The aspirants who are good with the logical applications of Mathematics, keep it as a compulsory option. While others who require practice and are not that good with mathematical applications keep it as an optional subject. Thus when you get qualified for an IAS interview, you are asked questions by the interviewer depending on whether you have Mathematics as a compulsory or optional paper. The set of questions are different but the objective is the same- to know how much you understand about Mathematics as a subject. Following are some tricky IAS questions asked in the field of Mathematics-
Your optional subject was Mathematics. Tell me how you will use mathematical knowledge in Governance and Administration?
Answer- Lean how to optimally utilize given resources through linear programming models such as simplex and will utilize in a wide range of governing areas such as health and education. Computing models such as Newton-Raphsons can help us effectively handle inflation, unemployment. They can also help us in how we can better re the benefits of demographic dividend. Integral and calculus can help us to understand the frequency and solve problems of congestion, transportation, and infrastructure bottlenecks. Children face problems in understanding mathematics and I can help departments learn how innovative and exciting learning models can make learning more attractive.
Who is this Manjul Bhargava?
Answer- Manjul Bhargava is a Canadian-American Mathematician of Indian Origin, who got the Fields Medal in 2014. His PhD thesis was the first major contribution to Gauss’ theory of the composition of binary forms for 200 years.
Have you heard of the movie “The man who knew infinity”?
Answer- “The man who knew infinity” is a movie about the life of S.Ramanujan and his time under Prof. G.H.Hardy.
What according to you is the Quality of maths taught in schools?
Answer- Only 40% of class VIII students in government schools can do simple division (ASER report 2018).
In a school in village children of 9th and 10th are afraid of maths, you are asked to give a speech to encourage them as a DM. What will be that speech?
Answer- Maths is like playing cricket. Some would be naturally better than others. But everyone can get better at it by practice. We are afraid of that which we do not understand – like Ghosts or darkness. As we practice more, we will understand more and the fear will go away. Students should pair up based on their complementary strengths. Those who are good at maths can help out those who are bad at it and learn something else in return. And never be afraid to say – I didn’t understand this. If you don’t understand something a second time, meet your teacher personally. You don’t have to be perfect at it. But if today you are better than tomorrow and even better the day after, nothing like it.
How will you explain how geometric and harmonic mean is better than the arithmetic mean? Does arithmetic mean the thorough application of principles?
Answer- There are a lot of situations where numbers don’t add up as sums. Their combined effect works through their product or reciprocals. For eg. If we want to find the average speed of a vehicle going to and fro between two points, we have to take the harmonic mean of the two speeds. Also, the geometric mean is frequently used in development studies and economics as a Compound Annual Growth Rate (CAGR).
Is the universe finite or infinite for a mathematician?
Answer- It is yet an unanswered question. As a mathematician, we can say that the universe is likely to be infinite but bounded. Like a fractal (A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. Fractals can be thought of as never-ending patterns).
How is maths relevant to encryption? Why is Whatsapp’s end-to-end encryption so difficult to crack? Have you heard of the unhackable method of encryption developed by China recently?
Answer- The entire field of cryptography is heavily dependent on mathematics.
Whatsapp: Whatsapp’s end-to-end encryption is hard to crack for the simple reason that it is end-to-end meaning even WhatsApp does not have a key to the encrypted message.
Chinese encryption: In 2017, Chinese scientists made the first ‘unhackable’ call to Vienna. It uses the method of Quantum communications, which sends information embedded in entangled particles of light via satellite. If someone tries to intercept the photons exchanged between the satellite and the ground station and to measure their polarization, the quantum state of the photons will be changed by this measurement attempt. So it is always possible to tell if the information has been intercepted.
Quantum encryption: Quantum encryption doesn’t encrypt user data, but makes it possible for users to securely distribute keys to each other, which can then be used for encrypted communication. Here the key was based on quantum entanglement. Essentially photons from the transmitter are polarised using filters. If an interceptor uses a different filter, then it will change the spin of the photons and thus leave its mark on the key.
Do you know the ASER statistics on maths? Why are kids in primary sections so bad in basic maths?
Answer- Studies have shown that an intuitive sense of numbers is transferred from parents to children. There is a strong correlation between parents who were bad at mathematics and children who are too. Therefore children in primary sections have a wide variation in their development of ‘number sense. Our current system is unable to deal with this variation. Children who need time just end up developing aversion towards the subject. Naturally, they are unable to use these unconventional methods.
With the onset of tablet-based learning, do you think kids can learn maths without the help of a teacher?
Answer- Experience from around the world shows that, over time, teachers’ role becomes more central – and not peripheral- as a result of the introduction of new technologies.
Introducing new technologies will replace some of the things that teachers do and will require teachers to take up newer duties and responsibilities. Nevertheless, teachers who aren’t comfortable with technologies will be replaced by teachers who are.
What is Chaos theory? Can we apply it in administration?
Answer- Chaos theory is an attempt to see and understand the underlying order of complex systems that may appear to be without order at first glance. The main idea is that small differences in the initial state of a system can cause large differences in the future state of the system. This is also termed “nonlinear dynamics”. This is one of the reasons why even the largest computers cannot predict the weather accurately over the medium term. Minor differences in the measurement of the current state of the weather can cause wide variation in the possible weather a few weeks in the future.
Other examples: Stock markets are inherently chaotic. This is one of the reasons why even the brightest minds can sometimes not see an upcoming market crash. Also, no one can predict the market accurately for the same reason.
Similarly, turbulence is a field where chaotic nature seems inherent, causing enormous difficulty to mathematicians in predicting the behavior of the system. Another simple example would be the double pendulum. Its behavior depends on the starting point, and no single equation can predict its motion.
Administration: Chaos theory can deal with uncertainty in a way previously established deterministic mathematics was not able to. This makes chaos theory extremely useful in understanding, modeling, and predicting the behavior of complex organizations and their administration. This is primarily due to the non-linear dynamics of modern organizations including cities and societies.
Therefore if you know the answer to the aforementioned tricky questions in Mathematics, you are sure to pass the interview round with flying colors. Have a logical mindset and an analyzed thought process helps in IAS interviews about Mathematics.