Presentation topics, Mathematical Computation, Math 9171
Each student will give one presentation during the course.
I would like to have them spread through the second half of the
course, so I encourage people choosing topics near the top of
the list to speak earlier.
All students are expected to attend all presentations and to arrive on time.
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.
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.
The presentations will be worth 40% of the overall mark in the course.
They will be graded on:
Note that knowledge of material is just a small part of the grade.
The presentation itself is much more important. Because of this, you
should practice the talk at least once or twice beforehand, with someone listening, and you should time how long
it takes. This is extremely important. You should also address
your presentation to your fellow students, not to me; students in the audience
are strongly encouraged to ask questions during and after the talk.
- 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
- 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.
- 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
- Talks will take place June 22 to July 8.
Course home page.