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Register a new userMathematical Modeling as a Means to Capacity Building in 21st Century STEM Careers
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Mathematicians have traditionally been a select group of academics that produce high-impact ideas allowing substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have represented a nearly constant rate of approximately 1% of bachelor degrees awarded in the United States. Even within STEM majors, mathematics or statistics only constitute about 6% of undergraduate degrees awarded nationally. However, the need for STEM professionals continues to grow and the list of needed occupational skills rests heavily in foundational concepts of mathematical modeling curricula, where the interplay of measurements, computer simulation and underlying theoretical frameworks takes center stage. It is not viable to expect a majority of these STEM undergraduates would pursue a double-major that includes mathematics. Here we present our solution, some early results of implementation, and a plan for nationwide adoption.
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Data volumes from multiple sky surveys have grown from gigabytes into terabytes during the past decade, and will grow from terabytes into tens (or hundreds) of petabytes in the next decade. This exponential growth of new data both enables and challenges effective astronomical research, requiring new approaches. Thus far, astronomy has tended to address these challenges in an informal and ad hoc manner, with the necessary special expertise being assigned to e-Science or survey science. However, we see an even wider scope and therefore promote a broader vision of this data-driven revolution in astronomical research. For astronomy to effectively cope with and reap the maximum scientific return from existing and future large sky surveys, facilities, and data-producing projects, we need our own information science specialists. We therefore recommend the formal creation, recognition, and support of a major new discipline, which we call Astroinformatics. Astroinformatics includes a set of naturally-related specialties including data organization, data description, astronomical classification taxonomies, astronomical concept ontologies, data mining, machine learning, visualization, and astrostatistics. By virtue of its new stature, we propose that astronomy now needs to integrate Astroinformatics as a formal sub-discipline within agency funding plans, university departments, research programs, graduate training, and undergraduate education. Now is the time for the recognition of Astroinformatics as an essential methodology of astronomical research. The future of astronomy depends on it.
The traditional university science curriculum was designed to train specialists in specific disciplines. However, in universities all over the world, science students are going into increasingly diverse careers and the current model does not fit their needs. Advances in technology also make certain modes of learning obsolete. In the last 10 years, the Faculty of Science of the University of Hong Kong has undertaken major curriculum reforms. A sequence of science foundation courses required of all incoming science students are designed to teach science in an integrated manner, and to emphasize the concepts and utilities, not computational techniques, of mathematics. A number of non-discipline specific common core courses have been developed to broaden students awareness of the relevance of science to society and the interdisciplinary nature of science. By putting the emphasis on the scientific process rather than the outcome, students are taught how to identify, formulate, and solve diverse problems.
The answers to fundamental science questions in astrophysics, ranging from the history of the expansion of the universe to the sizes of nearby stars, hinge on our ability to make precise measurements of diverse astronomical objects. As our knowledge of the underlying physics of objects improves along with advances in detectors and instrumentation, the limits on our capability to extract science from measurements is set, not by our lack of understanding of the nature of these objects, but rather by the most mundane of all issues: the precision with which we can calibrate observations in physical units. We stress the need for a program to improve upon and expand the current networks of spectrophotometrically calibrated stars to provide precise calibration with an accuracy of equal to and better than 1% in the ultraviolet, visible and near-infrared portions of the spectrum, with excellent sky coverage and large dynamic range.
We use the data of tenured and tenure-track faculty at ten public and private math departments of various tiered rankings in the United States, as a case study to demonstrate the statistical and mathematical relationships among several variables, e.g., the number of publications and citations, the rank of professorship and AMS fellow status. At first we do an exploratory data analysis of the math departments. Then various statistical tools, including regression, artificial neural network, and unsupervised learning, are applied and the results obtained from different methods are compared. We conclude that with more advanced models, it may be possible to design an automatic promotion algorithm that has the potential to be fairer, more efficient and more consistent than human approach.
Modern astronomy has been rapidly increasing our ability to see deeper into the universe, acquiring enormous samples of cosmic populations. Gaining astrophysical insights from these datasets requires a wide range of sophisticated statistical and machine learning methods. Long-standing problems in cosmology include characterization of galaxy clustering and estimation of galaxy distances from photometric colors. Bayesian inference, central to linking astronomical data to nonlinear astrophysical models, addresses problems in solar physics, properties of star clusters, and exoplanet systems. Likelihood-free methods are growing in importance. Detection of faint signals in complicated noise is needed to find periodic behaviors in stars and detect explosive gravitational wave events. Open issues concern treatment of heteroscedastic measurement errors and understanding probability distributions characterizing astrophysical systems. The field of astrostatistics needs increased collaboration with statisticians in the design and analysis stages of research projects, and to jointly develop new statistical methodologies. Together, they will draw more astrophysical insights into astronomical populations and the cosmos itself.
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