Detailed Course Contents
Math 4707 Probability and Stochastic Processes
Probability Law: Sets, Probabilistic Models, Conditional Probability, Independence, Total Probability Theorem, Bayes’ Theorem, Counting.
Discrete Random variables: Probability Mass Functions (PMF), Cumulative Distribution Functions (CDF), Expectation, Variance; Well known distributions (Uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution. etc.)
Continuous Random variables: Probability Density Functions (PDF), Cumulative Distribution Functions (CDF), Expectation, Variance; Well known distributions (Uniform distribution, Exponential distribution, Gaussian distribution).
Joint Random Variables: Joint PMFs, PDFs, Conditional Expectation, Covariance, Correlation, Independence of random Variables.
Stochastic Process: Counting Process (Discrete Time and Continuous Time), Independence, Fresh Start Property, Memoryless Property.
Bernoulli Process: Interarrival times, K-th arrival times, Splitting and merging of Bernoulli process.
Poisson Process: Exponential distribution, Memoryless property, Gamma distribution, Comparison of Exponential Random variables, Hypo-exponential distribution, Definition of Poisson process, Interarrival waiting time distribution.
Discrete time Markov Chains: Introduction, Classification of states, Chapman-Kolmogorov equations, Steady state behavior, Absorption probabilities and Expected time to absorption
Continuous time Markov Chains: Introduction, Birth-death processes, Transition probability function, Limiting probabilities.
Queuing Theory: Little’s formula, Kendall’s notation, M/M/1, M/M/K, M/M/1/K Queuing systems.
1. Introduction to Probability, Second Edition Author: Dimitri P. Bertsekas and John N. Tsitsiklis
2. Introduction to Probability Models, Eighth Edition Author: Sheldon M. Ross
3. Probability and Stochastic Processes Author: Roy D. Yates and David J. Goodman
4. Quivering Theory Author: Leonard Kleinrock.
Hum 4705 Accounting
Hum 4705 Accounting 3-0-0 Credit 3.00
The accounting profession, accounting concept, introduction to book keeping, rules of double entry, preparing balance sheets and profit and loss statement, balance-day adjustments, closing accounts, computerized accounting systems, accounting for companies, analysis of financial reports, product costing, cost planning and control, time value of money.
1. Principles of financial decision making, Ratnatunga J and others (Eds.), John Wiley, 1994
2. Accounting for financial decision making study guide, Waldman E and others (Eds.), John Wiley, 1994
CSE 4701 Artificial Intelligence and Expert Systems
Survey of concepts in artificial intelligence. Knowledge representation, search and control techniques. All machines and features of the LISP and PROLOG languages.
Problem representation: search, inference and learning in intelligent systems; systems for general problems solving, game playing, expert consultation, concept formation and natural language procession: recognition, understanding and translation. Case Study on Expert Systems.
1. Artificial Intelligence: A Modern Approach, Author: Stuart Russell and Peter Norvig
CSE 4702 Artificial Intelligence and Expert Systems Lab
Sessional Work base on course CSE 4701
CSE 4703 Theory of Computing
Formal methods of automata language and computability, Finite automata and regular expressions, Properties of regular sets, Context-free grammars, Push-down automata, Properties of context-free languages, Turing machines, Halting problem, Undecidability and Computability, Recursion function theory, Chomsky hierarchy, Deterministic context-free languages, Closure properties of families of languages, Computational complexity theory, Intractable problems, Applications in parsing, pattern matching and the design of efficient algorithms.
Finite state machines, Introduction to sequential circuits, basic definition of finite state model, memory elements and their excitation functions, synthesis of synchronous sequential circuits, iterative networks, definition and realization of Moore and Mealey machines.
1. Theory of Computation, Author: Michael Sipser
2. Introduction to Automata Theory, Languages and Computation, Author: Hopcroft and Ullman, Fourth edition, Narosa, 1998
3. Automata and Algebras, Author: Adamek, Kluwer, 1990