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15-259/559 Probability and Computing (PnC)
12 Units, FALL 2026

Where probability meets chocolate!
Probability theory has become indispensable in computer science:
  • It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty.

  • It is integral to CS theory, where probabilistic analysis and randomization form the basis of 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.

TEXTBOOK FOR CLASS

The course textbook is Introduction to Probability for Computing, 2024. The book is freely available here: www.probabilitybook.org . We will cover Chapters 1-18 of this book and parts of Chapter 19.

Discrete & Continuous Probability

  • Probability on events.
  • Discrete and continuous random variables.
  • Conditioning and Bayes.
  • Variance and higher moments.
  • Laplace transforms and z-transforms.
  • Gaussians and Central Limit Theorem.
  • Tails and stochastic dominance.

Systems Modeling

  • Heavy-tailed distributions.
  • Poisson processes.
  • Simulation of random variables.
  • Event-driven simulation.

Statistics

  • Estimators for mean and variance.
  • Maximum likelihood estimation (MLE).
  • MAP estimation.
  • Bayesian statistical inference.
  • Confidence intervals.
If you like this class, consider taking the follow-on class with the same textbook: 15-359 PnC II. That class covers Chapters 18-27: Chernoff bounds, Hoeffding Bounds, Balls-and-Bins Problems, Hashing, Randomized Algorithms, Discrete-Time Markov Chains, Ergodicity Theory.

CLASS/RECITATION TIMES:

  • Lectures: TUESDAY and THURSDAY 2:00 pm - 3:20 pm, WEH 7500

  • Recitations:

    • A: FRIDAY 9:00 am - 9:50 am, DH 1112, TAs: George + Michael F.
    • B: FRIDAY 1:00 pm - 1:50 pm, GHC 4211, TA : Pranav
    • C: FRIDAY 1:00 pm - 1:50 pm, GHC 4102, TAs: Max L. + Michael L.
    • D: FRIDAY 2:00 pm - 2:50 pm, PH A18C, TA: Max G.
    • E: FRIDAY 9:00 am - 9:50 am, Merged with Recitation A
    • F: FRIDAY 1:00 pm - 1:50 pm, PH A18A, TAs: Minerva + Megha
    • G: FRIDAY 2:00 pm - 2:50 pm, WEH 8427, TA: Nikhil + Nina

PROFESSORS:


Mor Harchol-Balter
harchol@cs.cmu.edu
OH: WED 5:30 - 7 pm, GHC 7207

Feras Saad
fsaad@cs.cmu.edu
OH: TUES 3:30 - 5 p.m., GHC 9225

TAs:


George Liu
georgeli@andrew
OH: TUES 6-7:30 p.m.
Location: 5th floor GHC, Carrel 2
Minerva You
minervay@andrew
OH: THURS 11:30 - 1 p.m.
Location: GHC 9115

Pranav Sangwan
psangwan@andrew
OH: THURS 3:30 - 5 p.m.
Location: 5th floor GHC, Table 1
Max Gao
maxgao@cmu.edu
OH: WED 1:30 - 3 p.m.
Location: 5th floor GHC, Table 1

Max Lee
maxwe@cmu.edu
OH: THURS 6-7:30 p.m.
Location: 5th floor GHC, Carrel 1
Megha Narayanan
meghanar@andrew
OH: MON 5-6:30 p.m.
Location: 5th floor GHC, Carrel 1

Michael Fryburg
mfryburg@andrew
OH: FRI 10-11:30 a.m.
Location: 5th floor GHC, Table 5 		-
Michael Liang
mliang4@andrew
OH: WED 3:30-5 p.m.
Location: 5th floor GHC, Table 1

Nikhil Sampath
nikhilsa@andrew
OH: MON 2:30 - 4 p.m.
Location: 5th floor GHC, Table 1 		-
Nina Yuan
mingyuyu@andrew
OH: WED 9:30 - 11 a.m.
Location: GHC 9115

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