Symbolic Dynamics: Projects

The Tuesday meetings can be used for project presentations. The idea is that one or two of the participants investigate a topic and report on their findings in class. Some of the projects are designed for students with expertise from other subjects, so that they in this way can educate the rest of us on interelations of that field with symbolic dynamics.

The list below consists of the basic projects I could think of. A presentation should be between 15 and 40 minutes; as our time is limited we need to plan this carefully. Later, we could compose more advanced projects in class based on the participants' interests.

Please consider volunteering for one of these projects. The ones that are color coded blue are still available.

Title Uses... Material Description Schedule
Data storage Computer science LM 2.5, [Mon], [MarSW]. Explain the relevance of shift spaces for data storage on media such as harddisks, zips, CD-roms etc. Investigate and report what storage schemes are currently in use. Thomas H.
Oct 12
Convolutional encoders Computer science, algebra LM 1.6 Give a lecture based on the contents of the relevant section of LM, explaining how we are using that in this case, the alphabet has extra mathematical structure. If possible, explain how such encoders are used. (Open)
Formal languages and automata Computer science, linguistics [BeaP], [HopU], [Per],... Give an overview of the theory of formal languages as you have learned it in your computer science or linguistics education. What are the basic results and how are they used? Explain what it has in common with symbolic dynamics, and what aspects differ. Torben
Sep 22
Symbolica Scientific computing Mathematica package Learn how to use the Symbolica package with Mathematica. Develop a Matematica worksheet which demonstrates the facilities. Use the worksheet to explain what it can do at an online presentation. Eik
Oct 13
Markov chains Statistics LM pp. 45-48, Give an overview of the theory of Markov chains and as you have learned it in your statistics or math/econ education. What are the basic results and how are they used? Anders
Niels
Sep 22
Perron-Frobenius theory Linear algebra
Statistics LM 4.2 Explain why you know this from your statistics or math/econ education, what you have been using it for. Give the proof of the PF-theorem that you have been taught. Give examples. Lola
Teresa
Nov 2
Billard systems Physics [Han1] [Han2] [Zhe] What are billard systems and why are they interesting in physics? What aspects of symbolic dynamics are used in their study? Thomas J.
Nov 16

Title	Uses...	Material	Description	Schedule
Data storage	Computer science	LM 2.5, [Mon], [MarSW].	Explain the relevance of shift spaces for data storage on media such as harddisks, zips, CD-roms etc. Investigate and report what storage schemes are currently in use.	Thomas H. Oct 12
Convolutional encoders	Computer science, algebra	LM 1.6	Give a lecture based on the contents of the relevant section of LM, explaining how we are using that in this case, the alphabet has extra mathematical structure. If possible, explain how such encoders are used.	(Open)
Formal languages and automata	Computer science, linguistics	[BeaP], [HopU], [Per],...	Give an overview of the theory of formal languages as you have learned it in your computer science or linguistics education. What are the basic results and how are they used? Explain what it has in common with symbolic dynamics, and what aspects differ.	Torben Sep 22
Symbolica	Scientific computing	Mathematica package	Learn how to use the Symbolica package with Mathematica. Develop a Matematica worksheet which demonstrates the facilities. Use the worksheet to explain what it can do at an online presentation.	Eik Oct 13
Markov chains	Statistics	LM pp. 45-48,	Give an overview of the theory of Markov chains and as you have learned it in your statistics or math/econ education. What are the basic results and how are they used?	Anders Niels Sep 22
Perron-Frobenius theory	Linear algebra Statistics	LM 4.2	Explain why you know this from your statistics or math/econ education, what you have been using it for. Give the proof of the PF-theorem that you have been taught. Give examples.	Lola Teresa Nov 2
Billard systems	Physics	[Han1] [Han2] [Zhe]	What are billard systems and why are they interesting in physics? What aspects of symbolic dynamics are used in their study?	Thomas J. Nov 16

Symbolic Dynamics/fall 99/eilers@math.ku.dk