Type of Document Dissertation Author Veliz-Cuba, Alan A. URN etd-07092010-144024 Title The Algebra of Systems Biology Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Laubenbacher, Reinhard C. Committee Chair Burns, John A. Committee Member Jarrah, Abdul Salam Committee Member Mortveit, Henning S. Committee Member Tyler, Brett M. Committee Member Keywords

- Polynomial Algebra
- Finite Fields
- Model Reduction
- Reverse Engineering
- Finite Dynamical Systems
- Systems Biology
- Discrete Models
- Mathematical Biology
Date of Defense 2010-07-05 Availability unrestricted AbstractIn order to understand biochemical networks we need to know not only how their partswork but also how they interact with each other. The goal of systems biology is to look

at biological systems as a whole to understand how interactions of the parts can give rise

to complex dynamics. In order to do this efficiently, new techniques have to be developed.

This work shows how tools from mathematics are suitable to study problems in systems

biology such as modeling, dynamics prediction, reverse engineering and many others. The

advantage of using mathematical tools is that there is a large number of theory, algorithms

and software available. This work focuses on how algebra can contribute to answer questions

arising from systems biology.

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