{"id":1649,"date":"2025-09-20T21:26:01","date_gmt":"2025-09-21T04:26:01","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mgsa\/?page_id=1649"},"modified":"2025-09-21T14:14:05","modified_gmt":"2025-09-21T21:14:05","slug":"real-analysis","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mgsa\/qualifying-exams\/real-analysis\/","title":{"rendered":"Real Analysis (525A)"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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To contribute solutions, corrections, notes, or other helpful resources, feel free to email mgsa@usc.edu<\/a> or submit a pull request to MGSA’s qualifying exams repository on GitHub<\/a>.<\/p>\n

Last update: 2025-09-21<\/em><\/p>\n

Back to Qualifying Exams Overview<\/em><\/a><\/p>\n<\/div>\n<\/div>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n \n \n\n\n\n\n\n\n\n

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\n \n <\/h2>\n\n\n<\/div>\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\n Exam\n <\/th>\n \n \n <\/th>\n \n Solutions\n <\/th>\n \n \n <\/th>\n \n Author\n <\/th>\n <\/tr>\n \n \n <\/thead>\n
\n Fall 2025<\/a>
\nFall 2024<\/a>
\nFall 2023<\/a>
\nFall 2022<\/a>
\nFall 2021<\/a>\n <\/td>\n \n \n 		\n Spring 2025<\/a>
\nSpring 2024<\/a>
\nSpring 2023<\/a>
\nSpring 2022<\/a>
\nSpring 2021<\/a>\n <\/td>\n \n \n 		\n Fall 2025<\/a>
\nFall 2024<\/a>
\nFall 2023<\/a>
\nFall 2022<\/a>
\nFall 2021<\/a>\n <\/td>\n \n \n 		\n Spring 2025<\/a>
\nSpring 2024<\/a>
\nSpring 2023<\/a>
\nSpring 2022<\/a>
\nSpring 2021<\/a>\n <\/td>\n \n \n 		\n Alex Fu\n <\/td>\n \n <\/tr>\n
\n Fall 2020<\/a>
\nFall 2019<\/a>\n <\/td>\n \n \n 		\n Spring 2020<\/a>
\nSpring 2019<\/a>\n <\/td>\n \n \n 		\n Fall 2020<\/a>
\nFall 2019<\/a>\n <\/td>\n \n \n 		\n Spring 2020<\/a>
\nSpring 2019<\/a>\n <\/td>\n \n \n 		\n Jonathan Michala<\/a>\n <\/td>\n \n <\/tr>\n
\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n Fall 2019<\/a>\n <\/td>\n \n \n \n \n <\/td>\n \n \n \n Zejing Wang\n <\/td>\n \n <\/tr>\n
\n Fall 2018<\/a>
\nFall 2017<\/a>
\nFall 2016<\/a>
\nFall 2015<\/a>
\nFall 2014<\/a>
\nFall 2013<\/a>
\nFall 2012<\/a>
\nFall 2011<\/a>
\nFall 2010<\/a>\n <\/td>\n \n \n 		\n Spring 2018<\/a>
\nSpring 2017<\/a>
\nSpring 2016<\/a>
\nSpring 2015<\/a>
\nSpring 2014<\/a>
\nSpring 2013<\/a>
\nSpring 2012<\/a>
\nSpring 2011<\/a>
\nSpring 2010<\/a>\n <\/td>\n \n \n 		\n Fall 2018<\/a>
\nFall 2017<\/a>
\nFall 2016<\/a>
\nFall 2015<\/a>
\nFall 2014<\/a>
\nFall 2013<\/a>
\nFall 2012<\/a>
\nFall 2011<\/a>
\nFall 2010<\/a>\n <\/td>\n \n \n 		\n Spring 2018<\/a>
\nSpring 2017<\/a>
\nSpring 2016<\/a>
\nSpring 2015<\/a>
\nSpring 2014<\/a>
\nSpring 2013<\/a>
\nSpring 2012<\/a>
\nSpring 2011<\/a>
\nSpring 2010<\/a>\n <\/td>\n \n \n 		\n Kayla Orlinsky\n <\/td>\n \n <\/tr>\n
\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n Fall 2018<\/a>
\nFall 2017<\/a>
\nFall 2016<\/a>
\nFall 2015<\/a>
\nFall 2014<\/a>
\nFall 2013<\/a>
\nFall 2012
\nFall 2011
\nFall 2010\n <\/td>\n \n \n 		\n Spring 2018<\/a>
\nSpring 2017<\/a>
\nSpring 2016<\/a>
\nSpring 2015<\/a>
\nSpring 2014<\/a>
\nSpring 2013<\/a>
\nSpring 2012<\/a>
\nSpring 2011
\nSpring 2010<\/a>\n <\/td>\n \n \n 		\n Jonathan Michala<\/a>\n <\/td>\n \n <\/tr>\n
\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n Fall 2015<\/a>
\nFall 2013
\nFall 2012<\/a>
\nFall 2011<\/a>
\nFall 2010<\/a>\n <\/td>\n \n \n 		\n Spring 2015<\/a>
\nSpring 2013<\/a>
\nSpring 2012<\/a>
\nSpring 2011<\/a>
\nSpring 2010<\/a>\n <\/td>\n \n \n 		\n Dan Douglas\n <\/td>\n \n <\/tr>\n
\n Fall 2011<\/a>
\nFall 2010<\/a>
\nFall 2009<\/a>
\nFall 2008<\/a>
\nFall 2007<\/a>
\nFall 2006<\/a>\n <\/td>\n \n \n 		\n Spring 2011<\/a>
\nSpring 2010<\/a>
\nSpring 2009<\/a>
\nSpring 2008<\/a>
\nSpring 2007<\/a>
\nSpring 2006<\/a>\n <\/td>\n \n \n 		\n Fall 2011
\nFall 2010<\/a>
\nFall 2009
\nFall 2008<\/a>
\nFall 2007<\/a>
\nFall 2006<\/a>\n <\/td>\n \n \n 		\n Spring 2011<\/a>
\nSpring 2010<\/a>
\nSpring 2009<\/a>
\nSpring 2008<\/a>
\nSpring 2007<\/a>
\nSpring 2006<\/a>\n <\/td>\n \n \n 		\n Alec Sahakian<\/a>\n <\/td>\n \n <\/tr>\n
\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n Fall 2009<\/a>
\nFall 2008<\/a>
\nFall 2006<\/a>\n <\/td>\n \n \n 		\n Spring 2009<\/a>
\nSpring 2008<\/a>
\nSpring 2006<\/a>\n <\/td>\n \n \n 		\n Jonathan Michala<\/a>\n <\/td>\n \n <\/tr>\n
\n Fall 2013<\/a>
\nFall 2012<\/a>
\nFall 2011<\/a>
\nFall 2010<\/a>
\nFall 2009<\/a>
\nFall 2008<\/a>
\nFall 2007<\/a>
\nFall 2006<\/a>
\nFall 2005<\/a>
\nFall 2004<\/a>
\nFall 2003<\/a>\n <\/td>\n \n \n 		\n Spring 2013<\/a>
\nSpring 2012<\/a>
\nSpring 2011<\/a>
\nSpring 2010<\/a>
\nSpring 2009<\/a>
\nSpring 2008<\/a>
\nSpring 2007<\/a>
\nSpring 2006<\/a>
\nSpring 2005<\/a>
\nSpring 2004<\/a>
\n\u2014\n <\/td>\n \n \n 		\n Fall 2013
\nFall 2012<\/a>
\nFall 2011<\/a>
\nFall 2010<\/a>
\nFall 2009<\/a>
\nFall 2008<\/a>
\nFall 2007<\/a>
\nFall 2006<\/a>
\nFall 2005<\/a>
\nFall 2004<\/a>
\nFall 2003<\/a>\n <\/td>\n \n \n 		\n Spring 2013<\/a>
\nSpring 2012
\nSpring 2011<\/a>
\nSpring 2010<\/a>
\nSpring 2009<\/a>
\nSpring 2008<\/a>
\nSpring 2007<\/a>
\nSpring 2006<\/a>
\nSpring 2005<\/a>
\nSpring 2004<\/a>
\n\u2014\n <\/td>\n \n \n 		\n Henry Tucker<\/a>\n <\/td>\n \n <\/tr>\n
\n \u2014
\nFall 2002<\/a>
\nFall 2001<\/a>
\nFall 2000<\/a>
\nFall 1999<\/a>
\nFall 1998
\nFall 1997<\/a>
\nFall 1996<\/a>
\nFall 1995<\/a>
\nFall 1994<\/a>\n <\/td>\n \n \n 		\n Spring 2003<\/a>
\nSpring 2002<\/a>
\nSpring 2001<\/a>
\nSpring 2000<\/a>
\nSpring 1999<\/a>
\nSpring 1998<\/a>
\nSpring 1997<\/a>
\nSpring 1996<\/a>
\nSpring 1995<\/a>
\n\u2014\n <\/td>\n \n \n 		\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n \n <\/td>\n \n <\/tr>\n
\n \u2014
\nFall 1993<\/a>
\nFall 1992\n <\/td>\n \n \n 		\n Spring 1994<\/a>
\nSpring 1993
\nSpring 1992<\/a>\n <\/td>\n \n \n 		\n \u2014
\nFall 1993<\/a>
\nFall 1992\n <\/td>\n \n \n 		\n Spring 1994<\/a>
\nSpring 1993
\nSpring 1992<\/a>\n <\/td>\n \n \n 		\n Henry Tucker\n <\/td>\n \n <\/tr>\n
\n \n <\/td>\n \n \n \n \n <\/td>\n \n \n \n \u2014
\nFall 1993<\/a>
\nFall 1992\n <\/td>\n \n \n 		\n Spring 1994<\/a>
\nSpring 1993
\nSpring 1992<\/a>\n <\/td>\n \n \n 		\n William Chang\n <\/td>\n \n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <\/div><\/div>\n\n\n\n \n \n\n\n\n\n\n\n\n
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\n \n <\/h2>\n\n\n<\/div>\n\n \n \n \n \n \n \n \n \n \n
\n Extra material\n <\/th>\n \n Author\n <\/th>\n <\/tr>\n \n \n <\/thead>\n
\n Cheat sheet<\/a>\n <\/td>\n \n \n \n Kayla Orlinsky\n <\/td>\n \n <\/tr>\n
\n Cheat sheet<\/a>\n <\/td>\n \n \n \n Henry Tucker\n <\/td>\n \n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":990,"featured_media":0,"parent":192,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1649","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nReal Analysis (525A) - Mathematics Graduate Student Association<\/title>\n<meta name=\"description\" content=\"Student-contributed solutions to the Real Analysis (525A) qualifying exam for the Mathematics programs at USC.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/mgsa\/qualifying-exams\/real-analysis\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Real Analysis (525A) - 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