{"id":187,"date":"2015-01-05T11:00:28","date_gmt":"2015-01-05T16:00:28","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/alladik\/?page_id=187"},"modified":"2026-03-19T08:14:53","modified_gmt":"2026-03-19T12:14:53","slug":"mas-7216-analytic-number-theory-ii-spring-2015","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/alladik\/mas-7216-analytic-number-theory-ii-spring-2015\/","title":{"rendered":"MAS 7216 – Analytic Number Theory II – Spring 2015"},"content":{"rendered":"\r\n
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MAS 7216 – Analytic Number Theory II – Spring 2015<\/h1>\n\n\n\n
\n
\n

\nMWF 6th period (12:50-1:40pm) – LIT 235 – FALL 2014<\/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 7th period (1:55 – 2:45 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>
    \nAlthough this is a continuation of MAS 7215,
    \nI will make it self contained. Thus, while
    \nMAS 7215 is desirable, it is not necessary
    \nfor this course.

    In the last twelve months, there have been
    \nspectacular progress on both the small gap
    \nand large gap problems regarding primes.
    \nAlthough the twin prime conjecture is still
    \nunsolved, progress towards it has been dramatic.
    \nTo better understand this, I will begin by
    \ngiving an account of Sieve Methods of Brun
    \nand Selberg and establish several important
    \nresults on almost primes, which will be approximations
    \nto the celebrated prime twin and Goldbach conjectures.
    \nI will also discuss the results of Westzynthius-Erdos-Rankin
    \non the large gap problem of primes.
    \nIn connection with this, I will discuss next the distribution
    \nof integers with restrictions on their prime factors.
    \nAnother topic for discussion with be the beautiful
    \nsubject of Probabilistic Number Theory ushered
    \nin by Paul Erdos and Marc Kac – a subject whose
    \norigins can be traced back to the work of Hardy
    \nand Ramanujan. I will provide a novel sieve theoretic
    \napproach to probabilistic number theory. Finally
    \nI plan to discuss primes in arithmetic progressions
    \nand the famous Siegel-Walfisz theorem.<\/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-187","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/187","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=187"}],"version-history":[{"count":3,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/187\/revisions"}],"predecessor-version":[{"id":723,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/187\/revisions\/723"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/media?parent=187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}