Mathematics for linguists
Veranstaltungsart: Proseminar
Zeit: Tuesday/Thursday 4-6 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: meta-logic 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: meta-logic 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 |
context-free
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.