15259/659 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 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: MONDAY and WEDNESDAY 2:40 p.m.  4:00 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:
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: Friday 10 a.m. EST ZOOM .

SPONSORs:
Thanks to Intel Corporation for providing a chocolate fund!
