CSE 422/562: Modeling and Simulation

Course Information

Course Objectives

Upon successful completion of the course, students are expected to

• understand the basic concepts associated with the basic probability theory

• be familiar with random variables along with concepts such as the independence, mean, characteristic function, moment generating function, Markov chains, tail bounds etc. and apply the concepts to different problems.

• implement basic models on random processes used in different areas of science and engineering.

Instructor

Md. Shahriar Karim
Office location: SAC 1010C
Office hours: Click here

• Visit SAC 1010C during office hours, or send an e-mail for appointment

Textbooks

• Probability, Random Variables and Stochastic Processes, 4th Edition by A Papoulis, S Pillai

• Probability and Computing by Michael Mitzenmacher, Eli Upfal

Additional Textbooks

• Introduction to Probability Models by Sheldon M. Ross

• Probability, Statistics, and Random Processes for Electrical Engineering by Alberto Leon-Garcia

• Introduction to Probability, 2nd Edition by Dimitri P. Bertsekas and John N. Tsitsiklis

• Introduction to Probability for Data Science, by Stanley H. Chan

Additional Content

A few of the courses that are relevant to the content of this course, and may be useful to understand and practice the content better

• Introduction to Probability for Computing and Data Science, at Brown University by Professor Eli Upfal and Alessio Mazzetto

• Random Variables and Signals, by Professor Mark R. Bell, Purdue University

• ECE 302 by Professor Stanley Chan, Purdue University

• Probabilistic Systems Analysis And Applied Probability, OCW MIT

• ECE 302 by Professor Sujay Sanghavi, Purdue University

• Introduction to Probability, OCW MIT

• Algorithms, Probability, and Computing, ETH Zurich

Course Content and Policy

• Click here for details

Lecture Notes

Review of Math Background [notes]

• Sequence and Series

• Combinatorics

• Integration and Differentiation

• Real Analysis Preliminaries

Probability Theory

• Basics of Set Theory [notes]

• Axioms of Probabilty, Probability Mass Function (PMF) [notes]

• Conditional Probability and Bayes Theorem [notes]

• Statistical Independence [notes]

Random Variables (RV)

• Definition and Measurable Function [notes]

• Continuous and Discrete RV: PDF, CDF [notes]

• Mean, Variance of Random Variables [notes]

• Characteristic Functions and Moments [notes]

• Function of Random Variables [notes]

Jointly Distributed Random Variables

• Marginal PDFs

• Concepts of Correlation and covariance

• Sum of Two Random Variables

Limit Theorems

• Weak Law of Large Numbers

• Strong Law of Large Numbers

• Central Limit Theorem

Applications: Stochastic Process

• Basics of Stochastic Process and Point Process [notes]

• Markov Process, Markov Chain, Birth-Death Process [notes]

• Simples Queues: M/M/1, M/M/n/K [notes]

• Random Walk and Diffusion [notes]

• Markov Chain Approximation of Chemical Master Equation (CME)

Other Applications:

• Basics of Information Theory

• To be decided

Other Modeling Concepts

• Mathematics of Neural Network

• Image Analysis

Projects

• Individual Project: Simples Queues Modeling

Team Project

• To be decided

Assessment Tools and Grades

We follow the NSU grading standard with 93% for an 'A’ grade, and may curve the final letter grade a little (if needed).

• Homeworks: 10%

• Quizzes: 15-20%

• Individual Project: 5%

• Exam 1: 30-35%

• Exam 2: 30-35%

Homworks

• Homework 1: [Problems] [Solutions]

• Homework 2: [Problems] [Solutions]

• Homework 3: [Problems] [Solutions]

• Homework 4: [Problems] [Solutions]

• Homeowkr 5: [Problems] [Solutions]

• Homework 6: [Problems] [Solutions]

Projects

• Individual Project: Simples Queues Modeling

Team Project

• To be decided

Exams

Tentative schedules are as follows

• Quiz 1: After Lecture 7

• Exam 1: After Lecture 14

• Quiz 2: After Lecture 20

• Exam 2: As per NSU schedule, and the syllabus will be selectively comprehensive

Students’ Notes: [not edited by the course instructor]

• Lecture: 2, 3 [Notes]

• Lecture: 4, 5 [Notes]

• Lecture: 6, 7 [Notes]

• Lecture: 8, 9 [Notes]

Course Policies

This course will strictly follow the “NSU Code of Conduct”. However, a few important points you all should always remember, and follow, are as below:

• Failure to attend an exam or failure to submit an assignment on time receives zero except when it is unavoidable because of some genuine medical emergency (requires stringent proofs). In case of emergency, students should contact the instructor before the exam or before the stipulated date of assignment.

• Copying assignments are strictly prohibited; instead, discussion among students are encouraged. Please note down names of your peer classmates who you discussed during homework assignments. However, as the exams will largely follow the pattern of questions being asked in HW, solving those problems alone would help you during exams.

• Regrading requests for quiz, midterms should be conveyed within the 6 hours of the papers being returned in class.

• Unless the final grade is incorrectly computed, grade will NOT be changed once it is posted. There are no scopes of assigning additional works to improve your final grade.

• Your phone should be at silent mode.

• Please do not distract others by your non-academic and non-professional behaviors. This is the bare minimum civility that we expect.