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What is Number Theory?

Number theory is a field of pure mathematics and is considered to be one of the oldest still relevant and in use today. It is generally related to the properties of whole numbers and rational numbers but more specifically focuses on integers. Number theory asks questions about and derives theories regarding the divisibility and multiplicity of numbers.

This then gives rise to a wider class of studies. In the past the words arithmetic and higher arithmetic were used to describe this study but today the term number theory is most commonly used.

The study is further subdivided into branches including elementary number theory, analytic number theory, algebraic number theory, geometry of numbers, combinatorial number theory, computational number theory, arithmetic algebraic geometry, arithmetic topology, arithmetic dynamics and modular forms. Number theory was referred to by Gauss as the queen of mathematics. When referring to number theory Pythagoras stated that number is the within of all things.

Why study Number Theory?

Number theory is increasingly finding its place in the world of information technology. Most specifically it is used for the generation of random numbers and for coding. Therefore those seeking a career in advanced computer science should consider studying Number Theory. Number theory also has a very important role to play in cryptology and sheds light on many of the principles applied in physics and chemistry.

Should you wish to be a bio-physicist or bio-chemist, the study of number theory would be important. The applications of number theory actually extend well beyond basic mathematical fields. It is used in quantum physics, which is in turn used to explain phenomena in our universe and also predict new ones. Even the basic principles of mechanics, engineering and electricity relate to quantum physics and, consequently, number theory. Fundamental applications of number theory are also used in graphic and acoustic design. For example one would rely heavily on number theory when designing an acoustically perfect concert hall.