MAS 7215Analytic Number Theory - I - MWF 6th period (12:50-1:40pm)Section 1A35 - LIT 223 FAll 2012
INSTRUCTOR:
304 Little Hall 392-0281 extn 227 email: alladik@ufl.edu
HOME-PAGE FOR THIS COURSE:http://www.math.ufl.edu/~alladik/gradnumthy/fall2012/index.html
OFFICE HOURS:M and W 7th period (1:55 - 2:45 pm) in LIT 304 and by appointment.
PREREQUISITES:Undergraduate course in number theory and a course in complex variable theory
COURSE DESCRIPTION:The study of prime numbers which goes back to the golden age of Greece, continues to be an active area of investigation today with a number of deceptively simple looking but very hard problems remaining open. The course will begin with a discussion of various estimates for sums and counting functions involving prime numbers and arithmetical functions. This will serve as a motivation for the Prime Number Theorem conjectured by Gauss and Legendre. It was Riemann who first realized in the mid-nineteenth century that the properties of the zeta function as a function of the complex variable will provide information about the distribution of primes. The Prime Number Theorem was proved towards the end of the nineteenth century simultaneously and independently by Hadamard and de la vallee Poussin using the theory of functions of a complex variable and the zeta function. We shall give this proof which was one of the crowning achievements of the nineteenth century. From then on, great strides have been made in analytic number theory and we shall discuss some important problems. Since this is the 125-th birth anniversary of the Indian mathematical genius Srinivasa Ramanujan, we shall give an introduction to Probabilistic Number Theory whose origins can be traced to a fundamental 1917 paper of Hardy and Ramanujan on the normal number of prime factors of integers.There will be no assigned text. I will use my own notes and give several books as references.
TEXT:No assigned text. I will use my own notes. A number of texts will be given as references.GRADING:The course grade will be based on homework assigned periodically.
ACCOMODATION FOR STUDENTS WITH DISABILITIES:Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.
The url of this page is http://krishnaswami-alladi.com/gradnumthy/fall2012/syllabus.html.
alladik@ufl.edu
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