{"id":1013,"date":"2019-06-07T13:07:48","date_gmt":"2019-06-07T17:07:48","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?page_id=1013"},"modified":"2020-01-08T14:57:33","modified_gmt":"2020-01-08T19:57:33","slug":"inequalities","status":"publish","type":"page","link":"https:\/\/jasoncantarella.com\/wordpress\/courses\/inequalities\/","title":{"rendered":"Summer Minicourse: Inequalities"},"content":{"rendered":"

It is unfortunately rather easy to complete a math major, and even go to graduate school, without learning much about what one might call “practical real analysis”. In this course, we try to remedy that situation by presenting a week’s worth of material that every working mathematician (especially in applied math) would be helped by knowing.<\/p>\n

The basic text for the course is the classic Inequalities, <\/em>by Hardy-Littlewood-Polya, but I’ll supplement it rather generously with material from the (excellent) The <\/em>Cauchy-Schwartz Master Class<\/em> by Steele.<\/p>\n

Every day will have two lectures (about an hour each) and two problems to work on together (about an hour each).<\/p>\n

Lecture Notes:<\/h3>\n
    \n
  1. Introduction to the p-means.<\/a><\/li>\n
  2. H\u00f6lder’s Theorem.<\/a>\n
      \n
    1. Problem set 1.<\/a><\/li>\n
    2. Problem set 2.<\/a><\/li>\n<\/ol>\n<\/li>\n
    3. Minkowski’s Theorem and a theorem of Hadamard.<\/a><\/li>\n
    4. Chebyshev’s inequality, Resolving Powers.<\/a><\/li>\n
    5. Symmetrical Means and Muirhead’s Theorem.<\/a><\/li>\n
    6. More on symmetry and majorization<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      It is unfortunately rather easy to complete a math major, and even go to graduate school, without learning much about what one might call “practical real analysis”. In this course, we try to remedy that situation by presenting a week’s worth of material that every working mathematician (especially in applied math) would be helped by […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":78,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-notitle.php","meta":{"footnotes":""},"class_list":["post-1013","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/1013","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/comments?post=1013"}],"version-history":[{"count":7,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/1013\/revisions"}],"predecessor-version":[{"id":1052,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/1013\/revisions\/1052"}],"up":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/78"}],"wp:attachment":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/media?parent=1013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}