Algebra Qualifying Exam: Difference between revisions

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


= Summer 2023 SEP =
= Summer 2024 SEP =
Below are the notes, worksheets, and solutions that will be used during the Summer 2023 SEP, run by Owen Goff (ogoff@wisc.edu) and Ivan Aidun (aidun@wisc.edu).
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://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]
[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 ==
== Schedule ==
Line 18: Line 54:
'''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 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]
'''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]
'''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:'''
'''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 =
= Summer 2022 SEP =

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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