Algebra Qualifying Exam: Difference between revisions

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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].


= Past Qualifying Exams =
= Summer 2024 SEP =
Below are the notes that will be used during the Summer 2024 SEP, run by 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]
 
'''Write-up of past qual problems:''' [https://drive.google.com/file/d/1PPWL5WMluzzyEbsKLEPa7ejOADNcnHt0/view?usp=sharing Problems], [https://drive.google.com/file/d/1h32hJuBKEb7lMoE-rkYUxWIPY05lIo1e/view?usp=sharing Solutions]
 
'''Ivan's study guides:'''
 
[https://drive.google.com/file/d/1stn3VFbKEIdQoKxhF-tWS3NrcQ0DS0W_/view?usp=sharing Basic Linear Algebra]
 
[https://drive.google.com/file/d/1m3iZP-PubwpRKTFfIX5kgMYCS6PEdTnZ/view?usp=sharing Advanced Linear Algebra]
 
[https://drive.google.com/file/d/1PzcJb2y5fPo7Pg7qaBdvQ0bTXJRI2eSC/view?usp=sharing Ring Theory 1]
 
[https://drive.google.com/file/d/18OCnoiOW83MWhdeFIcBz9lMYxs5SQa0J/view?usp=sharing Ring Theory 2]
 
[https://drive.google.com/file/d/1_bi5m39mEN8jARe2kd4xKXUurXZyWfx7/view?usp=sharing Module Theory 1]
 
[https://drive.google.com/file/d/1jhYPxhHCFgs9BjC4do8g4X-7e2IXrAE-/view?usp=sharing Module Theory 2]
 
[https://drive.google.com/file/d/1IQBfO00U37ik5-pNHx-QdDDeZrNX6TaF/view?usp=sharing Module Theory 3]
 
[https://drive.google.com/file/d/1tOECwCtBW1dryPZRvkcUtIGqFEvEQcva/view?usp=sharing Group Theory 1]
 
[https://drive.google.com/file/d/1Y1pim2d4C_VAmqfqhinIC36USKZIi558/view?usp=sharing Group Theory 2: Group Actions]
 
[https://drive.google.com/file/d/1yJoPpX1OWPDfAKDe0Wa8cm3_98jPgNug/view?usp=sharing Group Theory 3]
 
[https://drive.google.com/file/d/1lo5-pnCPcuVgiMFl_wF891WeQKezHY6K/view?usp=sharing Fields and Galois Theory]
 
'''Evan Dummit's notes:'''
[https://drive.google.com/file/d/1tAiKY-zpox8c_P1AGDWReW_T9ZH-38jJ/view?usp=sharing Linear Algebra],
[https://drive.google.com/file/d/1c65blx-_ZK8qqwmPGZYEAhTK3RTepquj/view?usp=sharing Rings and Modules],
[https://drive.google.com/file/d/1XZhrPHgJeQ8RWQbbNWoHsOhSJ9WYHwoZ/view?usp=sharing Group Theory],
[https://drive.google.com/file/d/1opBVylqXmNuWA8LPZg3rcHclNYj8LJEj/view?usp=sharing Field and Galois Theory]
 
 
= Summer 2023 SEP =
Below are the notes, worksheets, and solutions that were used during the Summer 2023 SEP, run by Owen Goff and Ivan Aidun.
 
== Schedule ==
5 Weeks: July 18 - August 17
 
Meetings on Tuesdays and Thursdays 10:15am-12:30pm in VV B203.
 
'''Week 1 - Linear algebra:''' [https://drive.google.com/file/d/1tAiKY-zpox8c_P1AGDWReW_T9ZH-38jJ/view?usp=sharing Notes], July 18 ([https://drive.google.com/file/d/1IFpQ2G920zBJfid_Pfi4K30WroXRXv8V/view?usp=drive_link Worksheet] and [https://drive.google.com/file/d/1duxfMiRE98z4-l80GDyk7JhnnhPdom5E/view?usp=sharing Solutions]), July 20 ([https://drive.google.com/file/d/1gQlM8rT1k7U4fWy57ZsuRMl9ai28I_ry/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1oc36XZGqksBikIq5G8RC_crm33iDgN0m/view?usp=drive_link Solutions])
 
'''Week 2 - Groups:''' [https://drive.google.com/file/d/1XZhrPHgJeQ8RWQbbNWoHsOhSJ9WYHwoZ/view?usp=sharing Notes] and [https://drive.google.com/file/d/1Qf8svifg0pmbVVaou1L7XLYRqysh1zHw/view?usp=sharing Ivan's notes about some uncommon but important group constructions], July 25 ([https://drive.google.com/file/d/1OHkHcRcEIwrfuthKBb3XGMAy3huQraxj/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1AR_4qvJw99TNO6qU61N5ELr74xpRsHfk/view?usp=sharing Solutions]), July 27 ([https://drive.google.com/file/d/1gLar4AMAWHkaqwnQ5FxJZtmwn0JRZTyD/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1z7Gz3Remgife5oMwukyR6a5ozhC2Xxzv/view?usp=sharing Solutions])
 
'''Week 3 - Fields:''' [https://drive.google.com/file/d/1opBVylqXmNuWA8LPZg3rcHclNYj8LJEj/view?usp=sharing Notes], August 1 ([https://drive.google.com/file/d/1vVNWsTsi_oN64bLbSOSfXNpWVMqPS0Tb/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1Vs3-ni0PCYygKzqCl44iGIy422W07shj/view?usp=sharing Solutions]), August 3 ([https://drive.google.com/file/d/1ZAGMbGUxDCTfzP0uiD0-00p4pJFaKUqU/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1LRN9ZUJ24ixnoBcO98v6yISbs4HVjVE0/view?usp=sharing Solutions])
 
'''Week 4 - Rings & Modules:''' [https://drive.google.com/file/d/1c65blx-_ZK8qqwmPGZYEAhTK3RTepquj/view?usp=sharing Notes], August 8 ([https://drive.google.com/file/d/1fJWQCtjHqxWrNHclFn5vQinkRO7j4CS9/view?usp=sharing Worksheet] and [https://drive.google.com/file/d/1mCMIAqaCJ-eCSpaKcaElhRN5R_7dJhIB/view?usp=sharing Solutions]), August 10 ([https://drive.google.com/file/d/1l3joeopwvkQMSQQfP4u7XZki7gbiPc8j/view?usp=drive_link Worksheet] and [https://drive.google.com/file/d/1iWdi1V7c1SBbWy5Vl1O3hwSmYSdUGmjo/view?usp=drive_link Solutions])
 
'''Week 5 - Misc./Review:''' August 15 ([https://drive.google.com/file/d/1Rj1wOgjo7kTfOlb0dfvd2Ck6hhe2oJx_/view?usp=drive_link Worksheet] and [https://drive.google.com/file/d/18AmXof5U45OEKceCJcMlMxaED6TOwc6p/view?usp=drive_link Solutions]), August 17 ([https://drive.google.com/file/d/1adzmkS4rkFfAlXHeiJ5tCtTMRUQRyadH/view?usp=drive_link Worksheet] and [https://drive.google.com/file/d/1gC_i7ci2UcMI9slh6oFK0jmwQna9NC4z/view?usp=drive_link Solutions])
 
= Summer 2022 SEP =
 
Below are the notes, worksheets, and solutions that were used during the Summer 2022 SEP, run by Caitlyn Booms and Ivan Aidun.
 
== Schedule ==
 
5 Weeks: July 19 - August 18
 
Meetings on Tuesdays and Thursdays at 9:45am-12pm in VV B333.


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


* Linear Algebra
'''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])
** [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
= Past Qualifying Exams =
** [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 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/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]


* Field Theory
* [[Media:Algebra Qual Fall 2019.pdf| Summer 2019]]
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/BasicFields.pdf Field Theory I]
* [[Media:Algebra Qual January 2019.pdf| Winter 2019]]
** [http://www.math.wisc.edu/~dynerman/content/mantilla/galois/Fields2.pdf Field Theory II]
* [[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]


* Ring Theory
= SEP Notes =
** [http://www.math.wisc.edu/~dynerman/content/mantilla/ring/Modules.pdf Modules]
https://kb.wisc.edu/math/internal/122251 is the new repository for any SEP content from previous semesters.
** [http://www.math.wisc.edu/~dynerman/content/mantilla/commute/CommutativeAlg.pdf Commutative Rings]

Latest revision as of 17:06, 5 August 2024

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 2024 SEP

Below are the notes that will be used during the Summer 2024 SEP, run by Ivan Aidun (aidun@wisc.edu).

List of topics covered on exam

Online repository of past exams

Write-up of past qual problems: Problems, Solutions

Ivan's study guides:

Basic Linear Algebra

Advanced Linear Algebra

Ring Theory 1

Ring Theory 2

Module Theory 1

Module Theory 2

Module Theory 3

Group Theory 1

Group Theory 2: Group Actions

Group Theory 3

Fields and Galois Theory

Evan Dummit's notes: Linear Algebra, Rings and Modules, Group Theory, Field and Galois Theory


Summer 2023 SEP

Below are the notes, worksheets, and solutions that were used during the Summer 2023 SEP, run by Owen Goff and Ivan Aidun.

Schedule

5 Weeks: July 18 - August 17

Meetings on Tuesdays and Thursdays 10:15am-12:30pm in VV B203.

Week 1 - Linear algebra: Notes, July 18 (Worksheet and Solutions), July 20 (Worksheet and Solutions)

Week 2 - Groups: Notes and Ivan's notes about some uncommon but important group constructions, July 25 (Worksheet and Solutions), July 27 (Worksheet and Solutions)

Week 3 - Fields: Notes, August 1 (Worksheet and Solutions), August 3 (Worksheet and Solutions)

Week 4 - Rings & Modules: Notes, August 8 (Worksheet and Solutions), August 10 (Worksheet and Solutions)

Week 5 - Misc./Review: August 15 (Worksheet and Solutions), August 17 (Worksheet and Solutions)

Summer 2022 SEP

Below are the notes, worksheets, and solutions that were used during the Summer 2022 SEP, run by Caitlyn Booms and Ivan Aidun.

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

SEP Notes

https://kb.wisc.edu/math/internal/122251 is the new repository for any SEP content from previous semesters.

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