Algebra and Number Theory
See here for our Algebra and Number Theory Seminar Schedule.
|C.F. Gauß||E. Noether||D. Hilbert||F.J. MacWilliams|
|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)|
|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|
Graduate Courses in Algebra
- 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
- 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
- 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
- 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
- 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
- MA 561 - Algebra I - H. Gluesing-Luerssen
- MA 565 - Linear Algebra - U. Nagel
- Ma 764 - Selected Topics in Algebra - A. Sathaye
- 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
- MA 561 - Modern Algebra I - A. Sathaye
- MA 565 - Linear Algebra - E. Enochs
- Ma 764 - Selected Topics in Algebra - A. Corso
- 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
- MA 561 - Modern Algebra I - A. Corso
- MA 565 - Linear Algebra - D. Leep
- Ma 765 - Topics in Coding Theory - H. Gluesing-Luerssen
- 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
- MA 561 - Modern Algebra I - H. Gluesing-Luerssen
- MA 565 - Linear Algebra - A. Corso
- Ma 765 - Topics in Number Theory - D. Leep
Current and Former Events
- Mathematical Coding Theory in Multimedia Streaming, Workshop at the Banff International Research Station, October 2015; Co-organized by Heide Gluesing-Luerssen.
- 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 Hayden-Howard Lecture presented by Robert Lazarsfeld, SUNY Stony Brook;
- 3rd Bluegrass Algebra Conference, June 2012. Co-organized by Alberto Corso.
- Plato's Cave: How much can you tell from a shadow on the wall?, Tenth Annual Hayden-Howard Lecture presented by David Eisenbud, University of California at Berkeley, April 2010.
- AMS Sectional Meeting #1057, March 2010, Co-organized by Alberto Corso.
- PASI: Commutative Algebra and its interactions to Geometry, Olinda (Brazil), August 3-14, 2009
- 2nd Bluegrass Algebra Conference, March 7-8, 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 Hayden-Howard Lecture presented by Joachim Rosenthal, University of Zürich (Switzerland) , April, 2008. This talk is suitable for advanced undergraduates!
- UIC-Purdue Workshop, December 2-3, 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 7-11, 2005.
- Lipman-Fest, May 17-21, 2004.
- Bluegrass Algebra Conference and Hayden-Howard Lectureship, April 11-13, 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.
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
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:
Maintained by Heide Gluesing-Luerssen.
Last update: November 4, 2016