# 15-259/659 Probability and Computing (PnC), SPRING 2020, 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: MONDAY and WEDNESDAY 2:20 p.m. - 3:40 p.m. EST ZOOM
• ## Recitations:

• (A) FRIDAY 9:10 a.m.. - 10:00 a.m. EST ZOOM led by Tianxin and Tai
• (B) FRIDAY 2:10 p.m. - 3:00 p.m. EST ZOOM led by Ishani and Jalani
• (C) FRIDAY 3:20 p.m. - 4:00 p.m. EST ZOOM led by Vanshika and Josh

## PROFESSORS:

 Mor Harchol-Balter harchol@cs.cmu.edu OFF HRS: Wed 7 p.m. - 8:30 p.m. ZOOM Weina Wang weinaw@cs.cmu.edu OFF HRS: Thurs 11 a.m. - 12:30 p.m. ZOOM

## NEW! Extra Weekend Short Office Hours:

• OFF HRS: Saturday, 10:30 a.m. - 11:15 a.m., with Mor or Weina ZOOM
• OFF HRS: Sunday, 11 p.m. - 11:45 p.m., with Jalani ZOOM .

## TAs:

 Ishani Santurkar ivs@andrew OFF HRS: Monday 12 p.m. - 1:30 p.m. ZOOM . Tianxin Xu tianxinx@andrew OFF HRS: Monday 4 p.m. - 5:30 p.m. EST ZOOM . Taisuke Yasuda taisukey@andrew OFF HRS: Tuesdays 12 p.m. - 1:30 p.m. EST ZOOM . Joshua Abrams jaabrams@andrew OFF HRS: Tuesday 7 p.m. - 8:30 p.m. EST ZOOM . Jalani Williams jalaniw@cs OFF HRS: Wednesday 12 p.m. - 1:30 p.m. EST ZOOM . Vanshika Chowdhary vchowdha@andrew OFF HRS: Thursday 8 p.m. EST ZOOM .