ICM 2018 Lecture Sampler

Applied Logic - CS 4860 - 2018 - Lecture 2

In this lecture we will begin covering topics from Smullyan’s excellent textbook, First-Order Logic. Many people regard this as one of the best logic textbooks written for teaching the logic which is the title of the book. That topic is covered in Part II of the book. Part I is about Propositional Logic and certain simple facts about trees. Trees are important because Smullyan treats proofs as ...

Machine Learning Winter 2018 Lecture 8 : Regression

• y is the observable response of an experiment; typically represented via some vector in R for some m ≥ 1 • x are the “conditions under which the experiment is conducted”, which are freely chosen at the experimenter’s discretion prior to conducting the experiment; typically range over some experimental domain Ω such as (a subset of) R • θ is the vector of parameters that influence the experime...

Applied Logic - CS 4860 - 2018 - Lecture 1

For over two millennia logic developed as a distinct subject in philosophy and mathematics. It is now vitally important in computer science (CS) as well. Logic is essential to guarantee the correctness and safety of software systems on which society increasingly depends. A single coding error or misunderstanding in building a critical system component can and has resulted in disaster. Furthermo...

School of Mathematics Spring 2018 QUANTUM COMPUTATION Lecture notes

INFR 11102 : Computational Complexity 27 / 02 / 2018 Lecture 11 : Karp - Lipton Theorem , Randomized computation

To show L ∈ Σp2, we need to somehow change the order of quantifiers in (1). Our assumption is that NP ∈ P/poly, namely Sat has a polynomial-size circuit family C = {C1, C2, · · · }. For an input x, |x| = n, we give an Σp2 algorithm to decide whether x ∈ L. We first guess a circuit C for Sat. It may have two types of error: φ ∈ Sat but C(φ) = 0 or φ ̸∈ Sat but C(φ) = 1. There is at least one corr...