Applied and Computational Mathematics: A New Curriculum for 21st Century Discovery and Innovation

By Jeffrey Humpherys

The following is a short introduction to an invited lecture to be presented at the upcoming 2018 SIAM Annual Meeting (AN18) in Portland, Ore., from July 9-13.

In recent years, we have seen an unprecedented surge in discovery and innovation — led largely by advances in science and engineering. A central and unifying theme of these breakthroughs is the role of applied and computational mathematics. Our ability to use mathematical abstraction to cast real-world problems into quantitative investigations has led to many crowning achievements.

As the frontier of discovery and innovation continues to progress, our curricula must stay in sync so that students are well-prepared to engage the workforce, thrive in postgraduate research, and compete in a fast-moving global economy. This means that the applied mathematics curriculum must remain aligned with the demands of industry and the broader STEM community.

Brigham Young University’s new and completely redesigned undergraduate Applied and Computational Math Emphasis (ACME) program provides students with a rigorous foundation in mathematics, statistics, and computation. It runs as a two-year, upper-division lockstep curriculum consisting of 32 credit hours distributed evenly over four semesters. In addition, students select an area of specialization from over 25 topics in the pure and applied sciences and take additional coursework, apart from the core curriculum, to fulfill a concentration requirement.

The program’s first year devotes meticulous study to the design, analysis, and optimization of algorithms, and offers students a substantial arsenal of mathematical and statistical tools to make definitive and rigorous statements about the performance, complexity, and accuracy of algorithms. The second year focuses on the art and science of mathematical modeling, which gives students the ability to connect the real world with abstract mathematics and numerical simulation.

In terms of technical education, students become well-versed in numerical analysis, scientific computing, data processing, relational databases, advanced programming concepts, software development, and scientific visualization. These skills are important for today’s scientific workforce, and are sure to be crucial for that of the coming generation. The curriculum also immerses students in several big data and high-performance computing frameworks and technologies.

Although Python is the program’s primary computing platform, students focus on the basic principles of scientific computing and algorithm development in a way that transcends specific languages and technologies. Through computation, they explore many applications of mathematics and statistics and gain a broad collection of interdisciplinary experiences to provide context and stimulate diverse interests.

In addition to a robust mathematical foundation, exposure to applications, and a strong technical education, the ACME program also fosters personal development through close collaboration, coaching, and a soft-skills seminar. These efforts help shape students’ careers by teaching them how to thrive in group settings.

The program’s ultimate goal is to produce a solid and vibrant pipeline of young scholars in the mathematical and computational sciences well-equipped to meet the challenges of a globally competitive scientific workforce. During the 2018 SIAM Annual Meeting, I will present an overview of this program and the content, technical development, outcomes, and insights learned in the five years since its commencement.

Jeffrey Humpherys joined the Department of Mathematics’ faculty at Brigham Young University in 2005. He also serves on the SIAM Education Committee.