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 *  This course is especially suitable for students who are taking *
 *  or who have taken the graduate algebra courses.                *
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Course COMPUTER ALGEBRA offered in Fall 2006:
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MAS 5731   MWF 10:10am - 11:00am  Mark van Hoeij
  
What this course is about: At first sight you might be inclined to
think that algebra courses with topics like ideals, finite fields,
Galois theory or the Chinese remainder theorem are far away from any
practical application. But this is not the case: There are algorithms
to compute with almost everything you learn in algebra courses, and
these algorithms have many applications.
  
Learning how algebraic algorithms work will help you to gain a
better understanding of the concepts and constructions of algebra.
The ability to do algebraic computations makes the (often abstract)
concepts from algebra much more concrete, making them easier to  
understand. This will be of great value for students who are preparing
for the Algebra Prelim.
  
The topics covered in this course are:
  
1. Introduction to Maple, Euclidean algorithm.
2. Lattice reduction and applications in algebraic number theory.
3. Factoring polynomials and factoring integers.
4. Groebner basis techniques for computations in algebraic geometry.
  
Prerequisites: You have taken or are currently taking the graduate
algebra courses Groups, Rings, Vectorspaces. If you are not sure,
please contact the instructor.
  
Implementations: No prior programming experience is required for this
course. We will spend the first two weeks on learning how to use Maple and
how to implement algorithms in Maple.  If you have already taken a
computer algebra course then you will be given a different topic during
the first two weeks.
  
Textbook is optional, the necessary material will be handed out in
class (to see the course material from previous Computer Algebra courses,
go to my website and click on "Fall 2003" or on "Spring 2002"). For students
who want a textbook I recommend:
 http://www-math.uni-paderborn.de/~aggathen/mca/index.html
  
Instructor:  dr. Mark van Hoeij,   hoeij@math.fsu.edu 
                                   http://www.math.fsu.edu/~hoeij