{"id":79,"date":"2013-11-12T09:02:17","date_gmt":"2013-11-12T09:02:17","guid":{"rendered":"http:\/\/www.sjut.org\/math\/?page_id=79"},"modified":"2013-11-18T12:19:29","modified_gmt":"2013-11-18T09:19:29","slug":"mat202","status":"publish","type":"page","link":"http:\/\/www.sjut.org\/math\/index.php\/courselist\/mat202\/","title":{"rendered":"MAT202 Real Analysis"},"content":{"rendered":"

This course builds on the foundation of MAT110 and equips the student with the basic\u00a0ideas and concepts of Real Analysis<\/em>. It is a one-semester course that covers, in a brief and elementary way, the most important topics in the subject in real analysis rather than a lengthy, detailed, comprehensive treatment, which normally requires an entire academic year. Successful completion of this course should provide students with a foundation for their understanding of calculus, which will enhance teaching of mathematics up through secondary school level.<\/p>\n

Contents:<\/strong>
\nThe Real Number System<\/strong>: Axioms for a Field, the extended real numbers, sequences of real numbers, open and closed sets of real numbers, continuous functions, Borel Sets<\/p>\n

Basic Topology<\/strong>: Finite, Countable and Non-Countable Sets, Metric Spaces, Compact Sets, Perfect Sets, Connected Sets<\/p>\n

Integration<\/strong>: The Riemann Integral, the Lebesgue Integral.<\/p>\n

Textbook:
\n<\/strong>Lebl, Jiri, Basic Analysis: Introduction to Real Analysis<\/em>, Jiri Lebl: Univ of Wisconsin \u2013 Madison, 2013. (http:\/\/www.jirka.org\/ra\/<\/a>)<\/p>\n

References:<\/strong>
\nProtter, Murray H., Basic Elements of Real Analysis<\/em>, Springer-Verlag, 1998.
\n(http:\/\/ramanujan.math.trinity.edu\/wtrench\/texts\/TRENCH_REAL_ANALYSIS.PDF<\/a>)
\nRoyden, H.L., Real Analysis<\/em>, 3rd Ed. Prentice Hall 1988.
\nRudin, W., Principles of Mathematical Analysis<\/em>, 3rd Ed., McGraw-Hill. 1976.
\nTrench, William F., Introduction to Real Analysis<\/em>, William Trench: Trinity University, 2003.<\/p>\n

Web Resources:<\/strong>
\nInteractive Real Analysis,\u00a0 http:\/\/mathcs.org\/analysis\/reals\/index.html<\/a>
\nLarson, Lee, http:\/\/www.math.louisville.edu\/~lee\/RealAnalysis\/realanalysis.html<\/a>
\nLebl, Jiri, Basic Analysis: Introduction to Real Analysis, http:\/\/www.jirka.org\/ra\/<\/a>
\nO\u2019Connor John, A first Analysis course,\u00a0http:\/\/www-groups.mcs.st-andrews.ac.uk\/~john\/analysis\/index.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

This course builds on the foundation of MAT110 and equips the student with the basic\u00a0ideas and concepts of Real Analysis. It is a one-semester course that covers, in a brief […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":18,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"categories":[16,15,14],"_links":{"self":[{"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/pages\/79"}],"collection":[{"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/comments?post=79"}],"version-history":[{"count":2,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/pages\/79\/revisions"}],"predecessor-version":[{"id":118,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/pages\/79\/revisions\/118"}],"up":[{"embeddable":true,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/pages\/18"}],"wp:attachment":[{"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/media?parent=79"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.sjut.org\/math\/index.php\/wp-json\/wp\/v2\/categories?post=79"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}