Mathematics of computation

Mathematics of Computation

For each prime p, let p# be the product of the primes less than or equal to p. We have greatly extended the range for which the primality of n!± 1 and p#± 1 are known and have found two new primes of the first form (6380! + 1, 6917!− 1) and one of the second (42209# + 1). We supply heuristic estimates on the expected number of such primes and compare these estimates to the number actually found.

Randomness, Computation and Mathematics

This article examines some of the recent advances in our understanding of algorithmic randomness. It also discusses connections with various areas of mathematics, computer science and other areas of science. Some questions and speculations will be discussed.

The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...

School of Mathematics Spring 2018 QUANTUM COMPUTATION

the principle of relativity: from ungar’s gyrolanguage for physics to weaving computation in mathematics

this paper extends the scope of algebraic computation based on a non standard × to the more basic case of a non standard +, where standard means associative and commutative. two physically meaningful examples of a non standard + are provided by the observation of motion in special relativity, from either outside (3d) or inside (2d or more), we revisit the “gyro”-theory of ungar to present the m...