The Mathematical Sciences in the 21st century

In the last day of 2013 it seems appropriate to browse two books published by the National Academies Press – both of them represent reports of an interesting project The Mathematical Sciences in 2025. They can be read online freely (and after a registration a PDF version can be downloaded as well).

I find particularly interesting and informative the first report Fueling Innovation and Discovery:The Mathematical Sciences in the 21st Century

It aims to “describe recent advances in the mathematical sciences and advances enabled by mathematical sciences research” and I believe our students will find many of the topics surprisingly applicable to their day-to-day use of technology. To illustrate this here are the first two paragraphs of the first topic:

In the last two decades, two separate revolutions have brought digital media out of the pre-Internet age. Both revolutions were deeply grounded in the mathematical sciences. One of them is now mature, and you benefit whenever you go to a movie with computer-generated animation. The other revolution has just begun but is already redefining the limits of feasibility in some areas of biological imaging, communication, remote sensing, and other fields of science.

The first could be called the “wavelet revolution.” Wavelets are a mathematical method for isolating the most relevant pieces of information in an image or in a signal of any kind (acoustic, seismic, infrared, etc.). There are coarse wavelets for identifying general features and fine wavelets for identifying particular details. Prior to wavelets, information was represented in long, cumbersome strings of bits that did not distinguish importance.

Some of the other topics discussed in an accessible and highly stimulating manner are: Mathematical simulations/When the lab is not big enough, Bioinformatics/Interpreting the human genome etc.

The second report of the project is The Mathematical Sciences in 2025 and its recommendations “that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences” may soon become quite relevant for our teaching in the IB programme.

Wishing you a prosperous and successful 2014!

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