Mathematics for linguists

Veranstaltungsart: Proseminar
Zeit: Tuesday/Thursday 4-6 p.m.
Raum: SfS, room 1.13

Gerhard Jäger
office: SfS, room 1.20
secretary: 1.22 (Christine Clauder)

Course description

Mathematical methods are essential for understanding and working in theoretical and computational linguistics. This course introduces the key concepts from the areas of set theory, algebra and logic, which belong to the basic repertoire of linguistic methods. The main goal of the course is to provide the students with sufficient competence in basic notations, terminology and concepts of discrete mathematics for their studies in theoretical and computational linguistics. Familiarity with concepts such as sets, functions and propositions, and the ability to work with simple proof techniques are a crucial prerequisite for subsequent courses.

The content of the course largely coincides with the courses "Formale Methoden I" and "Formale Methoden II" that I tought at Bielefeld University. At the homepages of these courses, you find course material in German.

syllabus

date topic literature
10/27
introduction set theory
PtMW, chapter 1 
10/29
relations and functions I
PtMW, chapter 1
11/3
relations and functions II
PtMW, chapter 1
11/5
orderings
PtMW, chapter 1
11/10
formal languages: foundations
PtMW, chapter 16
11/12
trees I, constituency
PtMW, chapter 16 
11/17
trees II, Chomsky hierarchy
PtMW, chapter 16
11/19
Finite automata
PtMW, chapter 17
11/24
regular expressions
HU, chapter 2
11/26
The pumping lemma
PtMW, chapter 17
12/1
context-free languages
PtMW, chapter 18
12/3
context-free languages (cont.)

12/8
statement logic: syntax and semantics
PtMW, chapter 6
12/10
statement logic: translation

12/15
statement logic: meta-logic and calculus of truth trees

12/17
practise test

1/7
statement logic: truth trees, natural deduction

1/12


1/14
statement logic: natural deduction

1/19


1/21
predicate logic: introduction

1/26
predicate logic: quantification

1/28
predicate logic: meta-logic and truth trees

2/2


2/4
predicate logic: natural deduction

2/9


2/11


2/16


2/18 written exam


literature:

[PtMW] Partee, B. H.., A. ter Meulen & R. E. Wall, Mathematical Methods in Linguistics, Kluwer, Dordrecht 1990.
[HU] Hopcroft, J. E. and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison Wesley 1979.