Algebra and Number Theory

See here for our Algebra and Number Theory Seminar Schedule.

Gauss Emmy Noether
Algebra
&
Number Theory
David Hilbert J. MacWilliams
      C.F. Gauß       E. Noether           D. Hilbert F.J. MacWilliams

 

Faculty
Alberto Corso Commutative Algebra
Paul Eakin Commutative Algebra
Heide Gluesing-Luerssen Algebraic Coding Theory
Dave Jensen Algebraic Geometry
David Leep Quadratic Forms
Uwe Nagel Commutative Algebra and Algebraic Geometry
Avinash Sathaye Algebraic Geometry

 

Current Doctoral Students (Post Qualifying Exam)
Isaiah Harney (Gluesing-Luerssen)
Eric Kaper (Nagel)
Theodoros Kyriopoulos (Enochs)
Tefjol Pllaha (Gluesing-Luerssen)
Luis Sordo Vieira (Leep)
Bill Trok (Nagel)

Former Doctoral Students >>

Emeriti and Former Members
James Beidleman (Emeritus) Group Theory
Donald Coleman (Emeritus) Group Rings
Edgar Enochs Homological Algebra
Cornelia Yuen(PostDoc) Commutative Algebra and Algebraic Geometry
Bonnie Smith (PostDoc) Commutative Algebra
Augustine O'Keefe (PostDoc) Commutative Algebra


Seminar

In Spring 2017 the seminar takes place Wednesdays, 2:00 - 3:00 pm, in POT 745. Coordinator: Dave Jensen. A tentative list of scheduled talks can be found here.

List of talks/abstracts since Summer 2009
Seminar events before Summer 2009


Graduate Courses in Algebra

Spring 2017:

  • MA 661 - Algebra II - D. Jensen
  • MA 764 - Selected Topics in Algebra: Coding Theory - H. Gluesing-Luerssen
  • Ma 765 - Selected Topics in Algebra: Hilbert Functions - U. Nagel

Fall 2016:

  • MA 561 - Algebra I - D. Jensen
  • MA 565 - Linear Algebra - H. Gluesing-Luerssen
  • Ma 665 - Rings and Modules - U. Nagel
  • Ma 765 - Selected Topics in Algebra - D. Leep

Spring 2016:

  • MA 661 - Algebra II - U. Nagel
  • MA 764 - Selected Topics in Algebra - A. Corso
  • Ma 765 - Selected Topics in Algebra: Duality Theory for Modules over Finite Frobenius Rings - H. Gluesing-Luerssen

Fall 2015:

  • MA 561 - Algebra I - U. Nagel
  • MA 565 - Linear Algebra - D. Jensen
  • Ma 764 - Selected Topics in Algebra: Finite Frobenius Rings and Character Theory - H. Gluesing-Luerssen

Spring 2015:

  • MA 661 - Algebra II - H. Gluesing-Luerssen
  • Ma 764 - Selected Topics in Algebra: Intro to Algebraic Curves - D. Jensen
  • Ma 765 - Selected Topics in Algebra: Commutative Algebra - A. Corso

Fall 2014:

  • MA 561 - Algebra I - H. Gluesing-Luerssen
  • MA 565 - Linear Algebra - U. Nagel
  • Ma 764 - Selected Topics in Algebra - A. Sathaye

Spring 2014:

  • MA 562 - Modern Algebra II - A. Sathaye
  • MA 764 - Selected Topics in Algebra: Integral Quadratic Forms - D. Leep
  • Ma 765 - Selected Topics in Algebra: Representation Theory - U. Nagel

Fall 2013:

  • MA 561 - Modern Algebra I - A. Sathaye
  • MA 565 - Linear Algebra - E. Enochs
  • Ma 764 - Selected Topics in Algebra - A. Corso

Spring 2013:

  • MA 562 - Modern Algebra II - A. Corso
  • MA 764 - Selected Topics in Algebra: Algebras, Coalgebras and Bialgebras - E. Enochs
  • Ma 765 - Selected Topics in Algebra: Algebraic Geometry and Commutative Algebra - U. Nagel

Fall 2012:

  • MA 561 - Modern Algebra I - A. Corso
  • MA 565 - Linear Algebra - D. Leep
  • Ma 765 - Topics in Coding Theory - H. Gluesing-Luerssen

Spring 2012:

  • MA 661 - Modern Algebra II - H. Gluesing-Luerssen
  • MA 764 - Selected Topics in Algebra - E. Enochs
  • Ma 765 - Selected Topics in Algebra: Schubert Varieties - U. Nagel

Fall 2011:

  • MA 561 - Modern Algebra I - H. Gluesing-Luerssen
  • MA 565 - Linear Algebra - A. Corso
  • Ma 765 - Topics in Number Theory - D. Leep

Previous Graduate Courses in Algebra >>


Current and Former Events


Sample Qualifying Coursework for Doctoral Students

  • MA 565 - Linear Algebra
    Vector spaces:  Basic definitions, dimension, matrices and linear transformations.
  • MA 561 - Modern Algebra I
    Groups:  Basic definitions, isomorphism theorems, permutation groups, structure of finitely generated abelian groups, groups acting on sets, the Sylow theorems, solvable groups.
    Rings:  Basic definitions, ideals, prime and maximal ideals, quotient rings, Euclidean rings, PID's and UFD's, field of fractions, polynomial rings, irreducibility criteria.
  • MA 661 - Modern Algebra II
    Fields:  Algebraic extensions, splitting fields, separable extensions, finite fields.
    Galois Theory:  Fundamental Theorem of Galois Theory, Galois group of polynomials, solvability of polynomial equations, symmetric polynomials.

Suggested text:
1) Abstract Algebra (3rd edition), by D. Dummit and R. Foote
Preliminaries; Ch. 1; Ch. 2; Ch. 3; Ch. 4; Ch. 6 (sect. 1); Ch. 7; Ch. 8; Ch. 9; Ch. 13; Ch. 14

Additional texts:
2) Algebra, by T. Hungerford
Ch. 1 (sec. 2-6); Ch. 2 (sec. 1, 2, 4-8); Ch. 3; Ch. 4 (sec. 1, 2, 6); Ch. 5 (sec. 1-6, 9); Ch. 8 (sec. 1-3)

3) Algebra (2nd edition), by S. Lang
Ch. 1 (sec. 1-6, 10); Ch. 2; Ch. 3 (sec. 1,2, 5); Ch. 5; Ch. 6 (sec. 1-5); Ch. 7; Ch. 8 (sec. 1-3, 7); Ch. 15 (sec. 2)

Here are some old prelim exams:

  Exam January 1995
Exam June 1995 Exam January 1996
Exam June 1996 Exam January 1997
Exam June 1997  
Exam June 1998  
  Exam January 2000
Exam June 2000 Exam January 2001
  Exam January 2002
Exam June 2002 Exam January 2003
Exam June 2003 Exam January 2004
Exam June 2004  
Exam June 2005 Exam January 2006
Exam June 2006 Exam January 2007
Exam June 2007 Exam January 2008
Exam May 2008 Exam January 2009
Exam June 2009 Exam January 2010
Exam June 2010 Exam January 2011
Exam June 2011 Exam January 2012
Exam June 2012 Exam January 2013
Exam June 2013  
Exam June 2014 Exam January 2015
Exam June 2015  

Maintained by Heide Gluesing-Luerssen.
Last update: November 4, 2016

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