# 15-259/659 Probability and Computing (PnC), SPRING 2022, 12 Units

## THE COOLEST of PROBABILITY CLASSES: Where probability meets chocolate

### Probability theory has become indispensable in computer science. It is at the core of machine learning, where one often needs to make decisions under stochastic uncertainty. It is also integral to computer science theory, where probabilistic analysis and ideas based on randomization appear in many algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

This is a FAST-PACED class which will cover MORE MATERIAL than the other probability options and will cover it in GREATER DEPTH.

### Part I: Everything You Ever Wanted to Know About Probability in 1 Month

 Probability on Events. Discrete and Continuous Random Variables. Conditioning and Bayes. Higher Moments. Laplace transforms and z-transforms. Gaussians and Central Limit Theorem. Tails and Stochastic dominance. Simulation of random variables. Heavy-tailed distributions.

### Part II: Randomized Algorithms with Full Proofs

 Concentration inequalities: Markov, Chebyshev, Chernoff Bounds. Las Vegas and Monte Carlo randomized algorithms. Randomized Sorting, Min-cuts, Balls-and-bins. Randomized Matrix-multiplication checking. Randomized Primality testing, Hashing, Tournament ranking, etc.

### Part III: Markov Chains with a side of Queueing Theory

 Discrete-time Markov Chains Ergodicity (with proofs) Continuous-time Markov chains. Poisson process. Elementary queueing theory with applications to modeling server farms, buffer provisioning, and capacity provisioning for data centers. Inspection paradox. PASTA.

## CLASS and RECITATION TIMES:

• Lectures: TUESDAY and THURSDAY 11:50 a.m. - 1:10 p.m. EST in Wean 7500.
• ## Recitations:

• (A) FRIDAY 9:05 a.m.. - 9:55 a.m. EST in GHC 4303 with Keshav
• (B) FRIDAY 1:25 p.m. - 2:15 p.m. EST in GHC 4215 with Vanshika and Tianxin
• (C) FRIDAY 2:30 p.m. - 3:20 p.m. EST in GHC 6115 with Alec
• (D) FRIDAY 1:25 p.m. - 2:15 p.m. EST in Wean 6403 with Carol and Adrian

## PROFESSORS:

 Mor Harchol-Balter harchol@cs.cmu.edu OFF HRS: Wed 5:30 - 7:00 p.m., GHC 7207 Weina Wang weinaw@cs.cmu.edu OFF HRS: Mon 5:00 p.m. - 6:30 p.m. GHC 9231

## TAs:

 Alec Sun alecsun@andrew OFF HRS: Tuesday 3:00 p.m. - 4:30 p.m. EST in Wean 8211. Tianxin Xu tianxinx@andrew OFF HRS: Wednesday 11:30 a.m. - 1:00 p.m. EST in 5th Floor Commons Carol Xinyi Zheng xinyizhe@andrew OFF HRS: Tuesday 6 p.m. - 7:30 p.m. EST in GHC 6023. Keshav Narayan ksnaraya@andrew OFF HRS: Thursday 10 a.m. - 11:30 a.m. EST in 5th floor commons. Adrian Abedon aabedon@andrew OFF HRS: Wednesday 1:00 p.m. - 2:30 p.m. in 5th floor commons. Vanshika Chowdhary vchowdha@andrew OFF HRS: Thursday 8:30 p.m. - 10:00 p.m. EST at GHC Carrel 3 on 5th floor.