Difference between revisions of "Algebra Qualifying Exam"

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Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the [http://www.math.wisc.edu/graduate/ official graduate program page] for official information.
 
Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the [http://www.math.wisc.edu/graduate/ official graduate program page] for official information.
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= Past Qualifying Exams =
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* [[Media:Aug 2017 Algebra Quals.pdf | Summer 2017]] ([[Media:Aug 2017 Algebra Quals solution.pdf | Solutions]])
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* [[Media:Jan 2017 Algebra Quals.pdf | Winter 2017]] ([[Media:Jan 2017 Algebra Quals solution.pdf | Solutions]])
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* [[Media:Aug 2016 Algebra Quals.pdf | Summer 2016]]
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* [[Media:Jan 2016 Algebra Quals.pdf | Winter 2016]]
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* [[Media:Aug 2015 Algebra Quals.pdf | Summer 2015]]
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* [[Media:Jan 2015 Algebra Quals.pdf | Winter 2015]]
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* [[Media:Aug 2014 Algebra Quals.pdf | Summer 2014]]
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* [[Media:Jan 2014 Algebra Quals.pdf | Winter 2014]]
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* Pre-2014 exams are available [http://www.math.wisc.edu/~passman/algquals.html here], there is also a file with 1991-2013 quals on Atrium.
  
 
= Guillermo Mantilla's SEP Notes =
 
= Guillermo Mantilla's SEP Notes =
In the summers of 2007?, 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam.
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In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.
  
* Group Theory
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Note: the links below are broken. The files themselves are available on Atrium, there are also 2016 SEP [https://www.math.wisc.edu/~eramos/teaching/SEP.html notes by Eric Ramos].  
** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf Group Theory I]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf Group Theory II]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity]
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*** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000]
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* Ring Theory
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules]
 
  
 
* Linear Algebra
 
* Linear Algebra
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Linear.pdf Linear Algebra I]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Linear.pdf Linear Algebra I]
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/inner.pdf Linear Algebra II]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/inner.pdf Linear Algebra II (inner products)]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Jform.pdf Linear Algebra III (Jordan Form)]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Jform.pdf Linear Algebra III (Jordan Form)]
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* Group Theory
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf Group Theory I]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf Group Theory II (group actions)]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity]
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*** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000]
  
 
* Field Theory
 
* Field Theory
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/BasicFields.pdf Field Theory I]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/BasicFields.pdf Field Theory I]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/Fields2.pdf Field Theory II]
 
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/Fields2.pdf Field Theory II]
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* Ring Theory
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules]
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** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings]

Revision as of 15:04, 28 December 2017

Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the official graduate program page for official information.

Past Qualifying Exams

Guillermo Mantilla's SEP Notes

In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.

Note: the links below are broken. The files themselves are available on Atrium, there are also 2016 SEP notes by Eric Ramos.