- We will look at this Maple worksheet on sequences in class.
- We will look at this worksheet on polynomials and the use of the quotes: ' ' in class. If there's enough time we'll also look at the following worksheets: worksheet on rational functions, worksheet on modular arithmetic. Study the remaining worksheets for next time.
- Homework week 1.
- Programming in Maple.
- Another introduction to Maple and some exercises to test yourself (in the form of a pdf-file) with some of the answers.
- Programming assignment: multiplication of polynomials
(this contains the
**homework for week 2**). - A sorting algorithm (called merge sort) based on the "divide and conquer" approach.
- Multiplying polynomials with the "divide and conquer" approach: the Karatsuba algorithm (next week).
- The Euclidean Algorithm.
- On Tuesday we explain the Karatsuba algorithm and then practise programming in the classroom.
- Thursday: You can read the worksheet
The Extended Euclidean Algorithm
at home.
To practise the method of "ansatz with undetermined coefficients"
we will implement the computation of the polynomials s,t in a different
way. Furthermore, we will work on "partial fraction decomposition"
of rational functions. The
**homework for week 3**will be to do at least one out of these three: computing the s and t in the extended Euclidean Algorithm using the ansatz method, or partial fraction decomposition, or Karatsuba. - Integration of rational functions.
**Homework week 4**: do the exercise in this worksheet. - More on integration of rational functions.
- Short introduction to resultants. For more on resultants see the course from fall 1999.
- The residue.
- More on residues.
- One more example on integration of rational functions.
- Differential fields,
logarithms polynomial case (contains the
**homework week 6**). - Logarithms general case.
- Another example for a logarithmic extension.
- valuations, Liouvilles Principle.
- The exponential case example 1. Example 2
- Differential operators
- Exponents (contains an assignment (optional)).
- Solving polynomial equations, polynomial ideals: Groebner basis. Here is a text file that explains the notion of polynomial ideals.
- Buchberger's criterium (contains an assignment) and applications.
- in class assignments.

**Week 1.**
Note: Some of these documents are for Maple 5 and higher, some are
only for Maple 6 and higher. I'll change that later today.