Pure and applied Mathematics – Applied Mathematics
Although the fields of pure and applied mathematics overlap, the latter can be said to be most occupied with the solutions to problems and application of methods, in concert with other sciences such as physics or economics.
Due to its analytical properties mathematics can be used as a tool in various fields. Several sub areas and disciplines have also emerged on the basis of mathematical theories or methods.
Mathematics in the insurance industry
Insurances are based on the principle of taking on a communal risk where several insurance holders pay a monetary sum to ensure coverage of a random or relatively unlikely cash requirement. To make sure that the total sum of money paid by all members will be sufficient, the contribution required by each policy holder can be estimated by statistically analyzing the extent of damages.
Here statistics and probability theory play an important role. Lets assume that a corporation decides to pay out the following amounts for a new three dice game: three dollars for one six, six dollars for two sixes, and ten dollars for three sixes.
The money at stake is two dollars. In this case, the random value is the average net gain of a player and the question of whether the stake value covers payout. The average frequency of paid combinations appearing and the expected net gain (E(G)) can be calculated using probability theory. The net gain depends on the number of sixes and is negative two, one, four, or eight dollars and the formula of the expected value coupling the probability with the corresponding net gain is: E(G) = -2-125/216 + 1-75/216 + 4-15/216 + 8-1/216 = -0.51.
As a result, the player loses on average $0.51. This is how an insurance company can, for example, calculate the premium for a life insurance plan. However, calculating the probability of death or fire is much more complicated due to the many factors that it depends on.
Cryptology
Information protection is becoming more and more important during the modern times of global networking. Personal data, company data, and military and strategic information must have limited access only. Cryptology deals with technical processes required to limit data access. This subject area developed when secret messages needed to be protected from the enemy.
Some cryptographic procedures were already used by the Egyptians. Today’s cryptology has many applications, for example, data encryption, user identification for computer systems and digital banking. These applications are based on mathematical theories such as algebra, numeric theory, and probability theory.
THE NOBEL PRIZE FOR A MATHEMATICIAN
The American John Forbes Nash (born in 1928) is one of the few mathematicians who has been awarded the Nobel Prize. After he completed his studies and several outstanding works in game theory, differential calculus, and partial differential equations, he was nominated for the Fields Medal At the end of the 1950s, he was diagnosed with paranoid schizophrenia.
It took him 30 years to manage his disease and, finally, he was able to return to mathematics. In 1994 he and two other mathematicians studying game theory were awarded the Nobel Prize for economics. In 2001 his story was released as a movie called A Beautiful Mind.