Algebra and Number Theory
See here for our Algebra and Number Theory Seminar Schedule.
& Number Theory 

C.F. Gauß  E. Noether  D. Hilbert  F.J. MacWilliams 
Faculty  

Alberto Corso  Commutative Algebra 
Heide GluesingLuerssen  Algebraic Coding Theory 
Dave Jensen  Algebraic Geometry 
David Leep  Quadratic Forms 
Christopher Manon  Algebraic Geometry 
Uwe Nagel  Commutative Algebra and Algebraic Geometry 
Avinash Sathaye  Algebraic Geometry 
Fernando Xuancheng Shao  Analytic Number Theory 
PostDocs  

Nathan Fieldsteel  Computational Alg. Geometry 
Current Doctoral Students (Post Qualifying Exam) 

Jared Antrobus (GluesingLuerssen) 
Eric Kaper (Nagel) 
Theodoros Kyriopoulos (Enochs) 
Aida Maraj (Nagel) 
Rachel Petrik (Leep) 
Tefjol Pllaha (GluesingLuerssen) 
Nandita Sahajpal (Leep) 
Bill Trok (Nagel) 
Jay White (Nagel) 
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 Fall 2017 the seminar takes place Wednesdays, 2:00  3:00 pm, in POT 745. Coordinator: Uwe Nagel. 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
Fall 2017:
 MA 565  Linear Algebra  H. GluesingLuerssen
 MA 561  Algebra I  D. Leep
 Ma 665  Rings and Modules  U. Nagel
 Ma 765  Selected Topics in Algebra: Combinatorial Commutative Algebra  C. Manon
Spring 2017:
 MA 661  Algebra II  D. Jensen
 MA 764  Selected Topics in Algebra: Coding Theory  H. GluesingLuerssen
 Ma 765  Selected Topics in Algebra: Hilbert Functions  U. Nagel
Fall 2016:
 MA 561  Algebra I  D. Jensen
 MA 565  Linear Algebra  H. GluesingLuerssen
 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. GluesingLuerssen
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. GluesingLuerssen
Spring 2015:
 MA 661  Algebra II  H. GluesingLuerssen
 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. GluesingLuerssen
 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. GluesingLuerssen
Spring 2012:
 MA 661  Modern Algebra II  H. GluesingLuerssen
 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. GluesingLuerssen
 MA 565  Linear Algebra  A. Corso
 Ma 765  Topics in Number Theory  D. Leep
Previous Graduate Courses in Algebra >>
Current and Former Events
 Mathematical Coding Theory in Multimedia Streaming, Workshop at the Banff International Research Station, October 2015; Coorganized by Heide GluesingLuerssen.
 International Conference in Homological Algebra; Including one day honoring Professor Edgar Enochs' career, July 2015;
 Singularities in algebraic geometry: how many times does a polynomial vanish at a point?, March 2015, Fifteenth Annual HaydenHoward Lecture presented by Robert Lazarsfeld, SUNY Stony Brook;
 3rd Bluegrass Algebra Conference, June 2012. Coorganized by Alberto Corso.
 Plato's Cave: How much can you tell from a shadow on the wall?, Tenth Annual HaydenHoward Lecture presented by David Eisenbud, University of California at Berkeley, April 2010.
 AMS Sectional Meeting #1057, March 2010, Coorganized by Alberto Corso.
 PASI: Commutative Algebra and its interactions to Geometry, Olinda (Brazil), August 314, 2009
 2nd Bluegrass Algebra Conference, March 78, 2009. Organized by Alberto Corso and Uwe Nagel.
 Math Club talk given by David Cox: Tangents to four unit spheres, March 5, 2009.
 Three Challenges of Claude Shannon, Eighth Annual HaydenHoward Lecture presented by Joachim Rosenthal, University of Zürich (Switzerland) , April, 2008. This talk is suitable for advanced undergraduates!
 UICPurdue Workshop, December 23, 2006.
 The History of Imaginary Numbers, presented by Robin Hartshorne, University of California (Berkeley). April 6, 2006. This talk is suitable for all undergraduates!
 Midwest Algebra, Geometry and their Interactions Conference (MAGIC 05), October 711, 2005.
 LipmanFest, May 1721, 2004.
 Bluegrass Algebra Conference and HaydenHoward Lectureship, April 1113, 2003.
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. 26); Ch. 2 (sec. 1, 2, 48); Ch. 3; Ch. 4 (sec. 1, 2, 6); Ch. 5 (sec. 16, 9); Ch. 8 (sec. 13)
3) Algebra (2nd edition), by S. Lang
Ch. 1 (sec. 16, 10); Ch. 2; Ch. 3 (sec. 1,2, 5); Ch. 5; Ch. 6 (sec. 15); Ch. 7; Ch. 8 (sec. 13, 7); Ch. 15 (sec. 2)
Here are some old prelim exams:
Maintained by Heide GluesingLuerssen.
Last update: July 31, 2017