Mathematics for linguists
Veranstaltungsart: Proseminar
Zeit: Tuesday/Thursday 46 p.m.
Raum: SfS, room 1.13
Gerhard
Jäger, Jason Quinley
office: SfS, room 1.20
secretary: 1.22 (Christine Glauder)
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 

10/19 
statement logic: syntax
and
semantics 
PtMW, chapter 6 
10/21 
statement logic:
translation 

10/26 
statement logic: metalogic and calculus of truth trees  
10/28 
statement logic: truth trees, natural deduction  
11/2 
statement logic: natural deduction, inductive proof  
11/4 

11/9 
predicate logic:
introduction 
PtMW, chapter 7 
11/11 
predicate logic:
quantification 

11/16 
predicate logic: metalogic and truth trees  
11/18 

11/23 
predicate logic: natural deduction  
11/25 

11/30 

12/2 
intermediate test 

12/7 
introduction set theory  PtMW, chapter 1 
12/9 
relations and functions I 

12/14 
relations
and
functions
II; orderings 

12/16 

12/21 
Formal language theory:
basics 

12/23 

1/11 
derivations,
automata 

1/13 

1/18 
regular
expressions 

1/20 

1/25 

1/27 
Pumping
Lemma 

2/1 
contextfree
languages 

2/3 
final test 
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.