CS 680-501 Computer Algebra II Syllabus

Course Description

This course continues the survey of fundamental ideas in symbolic mathematical computation. Topics typically covered include: p-adic lifting, polynomial factorization, solution of systems of polynomial equations, Grobner bases. Additional topics may include: polynomial real and complex zero isolation, the CAD algorithm and its application to quantifier elimination, algorithms for symbolic integration.

Course Objective

To obtain an understanding of the design, implementation, and analysis of computer algebra algorithms. More specifically students will become familiar with the underlying mathematics and algorithm design, implementation and analysis of algorithms for the exact solution of polynomial equations. Students should be able to use, implement and analyze the fundamental algorithms for polynomial factorization, root isolation and refinement, and the exact solution of systems of polynomial equations using Groebner bases and resultant techniques.

The course will require several computational assignments utilizing Maple, and several programming assignments using both Maple and C or C++.

Prerequisites

Computer Algebra I.

Instructor

Jeremy Johnson

Office: 271 Korman Center
phone: 895-2893
e-mail: jjohnson@mcs.drexel.edu
office hours: MW 1-3 and T 4-6, additional hours by appointment.
 

Meeting Time

W 6:00-9:00 in Commonwealth 306

Textbook

Keith Geddes, Stephen Czapor, and George Labahn Algorithms for Computer Algebra. Kluwer Academic Publishers, 1992.

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Topics

1. Interpolation and Hensel Lifting
2. Polynomial factorization
3. Root Isolation and Refinement
4. Solving Systems of Equations
5. Resultants
6. Groebner Bases
7. Quantifier Elimination

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Grading

1. Homework assignments (five) 50% (10% each)
2. Programming project 50%