Previous editions
Semester 2 2019
Lie Groups and
Physics
Semester 1 2019
Coxeter Groups and
Hecke Algebras
The undergraduate seminar is back! This year the seminar will be
aimed at first year students. A seminar is an extracurricular activity
in which students work as teams to understand a topic and give a
presentation to the larger group about their work and write a
little essay about the topics covered. The work of
different teams builds on each other, wich will mean that you have
to speak to each other. Besides offering the opportunity of studying a topic
at greater depth and learning higher level oral and written
presentation skills than we cannot easily teach you in a regular class, our
seminars have an important social function in the department
life. This is where the community comes together as learners and
where the different study cohorts really start to take shape.
This year we would like to extend this experience to interested
first year students. In a normal year we would love to bring you
all together, and we would work on the chalk board. This year, we
will be working online.
The idea is to get you to work together in groups remotely, under
the guidance of some more experienced students and lecturers, so
that we have a chance to all grow together as a
community, even when we are apart physically.
We have extended this invitation also to a group of students from
Tsinghua, who had to cancel their visit to Melbourne in
February. We are excited to finally get to meet you.
Our seminar topic will be the mathematics underlying modern
cryptography.
Participants
will prepare their presentations under the guidance of one expert or
another, and give a practice talk in advance. Great emphasis is put
on clear and compelling exposition.
The material is designed for beginners, but
students of all levels are welcome to be involved.
If you have a different topic that you are interested in and would
like to organize something yourself, please do contact the
organizers and we will try to help you make it happen.
This seminar is coorganized by
Majid Alamudi, Nora Ganter, Rohan Hitchcock, Adam Walsh, Chengjing Zhang
and Gufang Zhao.
Here is the
the email
list for this seminar, to subscribe,
enter enter your email address and then click the link in the
confirmation email to subscribe (the website is not very clear on this).
If you have questions, contact
rhitchcock@student.unimelb.edu.au
Topics are as follows. (The list is likely to evolve once we have
an idea of participant numbers).
| Week |
Topics |
Speaker |
| 4
|
The Pascal triangle and binomial coefficients factorials and
counting. Lemma: p divides "p choose k" when p is a prime. [McC]
Fermat's Little Theorem: proof by induction, using Lemma. [Maz,3.2]
|
tba |
| 5 |
Modular arithmetic and the extended Euclidean algorithm. Bezout's
Lemma. Invertibility modulo m. [Maz,5] [Chi, Chapters 2 and 3]
|
tba |
| 6
|
Euclid's Lemma and Chinese remainder theorem. [Hutz]
|
tba |
| 7
|
Prime factorization, existence and uniqueness. [Chi, Chapter 4] |
tba |
| 8
|
RSA. Prove from Fermat. [Chi, Chapter 9]. |
tba |
| 9
|
Groups, cosets, Lagrange's Theorem and Euclid's
theorem. [Chi, Chapter 10] |
tba |
10
|
Discrete logarithm, Part1: ElGamal encryption [She] |
|
| 11
|
Discrete logariathm, Part 2: elliptic curve
encryption.[Hutz,Chapter 9][She] |
|
| References
|
[Chi] Lindsey N. Childs: Cryptology and Error Correction
-- An Algebraic Introduction and Real World Applications
[Hutz] Benjamin Hutz: An Experimental Introduction to
Number Theory
[Maz] David R. Mazur: Combinatorics, A Guided Tour
[McC] John McCleary: Exercises in (Mathematical Style) -- Stories
of Binomial Coefficients
[She] Thomas R. Shemanske: Modern Croptography and Elliptic
Curves: A Beginner's Guide.
|