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Full-Text Articles in Physical Sciences and Mathematics
Algebraic Complexity Theory, Jerzy Weyman
Algebraic Complexity Theory, Jerzy Weyman
Dalrymple Lecture Series
I will discuss the basic notions related to the complexity theory. The classes of P and NP problems will be defined, with examples given. Besides discussing the statements of the problems, I will talk about the effectiveness of algorithms used in linear algebra (multiplying matrices and solving the systems of linear equations). No previous knowledge of complexity theory will be assumed, however some knowledge of linear algebra (matrices and their multiplication) will be needed.
Primes And Zeros: A Million Dollar Mystery, Brian Conrey
Primes And Zeros: A Million Dollar Mystery, Brian Conrey
Dalrymple Lecture Series
A prime number is an integer greater than one whose only positive divisors are 1 and itself. In 1859 G. F. B. Riemann proposed a way to understand how the prime numbers are distributed among the natural numbers. More than 150 years later mathematicians still have not proven Riemann's Hypothesis. The stature of this problem has continued to rise so that today it is widely regarded as the most important unsolved problem in all of mathematics. In this talk I will describe some of the colorful history that surrounds this question.