# 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. | ||

+ | The syllabus can be found [https://www.math.wisc.edu/graduate/quals/guide#algebra here]. | ||

+ | |||

+ | = Summer 2022 SEP = | ||

+ | |||

+ | Below are the notes, worksheets, and solutions that will be used during the Summer 2022 SEP, run by Caitlyn Booms (cbooms@wisc.edu) and Ivan Aidun (aidun@wisc.edu). | ||

+ | |||

+ | [https://math.wisc.edu/graduate/current-phd/qualifying-exams/topics/ List of topics covered on exam] | ||

+ | |||

+ | [https://uwmadison.app.box.com/v/algebra Online repository of past exams] | ||

+ | |||

+ | == Schedule == | ||

+ | |||

+ | 5 Weeks: July 19 - August 18 | ||

+ | |||

+ | Meetings on Tuesdays and Thursdays at 9:45am-12pm in VV B333. | ||

+ | |||

+ | '''Week 1 - Linear Algebra:''' [https://drive.google.com/file/d/1tAiKY-zpox8c_P1AGDWReW_T9ZH-38jJ/view?usp=sharing Notes], July 19 ([https://drive.google.com/file/d/1M9S-qSnLZ3VBjbE-52W_6CjsXkXdgDqW/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1Y5U5fmR4torgj7HqTqmit50ZiOXEPIb9/view?usp=sharing Solutions]), July 21 ([https://drive.google.com/file/d/1F3LlfQlgF0UKMaSPzsO_rf403U7ljcgP/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1t8YtDeWPfzZL9cVQPpRGPzSDYSEkYrvB/view?usp=sharing Solutions]) | ||

+ | |||

+ | '''Week 2 - Fields:''' [https://drive.google.com/file/d/1opBVylqXmNuWA8LPZg3rcHclNYj8LJEj/view?usp=sharing Notes], July 26 ([https://drive.google.com/file/d/1RsqJt15rvftahqiToLCzwwKrGV_RiWBY/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/13TZfuwcbGHLR1bHWm2_QH24dFlDTs1xV/view?usp=sharing Solutions]), July 28 ([https://drive.google.com/file/d/1T6HQsfI8yrFGKDooAGvkpOW7-x3V54QY/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1-bQMJ-8GijK1xovYRjzUO1Jl9Yml8ksf/view?usp=sharing Solutions]) | ||

+ | |||

+ | '''Week 3 - Rings & Modules:''' [https://drive.google.com/file/d/1c65blx-_ZK8qqwmPGZYEAhTK3RTepquj/view?usp=sharing Notes], August 2 ([https://drive.google.com/file/d/1aEo5LRudziEnaatRdEl3FAccYi42HXYb/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1Edh5skIIP68oGmwfDSovMz88oUgFu5DO/view?usp=sharing Solutions]), August 4 ([https://drive.google.com/file/d/1JHph47aS4RgM2tfIYiil0t5v8r74caXT/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/141f92uK7OVBFTzyvMAw8dZvPyaC2iBGc/view?usp=sharing Solutions]) | ||

+ | |||

+ | '''Week 4 - Groups:''' [https://drive.google.com/file/d/1XZhrPHgJeQ8RWQbbNWoHsOhSJ9WYHwoZ/view?usp=sharing Notes], August 9 ([https://drive.google.com/file/d/1RbzUzfbPNLkqjvxcXH7fz77vd5ee-gd0/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1YOBzo-sG6HS_VOvj21ve6u7b30b8C3nH/view?usp=sharing Solutions]), August 11 ([https://drive.google.com/file/d/1wTSC-Jefnbqw7jgf9i69hcQTcViJWgWJ/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1m3VRBxIDCChO-NkkCr74d2jHmxZQk8XZ/view?usp=sharing Solutions]) | ||

+ | |||

+ | '''Week 5 Misc./Review:''' August 16 ([https://drive.google.com/file/d/1qWmI-QnH1ffW2c3noMV5MdWB8QbG9B8Q/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/18N19hQS0ZLsn2bMPpLh02Y5TxH8stGuv/view?usp=sharing Solutions]), August 18 ([https://drive.google.com/file/d/16HEfOGRfL7P1xRmoH3ERY7XS-bw6kkEq/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1hU2Oc7AD2XMyckc99I2YcJH65JEgrzHq/view?usp=sharing Solutions]) | ||

+ | |||

+ | = Past Qualifying Exams = | ||

+ | |||

+ | * [[Media:Algebra Qual Fall 2019.pdf| Summer 2019]] | ||

+ | * [[Media:Algebra Qual January 2019.pdf| Winter 2019]] | ||

+ | * [[Media:Aug 2018 Algebra Quals.pdf| Summer 2018]] ([[Media:Aug 2018 Algebra Quals solution.pdf| Solutions]]) | ||

+ | * [[Media:Jan 2018 Algebra Quals.pdf| Winter 2018]] ([[Media:Jan 2018 Algebra Quals solution.pdf| Solutions]]) | ||

+ | * [[Media:Aug 2017 Algebra Quals.pdf| Summer 2017]] ([[Media:Aug 2017 Algebra Quals solution.pdf| Solutions]]) | ||

+ | * [[Media:Jan 2017 Algebra Quals.pdf| Winter 2017]] ([[Media:Jan 2017 Algebra Quals solution.pdf| Solutions]]) | ||

+ | * [[Media:Aug 2016 Algebra Quals.pdf| Summer 2016]] | ||

+ | * [[Media:Jan 2016 Algebra Quals.pdf| Winter 2016]] | ||

+ | * [[Media:Aug 2015 Algebra Quals.pdf| Summer 2015]] | ||

+ | * [[Media:Jan 2015 Algebra Quals.pdf| Winter 2015]] | ||

+ | * [[Media:Aug 2014 Algebra Quals.pdf| Summer 2014]] | ||

+ | * [[Media:Jan 2014 Algebra Quals.pdf| Winter 2014]] | ||

+ | * 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 | + | 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 [https://www.math.wisc.edu/~eramos/teaching/SEP.html notes by Eric Ramos]. | ||

+ | |||

+ | * 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/inner.pdf Linear Algebra II (inner products)] | ||

+ | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/linear/Jform.pdf Linear Algebra III (Jordan Form)] | ||

* Group Theory | * Group Theory | ||

− | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf | + | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/BasicGroups.pdf Group Theory I] |

− | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf | + | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/MoreGroups.pdf Group Theory II (group actions)] |

** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups] | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/SolNil.pdf Solvable & Nilpotent Groups] | ||

** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity] | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/ThmsGroups.pdf Theorems for non-simplicity] | ||

*** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000] | *** [http://www.math.wisc.edu/~dynerman/content/mantilla/group/less1000.pdf Non-simplicity proofs for groups of order < 1000] | ||

+ | |||

+ | * 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/Fields2.pdf Field Theory II] | ||

* Ring Theory | * Ring Theory | ||

+ | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules] | ||

** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings] | ** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings] | ||

− |

## Latest revision as of 13:50, 18 August 2022

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. The syllabus can be found here.

# Summer 2022 SEP

Below are the notes, worksheets, and solutions that will be used during the Summer 2022 SEP, run by Caitlyn Booms (cbooms@wisc.edu) and Ivan Aidun (aidun@wisc.edu).

List of topics covered on exam

Online repository of past exams

## Schedule

5 Weeks: July 19 - August 18

Meetings on Tuesdays and Thursdays at 9:45am-12pm in VV B333.

**Week 1 - Linear Algebra:** Notes, July 19 (Worksheet and Solutions), July 21 (Worksheet and Solutions)

**Week 2 - Fields:** Notes, July 26 (Worksheet and Solutions), July 28 (Worksheet and Solutions)

**Week 3 - Rings & Modules:** Notes, August 2 (Worksheet and Solutions), August 4 (Worksheet and Solutions)

**Week 4 - Groups:** Notes, August 9 (Worksheet and Solutions), August 11 (Worksheet and Solutions)

**Week 5 Misc./Review:** August 16 (Worksheet and Solutions), August 18 (Worksheet and Solutions)

# Past Qualifying Exams

- Summer 2019
- Winter 2019
- Summer 2018 ( Solutions)
- Winter 2018 ( Solutions)
- Summer 2017 ( Solutions)
- Winter 2017 ( Solutions)
- Summer 2016
- Winter 2016
- Summer 2015
- Winter 2015
- Summer 2014
- Winter 2014
- Pre-2014 exams are available here, there is also a file with 1991-2013 quals on Atrium.

# 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.

- Group Theory

- Field Theory

- Ring Theory