My Lecture Notes on Calculus

Lecture Notes on Stochastic Calculus (Part I)

1 Probability “review” 3 1.1 σ-fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Probability measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Distribution of a random variable . . . . . . . ....

Lecture Notes on Stochastic Calculus (Part II)

2 Ito-Doeblin’s formula(s) 7 2.1 First formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Continuous semi-martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Integration by parts formula . . . . . . . . . . . ...

Lecture notes on the lambda calculus

This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, type inference,...

Mth142 College Calculus 2 Lecture Notes

Substitution in Lambda Calculus Lecture Notes

We study the formalization of lambda calculus based on De Bruijn terms. The most interesting aspect is a system of substitution primitives and an accompanying equational theory providing for algebraic proofs. The equational theory can be presented as a confluent and terminating rewriting system providing for proof automation. We prove that parallel reduction is strongly substitutive, the key pr...