Mathematical Linguistics Syllabus

Course Outline

Linguistics 570

Day

Reading

Assignment

Lecture

Background
Mon Aug 29   Assignment 1 Lecture  
Wed Aug 31 Chapter 1. Featured and important: pp 7,8. Laws of set theory.   Lecture  
Mon Sep 05 H'day H'day H'day H'day
Wed Sep 07 Chapter 2: Relations, functions. The main point: Defining sets. Predicates. Necessary and sufficient conditions.

Recursive definitions of sets.

Assignment 2 Predicate definitions and Russell's Pair of docks Recursion slides. Relations Slides. Functions Lecture (ctd).  
Mon Sep 12 Chapter 3: Equivalence relations Assignment: Chapter 3, Ex 1,2,3, Think about 4. Lecture Equivalence relations slides  
Wed Sep 14        
Mon Sep 19        
Wed Sep 21   Assignment. Ch. 6. P128. Exercises. 1a,c,d,e,f,g,h,i. 2a,b,c,e,f[!]. (Note: '!' means: watch out! Tricky!). 3a,b,c. 6[all] (use truth tables to decide!) 8a. Read but discuss later: Basic concepts of Logic. Chapter 5

Chapter 6, statement logic Logic lecture Laws of logic (ps, pdf). Logical laws and linguistic intuitions.

 
Mon Sep 26        
Wed Sep 28 Chapter 6. Proofs in statement logic Assignment. Ch. 6. (ctd) 9a,b,e,f. 10a, c, e    
Mon Oct 03        
Wed Oct 05 Chapter 7. Predicate logic: Assignment (pp 174-177):
  1. 1a,d,e,f,l,m,,r,x, y.
  2. 2a, c, d, e,f,h
  3. 3e.
  4. 7a,b,d
  5. 8a,b
Lecture slides.  
Mon Oct 10        
Wed Oct 12        
Mon Oct 17        
Wed Oct 19        
Mon Oct 24 Chapter 9 (which is short), focusing on 9.1, 9.2, 9.3. Algebra. Also read 10.1, which introduces groups by way of symmetries of the square. Midterm (pdf). Extended Examples: Symmetries of the Square.

Lecture slides.

Extra! Don't read it unless you're a real geek! Groups and Cryptography (ps, pdf).
Wed Oct 26        
Mon Oct 31 Chapter 11 (skipping 11.3, 11.4). Posets and Lattices. Examples with sets, logic. Distributivity. Groups assignment (this document summarizes the assignment given in class). Lecture (ps, pdf) Lecture.  
Wed Nov 02        
Mon Nov 07 Chapter 11 continued. Lattices. Lattice assignment (with feature structures). lattices. Linguistic applications

Lecture 3 on lattices:Feature structures (revised 10/15). Diagrams of feature structure lattices.

 
Wed Nov 09        
Mon Nov 14 Chapter 16, 17 Languages, grammars, automata. Finite-state automata. Introduction. What is an ATM? \Finite-state languages. Regular languages. Using set theory on strings.

Recursive definition of regular languages.

  Chapter 17.

Limitations of finite-state languages. The pumping lemma. Regular language intro Lecture on Regular languages, FSAs.

 
Wed Nov 16        
Mon Nov 21   Assignment: Ch 17: 8(all); 12e [construct the FSA for 11e]; Ch 18 1 (all); 3a; 7;8 Context free grammars and pda's. anbn, recursion versus iteration. Lecture on Everett on recursion.
Wed Nov 23        
Mon Nov 28   Final (pdf). Lecture (Are human languages context-free?). Review.