NumberFields@Home: Difference between revisions

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Fields are important mathematical constructs that have far reaching applications to many branches of mathematics. Many people are familiar with the fields of rational numbers, real numbers, and complex numbers. The fields we are concerned with in this project are number fields: subsets of the complex numbers which contain the root of a given polynomial and are minimal for then being closed under addition, subtraction, multiplication, and division (except for division by 0). In particular, we are interested in imprimitive degree 10 fields (called decic fields), which correspond to certain degree 10 polynomials.

Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields. Ultimately, this research will lead to a deeper understanding of the properties of numbers, the basic building blocks of all mathematics. Another application of number fields is in [[wikipedia:Cryptography|cryptography]], where they are used in sophisticated factoring algorithms and as the basis for new cryptosystems. There are also distant applications to mathematical physics, including [[wikipedia:Quantum_mechanics|'''''quantum mechanics''''']] and [[wikipedia:String_theory|'''''string theory''''']].

Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields. Ultimately, this research will lead to a deeper understanding of the properties of numbers, the basic building blocks of all mathematics. Another application of number fields is in [[wikipedia:Cryptography|'''''cryptography''''']], where they are used in sophisticated factoring algorithms and as the basis for new cryptosystems. There are also distant applications to mathematical physics, including [[wikipedia:Quantum_mechanics|'''''quantum mechanics''''']] and [[wikipedia:String_theory|'''''string theory''''']].

== Goals ==

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 Fields are important mathematical constructs that have far reaching applications to many branches of mathematics. Many people are familiar with the fields of rational numbers, real numbers, and complex numbers. The fields we are concerned with in this project are number fields: subsets of the complex numbers which contain the root of a given polynomial and are minimal for then being closed under addition, subtraction, multiplication, and division (except for division by 0). In particular, we are interested in imprimitive degree 10 fields (called decic fields), which correspond to certain degree 10 polynomials.
-Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields. Ultimately, this research will lead to a deeper understanding of the properties of numbers, the basic building blocks of all mathematics. Another application of number fields is in [[wikipedia:Cryptography|cryptography]], where they are used in sophisticated factoring algorithms and as the basis for new cryptosystems. There are also distant applications to mathematical physics, including [[wikipedia:Quantum_mechanics|'''''quantum mechanics''''']] and [[wikipedia:String_theory|'''''string theory''''']].
+Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields. Ultimately, this research will lead to a deeper understanding of the properties of numbers, the basic building blocks of all mathematics. Another application of number fields is in [[wikipedia:Cryptography|'''''cryptography''''']], where they are used in sophisticated factoring algorithms and as the basis for new cryptosystems. There are also distant applications to mathematical physics, including [[wikipedia:Quantum_mechanics|'''''quantum mechanics''''']] and [[wikipedia:String_theory|'''''string theory''''']].
 == Goals ==