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Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Honors Scholar Theses
Finite fields, and the polynomial rings over them, have many neat algebraic properties and identities that are very convenient to work with. In this paper we will start by exploring said properties with the goal in mind of being able to use said properties to efficiently irreducibly factorize polynomials over these fields, an important action in the fields of discrete mathematics and computer science. Necessarily, we must also introduce the concept of an algorithm’s speed as well as particularly speeds of basic modular and integral arithmetic opera- tions. Outlining these concepts will have laid the groundwork for us to introduce …
Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.
Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.
Mr. Mohd Rezuan Masran
There are numerous verses in the Quran that encourage Muslims to observe the many creations of Allah. This article is an exploratory discuss ion on the observation of a sequence of numbers known as the Fibonacci sequence (also known as the Fibonacci numbers ) which can be observed in the creations of Allah. The history of Fibonacci sequence dated back to 1202 in the magnum opus of the Italian mathematician, Leonardo Pisano Fibonacci, entitled Liber Abaci ( Book of Calculation ). This article discusses verses in the Quran that encourage us to observe Allah’s creations. T here are many occurrences …
A Frobenius Question Related To Actions On Curves In Characteristic P, Darren B. Glass
A Frobenius Question Related To Actions On Curves In Characteristic P, Darren B. Glass
Math Faculty Publications
We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases.