Introduction to Probability for Computing

A highly engaging and interactive undergraduate textbook specifically written for computer science courses.

Mor Harchol-Balter (Author)

9781009309073, Cambridge University Press

Hardback, published 28 September 2023

555 pages
25 x 17.5 x 3 cm, 1.23 kg

'I know probability theory, and have taught it to undergrads and grads at MIT, UC Berkeley, and Carnegie Mellon University. Yet this book has taught me some wonderfully interesting important material that I did not know. Mor is a great thinker, lecturer, and writer. I would love to have learned from this book as a student - and to have taught from it as an instructor!' Manuel Blum, University of California, Berkeley, and Carnegie Mellon University

Learn about probability as it is used in computer science with this rigorous, yet highly accessible, undergraduate textbook. Fundamental probability concepts are explained in depth, prerequisite mathematics is summarized, and a wide range of computer science applications is described. Throughout, the material is presented in a “question and answer” style designed to encourage student engagement and understanding. Replete with almost 400 exercises, real-world computer science examples, and covering a wide range of topics from simulation with computer science workloads, to statistical inference, to randomized algorithms, to Markov models and queues, this interactive text is an invaluable learning tool whether your course covers probability with statistics, with stochastic processes, with randomized algorithms, or with simulation. The teaching package includes solutions, lecture slides, and lecture notes for students.

Preface
Part I. Fundamentals and Probability on Events: 1. Before we start ... some mathematical basics
2. Probability on events
Part II. Discrete Random Variables: 3. Probability and discrete random variables
4. Expectations
5. Variance, higher moments, and random sums
6. z-Transforms
Part III. Continuous Random Variables: 7. Continuous random variables: single distribution
8. Continuous random variables: joint distributions
9. Normal distribution
10. Heavy tails: the distributions of computing
11. Laplace transforms
Part IV. Computer Systems Modeling and Simulation: 12. The Poisson process
13. Generating random variables for simulation
14. Event-driven simulation
Part V. Statistical Inference
15. Estimators for mean and variance
16. Classical statistical inference
17. Bayesian statistical inference
Part VI. Tail Bounds and Applications: 18. Tail bounds
19. Applications of tail bounds: confidence intervals and balls-and-bins
20. Hashing algorithms
Part VII. Randomized Algorithms: 21. Las Vegas randomized algorithms
22. Monte Carlo randomized algorithms
23. Primality testing
Part VIII. Discrete-time Markov Chains
24. Discrete-time Markov chains: finite-state
25. Ergodicity for finite-state discrete-time Markov chains
26. Discrete-time Markov chains: infinite-state
27. A little bit of queueing theory
References
Index.

Subject Areas: Algorithms & data structures [UMB]