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Next offered in Spring 2020.

Course Description

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 to include 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, and semantics.

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 areas to be covered include the following:

  • Algebraic concepts – logic, Boolean algebra, order and lattices
  • Cardinality – counting and infinite sets
  • Computation – formal languages and automata, prolog programming
  • Mathematical Reasoning – automatic theorem proving, parsing as proof
  • Mathematical Analysis – a brief introduction to calculus
  • Probability and Statistics – discrete/continuous distributions, estimators, confidence intervals

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
  • Continuous models of phonetic coarticulation
  • Probabilistic grammar models

The software packages used in this course, SWI-prolog and R, are open source and freely available for a variety of computing platforms.

Example Syllabus

Fall 2016