Question

would you tell me some list of topic that is not mathematics but can be discussed how mathematics can be used to understand?

something like egnima or turing machine, the golden ratio

Answer 1

Answer:) What I understand from the question is we need a set of topics that are not essentially in the purview of mathematics as a field, but can be understood better if we use mathematics as a diagnostic tool. There are several such problems :

1.) Population growth : the logistic model is a model that describe how a given population (of people, bacteria etc.) grows when there is a creation mechanism (birth, cell division etc.) as well as scarce resources. The logistic equation is given as :

Here, the left hand side is the rate of growth of population P with time t, the right hand side contains two terms :

• signifies the the relative growth of the population, which is faster if there is more people to begin with and hence it is proportional to P
• is a term that signifies a negative growth term, which is due to the finite amount of resources in the environment of the population. As this term is proportional to , as P increases, the growth rate goes down and finally a stable population is reached, which is given by K.

2.) Cryptography : cryptography is a field which studies the creation and deciphering of codes. Majorly, cryptography involves using a cipher and a key, which are used to encode and decode a certain piece of information respectively. For the encryption to be hard to decrypt, modern day cryptography uses tools from Number Theory, a mathematical field concerned with the study of numbers, for getting the encryption algorithms. These algorithms make encryption easy, but decryption very hard, thus ensuring a safe communication between two parties.

3.) Social Networks and Epidemic research : Social networks are networks of people with similar interests, hobbies or day-to-day activities. Every person can be thought of having a social network of their own, which can be said to be true for any other person, and so this sets up a wide network of interconnected individuals. Studying the diversity and connectivity of such social networks gives important implications on the spread rate and effective methodologies for curbing the spread of epidemics. This is enabled by the use of graph theory, a field of mathematics which uses connected graphs to analyse the interrelations (drawn as edges) between different objects (drawn as nodes).