November 18, 2017 – 11:34 am
**Reference:**

**Geometric Inequalities, Vol 12, Mathematical Olympiad Series, Gangsong Leng, translated by Yongming Liu, East China Normal University Press, World Scientific.**

“God is always doing geometry”, said Plato. But, the deep investigation and extensive attention to geometric inequalities as an independent field is a matter of modern times.

Many geometric inequalities are not only typical examples of mathematical beauty but also tools for applications as well. The well known Brunn-Minkowski’s inequality is such an example. “It is like a large octopus, whose tentacles stretches out into almost every field of mathematics. It has not only relation with advanced mathematics such as the Hodge index theorem in algebraic geometry, but also plays an important role in applied subjects such as stereology, statistical mechanics and information theory.”

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Amazon India link:

November 18, 2017 – 11:21 am
http://www.ams.org/news?news_id=3821

*Cheers to Prof. Christiane Rousseau and her team !*

November 5, 2017 – 5:36 pm
October 22, 2017 – 12:08 am
October 15, 2017 – 11:57 pm
October 15, 2017 – 11:54 pm
September 18, 2017 – 1:02 am
In the following problems, each year is assumed to be consisting of 365 days (no leap year):

- What is the least number of people in a room such that it is more likely than not that at least two people will share the same birthday?
- You are in a conference. What is the least number of people in the conference (besides you) such that it is more likely than not that there is at least another person having the same birthday as yours?
- A theatre owner announces that the first person in the queue having the same birthday as the one who has already purchased a ticket will be given a free entry. Where (which position in the queue) should one stand to maximize the chance of earning a free entry?

*I will put up the solutions on this blog tomorrow. First, you need to make a whole-hearted attempt.*

Nalin Pithwa.

April 29, 2017 – 11:51 pm
Applications of math are everywhere…anywhere we see, use, test/taste, touch, etc…

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

- Crystallography
- 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.
- Medicine: MRI, cancer detection, Tomography,etc.
- Image processing: JPEG2000; Digital enhancement etc.
- Regulating traffic: use of probability theory and queuing theory
- Improving performance in sports
- Betting and bidding; including spectrum auction using John Nash’s game theory.
- Robotics
- Space Exploration
- 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.
- DNA Analysis
- Exploring oceans (example, with unmanned underwater vehicles)
- Packing (physical and electronic)
- Aircraft designing
- Pattern identification
- Weather forecasting.
- GPS also uses math. It uses physics also. Perhaps, just to satisfy your curiosity, GPS uses special relativity.
- 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.)
- Architecture, of course, uses geometry. For example, Golden ratio.
- Analyzing fluid flows.
- Designing contact lenses for the eyes. Including coloured contact lenses to enhance beauty or for fashion.
- Artificial Intelligence and Machine Intelligence.
- Internet Security.
- Astronomy, of course. Who can ever forget this?Â
*Get yourself a nice telescope and get hooked. You can also Stellarium.org freeware to learn to identify stars and planets, and constellations.*
- Analyzing chaos and fractals: the classic movie “Jurassic Park” was based on fractal geometry. The dino’s were, of course, simulations!
- Forensics
- Combinatorial optimization; the travelling salesman problem.
- 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 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.

“maths: make your career count”

AMSI (Australian Mathematical Sciences Institute) and ICE-EM have done a commendable job …to motivate all high students interested in various careers to excel in maths also:

Have a look at the following, for example:

http://mathscareers.org.au/index.php?option=com_content&view=article&id=19&Itemid=19

*Cheers to maths!*

Nalin Pithwa.