University of Kansas Algebra Qualifying Exam Study Group (2021-2022)

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Useful Links:

Collected KU Algebra Qualifying Exams

List of Qualifying Exam Topics

Practice Algebra Qualifying Exam I (Written by Dylan C. Beck and Souvik Dey.)

Practice Algebra Qualifying Exam II (Written by Dylan C. Beck and Souvik Dey.)


Expository Notes by Dylan C. Beck:

Groups, Group Actions, and the Class Equation

Finite (Abelian) Groups and Sylow's Theorems

Finitely Generated Abelian Groups and the Smith Normal Form

Permutation Groups and the Semidirect Product

Rings, Ideals, and Homomorphisms

The Hierarchy of Integral Domains

The Jordan Canonical Form, the Rational Canonical Form, and the Smith Normal Form


Schedule (Fall 2021)

Date

Topic

 Assigned Problems

Video

Hints
6 / 7 October

organizational meeting

13 / 14 October

  • the minimal polynomial of an algebraic element

  • the inverse of an element in a simple field extension
  • Q3, August 2018
  • Q3, January 2018
  • Q4, January 2017
  • Q4, January 2015
  • Q6, August 2014
  • Q2, August 2012
  • Q3, August 2011
  • Q3, January 2010
 hints
20 / 21 October

  • the degree of a (finite) field extension

  • the splitting field of a polynomial
  • Q6, January 2020
  • Q6, August 2019
  • Q3, January 2019
  • Q3, August 2017
  • Q2, August 2016
  • Q2, January 2016
  • Q3, January 2014
  • Q4(a, b), August 2013
  • Q3, January 2013
  • Q3, August 2010
 hints
27 / 28 October

  • the minimal polynomial of an algebraic element

  • the inverse of an element in a simple field extension

  • the degree of a (finite) field extension

  • the splitting field of a polynomial
  • Q4, January 2017
  • Q2, August 2016
  • Q2, January 2016
  • Q4, January 2015
  • Q3, January 2014
  • Q4(a, b), August 2013
  • Q3, January 2013
  • Q2, August 2012
  • Q3, August 2011
  • Q3, January 2010
  • Q3, August 2010
 hints
10 / 11 November

  • Smith Normal Form

  • Jordan Canonical Form

  • Rational Canonical Form
  • Q1(a), January 2021
  • Q3(a), January 2021
  • Q1, January 2020
  • Q5, January 2018
  • Q6, January 2017
  • Q6, January 2013
  • Q6, August 2011
  • Q5, January 2010
  • Q5(i), August 2009
  • Q4, January 2009
  • Q5, January 2009
  • Q4(a, b), August 2008
  • Q4, January 2008
 hints
17 / 18 November

  • Smith Normal Form

  • Jordan Canonical Form

  • Rational Canonical Form
  • Q3(b), January 2021
  • Q3, Fall 2020
  • Q6, August 2018
  • Q6, August 2017
  • Q4, January 2016
  • Q2, August 2014
  • Q6, January 2014
  • Q4, January 2011
  • Q4, August 2010
 hints
1 / 2 December

  • the characteristic and minimal polynomials of a linear operator

  • T-invariant subspaces
  • Q4, August 2016
  • Q4, August 2015
  • Q6, August 2015
  • Q6(a, b), January 2015
  • Q6(a), August 2013
  • Q5, August 2010
  • Q5(ii, iii), August 2009
 hints
22 / 23 December

  • general Q&A from previous exams
  • Q1, January 2018
  • Q2, January 2018
  • Q1, August 2016
6 / 7 January

  • general Q&A from previous exams
  • TBD

 

Last updated at 2:45 PM on Tuesday, 19 May 2022.