Computational Number Theory ?

In summary, Computational Number Theory is a branch of mathematics that uses computational tools and techniques to study the properties of numbers, particularly integers, and their relationships with one another. It has many practical applications in fields such as cryptography, data encryption, and prime number generation. It differs from traditional Number Theory by using computers and computational methods to solve problems and prove theorems. Common computational tools used in this field include factoring algorithms, prime number finding algorithms, and computer programming languages like Python and Mathematica. However, there are challenges in efficiently computing large numbers and developing algorithms for complex problems in Computational Number Theory.
  • #1
Moni
181
1
Computational Number Theory ?!?

I am a student of Computer Science and found many good algorithms on Number Theory while working...

But actually...honestly speaking...I don't find good sites on this particular important field...:frown:

Or even new works or research... what do you think ?
 
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  • #2
have you tried mathforum.org they have good links to website about most of the branches of mathematics.
 
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Computational Number Theory is a fascinating and important field that combines the principles of number theory with the power of computation. It involves the study of algorithms and methods for solving problems related to prime numbers, factorization, cryptography, and many other areas of number theory. As a student of Computer Science, I can understand your frustration in finding good resources on this topic. However, there are many great sites and research papers available that delve into the depths of computational number theory.

Some popular sites for computational number theory include MathWorld, Number Theory Web, and the Online Encyclopedia of Integer Sequences. These sites offer a wealth of information on different algorithms, theories, and applications of number theory in computation.

As for new works and research in this field, there is a lot of ongoing research happening in computational number theory. Many universities and research institutes have dedicated teams working on this topic, constantly developing new algorithms and methods to solve complex problems. You can also find numerous research papers published in journals and conferences that cover the latest advancements in this field.

In conclusion, computational number theory is a constantly evolving field with a lot of potential for further research. With the increasing use of technology in modern society, the importance of this field will only continue to grow. So, keep exploring and learning about this fascinating topic, and who knows, maybe you'll be the one to make groundbreaking discoveries in computational number theory!
 

1. What is Computational Number Theory?

Computational Number Theory is a branch of mathematics that uses computational tools and techniques to study the properties of numbers, particularly integers, and their relationships with one another. It involves using algorithms, computer programming, and other computational methods to solve problems and prove theorems in number theory.

2. What are some applications of Computational Number Theory?

Computational Number Theory has many practical applications, including cryptography, data encryption, error-correcting codes, and prime number generation. It also has applications in other fields such as physics, engineering, and computer science.

3. How is Computational Number Theory different from traditional Number Theory?

Traditional Number Theory focuses on studying the properties of numbers and proving mathematical theorems using pen and paper. Computational Number Theory, on the other hand, uses computers and computational methods to solve problems and prove theorems. It allows for the study of larger numbers and more complex problems that would be difficult or impossible to solve by hand.

4. What are some common computational tools used in Computational Number Theory?

Some common computational tools used in Computational Number Theory include algorithms for factoring large integers, algorithms for finding prime numbers, and algorithms for solving Diophantine equations. Other tools include computer programming languages such as Python and Mathematica, as well as specialized software designed for number theory calculations.

5. What are some challenges in Computational Number Theory?

One of the main challenges in Computational Number Theory is the efficient computation of large numbers. Many problems in number theory involve extremely large numbers, which can be difficult and time-consuming to compute. Another challenge is the development of efficient algorithms for solving complex problems, as well as the analysis and verification of the results obtained from these algorithms.

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