied Science PhD
program. This program stands to be in good stead with respect to opportunities for students to receive
high quality faculty research guidance. The Department organizes a vigorous series of colloquia as well
as an annual Distinguished Math Lecture, and strongly encourages “Math Incliner” undergraduates and
graduate students to participate in these colloquia.
Over many years the math faculty have established themselves as excellent organizers of mathematics
conferences. Recent examples of conferences hosted at UCCS are: Frontier Probability Days (2007) and
the International Conference on Nonlinear Waves, Integrable Systems and Their Applications (2005).
Over the past few years, instead of hosting conferences locally, a number of math faculty (Abrams,
Chakravarty, Mesyan, Oman, Prinari) have been active in organizing special sessions at conferences or
international workshops outside Colorado Springs.
Yet, despite the strengths mentioned above, the Department could use some added research in certain
areas of mathematics such as: statistics, numerical analysis/scientific computing, and
geometry/topology. This is especially true due to the need for a diversification of courses to be offered
to undergraduate and graduate students alike.
4. University/Community Service
The mathematics faculty serves a diverse community. Besides dedication to the department, college and
campus committees, the faculty serve the professional community by refereeing mathematical papers
and organizing conferences and special sessions. Two examples that cross over to the secondary school
community are: Gene Abrams’ service as the Principal Investigator of the Partnership for Innovative
Preparation of Educators and Students (PIPES) grant at the campus level (continuing since June, 2008),
and Rinaldo Schinazi’s recent service as the Co-director of the UCCS Teach program for secondary
school teacher licensure in math and science. The Department makes several contributions in the way of
community outreach (see Appendix X). Math communicates with its alumni to engage them in
department life by publishing an annual newsletter. One such alumnus is Professor John Lorch of
Mathematics at Ball State University whose family created an endowed undergraduate student
scholarship in the Math Department about 5 years ago.
5. Available Resources
Staff: The Math Department staff currently consists of one full-time administrative assistant,
Emanuelita Martinez, and two student office workers who handle various tasks. One of these student
workers is a graduate student who, while playing the role of retention specialist, advises at-risk students
on appropriate actions to succeed in their math courses. Another student office worker is a graduate
program liaison who manages the mathematics graduate files, and does paperwork for the math graduate
committee.
Budget:
The 2011-12 budget for the Mathematics Department (apart from faculty salaries) is given below:
Category
Budget
Instructional Budget (lecturers)
$119,625
GTF stipends
$ 18,186
Student Office Support
$ 8,300
Operating Expense
$ 15,000
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Mathematics Colloquia
Travel
Computers
Visiting Scholars Program
Math Program Fee
$ 5,149
$ 6,200
$ 3,000
$ 3,570
$121,851
The Math Department budget consists of an instructional budget for paying for all instruction that is not
paid for by a salary line (Instructor and Tenure Track faculty salary lines not shown). The Colloquium
budget pays for travel for short-term stays of research visitors who give a talk, as well as accompanying
costs for colloquium teas. The Visiting Scholars budget pays for travel associated with longer term
research visits. About 80% of the Math program fee pays for student wages; these include pay for
Supplemental Instruction. The other 20% of the program fee is used for operating expenses. Travel in
AY 2011-2012 was $620 per tenure track faculty. The Math department uses its portion of Indirect Cost
Recovery (ICR) funds coming from external grants to fund additional research travel or travel of
research visitors. These departmental ICR monies have come to about $3,000 to $4,000 per year over
the past few years. The GTF stipend is used to support Graduate Teaching Fellows –there is a two-year
time limit for any given student on GTF support.
Library Resources: The library spends about $10,000 per year to pay for Mathematics books and ebooks. Faculty may make requests for certain books to be purchased. Additionally books may be
borrowed from regional libraries using the Prospector interlibrary loan system. Most research papers
may be found via one of the electronic journal subscriptions covered by the library. For older papers not
covered by these subscriptions, one may use an electronic request system to obtain a scanned copy of the
print version. Overall, with internet access to electronically stored papers, the library is a fully
functioning research library. There are fewer books in the UCCS library than one may find at a large
research library, so one has to use the Prospector system to browse on occasion.
6. Diversity and Inclusiveness.
The Department of Mathematics is committed to helping each person realize his or her full potential in
mathematics education. The Department believes that in order to achieve equal opportunity for all, an
important curricular goal must be to provide individuals with role models, tutoring, and peer group
support, in an environment sensitive to diverse reactions to teaching and learning styles. A review of the
math faculty during the last five years indicates that there has been a significant multi-cultural, ethnic
and gender diversity in both its regular and honoraria faculty. Currently, the Department’s regular
faculty represents a diversity of international backgrounds, including roots in China, India, Brazil, and
Europe and Eastern Europe. The current gender makeup of mathematics regular faculty (including the
Math Center Director) is three females and eleven males. The current gender makeup of mathematics
lecturers is six females and six males; and of the graduate teaching fellows, one female and three males.
Of the 96 Mathematics majors as of census date in Fall 2012, 49 are female and 47 are male. Also, 24 of
these 96 students identify themselves with minority (non-caucasian) populations. Some members of the
Department have participated in diversity and inclusiveness training, either at the campus level (e.g. via
the BIG Idea Building Inclusiveness Workshop)"or in outside venues.
III.
STUDENT OUTCOME ASSESSMENT
There are three major stakeholders involved in the earning of an undergraduate degree in mathematics:
the students, the faculty, and potential employers of the students. The assessment program of the
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mathematics Department is designed to measure the extent to which students are achieving the four
Student Learning Objectives listed below. Students must have a firm grasp of each of these outcomes
before they are considered to be competent in mathematics at the bachelor’s level. Faculty must have
appropriate vehicles by which they can assess the effectiveness of various educational and pedagogical
techniques, in order to improve the learning process. Potential employers (most commonly in the
education or high technology industries) need employees who are skilled in the four indicated
objectives.
The Student Learning Objectives:
1. Students will be able to apply both theoretical and computational techniques to the solution of
mathematical problems.
2. Students will be able to comprehend, formulate, and produce mathematical proof.
3. Students will be able to communicate correct mathematical content in both written and oral form.
4. Students will understand that mathematics comprises a broad array of interconnected concepts.
Assessment Instruments: To determine the level of achievement of the outcomes, the Department
utilizes the following types of assessment instruments.
(a) Course mapping rubric. The student learning objectives are assessed via rating each student on
specific content areas of the course. A matrix with objectives as rows and content areas as
columns provides the structure- not all objectives need be addressed by each content area, but
every objective is covered by some of the content areas. The following capstone courses are
mapped in this way: Modern Analysis I, Mathematical Modeling, and Stochastic Modeling.
(b) Graduating student surveys. Annual surveys to seniors ask for students to provide self
assessment in certain areas that cover student learning objectives. The structure is again to map
each question to certain of the learning objectives.
Assessment process: The department has of late become much more engaged in its assessment activities,
with two tenured faculty (Cascaval and Chakravarty) recently coming into the role of program
assessment coordinator, Cascaval for the undergraduate program and Chakravarty for the graduate
program. The Mathematics chair continues to be involved in helping coordinate assessments as well.
The monthly meetings of the Math department are a good vehicle for discussions of this process.
IV.
PROGRAM/UNIT PLANNING
The description of the Mathematics programs above shows that the Department has succeeded in its
quest for excellence in several significant ways in its teaching, research and service mission. The
Department takes painstaking care in ever reviewing its teaching processes, and needs for improvement
in the curriculum. The research activity of the faculty is vigorous and there is a strong impetus for
discussing new ideas and for dissemination of work in publications and in talks at conferences and
colloquia. The math faculty is firmly committed to working with the various university systems and
committees to move the math program and campus forward. The Department is actively involved in the
community at several levels, including its role in making strong connections with regional educational
institutions. Despite these accomplishments, the Department strives to improve. To effect such
improvement, we have identified the following non-prioritized ventures which we intend to pursue.
1. Increase enrollments and graduates in the degree programs supported by the Mathematics
Department. In addition to aggressive recruitment and retention efforts, the Department intends to
enhance the Math Majors’ experience as follows. Design sections geared more towards Math
Majors (such as Calculus, Discrete Math etc), with a stronger emphasis on proof development and
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more in-depth coverage of topics. Since many of our Math required courses double as service
courses to other departments (all calculus courses, Math 3130, Math 3400, Math 3810), we find that
some majors may remain under the radar screen until the second semester of their junior year (when
they take Math 3110 and Math 3410, if at all).
2. Reduce the extent of the Department’s reliance on lecturers. Currently, lecturers and Graduate
Teaching Fellows teach 50% of the Department’s student credit hours. Although the lecturing staff
is certainly a valuable asset to the Department, in order to ensure a stable teaching program with
continued (4% to 5%) campus growth, it is necessary to hire permanent faculty to provide
sophisticated teaching of the Mathematics curriculum starting from Calculus 1. Over the current
academic year there will have been 6 courses (counting 23 hours) at the level of Calculus and above
taught by lecturers. This does not count several courses of this type (including 3000 level courses)
taught by non-PhD level instructors nor does it count a couple of 1 hour Computational Math
courses taught by a graduate student. Thus currently the equivalent of two lecturers are currently
teaching courses that the Math department would like to be taught by professors. Finally, the
lecturers who have attained a senior status can be given more acknowledgment for the role they
play as well, since indeed lecturers will remain an active part of the Department.
3. Incorporate more computing in the undergraduate curriculum, since many students would benefit in
learning the math concepts if aided by computer simulations and illustrations (Math 3130 (Linear
Algebra) and Math 3400 (Differential Equations) could use Matlab, Calculus sequence could use
some applets, e.g. Math Visualization Toolkit).
4. Create a Math Computing Lab. This requires a physical space, dedicated to Math Majors. This
room would accommodate computational needs of math students, with support for specialized
software (such as Matlab, Matematica, etc.), and staffed by graduate (MS or PhD) students who
would act as tutors. For example a Matlab tutor would be on staff there. Courses with a strong
computational component could use the Computing Lab to schedule exams, or one-time demos.
Such a Lab would also accommodate computing activities for student research. It is felt that a
computing lab would attract more students to the BS Mathematics degree track and thus bolster the
number of Mathematics majors.
5. Offer a BS/MS degree for our stronger undergraduate students, who are capable of taking our Math
4/5000 level courses at the 5000 level.
6. Increase the range of research expertise in the Department, to provide for a diversification in the
courses offered at both the undergraduate and graduate levels. The Department seeks to diversify its
research expertise in the following areas: statistics, numerical analysis/scientific computing, and
geometry/topology.
7. Establish a multi-purpose seminar room for Mathematics that will support Seminars, Supplemental
Instruction sessions, Math Incline meetings, Math club, Department meetings, Math Contest
preparation, group Math advising, Graduate Oral presentations, and other events.
8. Improve the resources for graduate students of the Department, including office space and graduate
course availability. Currently there is one standard sized office to accommodate all the lecturers and
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Graduate Teaching Fellows. Therefore the need for space is clear. Additionally, the range and
frequency of courses offered to graduate students is limited due to the teaching demands placed on
a small research department. In particular the graduate students need to see more consistent
offerings of courses that involve the use of computers and computing.
9. Identify resources to allow for smaller sections of various courses (this includes service courses,
and even precalculus courses). Note that due to the fast growth of the campus, lower division
mathematics class sizes, as well as 3000 level math service course class sizes, have been running up
to 60 as recently as two years ago. Some remnants of this fairly recent adjustment of larger class
sizes due to student number increases still exist for the Department to date. Thus the needed
resource is more instructional capacity in not only the lecturer rank (for all precalculus courses) but
also in the permanent faculty ranks (for calculus and above). For example recently Math has been
trying to split the one section of MATH 3810, Probability and Statistics, into two sections in at least
the Fall semester but has been hampered in this effort due to the lack of instructional capacity. Math
would like to be able to offer a second section of the capstone course MATH 4310, Modern
Analysis I, in Spring semesters (the course is currently Fall only) to help students manage their
schedules and so graduate in a timely fashion. One result of the current campus growth is that Math
is adding approximately two sections per semester to accommodate all the lower division students
coming in (combining calculus and all precalculus courses).
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