MATH
4LT3/6LT3 Project:
- Each student in the class will be expected to submit an
video presentation on
some
topic related to the course material. The presentation should not be
a
technical document that merely produces the proof of some
theorem. Ideally, it will deal with some aspect of the theory
of
computability not covered in the lectures or it will explore the
connection between some of
the material covered in the course with some other branch of
mathematics, computer science,
philosophy, psychology, history, etc, or with popular
culture.
The presentation could be historical in nature, for example, covering the
motivation and/or circumstances leading up to the development of the
formal notion of an
algorithm.
- The course textbook may provide some ideas
for topics, but you might be better off looking through other sources.
See below for a few suggestions. Dr. Valeriote may
also be
able to provide
assistance with this.
- Once you have settled on a topic, please send it in an
email to
Dr. Valeriote.
- Ideally,
the same topic won't be selected by more than one or two students, so
you should come up with a short list of possible esssay topics.
- The length of the video should be around 15 minutes.
- All sources used in your presentation should be properly
referenced and you should reference at least two separate, published
sources.
- Videos should be submitted in a standard video format to a dropbox
that will be set up on the Avenue To Learn site for this course.
- Once the videos have been submitted, they will be made available to the class for viewing.
Deadlines:
- Friday, 14
November: send your presentation topic in an email to Dr.
Valeriote.
- Wednesday, 3
December by 11:59pm: submit a copy of your presentation to the Avenue to learn course site.
Some
Resources:
- "The
Emperor's New Mind: Concerning
Computers, Minds, and the Laws of Physics" by Roger
Penrose,
published by Oxford University Press.
- "Shadows
of the Mind, a search for the Missing Science of Consciousness" by
Roger Penrose, published by Oxford University Press.
- The Stanford Encyclopedia of Philosophy website entries
on computability, the Church-Turing thesis, complexity theory, Alan
Turing, Alonzo Church, ...
- Introductory
books on the theory of computation, such as "Introduction to
the
Theory of Computation" by Michael Sipser, or "Elements of the Theory of
Computation" by Lewis and Papadimitriou.
- "Godel, Escher, Bach" by Douglas Hofstadter
- Turing's original paper on computability: “On
Computable Numbers, with an Application
to the Entscheidungsproblem”, Proceedings of the London
Mathematical Society, 2(42): 230–265 (this can be downloaded
here.)
- "The Golden Ticket" by Lance Fortnow (available as an ebook
from the McMaster Library system)
- "Quantum Computing since Democritus" by Scottt Aaronson
(available as an ebook from the McMaster Library system)
- "Turing's
Revolution", edited by G. Sommaruga and T. Strahm. This book
is
available as an ebook through
the McMaster Library system
Some
potential topics:
- The Turing Test
- Machine Learning
- The undecidable
- Other models of computation (lambda-calculus, Minsky
machines, recursive functions ...)
- Artificial Intelligence
- Chomsky Hierarchy
- Push down automata
- Grammars
- Complexity classes besides P and NP
- Cellular Automata
- Hilbert's Program
- NP complete problems
- Quantum Computing
- Connections with mathematical logic