1. Historical perspective

To address the interdisciplinary research and education mission for this campus, the School of Natural Sciences sought to develop applied mathematics instead of a more traditional, “pure” mathematics discipline. The Applied Mathematics group of faculty have contributed to the campus mission through development of undergraduate and graduate research and education programs. All faculty in the Applied Mathematics Unit are also faculty in the Applied Mathematics Graduate Group. In speaking of the Applied Mathematics faculty below, we refer to those in the Unit and the Graduate Group.

The Applied Mathematics faculty has been active in collaborating with faculty across the entire campus. It is for all of these reasons that the Strategic Academic Vision for UC Merced, states that Applied Mathematics is an essential core discipline to be “present and nurtured at UC Merced in 20 years.” Because Applied Mathematics is a theoretical and computational scientific endeavor, the Applied Mathematics program has grown and may continue to grow with minimal competition for resources with other developing programs on campus.

In keeping its alignment with the interdisciplinary mission of UC Merced, Applied Mathematics is well poised to enable other programs on campus to develop further through innovative, cross-linking collaborations. The Applied Mathematics faculty currently participate in other research programs on campus including Quantitative and Systems Biology, Physics, Chemistry and Chemical Biology, Electrical Engineering and Computer Sciences, and Mechanical Engineering and Applied Mechanics. Specific activities include participating in doctoral thesis committees, co-advising students, and collaborative funding endeavors. Currently, there are emerging areas of cooperation and collaboration between Applied Mathematics faculty members and those in the Environmental Systems, and Biological Engineering and Small-scale Technologies graduate programs. Moreover, Applied Mathematics faculty have been actively engaged in the development of the Management program. The Applied Mathematics faculty is intent on increasing the activity in innovative, cross-disciplinary collaborations across campus.

2. Applied Mathematics at UC Merced

The Applied Mathematics program at UC Merced defines applied mathematics as the application of modeling, analysis, and scientific computing to solve problems relevant and important to the real world.  To that end, the Applied Math program at UC Merced has identified the following three strategic foci. 

• Modeling complex systems
• Scientific computing
• Data science

These three strategic foci are guides for future growth and development. Moreover, these three strategic foci provide rich opportunities for contributing to other disciplines and foster interdisciplinary and multidisciplinary research and education. At present, the Applied Mathematics faculty have expertise in all three of these strategic foci with most faculty representing modeling complex systems, then scientific computing, followed by data science. The educational programs reflect this current emphasis, as well. While contributing to the campus’ 2020 Project goals for overall growth, our objective in Applied Mathematics is to broaden and deepen the expertise of Applied Mathematics faculty across these three foci, and cross-cutting, collaborations across campus.

We assess applied mathematics research using two criteria: (1) sophistication of the mathematics used and (2) novelty and importance of the application. We have built, and continue to build a program comprised of broad-minded interdisciplinary researchers who contribute to the core applied mathematics program as well as a number of other programs at UC Merced. This approach is in stark contrast to developing a program by defining a specific set of traditional mathematics sub-fields. By developing the applied mathematics program in this way, we plan to develop a truly modern applied mathematics program at this new campus. We seek to strengthen this program through cross-disciplinary collaborations, which allow for applied mathematicians to contribute also the development of other academic programs. Moreover, these cross-disciplinary collaborations allow for a broadening and diversification of funding opportunities for research and education initiatives.

3. Resource needs for Applied Mathematics

At present, the applied mathematics program has 10 core, ladder-rank faculty (2 Full, 4 Associate, 3 Assistant, and 1 Lecturer with Security of Employment), and 2 Visiting Assistant Professors. We propose here a plan to grow to 23 ladder-rank faculty and 4 Visiting Assistant Professors by the 2020-2021 Academic Year. This growth in faculty is accompanied by the following growth projections. 

• 180 Undergraduate Majors (consistent with campus history of 2% of total undergraduate population corresponding to an undergraduate student-to-faculty ratio of 9-to-1);

• 60 Graduate Students (consistent with campus history of 6% of total graduate student population corresponding to a graduate student-to-faculty ratio of 3-to-1);

Our faculty growth plan will enhance, and deepen our fields of expertise within the three strategic foci listed in Section 2.  In particular, our future faculty search will include (but not be limited to) researchers in (1) atmospheric science, epidemiology, neuroscience, and conservative and dissipative chaos for modeling complex systems; (2) asymptotic and perturbation methods, applied analysis, optimal control, numerical linear algebra, multigrid methods for numerical partial differential equations, stochastic differential equations, and high performance computing for numerical analysis and scientific computing; and (3) financial mathematics, climate modeling, signal processing, inverse problems, computational genomics and bioinformatics for data science.  This growth plan is aggressive, but reasonable. It puts the Applied Mathematics program well on track to become a nationally recognized program for its research and educational excellence. 

3.1 Space Requirements

At present, the Applied Mathematics faculty and students are distributed across the Science and Engineering Building, the Classroom and Office Building, and the Academic Offices Annex. To meet the objectives listed in Section 2, Applied Mathematics program must have the following. 

1. Clustered offices for Applied Mathematics faculty, graduate students, postdoctoral researchers, and undergraduate student researchers.
2. Collaborative research work spaces for purposes including, but not limited to, holding group meetings, facilitating collaborative research discussions, and hosting education and research computing;
3. Ease of access to meet and work with collaborators in other research units and groups elsewhere on campus.

The types of research space listed above are absolutely critical to the success of this program. Moreover, we believe that meeting these requests for space resources is quite feasible for this campus.

3.2 Integrating space needs in a multi-use building with other programs

The Applied Mathematics group would welcome the opportunity to be co-housed with other theoretical and computational colleagues across campus. For example, the entirety of the Applied Mathematics group is participating in an initiative to establish a research theme called Computational and Data Science. It may be most effective from a campus perspective to house a variety of theoretical and computational faculty, postdoctoral researchers, and graduate students together. In that situation, the Applied Mathematics program personnel will need to be in contiguous office spaces to facilitate the Applied Mathematics Unit’s and Graduate Group’s activities.

3.3 Local research computing resource needs

All Applied Mathematics faculty, students, and postdoctoral researchers require local research computing resources. These research computing resource needs are commensurate with those described in the research theme proposal for Computational and Data Science to which all Applied Mathematics faculty are associated.  Specifically, these research computing resources include on-site hardware, software, and administrative support staff.  For hardware, we will need a few shared small- and medium-scale computing platforms for development and testing of codes and training of students.  Moreover, such local research computing resources are absolutely necessary for performing scale studies which are required for transitioning to large-scale computing platforms.  A sharing strategy will be used to purchase software licenses.  Staff support is needed to provide maintenance to the computing hardware and software, to ensure stability in data storage and backup, and to monitor the security of the campus research computing systems.

4. Comparison programs

There are a few notable programs in applied mathematics nationally, for example, the Departments of Applied Mathematics at University of Washington and University of Colorado at Boulder. Both programs are consistently ranked in the top ten applied math programs in the country, with University of Washington tying for first in 2010.  However, these two programs as well as nearly all other comparable programs co-exist with a traditional pure mathematics program. At UC Merced, we have been developing the Applied Mathematics program alongside the other innovative programs on campus. This co-development of applied mathematical sciences with other programs on campus is a signature for this program and for UC Merced.

All of the other eight regular UC campuses have graduate programs in Mathematics. Nearly all of the Applied Mathematics programs are specializations within their respective Mathematics doctoral programs. A direct comparison of the Applied Mathematics Graduate program at UC Merced with other UC programs is inherently difficult because the structure here is completely different. This difference is not accidental. We have chosen deliberately to position ourselves in a way that emphasizes modeling complex systems, scientific computing and data science. However, many campuses have initiated new graduate programs related to computational science and engineering that align closely with what we are building here at UC Merced.

As a small group within a relatively new campus, we are able to implement curricular changes on a relatively short time scale. This flexibility allows us to implement substantive changes and additions to the curriculum within an academic year's time. By taking advantage of this situation, we are introducing a new emphasis track in Computational and Data Enabled Science for our applied math majors, with four new courses: Introduction to R, Scientific Computing, Numerical Linear Algebra and Cloud Computing. All of these courses are aligned with other academic programs on campus. Thus, they will also serve a broader audience of students in other programs in science and engineering thereby contributing to the campus mission to provide interdisciplinary educational experiences for its students.

5. Contributions to the campus

Mathematics courses train students in the fundamental skills needed to solve problems using analytical reasoning and computational methods. Approximately 2% of undergraduates declare Applied Mathematical Sciences as their major. However, lower-division mathematics courses account for very large number hours taught on campus each academic year largely due to the fact that nearly all the undergraduate students are required to enroll in these courses. For example, the Math 5, 15, and 18 courses almost entirely serve students in other programs. In addition, upper-division and graduate mathematics courses serve a number of other programs such as chemistry, physics and engineering. There are plans in place to expand the course offerings and training programs to include scientific computing, probability, and computational statistics, to name a few.

Individuals who have rigorous training in the subject and use the methods being taught in their own research best achieve effective teaching of mathematics courses. All Applied Mathematics faculty contribute to teaching undergraduate and graduate mathematics courses. Additional Applied Mathematics faculty will add new areas of research expertise, and will provide the means to offer broader and deeper curricula at both the undergraduate and graduate levels. Growing the number of faculty is absolutely crucial for achieving satisfactory student-to-faculty and lecturer-to-ladder-rank faculty ratios associated with these mathematics courses. At present, both ratios are largely off-balance from what we would like to achieve as this campus grows and develops. The proposed growth plan is designed to address the rebalancing of these ratios.

Presently, the Applied Mathematics group must rely heavily on Unit 18 Lecturers for lower-division mathematics instruction. Even with the growth proposed here, this group will continue to need Unit 18 lecturers for instruction, but the proposed growth will reduce the overall ratio of lecturers-to-faculty to be more reasonable. Furthermore, the proposed growth in ladder-rank faculty and Visiting Assistant Professors will lead to more of these faculty teaching lower-division mathematics courses.