15259/659 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 FASTPACED 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 ztransforms.

 Gaussians and Central Limit Theorem.
 Tails and Stochastic dominance.
 Simulation of random variables.
 Heavytailed distributions.

Part II: Randomized Algorithms with Full Proofs
 Concentration inequalities: Markov, Chebyshev, Chernoff Bounds.
 Las Vegas and Monte Carlo randomized algorithms.

 Randomized Sorting, Mincuts, Ballsandbins.
 Randomized Matrixmultiplication checking.
 Randomized Primality testing, Hashing, Tournament ranking, etc.

Part III: Markov Chains with a side of Queueing Theory
 Discretetime Markov Chains
 Ergodicity (with proofs)
 Continuoustime Markov chains.
 Poisson process.

 Elementary queueing theory with
applications to modeling server farms, buffer provisioning,
and capacity provisioning for data centers.
 Inspection paradox. PASTA.

Optional 3unit Mini class, 15260 Statistics and Computing, provides a statistics supplement for students wishing to receive an ML minor or do an ML concentration.
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 HarcholBalter
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.

SPONSORs:
Thanks to Citadel for covering all textbooks and chocolate!

