Category Archives: applications of maths

Birthday Probability Problems: IITJEE Advanced Mathematics

In the following problems, each year is assumed to be consisting of 365 days (no leap year):

  1. 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?
  2. 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?
  3. 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.

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.

Use of mathematics by a financial analyst

“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.

Movie Magic: The Mathematics Behind Hollywood’s Visual Effects

Distinguished Lecture Series: The Mathematical Association of America

Mathematics that Swings: The Math Behind Golf

Mathematics that Swings: the Math Behind Golf, by Douglas N. Arnold, Professor of Mathematics, University of Minnesota: 

The Mathematical Association of America, Distinguished Lecture Series:

Math is everywhere. Some time back, I had written smallish blog article(s) on stuff like math in our taste buds, math in hearing, etc. If you aspire to become an ace pure or applied mathematician, or even a very good engineer, it helps to see math (and/or physics) everywhere; this will help you to “churn”. Some body had asked Newton the secret behind his success, Newton had said:” I constantly keep the subject before me, and wait till the dawnings emerge into a full and clear light.” Gauss, had also, said, “I just think constantly about math.”

Thanks to Dr. Douglas N. Arnold, and of course, the Mathematical Association of America.

Nalin Pithwa.

Huygen’s Clock

Ref: Calculus and Analytic Geometry, G B Thomas and Finney, 9th edition.

The problem with a pendulum clock whose bob swings in a circular arc is that the frequency of the swing depends on the amplitude of the spring. The wider the swing, the longer it takes the bob to return to centre.

This does not happen if the bob can be made to swing in a cycloid. In 1673, Chritiaan Huygens (1629-1695), the Dutch mathematician, physicist and astronomer who discovered the rings of Saturn, driven by a need to make accurate determinations of longitude at sea, designed a pendulum clock whose bob would swing in a cycloid. He  hung the bob from a fine wire constrained by guards that caused it to draw up as it swung away from the centre. How were the guards shaped? They were cycloids, too.

Aufwiedersehen,

Nalin Pithwa.

Are kids no longer learning multiplication tables in school?

This topic is very close to my heart and head. I had written a remark about this in an earlier blog article. 

Today, I suddenly found some “echoes” or “resemblances” to my views. Kindly let me re-blog, or share the opinions about this from today’s EETimes, authored by Max Maxfield, Designline Editor. The URL is pasted below:

http://www.eetimes.com/author.asp?section_id=216&doc_id=1331382&

Thanks Max and EETimes !

From Nalin Pithwa.

Mathematics that we can taste, touch, see, smell, and hear !!

In some blog article earlier, I had claimed that we can see, taste, touch, smell, and hear mathematics every where around us! Well, to be precise, I had explained that ‘sweetness’ or ‘sourness’ of what we eat or drink can be measured with the pH value, which uses the tool of common logarithms !

Now, we all love mp3 music. It uses a special algorithm to measure the sensitivity of the human ear to various frequencies and intensities. It masks out certain pieces of the sound or music signal (called information signal, in the language of engineering) and thus achieves “compression” of the music signal. So, the creators of the mp3 algorithm actually created a mathematical model of the human ear.

And, of course, the loudness of sound is measured in terms of decibels, which is again a logarithmic quantity.

Architects use “golden ratio” to create a majestic structure that we can see/marvel at. This golden ratio is a special number.

The pain that human skin/body feels is measured in terms of “bols”. ( Go ahead and google this term).

And, of course, smell, obnoxious or aromatic, is measured in terms of the concentration of special molecules in the immediate vicinity.

Nature also loves math! Do you know that the spirals of a daisy flower are arranged like Fibonacci numbers/sequences?

More on each of these topics later,

Nalin Pithwa