Curriculum

Textbook: Sheldon M. Ross: "Introduction to Probability Models", 11th edition (2014), Academic Press, ISBN: 978-0-12-407948-9

Final curriculum

• Chapters 1-3: Only 2.9 (excluding example 2.53) is formal curriculum, but results from these chapters that we refer to in later chapters are assumed to be known 
• Chapter 4:
  • 4.1
  • 4.2, excluding examples 4.10 and 4.11. Excluding also pages 193-194 until the Remark on page 194
  • 4.3, excluding the last part of 4.3 from the last 1/3 of page 199, from random-walk in 2 dimensions
  • 4.4, excluding examples 4.24, 4.25 and 4.26
  • 4.5.1: The gambler's ruin problem
  • 4.6: Mean time spent in transient states 
  • 4.7: Branching processes
  • 4.8: Time reversible Markov Chains, until Example 4.35
  • 4.9: Markov Chain Monte Carlo Methods, until example 4.39
• Chapter 5:
  • 5.1
  • 5.2: The exponential distribution. Excluding middle of page 282-283, and excluding examples 5.1, 5.5, 5.7, 5.9, 5.10 and 5.11
  • 5.3: The Poisson Process. Excluding Remark (i) on page 301, examples 5.16, 5.17, the rest of 5.3.4, examples 5.19, 5.20, 5.21 and 5.22 and subsection 5.3.6
  • 5:4: Generalizations of the Poisson process. Excluding subsection 5.4.3
• Chapter 6:
  • 6.1
  • 6.2: Continuous-time Markov Chains
  • 6.3: Birth and death processes, excluding the rest after Example 6.7
  • 6.4: The transition probability function P_ij(t)
  • 6.5 Limiting probabilities, excluding Example 6.16
  • 6.8: Uniformization
  • 6.9: Computing the transition probabilities
• Chapter 7:
  • 7.1: Introduction
  • 7.2: Distribution of N(t)
• Chapter 10:
  • 10.1: Brownian motion
  • 10.2: Hitting times, maximum variable, and the gambler's ruin problem
  • 10.3: Variations on Brownian motion