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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:

1. differential and integral calculus in one and several variables;
2. vector spaces and matrix algebra;
3. ordinary and partial differential equations;
4. at least one programming language;
5. at least one applications software package in either mathematics or statistics;
6. methods of complex variables as used in applications;
7. numerical methods to solve problems approximately.

In addition, students completing a degree in applied mathematics must acquire:

1. 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;
2. problem-solving and modeling techniques and strategies central to applications; and
3. 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 under review.

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 Participant.

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 contest.

Internships: 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.

Graduate Schools: 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 continued input.

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Last revision 01/28/03