COURSE SYLLABUS

Course Number: MATH 6670
Course Title: PROBABILITY AND STOCHASTIC PROCESSES I
Credit Hours: 3
Prerequisites: MATH 2630
 
I.	Course Objectives: To introduce students to the fundamental concepts
and techniques of probability theory and stochastic processes. The course will emphasize the use of probabilistic (intuitive) reasoning to create probability models for applications to queuing systems, inventory models etc. Simulation will be used to help students to develop their intuition.

	Schedule and Outline of Course Content: (Individual instructors may re-arrange the material and use different
headings.)
	Probability (6 classes)
Properties of probability, conditional probability, Law of Total Probability, independent events, Bayes Theorem  
Discrete random variables (8 classes)
Discrete random variables, expectations, variance, uniform, hypergeometric, binomial, and Poisson distributions, Laplace transforms.
	Random variables with absolutely continuous distributions (6 classes)
Expectations, variances, uniform, exponential, and normal distributions.
Simulation and the Law of Large Numbers (3 classes)
Simulating probabilities, expectations, discrete and absolutely continuous distributions.
	Discrete time Markov chains (12 classes)
Transition probabilities, classification of states, ergodic and periodic chains, absorbing chains, Markov reward processes, reversible chains, simulation.
	The Poisson Process (6 classes)
Arrival times and their properties, compound and filtered Poisson Processes, the Poisson renewal process, simulation.

	3. Possible Textbooks: 
		The Essentials of Probability, Durrett (1994);
		Probability, Pitman (1993)
		An Introduction to Stochastic Processes, Kao (1997).
		An Introduction to Stochastic Modeling, 3rd edition, Karlin and Taylor (1998)	Other texts may be used by individual instructors.

II.	Grading and Evaluation Procedures:
1. Course requirements: Typically tests, midterm exam, final exam are used with other methods of evaluation employed at the discretion of the instructor.
2. Grading system and percentages are determined by the instructor.

III. 	Policies related to the conduct of the class are set by individual instructors.