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Applied Mathematics Program
Applied Mathematics Program
Last updated 10/8/2002
The undergraduate major in Applied Mathematics is designed to
prepare graduates for diverse professional careers in areas where
mathematics is applied as well as for graduate study in a wide
variety of disciplines. The Applied Math major requires certain
core courses and also requires that students take a concentration of
24 credits in an area that uses applied mathematics. Areas of
concentration from previous students include economics, business,
physics, biology, computer science and all areas of engineering.
Students then take more math and applied math courses to complement
their chosen area of application. This flexibility makes it
possible for students to obtain the mathematical skills needed for a
wide range of applications.
This flexibility also allows Applied Math graduates to be
competitive for a variety of careers. Some of the companies which
have most recently recruited our students include Boeing, Raytheon
and Lockheed Martin and others from the aerospace industry;
Consolidated Graphics, ADAPTEC, Sun Microsystems and Microsoft from
the computer industry; Lehman Brothers and Milliman USA from
insurance and finance; and the national labs Sandia, Los Alamos,
MIT Lincoln Labs, NOAA and NCAR. Applied Math graduates have also
embarked on satisfying careers with a host of smaller firms.
In an effort to prepare our students for the rapidly changing technological field, Applied Math has
identified the following areas of knowledge as central to the undergraduate degree in applied mathematics:
- differential and integral calculus in one and several variables;
- vector spaces and matrix algebra;
- ordinary and partial differential equations;
- at least one programming language;
- at least one applications software package in either mathematics or statistics;
- methods of complex variables as used in applications;
- numerical methods to solve problems approximately.
In addition, students completing a degree in applied mathematics must
- an in-depth knowledge of an area of application such as an
engineering discipline, one of the natural science fields or one of the
quantitative areas of business and economics;
- problem-solving and modeling techniques and strategies central to
- the ability to communicate analytic arguments clearly and concisely
both orally and in writing.
The flexibility of the degree makes it difficult to identify any one
national exam to assess adequately and accurately the knowledge and
skills of graduating Applied Math seniors. Consequently, the Applied
Math faculty have developed a suite of assessment techniques which
we believe more fully captures the breadth of the degree program.
Twenty-six (26) students have graduated with a Bachelor of Science
degree in Applied Mathematics in the two year period from December
2000 to August 2002. The following information is based on data
collected from these students and assesses how the preceding goals
have been met.
Senior survey and exit interview:
Every graduating senior has passed at least one course in each of
the areas specified by items 1, 2, 3, 6 and 7. Further, every
graduating senior knows at least one programming language (item 4),
specifically C/C++, Fortran or Java. Most students know at least
two. All graduating seniors are familiar with either Matlab or
Mathematica (item 5) and most know both.
Senior research (capstone) project:
As a result of an NSF VIGRE research grant received by the
Department in 1998, an increasing number of our junior and senior
applied math majors are participating in research projects. Of the
26 students covered in the period of this assessment, almost 40% (10
students) worked on an independent research project with a faculty
member or postdoctoral fellow. Each student gave at least one
public presentation and most wrote reports on their work. One
student's report was published in a research journal and one is
Nationally-normed exams: Of the 26 students who graduated
with Applied Math degrees between December 2000 and August 2002, 7
took a national exam.
- GRE Subject exam in mathematics: This exam is most suitable for
students planning to attend certain graduate schools in
mathematics. Four students took this exam.
- General GRE exam: Two students took this exam, which is appropriate for anyone
planning to attend graduate school.
- Actuarial exams: This is a
series of eight exams that an actuary would take during his/her
first few years of work, after receiving an undergraduate degree.
Most actuaries attempt only one or two exams before graduation and
the rest while on the job. The first exam covers calculus 1, 2 and
3, linear algebra, probability and risk analysis. The second
actuarial exam focuses on interest theory, economics and finance.
The passing rate is generally 35-45%. One student passed the first
two actuarial exams, each on the first try.
Mathematical Contest in Modeling:
The contest is sponsored by COMAP, The Consortium for Mathematics
and its Applications. It is a 4-day competition in which 3-person
teams answer an open-ended problem with mathematical modeling and
computer simulation. At the end of the four days, a written report
is submitted. This contest allows students to showcase their
mathematical, computational and communication skills---and clearly
requires students to demonstrate knowledge in areas A, B and C. It
draws over 500 entries from teams around the world. The solution
papers are graded as Outstanding (less than 2% of all papers),
Meritorious (next 17%), Honorable Mention (next 23%) and Successful
Applied Math has entered teams in recent years and been among the
most successful departments. Applied Math teams received the
Outstanding designation in 1993, 2000 and 2002. In addition, the
three other CU teams from 2002 each received a Meritorious
designation. Among the 26 graduating seniors evaluated during the
time period of this report, six participated in this international
Complete information on internships is often difficult to obtain since students do not always
report this activity. However, at least six of our students interned at Microsoft, Lehmann Brothers,
Milliman USA, Oak Ridge National Laboratory, Colorado Department of Public Health and LASP (Laboratory
for Atmospheric and Space Physics). The first 3 of these internships led to permanent
positions upon graduation.
A strong indicator of the success of any program is the quality of the graduate schools to which
its students are accepted. Of the 26 students evaluated during the period of this report, 7 are
enrolled in, or have graduated from, graduate programs at Berkeley, Brown University,
Columbia University, Courant Institute at NYU, MIT, Portland State University and the University of
Colorado at Boulder. An additional 3 students indicated that graduate school was likely
within the next couple of years.
We believe that the preceding analysis indicates that the Department
of Applied Mathematics is successful in educating its students.
Over the past five years, the Department has had an increased
emphasis on including projects in many of its courses. The projects
have focused on developing mathematical and computational models and
then communicating this in a written report. This change was
brought about because of feedback from previous assessments. We feel
that these projects have contributed to the increasing level of
success of our students in the Mathematical Contest in Modeling as
well as in internships and the job market. In the future, Applied
Math plans to maintain contact with our alumni and will value their