Analysis
Exams with (some) solutions

Analysishref.pdf updated: 2011.04.03
Analysisnohref.pdf updated: 2011.04.03
This document contains solutions to some problems that appeared on previous comprehensive exams in real and complex analysis given at University of Hawaii at Manoa.
Please inform me of any typos or mathematical errors you discover by emailing William DeMeo (williamdemeo at gmail). Credits will appear below.
Exams without solutions

ProblemsInAnalysis.pdf,
This document contain (reproductions of) some of the
analysis comprehensive exams given to graduate students in the
Math Department at
UH Manoa.
The main differences between my transcriptions and the originals are the fonts and the
footnotes I've inserted to point out possible typos or to note when a given problem appears on multiple exams.
Analysis References
In preparing for the comprehensive exam in analysis I found the following books invaluable,
and the solutions above contain many references to them. (You can support this web page by clicking
on the images below and purchasing a book from Barnes and Noble.)
Algebra
Exams without Solutions

ProblemsInGroupsAndRings.pdf
This document contains some of the
problems that appeared on previous comprehensive exams in group theory and ring theory given at
University of Hawaii at Manoa. (Updated 2010.09.10: added Nov 2003 & Nov 2004 Ring theory exams)
Exam with (some) Solutions
Algebra References
In preparing for the comprehensive exam in algebra I found the following books invaluable. (You can support this web page by clicking on the links below and purchasing a book from
Barnes and Noble.)
Status of Analysis.pdf as of 4/3/2011
Exam 
Solved & TeX'd 
Solved but unTeX'd 
Unsolved 
Real Nov 1991 
19 


Real April 1998 
3, 4, 6, 8, 9 
1, 2, 5 
7 
Real Nov 2000 
1 
27 

Real Nov 2001 
17 


Real April 2004 
1, 2, 3 
47 

Real Nov 2007 
16 


Complex April 1989 
14, 6 
5 

Complex Nov 1991 
1, 3, 5, 7 
2a, 4, 6, 811 
2b 
Complex April 1995 
16 


Complex Nov 2001 
15 


Complex Nov 2006 
13, 4a, 5 
4b 

Complex April 2007 
1, 36 
2 

Complex Nov 2007 

1, 2, 3a, 4, 5, 6 
3b 
Credits
 2011.04.03: Real April '04  Geoff Patterson noticed a typo in my solution to problem 2 (fixed).
 2010.06.09: Real Nov '91  Quinn Culver suggested a more efficient solution to 7 (added).
 2010.02.12: Real April '98  Mike Joyce noticed a typo in 4 (fixed).
 2010.02.11: Real April '91  Mike Joyce noticed a typo in 9 (fixed).
 2010.02.05: Complex April '89  Mike Joyce noticed a mistake in 4 (replaced with a ref. to correct solution).
 2009.02.19: Complex Nov '01  Yoshi noticed a typo in 1b: f'(z) should be f'(z_0) throughout (fixed).
 2008.08.15: Real Nov '91  Matt Chasse noticed the error in my original solution to 4 (fixed).
Author: William DeMeo
Design by:
Hyeyoung Shin
Last modified: 2011.04.03
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William DeMeo (williamdemeo at gmail)
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