Welcome to Mathematical Linguistics, a course covering the mathematics you need to know for Formal Linguistics. This course won’t be as rigorous as a math course, but you will be able to use all of this information and apply it to linguistics. If you have any questions or suggestions, please email them to contact@trevtutor.com

### Lectures

##### Introduction

##### Foundation of Mathematics

Basics of Set Theory

Power Sets

Set Operations

Set Laws

Ordered Pairs and Relations

Functions

Composition of Functions

Properties of Relations

Equivalence Relations and Partitions

##### Propositional Logic, Predicate Logic, and Compositional Semantics

Introduction to Propositional Logic and Truth Tables

Tautologies, Contradictions, and Contingencies

Logical Equivalence

Compositional Semantics with Propositional Logic

Compositional Semantics with Propositional Logic Examples

Introduction to Predicate Logic and Translation

Predicate Logic Syntax

Quantifier Raising and Logical Form

Compositional Semantics with Predicates

Compositional Semantics with Pronouns

##### Formal Languages and Automata

Introduction to Formal Languages and Finite State Machines

Formal Definition of Finite State Machines and Regular Operators

Regular Operations on Finite State Machines

Regular Expressions

Pumping Lemma for Regular Languages

Human Language is not Regular

Context-Free Grammar

Chomsky Normal Form

Pumping Lemma for Context-Free Languages

Context-Sensitive Grammar

Tree-Adjoining Grammar

##### Abstract Algebra

Algebras and Operations

Identity Elements, Inverse Elements, and Zero Elements

Groups

Subgroups, Semigroups, and Monoids

Integral Domains and Well-Ordering

Posets and Duality

Lattices and Semilattices

Filters and Ideals

Boolean Algebra

### Exams

Mathematical Linguistics – Exam 1 (Foundations of Mathematics, Propositional Logic, and Compositional Semantics)

Mathematical Linguistics – Exam 1 Solutions

Mathematical Linguistics – Exam 2 (Predicate Logic and Compositional Semantics)

Mathematical Linguistics – Exam 2 Solutions

Mathematical Linguistics – Exam 3 (Formal Languages and Automata)

Mathematical Linguistics – Exam 3 Solutions

Mathematical Linguistics – Exam 4 (Abstract Algebra)

Mathematical Linguistics – Exam 4 Solutions