Computer Algebra II (CS 680-501)

 Announcments  Lectures  Programs  Course Resources   Assignments  Grading Policy
Course Announcement
The department of Mathematics and Computer Science is offering a two term graduate sequence (Computer Algebra I & II) in computer algebra algorithms during the Winter 99-00 and Spring 99-00 terms.

This course is of interest to computer science, mathematics, science, and engineering students who are interested in understanding the algorithms underlying computer algebra systems such as Maple. It is also of interest to students interested in computational mathematics, algorithm design and analysis, and complexity theory.

This course is open to advanced undergraduates and may be used for either the numeric computing or the algorithms tracks.

See syllabus for more details.

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.
Graduate computer science, mathematics, engineering, and science students interested in learning about the algorithms underlying computer algebra systems such as MAPLE. The course is appropriate for students interested in computational mathematics, algorithm design and analysis, and complexity theory.

This course is also open to upper level undergraduates interested in algorithms design and analysis and computational mathematics. The course counts towards either the numeric and scientific computing track or the algorithms and data structures track for computer science students.
Computer Algebra I
Jeremy Johnson
Office: 271 Korman Center
phone: 895-2893
office hours: MW 1-3, and T 4-6. Additional hours by appointment.
Meeting Time
W 6:00-9:00 in Commonwealth 306
  1. Keith Geddes, Stephen Czapor, and George Labahn Algorithms for Computer Algebra. Kluwer Academic Publishers, 1992.
  2. Maple V Computer Algebra System. The student edition is available for purchase. Access to Maple is available through department and university computers.
  3. The text will be supplemented by several journal articles and readings from texts available in the library.


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


  1. Homework assignments (five @ 10%) (50%)
  2. Programming projects (50%)


Reference Books
  1. to be added.
Web Pages
  1. Waterloo Maple
  2. Maple V Application Center
  3. SymbolicNet -- Symbolic Mathematical Computation Information Center
  4. IMACS Conferences on Applications of Computer Algebra

Look Here for Important Announcemen ts

Announcements (Last posted May 28 @ 11:25 am)


This list is tentative and may be modified at the instructor's discretion.
  1. Mar. 29, 2000 (CRT, Interpolation and Modular Algorithms - Chapter 5)
  2. April 5, 2000 (P-adic Lifting and Hensel's Lemma - Chapter 6)
  3. April 12, 2000 (Integral Polynomial Factorization - Chapter 6 and 8)
  4. April 19, 2000 (Polynomial Factorization over Finite Fields - chapter 8)
  5. April 26, 2000 (Polynomial Factorization over Finite Fields - chapter 8)
  6. May 3, 2000 (Real Root Isolation and Refinement)
  7. May 10, 2000 (Real Root Isolation and Refinement)
  8. May 17, 2000 (Groebner Bases - Chapter 11)
  9. May 24, 2000 (Groebner Bases - Chapter 11)
  10. May 31, 2000 (Quantifier Elimination)

Programs and Worksheets

Created: 3/27/00 (revised Apr. 10) by