This graduate course presents a collection of ideas from mathematics and computer science that are of particular relevance to linguistics. The course does not require a strong background in mathematics, in fact it is intended for students with little or no advanced knowledge in mathematics and computer science. The relevance of these ideas for linguistics and language-related research will be a running theme of the class. Areas of linguistic relevance to be discussed will include phonetics, phonology, syntax, semantics, and learnability.
Graduate students from other departments who have an interest in language-related cognitive research are encouraged to register, and should feel free to contact the instructor with any questions.
The topics to be covered include the following:
- Algebraic concepts - logic, Boolean algebra, order and lattices
- Cardinality - counting and infinite sets
- Mathematical Reasoning - predicate calculus, mathematical induction
- Computation - formal languages and automata, language processing
- Mathematical Analysis - a brief introduction to calculus
- Statistics - probability, hypothesis testing, bias and variance
The linguistic applications to be discussed may include:
- Optimality Theory ERC entailment
- Semantics of plurals using semi-lattices
- Computational parsing (including prolog programming)
- Syntactic processing with agreement and filler/gap dependencies
- Reasoning over infinite candidate sets
- Continuous models of phonetic coarticulation
- Drawing statistically valid conclusions from linguistic data
- Formal Methods text, 2007 (NOTE: this will be heavily revised for Fall 2012)