Traditionally, a typical undergraduate student enrolled in a hydrology and atmospheric science major will take about six required mathematics and computing courses. This approach treats calculus, linear algebra, statistics, differential equations, and computer programming as isolated subjects. These subjects are taught to hydrology and atmospheric sciences students in the same way as to students in mechanical engineering and computer science, thus not providing useful tools and examples explicitly designed for hydrology and atmospheric sciences. The students are not taught how mathematics is used in solving actual hydrology and atmospheric science problems. Their major professors may be disappointed by the students’ weak mathematics backgrounds. The students in turn may be frustrated by having learned inappropriate and abstract mathematics taught by teachers who are unfamiliar with hydrology and atmospheric sciences. Is this now the right time to make a fundamental change in this teaching methodology? In other words, can we modernize mathematics education for hydrology and atmospheric sciences? You may have answers to this question. We suggest a specific modernization approach, replacing the six traditional courses by an integrated climate mathematics curriculum including real-world problems and data. Climate mathematics includes modern methods valuable in research and practice, such as singular value decomposition and empirical orthogonal functions. At the same time, we advocate eliminating many traditional and non-useful methods, e.g., convergence tests of infinite series and integration techniques for difficult functions. We can make these changes because of the availability of powerful computing resources and the popularity of R and Python programming. To emphasize the usefulness of this new approach to mathematics education, we illustrate all the most important mathematical and computing topics using examples and data from atmospheric science and related applications. We also provide specific suggestions for both students and faculty to help advance the modernization process.
Dr. Samuel S. P. Shen is Distinguished Professor of Mathematics and Statistics at San Diego State University, and Visiting Research Mathematician at Scripps Institution of Oceanography, University of California, San Diego. Formerly, he was McCalla Professor of Mathematical and Statistical Sciences at the University of Alberta, Canada, and President of the Canadian Applied and Industrial Mathematics Society. He has held visiting positions at the NASA Goddard Space Flight Center, the NOAA Climate Prediction Center, and the University of Tokyo. Shen holds a B.Sc. degree in Engineering Mechanics from Nanjing University of Science and Technology, and M.A. and Ph.D. degrees in Applied Mathematics from the University of Wisconsin–Madison.
Dr. Richard C. J. Somerville is Distinguished Professor Emeritus of Atmospheric and Climate Science at Scripps Institution of Oceanography, University of California, San Diego. He is a fellow of three scientific societies: the American Association for the Advancement of Science (AAAS), the American Geophysical Union (AGU), and the American Meteorological Society (AMS). He has received awards from the AMS for his research and his popular book, The Forgiving Air: Understanding Environmental Change. From the AGU, he has received two major honors, the Climate Communication Prize and the Ambassador Award. Somerville holds a B.S. degree in Meteorology from Pennsylvania State University and a Ph.D. degree in Meteorology from New York University.