Mathematics – The Subject of Mathematics
Mathematics is more than numbers and geometric figures, it is a logical science that deals with structure, space, quantity, and change. Mathematicians study the relationships between these concepts.
Mathematics is classified as a structural science and works on theories that it creates. A theory is a system of statements about an object. Mathematics takes the relationships between objects and generates a structure called a theorem.
A theorem, while derived from basic statements or axioms that are taken to be self-evidently true, can only be proved by making further assumptions. The power of its theorems gives mathematics its importance. If a question is able be described mathematically, then it can also be solved mathematically.
Process of abstraction
Mathematics allows abstraction and disengagement from concrete objects, while still providing for retranslation into everyday situations. For example, through observation the average number of times that a certain number would be rolled on a die with every sixth throw can be determined. To save time, mathematics can be used to determine the chances of rolling say a “six” without even having to throw the dice.
Fields of application
Mathematics is composed of many different branches, some of which may overlap. Mathematicians segregate into two groups, pure mathematics and applied mathematics. These divisions are based more on what their goals are than what branch of mathematics they study. Pure mathematicians study mathematics in an abstract form, with little thought given to practical application.
Applied mathematics, as the name implies, focuses on the ability to apply mathematical knowledge to solve real problems. The major branches of mathematics include number theory, topology (an extension of geometry), numerical analysis, and discrete mathematics (dealing with finite countable structures), along with the disciplines normally taught in school, such as algebra and geometry.
Numerical analysis and discrete mathematics are new fields of study that were developed in the 20th century with practical applications to sciences, business, and other domains in mind.
FIBONACCI NUMBERS
Leonardo da Pisa, also known as Fibonacci, was an arithmetician in Pisa and is considered the most influential mathematician of the Middle Ages. With his greatest work Liber Abaci he introduced Europe to Indian arithmetics and the Arabic number system we use today. In modern mathematics, his name is associated with a series of numbers. Attention was drawn to this series due to the famous rabbit problem, which was described in Liber Abaci.
The number series begins with zero and one and each of the following numbers is the sum of the two previous Fibonacci numbers. Amazingly this number series reemerges in many other areas, for example the so-called golden section, Pascal’s triangle, and the spiral-shaped alignment of leaves or seeds in many plants.
BASICS
AXIOMS are elementary statements that do not require any proof.
AN AXIOMATIC SYSTEM is a set of noncontradictory theorems of a mathematical theory.
MATHEMATICAL FACTS are derived from axioms, such as seen in classic geometry.