University of Minnesota
School of Mathematics
School of Mathematics         Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity.  
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Past Prelims




Ph.D. Written Prelim Examination Committee 2009-2010

Schedule for Spring 2010 Written Prelims (April 19 - 22)

The exams:

The grade distributions:

Note: There was no Riemannian Geometry exam in Spring 2009; no one took the exam.



Schedule for Fall 2009 Written Prelims (August 31 - September 03)

The exams:

The grade distributions:

Note: There was no Riemannian Geometry exam in Spring 2009; no one took the exam.


Ph.D. Written Prelim Examination Committee 2008-2009

Schedule for Spring 2009 Written Prelims (20 -23 April)

The exams:

The grade distributions:

Note: There was no Riemannian Geometry exam in Spring 2009; no one took the exam.



Schedule for Fall 2008 Written Prelims (25 -28 August)

The exams:

The grade distributions:

Note: There was no Riemannian Geometry exam in Fall 2008; no one took the exam.


Ph.D. Written Prelim Examination Committee 2007-2008

Schedule for Spring 2008 Written Prelims (21 -24 April)

The exams:

The grade distributions:

Note: There was no Riemannian Geometry exam in Spring 2008; no one took the exam.



Schedule for Fall 2007 Written Prelims (27 -30 August)

The exams:

Note: There was no Riemannian Geometry exam information for Fall 2007.


Ph.D. Written Prelim Examination Committee 2006-2007

Schedule for Spring 2007 Written Prelims (23 April - 27 April)

The exams:

The grade distributions:




Schedule for Fall 2006 Written Prelims (28 August - 1 September)

The exams:

The grade distributions:

Note:There was no Riemannian Geometry exam in Spring 2007 or Fall 2006; no one took the exam.


Ph.D. Written Prelim Examination Committee 2005-2006

Schedule for Spring 2006 Written Prelims (24-28 April 2005)

The exams:

The grade distributions:

Note:There was no Riemannian Geometry exam in Spring 2006; no one took the exam.


Schedule for Fall 2005 Written Prelims (25-29 April 2005)

The exams:

The grade distributions:



Ph.D. Written Prelim Examination 2004-2005

Schedule for Spring 2005 Written Prelims (25-29 April 2005)

The exams:



The grade distributions:


Schedule for Fall 2004 Written Prelims (30 August - 3 September)

The exams:


The grade distributions:

Note:There was no Riemannian Geometry exam in Fall 2004; no one took the exam.