{"id":157,"date":"2014-08-21T15:14:07","date_gmt":"2014-08-21T19:14:07","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/alladik\/?page_id=157"},"modified":"2026-03-19T08:14:53","modified_gmt":"2026-03-19T12:14:53","slug":"mas7215","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/alladik\/mas7215\/","title":{"rendered":"MAS 7215 – Analytic Number Theory I – Fall 2016"},"content":{"rendered":"\r\n
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MAS 7215 – Analytic Number Theory I – Fall 2016<\/h1>\n\n\n\n
\n
\n

\nMWF 6th period (12:50-1:40pm) – LIT 233 – FALL 2016<\/strong>
\n

INSTRUCTOR:<\/h3>
\n

    \nKrishnaswami Alladi

    \n304 Little Hall

    \n(352) 294-2290
    \nemail: alladik@ufl.edu
    \n<\/ul>
    \n

    OFFICE HOURS:<\/h3>
    \n M and W 8th period (3:00 – 3:50 pm) in LIT 304 and
    \n by appointment.
    \n

    PREREQUISITES:<\/h3>
    \nUndergraduate course in number theory and a course in complex variable theory
    \n

    COURSE DESCRIPTION:<\/h3>
    \n Number Theory is one of the two oldest subjects in mathematics, the other being geometry.
    \nYet, Number Theory is one of the most important and active areas of research today.
    \nAnalytic number theory deals with fundamental arithmetical questions which can be tackled
    \nusing analytic techniques. The subject has a wealth of outstanding open problems. In the
    \npast decade some dramatic advances have been made on some of these famous problems.
    \nThe course will start from scratch and will be self contained, but will reach great heights
    \nin a steady ascent. Topics to be covered will include (and not necessarily in the order
    \ngiven below): estimates involving prime numbers, arithmetical (number theoretic) functions
    \n– their algebra and asymptotic estimates concerning them, Dirichlet series, the Riemann zeta
    \nfunction, the prime number theorem and its proof(s), Dirichlet’s theorem on primes in
    \nprogressions, the Siegel-Walfisz strongform of the Prime Number Theorem for Arithmetic
    \nProgressions, introduction to sieve methods to understand the prime twins and Goldbach
    \nconjectures – important partial results towards these conjectures, The Erdos-Kac Theorem
    \nin Probabilistic Number Theory.

    NOTE: Naturally some of these topics will be covered in MAS 7216.<\/p>

    TEXT:<\/h3>
    \nNo assigned text. I will use my own notes. A number of texts will be given as
    \nreferences. All I expect is a background in complex variable theory.
    \n

    \n\u00a0
    \n

    GRADING:<\/h3>
    \nGrades will be based on a few homework assignments,
    \nand seminars that students will have an opportunity to give.

    ACCOMODATION FOR STUDENTS WITH DISABILITIES:<\/h3>
    \nStudents requesting classroom accommodation must first register with the Dean of
    \nStudents Office. The Dean of Students Office will provide documentation to the
    \nstudent who must then provide this documentation to the Instructor when requesting
    \naccommodation.
    \n<\/td>
    \n<\/tr>
    \n<\/table>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":283,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-157","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/users\/283"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/comments?post=157"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/157\/revisions"}],"predecessor-version":[{"id":727,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/157\/revisions\/727"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/media?parent=157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}