Computers in Number Theory

Random Number Generators for Parallel Computers

Random number generators are used in many applications, from slot machines to simulations of nuclear reactors. For many computational science applications, such as Monte Carlo simulation, it is crucial that the generators have good randomness properties. This is particularly true for large-scale simulations done on high-performance parallel computers. Good random number generators are hard to f...

Algorithms in Number Theory

Number Theory in Geometry

The topic of my talk is number theory in geometry. I will say a few words about history of mathematics to show how geometry has played an important role in the development of mathematics. I will also mention some contributions of Indian Mathematicians of antiquity since these are not widely known. Humans, and apparently some animals too, can and need to count. We count discrete objects, such as...

Undecidability in number theory

D oes the equation x + y + z = 29 have a solution in integers? Yes: (3,1,1), for instance. How about the equation x + y + z = 30? Again yes, although this was not known until 1999: the smallest solution is (−283059965,−2218888517, 2220422932). And how about x + y + z = 33? This is an unsolved problem. Of course, number theory does not end with the study of cubic equations in three variables: on...

Undecidability in number theory