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Project: Math 582b
Views: 476

Due: Sunday, January 10 (I'll collect it automatically)

1. How much have you used each of the following?

  • Python: never, [ ] a little, [ ] a lot

  • C/C++: never, [ ] a little, [ ] a lot

  • Sage: never, [ ] a little, [ ] a lot

  • Pari: never, [ ] a little, [ ] a lot

  • Magma: never, [ ] a little, [ ] a lot

Additional comments:

2. How familiar are you with each of the following topics? For each list, something you want to learn about that involves that topic.

  • Number fields:

  • Elliptic curves:

  • Exact linear algebra:

  • Modular forms:

3. What is your favorite algorithm in computational number theory that you basically understand?

Describe how it works.

4. Given an algorithm that you care about in computational number theory that you do not really feel you understand?

What does it do? What is confusing about it? Is there are slow algorithm that solves the same problem that you do understand?

5. Write code using each of Sage, Pari, and Magma that writes 2016 in binary. You can call any built-in functions. This is just to get you to try the programs.

Hints:

  • You can use Magma for free online here: http://magma.maths.usyd.edu.au/calc/ or with the magma_free command in Sage.

  • To run Pari in SMC, type gp on the command line, or %gp in a Sage worksheet cell.

6. Give an example of problem in number theory for which there is no currently known (or even conjectural) algorithm to solve that problem.

This is NOT a question about efficiency. It's a question about the existence of any algorithm at all. Make sure you understand what the word "algorithm" means.

7. Give an example of problem in number theory for which there is no currently known polynomial time algorithm to solve it.

This is a question about efficiency.