Linguistics 726 Mathematical Linguistics (really: mathematics for and in linguistics)

 syllabus | course description | lectures | homework | book errata | links | readings | LING 726 2001 Website

Barbara Partee and Vladimir Borschev
Fall 2004, University of Massachusetts, Amherst

 

Lecture correspondence
Overview 2004 vs. 2001

Lectures 1-3: Basic Concepts of Set Theory, Functions, and Relations

Lecture 4, Section 1: Algebra: Signature, algebra in a signature. Isomorphisms, homomorphisms, congruences and quotient algebras.
Lecture 4, Section 2: Algebra, continued. Lattices and Boolean algebras

Rajesh's 1st guest lecture: Formalizing Optimality Theory: Some Preliminaries

Lecture 5: Statement Logic

Lecture 6: Predicate Logic format

Chris' Handout on Tree definitions

Lecture 7: Model Theory. Consistency, independence, completeness, categoricity of axiom systems. Expanded with algebraic view.

Lecture 8: Axioms and theories, more examples. Axiomatic description of properties of relations.

Lecture 9: Proof by Induction

Lecture 10: Statement Logic as a word algebra on the set of atomic statements. Lindenbaum algebra

Lecture 11&12 (still under revision)

Lecture 13: Are Natural Languages finite-state languages? (and other questions) format

Lecture 14: Push-Down Storage Automata and Context-Free Grammars

Lecture 15: Finite State Transducers and OT Issues

Rajesh's 2nd guest lecture: Formalizing Optimality Theory: Complexity

Lecture 16: Infinities
Supplement: Is Language Infinite?