- 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.
**Home work for week 1.**Carefully study the worksheets we did in class. If anything is not clear, make sure to ask me about it. Do the following assignments during this week.-
**Turn in home work:**Compute the set of all cubes of all integers from 1 up to 25. Then compute the set of all numbers that are the sum of three of such cubes. Then determine the intersection so that you find: The set of all cubes of integers 1 .. 25 that are itself the sum of three (not necessarily distinct) cubes. Then e-mail me (hoeij@math.fsu.edu) the Maple commands that you used to find this set. Turn this in on or before Friday**August 31**. Hint: something very similar (but then the sum of 2 squares instead of 3 cubes) was done in the worksheet on sequences. - Whenever you have a question, do not wait, feel free to come to my office (105B LOV) at any time. You may even ask questions about an assignment.
- Programming in Maple.
- Programming assignment: multiplication of polynomials.
- The Euclidean Algorithm, a sorting algorithm based on divide and conquer. The Extended Euclidean Algorithm, an assignment.
- A worksheet on FFT.
- 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, due on Wednesday) and applications.
- in class assignments.
- Integration of rational functions. Homework: do the exercise in this worksheet.
- Integration of rational functions, part 2.
- Short introduction to resultants. For more on resultants see the course from fall 1999.
- The residue.
- More on residues.
- differential fields, logarithms polynomial case, logarithms general case.
- Valuations.
- One more example for integration with a logarithmic extension. Study this worksheet!
- Liouvilles principle.
- The exponential case.
- Another example for the exponential case.
- Programming: Study the following worksheet intro and rational functions.
- Multiplication, division, and GCRD
- Exponents of an operator.

**Week 1.**