PDF T6 Course Specifications 10 6 2017

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Course Title: Stochastic processes Course Code: MTHF3504

Program:

BSc. in Mathematics

Department:

Mathematics

College:

Jamoum University College

Institution:

Umm Al-Qura University

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3 A. Course Identification

1. Credit hours: 4 2. Course type

a. ^University ^College ^Department ✔ ^Others

b. ^Required ^Elective ✔

3. Level/year at which this course is offered:

4. Pre-requisites for this course (if any):

Introduction to real analysis and probability theory 5. Co-requisites for this course (if any):

Not applicable

6. Mode of Instruction (mark all that apply)

No Mode of Instruction Contact Hours Percentage

1 Traditional classroom Four hours/week %100

2 Blended 0 0

3 E-learning 0 0

4 Distance learning 0 0

5 Other 0 0

7. Contact Hours (based on academic semester)

No Activity Contact Hours

1 Lecture 40

2 Laboratory/Studio 0

3 Tutorial 0

4 Others (specify) 0

Total 40

B. Course Objectives and Learning Outcomes

1. Course Description

A stochastic process is a set of random variables indexed by time or space. Stochastic modelling is an interesting and challenging area of probability and statistics that is widely used in the applied sciences. In this course, you will acquire the theoretical knowledge and practical skills essential for the analysis of stochastic systems. You will learn the basic

concepts of the theory of stochastic processes and study different types of stochastic processes including Markov chains, Poisson processes and birth-and-death processes.

2. Course Main Objective

The course objective is to achieve an elementary knowledge of stochastic processes. This module provides a rigorous introduction to this topic. Students will develop a solid mathematical background in stochastic processes that will allow them to understand key results from modern mathematical finance.

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3. Course Learning Outcomes

CLOs Aligned

PLOs 1 Knowledge and Understanding: by the end of this course, the

student is expected to be able to

1.1 Identify and apply the most appropriate stochastic process technique for a given applied problem.

1.2 Define basic concepts from the theory of Markov chains and present proofs for the most important theorems.

1.3 Interpret and understand the solution for a stochastic process application.

1.4 Compute probabilities of transition between states and return to the initial state after long time intervals in Markov chains.

2 Skills : by the end of this course, the student is expected to be able to

2.1 Interpret and understand the solution for a stochastic process application.

2.2 Apply probability and matrix theory to solve stochastic models.

2.3 Determine limit probabilities in Markov chains after an infinitely long period.

3 Values: by the end of this course, the student is expected to be able to

3.1 Document and articulate the results and conclusions for stochastic process techniques applied to actual cases in a variety of disciplines.

3.2 Apply the theory to model real phenomena and answer some questions in applied mathematical finance.

3.3 Apply scientific models and tools effectively.

3.4 Apply knowledge gained during the course using computer applications

C. Course Content

No List of Topics Contact

Hours

1

Introduction : definition of stochastic process, type of stochastic processes, properties of stochastic processes, some common stochastic processes

4

2

Markov chain: definitions and examples,

multistep transition probabilities, classification of states, stationary distributions, limit behavior,

12 3 Poisson processes: defining the Poisson process, compound Poisson

processes, transformations, memoryless property 8

4 Branching processes: discrete time branching processes, extinction

probabilities, continuous time branching processes 8

5 Birth-and-death processes: pure birth process, pure death process 8

Total 40

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5 D. Teaching and Assessment

1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods

Code Course Learning Outcomes Teaching Strategies Assessment Methods K Knowledge and Understanding

K.1

Identify and apply the most appropriate stochastic process technique for a given applied

Lectures Tutorials Discussion Problem Solving

Exams(Midterm and Final).

Quizzes.

K.2

Apply probability and matrix theory to solve stochastic models.

Lectures Tutorials Discussion Problem Solving

Exams

(Midterm and Final).

Quizzes.

K.3 Interpret and understand the solution for a stochastic process application.

Lectures Tutorials Discussion Brain Storming

Quizzes.

S Skills

S.1 Interpret and understand the solution

for a stochastic process application. Small group work.^Lecture.

Quizzes.

S.2 Apply probability and matrix theory to

solve stochastic models. Small group work.^Lecture.

Quizzes.

S.3

Determine limit probabilities in Markov chains after an infinitely long period.

Lecture.

Small group work.

Quizzes.

V Values

V.1

Document and articulate the results and conclusions for stochastic process techniques applied to actual cases in a variety of disciplines.

Cooperative education Exams(Midterm and Final).

Quizzes.

V.2

Apply the theory to model real phenomena and answer some questions in applied mathematical finance.

Cooperative education Exams(Midterm and Final).

Quizzes.

V.3 Apply knowledge gained during the course using computer applications

Cooperative education Coursework Self-study 2. Assessment Tasks for Students

# Assessment task* Week Due Percentage of Total

Assessment Score

1 Midterm exam Sixth week %25

2 Quizzes and HomeWorks During semester %25

3 Final exam End of semester %50

*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)

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6 E. Student Academic Counseling and Support

Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice :

Each group of students is assigned to a faculty member where he or she will provide academic advising. All faculty members are required to be in their offices outside teaching hours. Each faculty member allocates at least 4 hours per week to give academic advice and to answer to the questions of students about concepts studied during the lectures.

F. Learning Resources and Facilities

1.Learning Resources

Required Textbooks

1- Essentials of Stochastic Processes (Springer Texts in Statistics) 3rd ed. 2016 Edition by Rick Durrett. ISBN- 13: 978-3319456133 ISBN-10: 331945613X.

2- A First Course in Stochastic Processes , 2nd Edition by, Samuel Karlin, Howard E. Taylor Published by Elsevier Science Publishing Co Inc, United States (1975) ISBN 10:

0123985528 ISBN 13: 9780123985521

Essential References Materials

1- Probability and Random Processes, 2nd Edition, by Geoffrey R. Grimmett , David R. Stirzaker , Publisher Oxford

University Press; 3rd edition (August 2, 2001), Language:

English ISBN-10 : 0198572220 ISBN-13 : 978- 0198572220

2- Understanding Markov Chains: Examples and Applications 3rd Edition , by Nicolas Privault, Publisher Springer, (2018) ،ISBN 978-9811306587

Electronic Materials

Other Learning Materials

2. Facilities Required

Item Resources

Accommodation

(Classrooms, laboratories, demonstration rooms/labs, etc.)

Technology Resources

(AV, data show, Smart Board, software, etc.)

Data Show, Smart Board Other Resources

(Specify, e.g. if specific laboratory equipment is required, list requirements or

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Item Resources

attach a list)

G. Course Quality Evaluation

Evaluation

Areas/Issues Evaluators Evaluation Methods

Effectiveness of teaching and assessment

Students Direct

Quality of learning resources ^Students ^Direct

Extent of achievement of

course learning outcomes Faculty member Direct

Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)

Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)

H. Specification Approval Data

Council / Committee Council of the Mathematics Department

Reference No.

Date

PDF T6 Course Specifications 10 6 2017

Course Title: Stochastic processes Course Code: MTHF3504

Program:

Department:

College:

Institution:

2

Table of Contents

3

A. Course Identification

B. Course Objectives and Learning Outcomes

4

C. Course Content

5

D. Teaching and Assessment

6

E. Student Academic Counseling and Support

F. Learning Resources and Facilities

7

G. Course Quality Evaluation

H. Specification Approval Data