## The power of the unseen, the abstract: applications of mathematics

Applications of math are everywhere…anywhere we see, use, test/taste, touch, etc…

I have made a quick compilation of some such examples below:

1. Crystallography
2. Coding Theory (Error Correction) (the stuff like Hamming codes, parity check codes; used in 3G, 4G etc.) Used in data storage also. Bar codes, QR codes, etc.
3. Medicine: MRI, cancer detection, Tomography,etc.
4. Image processing: JPEG2000; Digital enhancement etc.
5. Regulating traffic: use of probability theory and queuing theory
6. Improving performance in sports
7. Betting and bidding; including spectrum auction using John Nash’s game theory.
8. Robotics
9. Space Exploration
10. Wireless communications including cellular telephony. (You can Google search this; for example, Fourier Series is used in Digital Signal Processing (DSP). Even some concepts of convergence of a series are necessary!) Actually, this is a digital communications systems and each component of this requires heavy use of mathematical machinery: as the information bearing signal is passed from source to sink, it under goes several steps one-by-one: like Source Coding, encryption (like AES, or RSA or ECC), Error Control Coding and Modulation/Transmission via physical channel. On the receiver or sink side, the “opposite” steps are carried out. This is generally taught in Electrical Engineering. You can Google search these things.
11. DNA Analysis
12. Exploring oceans (example, with unmanned underwater vehicles)
13. Packing (physical and electronic)
14. Aircraft designing
15. Pattern identification
16. Weather forecasting.
17. GPS also uses math. It uses physics also. Perhaps, just to satisfy your curiosity, GPS uses special relativity.
18. Computer Networks: of course, they use Queuing theory. Long back, the TCP/IP slow start algorithm was designed and developed by van Jacobson.(You can Google search all this — but the stuff is arcande right now due to your current education level.)
19. Architecture, of course, uses geometry. For example, Golden ratio.
20. Analyzing fluid flows.
21. Designing contact lenses for the eyes. Including coloured contact lenses to enhance beauty or for fashion.
22. Artificial Intelligence and Machine Intelligence.
23. Internet Security.
24. Astronomy, of course. Who can ever forget this? Get yourself a nice telescope and get hooked. You can also Stellarium.org freeware to learn to identify stars and planets, and constellations.
25. Analyzing chaos and fractals: the classic movie “Jurassic Park” was based on fractal geometry. The dino’s were, of course, simulations!
26. Forensics
27. Combinatorial optimization; the travelling salesman problem.
28. Computational Biology

We will try to look at bit deeper into these applications in later blogs. And, yes, before I forget “Ramanujan’s algorithm to compute $\pi$ up to a million digits is used to test the efficacy and efficiency of supercomputers. Of course, there will be other testing procedures also, for testing supercomputers.

There will be several more. Kindly share your views.

-Nalin Pithwa.