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Number Theory Essay Assignment Help

Order ID53563633773 TypeEssay Writer LevelMasters StyleAPA Sources/References4 Perfect Number of Pages to Order5-10 Pages

Description/Paper InstructionsNumber Theory Essay Assignment Help

NUMBER THEORY 2

NUMBER THEORY 2

Number Theory

Joshua Sears

The Heart of Mathematics

MAT-135

November 10, 2019

Running head: NUMBER THEORY 2

Number Theory

The research topic that I have selected to do my research paper on is The Number Theory, also sometimes referred to as “higher arithmetic”. I chose this topic because I feel as it will help me establish a baseline in understanding how the different applications work.

Numbers have been the forefront of the mathematical world since the beginning of time. As Carl Gauss once described the Number Theory as “Queen of Mathematics” (Najera, n.d., p. 1). The origin of this theory dates back to B.C. times to a mathematician by the name of Euclid of Alexandria, also known as the “Father of Geometry” who put forth one of the oldest algorithms known as The Greatest Common Divisor (Najera, n.d., p. 1) which begins the journey of The Number Theory. To elaborate, what this is saying is that two lengths (a) and (b) is the greatest length (g) that measures a and b evenly while alternatively, both a and b are both integer multiples of the length g. Say you wanted to redo your floor in your house, and the room you wanted to do measured 15 feet by 18 feet. You would want to buy the product in the same size that is large enough to go into both integers in the same length and size. If you put these into fraction form, you see that 3 will go into both 15 and 18 equally, allowing you to only have to buy one size and not over ordering.

Two thousand years later a bright, young new mathematician brings us a new theory that utilizes the number theory. The Fundamental Theorem of Arithmetic was born by the name of Carl Gauss. This new theory states “any integer greater than 1 is either a prime, or can be written as a unique product of prime numbers (ignoring the older) (Najera, n.d., p. 3)”. What this is saying is that prime numbers are essentially the building blocks of integers, that it is like a guarantee that anything greater than 1 is prime or can be made a prime and there is only 1 way to do that in each case. For example, you can make 42 by only utilizing prime numbers as such: 2x3x7=42. As for ignoring the order, look at it like this, 2×11=22, where as 11×2=22. Regardless of the order we put it, we still ended up with the same outcome.

Today, in our modern technological world, the way that the number theory is used is by cryptography. Cryptography is the process of transferring information securely, in a way that no unwanted third party will be able to understand the message, essentially being crack proof. The way the number theory plays into this is that in some cryptologic systems, encryption is accomplished by choosing certain prime numbers and then products of those prime numbers as the basis for further mathematical operations (“Applications of Number Theory in Cryptography,” 2019, p. 3). During WWII, allied forces gained crucial strategic and tactical advantages by being able to intercept cryptical data (“Applications of Number Theory in Cryptography,” 2019, p. 4).

References

Applications of Number Theory in Cryptography. (2019). Retrieved from https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/applications-number-theory-cryptography

Najera, J. (n.d.). Number Theory — History & Overview. Retrieved from https://towardsdatascience.com/number-theory-history-overview-8cd0c40d0f01

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