A Universal Subject

Mathematics, in a very simple manner if approached means science about truth. However, the decline in its respect amongst the evolving youngsters has different causes. In earlier times, people who tend to study and carry on with Maths were regarded as people with high IQ, so only fewest of the total population would choose to go along with this subject. In the meantime, with the explosion of technology and Artificial Intelligence, this subject secures its rank in every manner, as Mathematics is thought of as the backbone of science. However, current times do not seem to comprehend the need to study Mathematics as a subject, rather it has become a part of engineering courses.

Being a Pure Mathematician, it becomes obligatory for me to contribute to the enhancement of Mathematics as a subject or re-attainment of its position in the academic system. Let’s commence from recognising the fields where Mathematics has played crucial role. The ground for the higher mathematics is set by the concept of Sets, Relations and Functions, Linear Algebra and Modern Algebra. Nonetheless, everyday life demands continuous use of basic mathematics as in terms of budgeting, driving, managing time, exercising, cooking, stitching, trading etc. No such an event that doesn’t require mathematics some or the other way.

Well, we can celebrate this National Mathematics Day by visualising different shades of math beyond classroom. Let’s first consider the concept of relations, which in maths means how the elements of one set are related to the elements of other set. This concept enables us to understand how the students are associated with their grades, another example being the temperature at different times in a day, a particular group of people and their ages and so on. The next very immediate concept being the subset of a relation itself called as function. Function, also being a relation, but the only difference that function generates exactly one output for one input but contrary to that a relation has many outputs for a single input. To see that in real life, we can consider the human appearances, one person with exactly one unique appearance. Moreover, students in a particular classroom with exactly one identification number, aadhar numbers etc.

Next, we study the concept of differentiation which in  layman’s language means the rate of change. To  further see that in real life we can consider a moving car, where we can see the change of distance with respect to time, the rate of change of speed with respect to time, or change of velocity with respect to time and what not. Similarly, we see the rotation of earth with respect to the sun and the rotation of other planets with respect to sun or earth and among themselves as well. Another most important concept is that of matrices which is used in geology for conducting seismic surveys, in computer sciences for programming 3D games etc.

Another prominent application of mathematics (in particular, Number Theory) lies in the field of Cryptography, which involves encryption and decryption of data for security purposes. As by the use of coding and decoding, one can secretly send a message from one place to another without anyone manipulating the same. For example, if we divide english alphabet in two sets, first 13 and later 13. Then  join them by a bijective function, so we can write HELLO by URYYB. So that message goes encrypted. This is a very basic way, we have advanced ways as well. This field itself has got many efficient uses for national or international level of confidential communications or transmission of sensitive information.

Fibonacci series in mathematics, is a sequence of numbers in which each consecutive number is equal to the sum of the two numbers that come before it. For instance, if you start with the number zero, this is what a Fibonacci series would look like: 0, 1, 1, 2, 3, 5, 8, 13, and so on. The Fibonacci series is famously found in nature--trees, flowers, and other naturally occurring spiral structures grow leaves and petals that follow the sequence. It's also particularly useful when it comes to cryptology, the study of codes and how to solve them. With modern technology, the Fibonacci series can be used to encrypt sensitive information over the internet for security purposes.

The toughest field of mathematics so far known is the Topology, which literally means the study of place, or the study of surfaces. In this field of mathematics, we study how we can transform one object into another without any cut-paste, yet one can mould, stretch, crumple, bend or tear the object with the use of proper transformation (preserving the features of the object, mathematically called as homeomorphism. Thus, for a topologist, a coffee mug and donut (also known as torus) are same, as each of these two objects possess a single hole which is preserved during the transformation (homeomorphism). Such things are mathematically termed as topologically equivalent. One more observation, as being a topologist, we believe in two perspectives of looking at a particular object, one is locally and another globally.  Thus, for us, Earth is flat (locally) but round (globally).

Another very eminent concept of mathematics is that of metric spaces, which leads to understand the distance between any two points in a space or a set. This metric being a distance measuring function has got direct application in the field of Biology. Since genotypes-phenotypes are of very primary importance in biology, we see how topology is even useful in sequencing the right nucleotides in DNA strand. Genotypes are the internally veiled and inheritable information of a living being while as phenotypes are the physical appearances of that information. Topology solves one most important problem in DNA research. As we know that DNA is composed of four nucleotides: Adenine, Cytosine, Guanine and Thymine. These are arranged in a manner that they resemble a sequence.

The sequence of nucleotides on every single chain of DNA decides the sequence of the other chain. The problem found in DNA research is in the comparison of distinct DNA sequences. So using the concept of metric spaces (a special type of topological spaces), we measure the distance between two sequences, where the distance function(metric) gives the intuition towards the nature of evolutionary history of species. Let’s consider x and y to be the two sequences of letters A, C, G and T. To calculate the distance between x and y, we fix the number of operations on x to turn it into y. We can apply three operations that is insertion, deletion and replacement for the sequence say P to turn x into y.

In current era, we owe Mathematics a standing ovation  for preserving the logic behinds theories. Let’s not underestimate the contribution of maths to all the fields of science and non-science.

Dr. Mir Aaliya, Mathematics Faculty in Govt. Degree College, Sopore