All students are expected to attend all presentations and to arrive on time.

**Possible Topics:**
These are suggestions, but **you can also propose other topics**.
Topics need to be discussed with me and approved.
You should choose a topic that is not something you already know about.
When you meet with me, I can give more information about
the topics and can suggest further references.
You should also do some research about the topics.

Some of these may be covered in class, as the final choice of course material is still being worked out.

- Number theory (in Sage or something else).
- Cryptography (in Sage or something else), e.g. RSA, lattice-based crypto, elliptic curve crypto, etc.
- Integer factorization algorithms.
- Grobner bases (in Sage or something else).
- Combinatorics and/or graph theory (in Sage or something else).
- Numerical integration and differential equations (in Sage or something else).
- An introduction to another mathematical software package, such as Macauley, Singular, Maxima, etc.
- Topological data analysis (studying large data sets using algebraic topology).
- Kenzo, a powerful tool for doing computations in algebraic topology. Available as part of Sage.
- SageManifolds, or some other software for studying manifolds.
- Software for knot theory and links. Sage has some support.
- Quantum computing.
- Haskell, functional programming, lazy evaluation.
- Prolog, a language for encoding problems using logic.

**Duration:**
45-55 minutes.
The presentations are not long, so you will need to carefully
select the appropriate amount of material to present.
You should focus on the key ideas, with illustrative examples,
motivation, necessary background, and history (e.g. attributions and years).
The presentations can involve writing on a tablet, prepared slides, computer software,
or some combination.

**Grading:**
The presentations will be worth 40% of the overall mark in the course.
They will be graded on:

- Knowledge of material. Be prepared to answer questions.
- Organization: Well-organized; appropriate choice of topics and amount of material; good outline, on time.
- Clarity and style of presentation: speaking clearly, looking at audience, giving clear explanations, appropriate use of tablet/slides/technology, etc.
- Duration: if you end within the time span given, you get full marks for this category; otherwise, you lose marks. You might want to build some flexibility into the end of your presentation so you can adjust on the fly. And take into account that there may be questions during your talk.

**Timeline:**

- Now: look over topics and read about a couple of them.
- In class on May 27 we'll discuss topics and dates.
Bring at least
**two**possible choices of topic. - Give me a
**brief**outline (1 to 2 pages) ≥ 1 week ahead of your date. - Talks will take place June 22 to July 8.