Sarjana Muda Sains (Matematik Teknologi) dengan KepujianBachelor of Science (Mathematics Technology) with Honours

Curriculum Structure According to Component

CATEGORY CODE COURSECREDIT

MATA PELAJARAN WAJIB UNIVERSITI

UWB 10202 Effective Communication 2UWB 10102

English For Academic Purposes 2

UWA 10302 TITAS 2UQX 1**01 Co-curiculum I 1UWB 10302 Technical Writing 2UWB 1**02 Foreign Language 2UQX 1**01 Co-curiculum II 1UWS 10103

Nationhood and Current Development of Malaysia 3

UWA 10102UWA 10202

Islamic Studies/Moral Studies

2

BWA 21002 Creativity and Innovation 2UWS 10202 Ethnic Relation 2  Jumlah 21

MATA PELAJARAN TERAS

BWA 10103 Computer Programming 1 3BWA 1020

Calculus I 3

1

3BWA 10303 Linear Algebra 3BWA 10403 Computer Programming 2 3BWA 10503 Calculus II 3BWA 10603 Discrete Mathematics 3BWA 20102 Basic Accounting 2BWB 10103 Statistics I 3BWA 20203 Graph Theory 3BWA 20303

Ordinary Differential Equations 3

BWA 20502 Scientific Computing Tools 2BWA 20702 Management 2BWB 10303 Statistics II 3BWA 20403 Linear Programming 3BWA 20603

Introduction To Fuzzy Set Theory 3

BWA 20803 Vector Calculus 3BWA 30102 Project Management 2BWB Data Analysis 3

2

21003BWA 30203

Topik-topik khas dan Isu semasa 3

BWA 20903 Numerical Analysis I 3BWA 30303

Partial Differential Equation 3

BWA 30503 Investment Analysis 3BWB 31403 Statistical Quality Control 3BWA 30603 Mathematical Modelling I 3

BWA 30403 Numerical Analysis II 3BWA 40103 Mathematical Modelling II 3BPK 20802 Entrepreneuship 2BWA 30702 Final Year Project 1 2BWA 40304 Final Year Project 2 4BWA 30804 Industrial Training 4

Total 86

ELECTIVE COURSE 

Computation BWA 31803

Java Programming 3

BWA Discrete Event Simulation 33

31703BWA 31903

Mathematics Element for Computer Graphics 3

BWA 41103

Metaheuristics Techniques in Mathematics 3

BWA 41003

Number Theory and Elementary Cryptography 3

Optimization

BWA 30903

Advanced Linear Programming 3

BWA 31203

Variation of Calculus 3

BWA 31303

Optimal Control 3

BWA 40603

Technique of Optimization I 3

BWA 40703

Technique of Optimization II 3

Operational Research

BWA 30903

Advanced Linear Programming 3

BWA 31103

Operation research in Transportation system 3

BWA 31003

Network Flow 3

BWA 40403

Inventory Control 3

BWA 40503

Queuing System 3

Actuarial Science BWA 31603

Mathematical Finance 3

BWA 31403

Actuarial Mathematics I 3

4

BWA 31503

Actuarial Mathematics II 3

BWA 40803

Risk Theory 3

BWA 40903

Stochactic Process 3

    Jumlah 15

5

COURSE COMPONENT CREDIT PERCENTAGE (%)

University 21 17.21 %Computer 8 6.55 %Mathematics 52 42.62 %Statistics 15 12.30 %Management and Entrepreneurship

11 9.02 %

Elective 15 12.30 %Total 122 100 %

6

YEAR 1, SEMESTER I

BWA 10103 Computer Programming 1

SynopsisIntroduction to Visual C++: Machine languages, object oriented programming, compilers, preprocessor directives. Input/ output, variable types, arithmetic and relational operations: Standard input and output commands, variable types, arithmetic and relational operators, precedence of operators, variable casting. Control structures and logical operators: Algorithms and pseudocodes, control structures, if, if-else, while, do-while and for statements. Functions and recursion: Math library functions, C++ standard library header files, function definitions, prototypes and arguments, storage classes, function call and argument passing, recursive functions. Arrays: Declaring single and multidimensional arrays, passing arrays to functions, searching and sorting arrays. Pointers and strings: Pointer variable declarations, passing arguments with pointers, pointer expressions and arithmetic, string manipulation functions. File processing: Creating a sequential file, opening files for input/ output, reading data and updating sequential files. Templates: Function templates and overloading function templates.

Reference1. Deitel, H. M. & Deitel, P. J. (2005). C++ How to Program. 5th Ed. New Jersey:

Prentice Hall.2. Horton, I. (2003). Beginning Visual C++ 6.0. USA, Indiana: Wiley Publishing,

Inc.3. Smith, M. (1999). Object-Oriented Software in ANSI C++. 2nd Ed. UK: McGraw-

Hill International.4. Bronson, G. J. (1999). A First Book of C++. USA: Brooks Cole Pub Co.5. Hyman, M. & Arnson, B. (1998). Visual C++ 6 for Dummies. USA: John Wilet &

Sons, Inc.

BWA 10203 Calculus I

SynopsisLimits and Continuity: Techniques of finding limits. Continuity. Differentiation: Techniques of differentiation: product rule, quotient rule. Chain rule. Implicit differentiation. Higher derivatives. Differentiation of trigonometric functions, logarithmic functions, exponential functions, implicit functions, parametric functions, hyperbolic functions and inverse functions. Applications of differentiation: approximate value and error, rates of change, motion along a line, gradient of curve at a point, maximum and minimum problems, curve sketching. L’Hopital’s Rule: Indeterminate form of type 0/0, /, 0 , 00, 0, 1, – . Integration: Techniques of integration: integration by substitution, integration by parts, integrating rational functions, integration of trigonometric functions, integration of hyperbolic functions and integration of irrational functions. Applications of integration: area of a region and volume of

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revolution. Further Differentiation and Integration: Derivatives and integrations involving inverse trigonometric and inverse hyperbolic functions. Applications: arc length, surface area of revolution, curvature

Reference1. Md. Raji, A. W., Rahmat, H., Kamis, I. Mohamad, M. N. & Ong, C. T. (2003).

Calculus for Science and Engineering Students. Malaysia: UTM Publication.2. Anton, H., Bivens, I. & Davis, S. (2002). Calculus. 7th Ed. USA: John Wiley &

Sons, Inc.3. Smith, M. (2006). Calculus: Concepts & Connections. 1st Ed. New York:

McGraw Hill. 4. Larson, R. E., Hostetler, R. P. & Edward, B. H. (1998). Calculus with Analytic

Geometry. 6th Ed. USA: Houghton Mifflin Company.5. Thomas, G. B. & Finney, R. L. (1996). Calculus and Analytic Geometry. 9th Ed.

USA: Addison-Wesley Publishing Company.6. Edward, C. H. & Penney, D. E. (1998). Calculus. 5th Ed. USA: Prentice-Hall,

Inc.

BWA 10303 Linear Algebra

SynopsisMatrices and Determinant: Matrix operations, elementary row operation and inverses, determinants of matrices. Linear system: solution using matrix inverse, Crammer’s rule, Gauss and Gauss Jordan elimination method. Vector Spaces: linear independence, spanning sets, bases, the rank of a matrix, orthogonal bases, Gram-Schmidt process. Linear Transformation: kernel and range. Eigenvalues and Eigenvectors: Diagonalization, Cayley-Hamilton Theorem

Reference1. Kolman, B. (1997). Introductory Linear Algebra with Applications. 6th Ed. USA:

Prentice Hall.2. Leon, S. J. (2006). Linear Algebra with Applications. 7th Ed. Upper Saddle

River, NJ: Pearson.3. Strang, G. (2006). Linear Algebra and its Applications. 4th Ed. CA: Thomson. 4. Lipschutz, S. & Lipson, M. L. (2001). Linear Algebra. 3rd Ed. New York:

McGraw Hill. 5. Anton, H. (2000). Elementary Linear Algebra. 8th Ed. USA: John Wiley.

YEAR 1, SEMESTER 2

BWA 10403 Computer Programming II

8

SynopsisA review of C++ fundamentals: Understanding data types, loops, conditional branching, mathematical functions, expressions and logical operators, file input/ output. Classes: Definition of structure and classes, data and array passing, inheritance and polymorphism. Windows programming for C++: Microsoft Foundation Classes (MFC), AppWizard, comments in AppWizard, improving output text. Menus and toolbars: Message maps and categories, creating and editing menus, adding toolbar buttons. Dialogs and controls: Create dialogs, spin button control, edit box control. Drawing curves: Drawing mechanisms in C++, drawing lines, rectangles, circles and curves.

Reference1. Deitel, H. M. & Deitel, P. J. (2005). C++ How to Program. 5th Ed. Upper Saddle

River: New Jersey Pearson Education, Inc.2. Horton, I. (2003). Beginning Visual C++ 6.0. Indianapolis, Indiana: Wiley

Publishing, Inc., 3. Smith, M. (1999). Object-Oriented Software in ANSI C++. 2nd Ed. UK: McGraw-

Hill International (UK) Limited.4. Bronson, G. J. (1999). First book of C++. USA: Brooks Cole Pub Co. 5. Hyman, M. & Arnson, B. (1998), Visual C++ 6 for Dummies. USA: John Wiley &

Sons., Inc.

9

BWA 10503 Calculus II

SynopsisSequence and series: Convergence/ divergence of sequences. Infinite series: Geometric series, p-series, alternating series and telescoping series. Convergence tests: divergence test, integral test, comparison test, limit comparison test, ratio test, root test, alternating series test and ratio test for absolute convergence. Absolute and conditional convergence. Power series. Taylor and Maclaurin series. Application of power series. Functions of Several Variables: Domain and range, contour lines, level curves and 3D-graphs. Limits and continuity. Partial derivatives and chain rules. Mixed derivatives. Rate of change. Total differentials and exact differentials. Local and absolute extreme values of functions of two variables. Lagrange multipliers. Multiple Integrations: Double integrals: Areas and volumes. Double integrals in polar coordinates. Surface areas. Triple integrals: Volumes. Triple integrals in cylindrical and spherical coordinates. Applications: Mass, moments of mass, centre of mass, centroid, centre of gravity, theorem of Pappus and moment of inertia. Change of variables in multiple integrals: Jacobians

Reference1. Anton, H., Bivens, I. & Davis, S. (2002). Calculus. 7th Edition. New York: John

Wiley. 2. Straud, K. A. (1996). Further Engineering Mathematics. 3rd Edition. England:

Macmillian Publication.3. Smith, R. T. & Minton, R. B. (2007). Calculus Early Transcendental Function. 3rd

Edition. New York: McGraw-Hill 4. Stewart, J. (2003). Calculus. 5th Edition. USA: Thomson Learning Inc.

BWA 10603 Discrete Mathematics

SynopsisSets and Logic: Sets, propositions, arguments, quantifiers. Proofs: Methods of proof, and mathematical induction. Functions, Sequences and Relations: Functions sequences, strings, and relations. Algorithms: Characteristics, examples, analysis, and recursive algorithms. Introduction to Number Theory: Divisors, integer algorithms, and Euclidean algorithm. Counting Methods: Combinations, permutations, and the Pigeonhole Principle. Recurrence Relations: Introduction, Solving recurrence relations, and the applications to the analysis of algorithms.

Reference1. Johnsonbaugh, R. (2009). Discrete Mathematics. 7th Ed. NJ: Pearson Education.2. Ross, K. A. & Wright, C. R. B. (1999). Discrete Mathematics. Upper Saddle

River, NJ: Prentice Hall.3. Truss, J. K. (1999). Discrete Mathematics for Computer Scientists. Harlow.

England: Addison-Wesley.10

4. Lovasz, L. (2003). Discrete Mathematics: Elementray and Beyond. New York: Springer.

5. Koshy, T. (2004). Discrete Mathematics With Applications. Burlington, MA: Elsevier Academic Press.

11

BWB 10103 Statistics 1

SynopsisStatistics and Probability I focus on The Nature of Statistics, Frequency Distributions and Graphs, Data Description, Index Number, Introduction to Probability and Probability Distributions.

Reference1. Khamis, A. et all. (2009). Introduction to Statistics. 1st Edition. Batu Pahat:

Pusat Pengajian Sains, UTHM2. Panel Statistics. (2009). Statistics Management. 1st Edition. Batu Pahat: Pusat

Pengajian Sains, UTHM3. Heng, C. Y. et all. (2003). Introduction to Probability & Statistics. Revised

Edition. FOSEE MMU. 4. Bluman, A. G. (2012). Elementary Statistics, A Step by Step Approach. New

York: MacGraw Hill International Edition.5. Triola, M. F. (2005). Essential of Statistics. 2nd Edition. Pearson Adison Wesley.

YEAR 2, SEMESTER I

BWA 20102 Basic Accounting

SynopsisBalance sheet, income statement, statement of cash flows, adjusting journal entries, financial statement analysis, cost behavior, cost-volume-profit analysis, budgeting, and relevant cost analysis.

Reference1. Lerner, J. J. & Cashin, J. A. (1999). Principles of Accounting I. 5th Ed. New York:

McGraw Hill. 2. Weygandt, J. J., Kieso, D. E., & Kimmel, P. D. (2005). Accounting Principles.

7th Ed. United States of America: John Wiley and Sons, Inc. 3. Abraham, A. et al. (2008). Accounting for Managers. 4th Ed. Australia: South-

Western/Cengage Learning.4. Zimmerman, J. L. (2009). Accounting for Decision Making and Control. 6th Ed.

Boston: McGraw-Hill.5. McLaney, E. J. (2007). Accounting: An Introduction. 4th Ed. Harlow: Financial

Times Prentice Hall.

BWB 10303 Statistics II

SynopsisStatistics and Probability II focuses on the Special Probability Distribution, Special Probability Densities, Estimation and Hypothesis Testing.

Reference

12

1. Panel Statistics. (2011). Statistics Management. 1st Edition. Batu Pahat: Fakulti Sains, Sastera & Warisan,UTHM.

2. Khamis, A. et all. (2009). Introduction to Statistics. 1st Edition. Batu Pahat: Pusat Pengajian Sains. UTHM.

3. Mendenhall, W., Beaver, R. J. & Beaver,B. M. (2006). Introduction to Probability & Statistics. Cengage Learning.

4. Bluman, A. G. (2012). Elementary Statistics, A Step By Step Approach. New York: MacGraw Hill. International Edition,

5. Triola, M. F. (2010). Essential of Statistics. 4th Edition. Pearson Education.

13

BWA 20203 Graph Theory

SynopsisGraphs: Introduction, definitions and types of graphs. Paths and Cycles: Connectivity, Eulerian graphs, Hamiltonian graphs. Trees: Properties and counting. Planarity: Planar graphs, Euler’s graphs, dual and infinite graphs. Colouring Graphs: Colouring vertices, Brooks’ theorem, colouring maps and edges, and chromatic polynomials. Digraphs: Eulerian digraphs and tournaments, and Markov chains. Matching, marriage and Menger’s Theorem: Hall’s theorem, transversal theory, Menger’s theorem and network flows.

Reference1. Wilson, R. J. (1996). Introduction to Graph Theory. 4th Edition. England:

Longman.2. Gross, J. L. & Yellen, J. (2006). Graph Theory and Its Applications. 2nd Edition.

Boca Raton: Chapman and Hall.3. Chartrand, G. & Zhang, P. (2004). Introduction to Graph Theory. 1st Edition.

Boston: McGraw-Hill.4. Sharma, S. C. (2007). Graph Theory. 1st Edition. New Delhi: Discovery

Publishing.5. Diestel, R. (2000). Graph Theory. 2nd Edition. New York: Springer.

BWA 20303 Ordinary Differential Equations

SynopsisFirst order differential equations: Origin of differential equations. Existence and uniqueness theorems. Methods of solution (separating the variables, homogeneous, linear and exact), Bernoulli and Riccati equation, initial and boundary value problems, applications of first order differential equations. Second order (and higher) linear differential equations: Methods of solution (undetermined coefficients and variation of parameters), applications of second order (and higher) linear differential equations. Series solutions of second order linear equations: Ordinary and singular points, powers series solution, Frobenius method. Laplace transforms: Definition, linearity, first shift theorem, multiplying by t. Unit step functions and Delta functions, second shift theorem. Inverse Laplace transform: Definition and properties, convolution theorem. Solve initial and boundary value problems for linear differential equations which involve unit step functions, Dirac Delta functions and periodic functions. System of ODEs: Theories of system of ODEs, homogeneous and nonhomogeneous system, critical points and stability, solution of system of ODEs by Laplace transforms.

Reference1. Md. Raji, A. W. & Mohamad, M. N. (2002). Differential Equations. Skudai: UTM

Publication.14

2. Boyce, W. E. & DiPrima, R. C. (2004). Elementary Differential Equations and Boundary Value Problems. USA: John Wiley & Sons, Inc.

3. Kuldeep Singh. (2003). Engineering Mathematics through Applications. USA: Industrial Press, Inc.

4. Lopez, R. J. (2001). Advanced Engineering Mathematics. USA: Addision Wesley.5. O’Neil, P. V. (2003). Advanced Engineering Mathematics. USA: Thomson

Brooks/ Cole.

15

BWA 20403 Linear Programming

SynopsisIntroduction: Brief history of linear programming, System of linear equations, System of linear inequalities, Linear programming formulations, Examples of linear programming models. Graphical Method: Graphical linear programming solutions, Graphical sensitivity analysis, Special cases of graphical solution, Computer solution. Simplex Method: Converting inequalities into equations, Primal simplex method, Pivot rules and operation, Artificial variable technique, Special cases in Simplex Method, Computer solution. Duality and Sensitivity Analysis: Definition of the dual problem, Primal-dual relationship, Economic interpretation of duality, Additional simplex algorithm, Post optimal / Sensitivity analysis.

Reference1. Dantzig,G. B. (1963). Linear Programming and Extensions. Princeton University Press.2. Taha, H. A. (1996). Operations Research: An Introduction. Prentice Hall.3. Strayer, J. K. (1989). Linear Programming and Applications. Springer-Verlag.4. Nordin, H. M. (2001). Pengaturcaraan Linear: Algoritma Simpleks Asas

Pengurusan Kuantitatif. Cetakan Pertama. Kuala Lumpur: NHM-ISM.5. Eiselt, H. A. & Sandblom, Carl-Louis. (2007). Linear programming and Its

Applications. Berlin: Springer.

YEAR 2, SEMESTER 2

BWA 20502 Scientific Computing Tools

SynopsisIntroduction to MATLAB: Command window. M-files. Variables, expressions and statements. File types in MATLAB. Mathematical operations in MATLAB: Mathematical operations. Logical and comparison operators. Symbolic calculations in MATLAB: Symbolic variables and expressions. Algebraic operations and equations. Manipulating algebraic expressions. Solving linear and nonlinear equations. Differentiations and integrations. Matrix operations in MATLAB: Matrices and arrays. Fundamental matrices. Matrix operations. Flow control structure: If, if-else, while, do-while, for, switch, break and continue. Functions: Functions in MATLAB and user defined functions. Graphics: 2D plot: Line, axis and colour control. 3D plot: Plotting surfaces. Contour plot. Solving ODEs with MATLAB: First and second order ODEs. Numerical methods. Solving linear algebra problems with MATLAB: Row operations. Eigenvalues and eigenvectors. Numerical methods.

Reference1. Kiryanov, D. (2003). The Mathcad 2001i Handbook. USA: Hingham.2. Frank, G. (2001). The Maple Book. USA: Boca Raton.

16

3. Amos, G. (2004). MATLAB: An Introduction With Applications. USA: Hoboken.4. Pritchard, P. J. (1998). Mathcad: A Tool for Engineering Problem Solving. USA:

Boston.5. Abell, M. L. & Braselton, J. P. (2005). Maple by Example. USA: Boston.6. Hunt, B. R. et all. (2006). A Guide to MATLAB: For Beginners and Experienced

Users. USA: New York.

17

BWA 20603 Introduction to Fuzzy Set Theory

SynopsisINTRODUCTION: Fuzzy sets;Basic types, Basic concepts: Additional properties of

-cuts, Representations of fuzzy sets, Extension principle for fuzzy sets. OPERATIONS ON FUZZY SETS: Types of operations, Fuzzy complements, Fuzzy intersections: t-norms – Fuzzy unions: t-co-norms – Combinations of operations. FUZZY ARITHMETIC: Fuzzy numbers, Linguistic variables, Arithmetic operations on Intervals, Arithmetic operations on fuzzy numbers. FUZZY RELATIONS: Crisp and fuzzy relations, Binary fuzzy relations, Binary relations on a single set, Fuzzy equivalence relations, Fuzzy compatibility relations, Fuzzy ordering relations. FUZZY RELATION EQUATIONS: Partition, Solution method, Fuzzy relation equations based on sup-i compositions and inf-wi compositions.

Reference1. Klir, G. J. & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic, Theory and

Applications. 1st Edition. Upper Saddle River, NJ: Prentice-Hall.2. Dubois, D. & Prade, H. (1980). Fuzzy Sets and Systems, Theory and

Applications. 1st Edition. Boston: Academic Press.3. Kaufmann A. (1975). Introduction to the theory of Fuzzy Subsets. Vol. I.,

Fundamental Theoretical Elements. 1st Ed. Boston: Academic Press.4. Zimmermann, H. J. (2001). Fuzzy Set Theory -- and Its Applications. Boston:

Kluwer Academic Publishers.5. Klir, G J., Clair, U. S & Yuan, B. (1997). Fuzzy Set Theory: Foundations and

Applications. Upper Saddle River, NJ: Prentice Hall.

BWA 20702 Management

SynopsisIntroduction to Management, Comparison between previous and present Management Practices, Decision Making, Planning, Strategic Management, Organizational Structure and Design, Change and Innovation Management, Human Resource Management, Basic Behavior, Group, Team Work, Motivation, Leadership and Monitoring.

Reference1. Holt, D. H. (1987). Management Principles and Practices. 5th Ed. New Jersey:

Prentice-Hall. 2. Griffin, R. W. ( 2000). Fundamentals of Management: Core Concepts and

Applications. 2nd Ed. Boston: Houghton Mifflin.3. Hill, J. G. (2000). Contemporary Management. 2nd Ed. New York: McGraw Hill.4. Morden, T. (2004). Principles of Management. 2nd Ed. Burlington, VT: Ashgate. 5. Morden, T. (2007). Principles of Strategic Management. 2nd Ed. Burlington, VT:

Ashgate.

18

19

BWB 21003 Data Analysis

SynopsisExploratory to data analysis: definition and interpretation, nature of statistical analysis, Review of Statistical Inference: variables and data, basic statistics, database fundamentals, collecting data, sampling, Data entry with package : introduction to SPSS and Minitab, using SPSS and Minitab for data entry, building a data file, running a simple analysis and obtaining the output, graphical method for describing data, numerical method for describing data (frequency distribution, measures of central tendency, measures of variability), Random Variables and Probability Distributions: random variables, probability distributions for discrete and continuous random variables, mean and standard deviation for random variables, binomial, geometric and normal distribution, checking for normality and normalizing transformations, Hypothesis Tests: Hypotheses and test procedures, errors in hypothesis testing, hypothesis tests for a population mean, Categorical Data: Chi-squared tests for univariate categorical data, tests of homogeneity and independence in a two way table, Simple Linear Regression & Correlation Analysis of Variance: single factor ANOVA and the F test, multiple comparison multicollinearity.

Reference1. Peck, R., Olsen, C. & Devore, J. (2001). Introduction to Statistics and Data

Analysis. Duxbury Thomson Learning.2. Foster, J. J. (2001). Data Analysis Using SPSS for Windows Versions 8 to 10: A

beginner’s Guide. SAGE Pub.3. Geoffrey, V. & Scott, K. (2006). Statistical Methods for Engineers. Thomson.4. Ott, R. L. and Longnecker, M. (2010). An introduction to Statistical Methods

and Data Analysis. Belmont, CA: Brooks/Cole Cengage Learning.5. Dunn, P. F. (2010). Measurement and Data Analysis forEengineering and

Science. Boca Raton: CRC Press.

BWA 20803 Vector Calculus

SynopsisVector-valued Functions: Definition and graphs. Operations, limits, differentiations and integrations. Unit tangent vectors, principal unit normal vectors, binormal vectors, arc length and curvature. Motion in a plane curves. Applications of vector-valued Functions. Vector Calculus: Directional derivatives and gradients of functions of several variables. Divergence and curl of vector field. Line integrals of scalar and vector field. Independence of path and conservative vector field. Green’s theorem. Surface integrals of scalar and vector field. Gauss’s theorem and Stokes’ theorem.

Reference1. Lovric, M. (2007). Vector Calculus. Hoboken, NJ: John Wiley.2. Colley, S. J. (2006). Vector Calculus. Upper Saddle River, NJ: Pearson.

20

3. Smith, R. T. & Minton, R. B. (2007). Calculus Early Transcendental Function. 3rd Ed. New York: McGraw-Hill

4. Matthews, P. C. (1998). Vector Calculus. London: Springer.5. Schey, H. M. (2005). Div, Grad, Curl and All That: An Informal Text On

Vector Calculus. New York: W.W. Norton.

21

BWA 20903 Numerical Analysis I

SynopsisIntroduction to numerical analysis and error: Review of calculus, round-off error, truncation error, absolute and relative error. Numerical solution for nonlinear equations: Intermediate Value Theorem, bisection, Newton-Raphson, secant, false position, fixed-point iteration, convergence analysis. Systems of linear equations: Gauss elimination, Gauss elimination with pivoting, LU decompositions, Thomas algorithm, Jacobi and Gauss-Seidel iteration, SOR iteration, norm and condition number of matrices, convergence criteria of iterative methods. Interpolation: Langrange polynomial, Newton’s divided difference method, cubic spline interpolation. Numerical Differentiation and Integration: First and second derivative, Trapezoidal rule, 1/3 and 3/8 Simpson’s Rule, Romberg integration, 2-point and 3-point Gauss Quadrature method, Monte Carlo integration. Eigenvalues: Power method, shifted and inverse power method, QR algorithm. Ordinary Differential Equations: Solution of initial value problem by Taylor’s series, Euler, Huen, Runge-Kutta and multistep methods.

Reference1. Burden, R. L. & Faires, J. D. (2005). Numerical Analysis. 8th Ed. USA: Thomson

Brooks/ Cole.2. Chapra, S. C. & Canale, R. P. (1998). Numerical Methods for Engineers. USA:

McGraw-Hill.3. Jain, M. K., Iyengar, S. R. K. & Jain, R. K. (1987). Numerical Methods for

Scientific and Engineering Computation. 2nd Ed. USA: Wiley Eastern Ltd.4. Matthew, J. H. (1992). Numerical Methods for Mathematics, Science and

Engineering. 2nd ed. USA: Prentice-Hall.5. Kreyszig, E. (2006). Advanced Engineering Mathematics. 9th Ed. USA: John

Wiley & Sons, Inc. 6. Kincaid, D. R., & Cheney, E. W. (2002). Numerical Analysis: Mathematics of

Scientific Computing, USA: Brooks/ Cole.

BWA 21002 Creativity & Innovation

SynopsisThis course focuses on developing a creative person who will eventually think strategically, creatively and critically. The knowledge and skills acquired throughout the course will later be applied by the students in solving problems and making decisions in the future. In this course, students will be exposed to various creativity and problem solving techniques. Some of the skills to be covered throughout the course are problem solving, techniques in creativity and techniques in innovation.

References

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1. Bernacki, E. (2002). Wow! That’s a Great Idea! Singapore: Prentice Hall.2. De Bono, E. (2003). Serious Creativity 1: Lateral Thinking Tools, Techniques

and Application. Singapore : Allscript Books.3. De Bono, E. (2003). Serious Creativity 2: Lateral Thinking Tools, Techniques

and Application. Singapore: Allscript Books.4. Ceserani, J. & Greatwood, P. (1995). Innovation and Creativity. London:

Kogan Page.5. Ceserani, J. & Greatwood, P. (2001). Innovation and Creativity. New Delhi:

Creast Publishing House.

23

YEAR 3, SEMESTER I

BWA 30102 Project Management

SynopsisIntroduction to Project Management : Project and Project Management definition, Project Management constraints, Importance of Project Management, Project Life Cycle, Project Management Field. Project Initiation : Project Selection, Project Manager and Organization. Project Planning : Initial Project Coordination, Relationship of Planning Process, Planning Element, Integration System, Work Breakdown Structure (WBS), Interface Coordination through Integration Management. Budgeting and Cost Estimation : Methods of Budgeting, Estimating Project Budgets, Improving Cost Estimation, Cost Control, Budget Uncertainty and Risk Management. Project Scheduling : Scheduling Defined, Scheduling Network Techniques, Project Uncertainty and Risk Management, The Gantt Chart. Project Resource Allocation : Critical Path Method - Crashing a Project, Resource Loading, Resource Leveling, Constrained Resource Scheduling, Multiproject Scheduling and Resource Allocation. Project Monitoring and Controlling : The Plan-Monitor-Control Cycle, Data Collection and Reporting, Earned Value, Project Control and Its purposes, Designing the Control System. Project Evaluation and Termination : Evaluation Criteria and Measurement, Project Auditing, Project Termination.

References1. Meredith, J. R. & Mantel, S. J. (2003). Project Management. A Managerial

Approach. New York: John Willey & Sons.2. Meredith, J. R., Mantel, S. J., Margaret, M.S. & Scott, M.S. (2001). Project

Management in Practice. New York: John Willey & Sons. 3. Gray, C. F. & Larson, E. W. (2006). Project Management. The Managerial

Process. New York: McGraw-Hill. 4. Pinto, J. K. (2007). Project Management: Achieving Competitive Advantage.

New Jersey: Pearson Prentice Hall.5. Kerzner, H. (2001). Project Management, A System Approach to Planning,

Scheduling and Controlling. New York: John Willey & Sons.6. Burke, R. (2003). Project Management, Planning and Control Techniques.

London: John Willey & Sons.7. Cleland, D. I. & Ireland, L. R. (2002). Project Management, Strategic Design

and Implementation. New Jersey: McGraw-Hill.

BWA 30203 SPECIAL TOPICS AND CURRENT ISSUSES

SynopsisThere is no set syllabus for this course. Students are required to attend the seminar and talk that will be organized by the lecturer. The seminar and talk will be based on the current topics and issues related to the ICT fields and work environment. The seminar and talk will be conducted within 8 weeks of lectures.

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The invited guest speakers which represent the industry will deliver the talk on current topics and issues from e-commerce and creative multimedia point of views.

25

BWA 30303 Partial Differential Equation

SynopsisThe major area of studies include: First-Order Partial Differential Equations linear, quasi-linear and non-linear first order equations, Second-Order Partial Differential Equations classification of linear second order equations, Fourier Series concept of Fourier series to solve partial differential equations, Wave Equation Derivation of wave equation, solving wave equation using method of separation variable, Heat equation Solution of heat equation problem based on some cases, Laplace Equation Laplace equations in one, two and three-dimensional spaces. Poisson equation.

Reference1. Greenberg, M. D. (1998). Advanced Engineering Mathematics. USA: Prentice-

Hall.2. Amaranath, T. (2003). An Elementary Course in Partial Differential Equations.

USA: Alpha Science International.3. O’neil, P. V. (1999). Beginning Partial Differential Equations. New York: John

Wiley.4. Pinsky, M. A. (1984). Introduction to Partial Differential Equations. USA: Mc-

Graw Hill.5. Williams, W. E. (1980). Partial Differential Equations. UK: Oxford University

Press.6. Berg, P. W. (1966). Elementary Partial Differential Equation. USA: Holden-Day.7. Isa, M. & Shafie, S. (2007). Partial Differential Equations for Science and

Engineering Students. Teaching Module. UTM.

BWB 31403 Statistical Quality Control

SynopsisIntroduction to quality control and techniques in the industry : What is quality, The needs and goals for SPC, Prevention vs Detection models, Basic tools and techniques for SPC. Management’s Problems and Solutions : Management problems, Deming’s 14 points and Deming’s Seven deadly diseases, Crosby’s 14 steps, Compare Deming’s 14 points for management and Crosby’s 14 steps, TQM and total customer satisfaction, International Standard Organization (ISO 9000). Introduction to Variation and Statistics : Measurement concepts, Error and round-off rules, Variation concepts, Data collection and organization, Measures of the centre distribution and spread, Distribution and three standard deviation. Introduction to Tables, Charts and Graphs : Stem plot, Tally Charts and frequency table, Histogram, Pareto Chart, Flow Charts, Storyboards, Cause-And-Effect Diagram. Normal Probability Distribution : Application normal and Central limit Theorem in SPC.

Reference

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1. Montgomery, D. C. (2005). Introduction to Statistical Quality Control. 5th Ed. John Wiley & Sons, Inc.

2. Chandra, M. J. (2001). Statistical Quality Control. Delhi: CRC Press.3. Grant, E. L. & Leavenworth, R. S. (1996). Statistical Quality Control. New York:

McGraw Hill. 4. Mitra, A. (1998). Fundamentals Of Quality Control And Improvement. New

York: Macmillan. 5. Smith, G. M. (1998). Statistical Process Control and Quality Improvement. New

Jersey: Prentice- Hall.

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BWA 30403 Numerical Analysis II

SynopsisBoundary value problems: Linear shooting method, finite difference method and Rayleigh-Ritz method. Multiple integrals: Simpson’s double integral, Gaussian double and triple integral. System of first order linear differential equations: Fourth order Runge-Kutta, reducing higher order differential equations to system of first order differential equations. Partial Differential Equations: Finite difference methods, elliptic PDE (Laplace and Poisson), parabolic PDE and hyperbolic PDE, explicit and implicit methods, irregular domain and Neumann boundary condition problems, consistency, stability and convergence of finite difference method. Finite element method: One dimensional heat flow problem. Discrete Fourier Transforms (DFT): Introduction to DFT, solving differential equations by DFT. Fast Fourier Transforms (FFT): Introduction to FFT, solving differential equations by FFT.

Reference1. Burden, R. L. and Faires, J. D. (2005). Numerical Analysis. 8th Ed. USA: Thomson

Brooks/ Cole.2. Chapra, S. C.& Canale, R. P. (1998). Numerical Methods for Engineers. USA:

McGraw-Hill.3. Jain, M. K., Iyengar, S. R. K. & Jain, R. K. (1987). Numerical Methods for

Scientific and Engineering Computation. 2nd Ed. USA: Wiley Eastern Ltd.4. Matthew J. H. (1992). Numerical Methods for Mathematics, Science and

Engineering. 2nd ed. USA: Prentice-Hall.5. Kreyszig, E. (2006). Advanced Engineering Mathematics. 9th ed. USA: John

Wiley & Sons, Inc. 6. Kincaid, D. R. & Cheney, E. W. (2002). Numerical Analysis: Mathematics of

Scientific Computing, USA: Brooks/ Cole.

YEAR 3, SEMESTER 2

BWA 30503 Investment Analysis

SynopsisA Brief History of Risk and Return: What is an investment, Measures of return and risk, Determinants of Required Rates of Return, Relationship between risk and return. Buying and Selling Securities: Use of Security market indexes differentiating factors in constructing market indexes Securities, Stock market indicator series, Bond market indicator series, Composite stock-bond indexes, Mean annual security risk-returns and correlations, Security Types. The Stock Market: The primary and secondary stock market, Dealers and Brokers, Common Stock Valuation, Earnings and cash flow analysis, Stock Price Behavior and Market Efficiency. Interest Rates and Bond Markets: Interest Rates, Bond Prices and Yields, Corporate Bonds, Government Bonds. Mutual Funds: Fund management Fees, Investment companies and fund types, Investment style and the classification of mutual funds, Mutual fund operations, Mutual fund costs and

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fees, Short-term funds, Long term funds, mutual fund performance. Portfolio Management: Diversification and asset allocation, Return, Risk (systematic and unsystematic) and the Security Market Line, Performance Evaluation and Risk Management

References1. Haugen, R. A. (1993). Modern Investment Theory. 3rd Ed. New Jersey:

Prentice Hall.2. Vierck, C. J. & Jordan, B. D. (2000). Fundamentals of Investments: Valuation

& Management. 2nd Ed. Boston: Irwin/McGraw-Hill. 3. Higgins, R. C. (1997). Analysis for Financial Management. 5th Ed. Homewood:

Irwin. 4. Mandell, L. & O’Brien, T. J. (1992). Investments. 3rd Ed. New York: Macmillan. 5. Reilly, F. (1989). Investment Analysis and Portfolio Management. 2nd Ed.

Forth Worth: The Dryden Press.

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BWA 30603 Mathematical Modelling I

SynopsisIntroduction to Modelling: Modelling process, overview of different kinds of models. Qualitative Modelling with Functions. Modelling with Dimensional Analysis. Modelling with Difference Equation: overview of basic concepts concerning matrices, fixed points, stability and iterative processes. Modelling with Ordinary Differential Equations: overview of basic concepts in ODE and stability of solutions, linear operators, coupled linear systems, phase plane, stability analysis. Empirical Modelling with Data Fitting: error function, least square method, fitting data with polynomials and splines. Modelling with Partial Differential Equations: overview of the key properties of some particular kinds of PDEs, separation of variables, equilibrium solutions, stability and linear stability, travelling waves, spatially periodic solutions.

Reference1. Giordano, F. R., Weir, M. D. & Fox, W. P. (2002). A First Course in Mathematical

Modeling. 3rd Ed. USA: Thomson Brooks/Cole.2. Simmons, G. & Ktantz, S. (2007). Differential Equations: Theory, Technique and

Practice. USA: McGraw-Hill.3. Henry, E. & David, E. P. (2000). Differential Equations: Computing and

Modeling. USA: Prentice-Hall, Inc.4. Edwards, D. & Hamson, M. (2007). Guide to Mathematical Modeling. New York:

Industrial Press.5. Thangavel, K. & Balasubramaniam, P. (2006). Computing and Mathematical

Modeling. New Delhi: Narosa.

BWA 30702 Final Year Project I

SynopsisStudents will be given a choice of research topics based on theory or practical, within mathematics area in the following categories: Operational research, computational, actuaries and optimization. This first half project involves the literature reviews and predicted outcomes to the proposed projects.

Reference1. Buku Panduan PSM Universiti Tun Hussein Onn.2. Guidelines for Thesis Writing UTHM.3. Antony, J. (2003). Design of Experiments for Engineers and Scientists.

Melbourne: Butterworth- Heinemann.4. Patten, M. L. (2005). Understanding Research Methods: An Overview Of The

Essentials. 9th Ed. New York: McGraw-Hill/Irwin.5. Doeblin, Ernest O., (1995). Engineering Experimentation: Planning, Execution,

Reporting. McGraw-Hill, Ohio6. Jones, D. & Lane, K. (2002). Technical Communication. New York: Longman.

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YEAR 3, SEMESTER 3

BWA 30804 Industrial Training

SynopsisStudents are required to undergo Industrial Training (LI) in selected local industries or government bodies for 8 weeks. At the end of their training, students are required to submit a written report on their work and present their work in a seminar. The evaluation of the subject is based on the Industrial Supervisor’s report, the Faculty Supervisor’s report, the student’s Log Book write-up, the work presentation and the written report.

YEAR 4, SEMESTER I

BWA 40103 Mathematical Modelling II

SynopsisMathematical Modelling: Introduction, Steps in Mathematical Modelling and examples. Mathematical tools in modeling (depends on case studies). Case studies: Problems in Nonlinear Transverse Vibration in an Elastic Medium, Nonlinear Phenomena by Dynamical System, Broadcasting and Gossiping in Communication Networks and Vertical Stabilization of a rocket on a Movable Plateform.

Reference1. Maccluer, C. M. (2000). Industrial Mathematics: Modeling in Industry, Science

and Government. New Jersey, USA: Prentice-Hall.2. Mark, M. M. (1993). Mathematical Modeling. USA: Academic Press, Inc.3. Fulford, G. R. & Broadbridge, P. (2002). Industrial Mathematics: Case Studies

in Diffusion of Heat and Matter. UK: Cambridge University Press.4. Svobodny, T. (1998). Mathematical Modeling for Industry and Engineering.

New Jersey, USA: Prentice-Hall.5. Shier, D. R. & Wallenius, K. T. (2000). Applied Mathematical Modeling: A

Multidisciplinary Approach. USA: Chapman & Hall/CRC.

BWA 40304 Final Year Project II

SynopsisThis course provides the platform for carrying out individual research on specific areas in mathematics; i.e. Operational research, computational, actuaries and optimization.  This project involves literature survey, theoretical analysis, computer modeling, data analysis and presentation of results in terms of oral and

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written report. Students will be expected to contribute to the research activity (e.g. seminars) of the host institution.

Reference1. Buku Panduan PSM Universiti Tun Hussein Onn.2. Guidelines for Thesis Writing UTHM.3. Antony, J. (2003). Design of Experiments for Engineers and Scientists.

Melbourne: Butterworth-Heinemann.4. Patten, M. L. (2005). Understanding Research Methods: An Overview of The

Essentials. 9th.Ed. New York: McGraw-Hill/Irwin.5. Doeblin, E. O. (1995). Engineering Experimentation: Planning, Execution,

Reporting. McGraw-Hill, Ohio.

6. Jones, D. & Lane, K. (2002). Technical Communication. New York: Longman.

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Elective A: Computation

BWA 31703 Discrete Event Simulation

SynopsisSimulation: Introduction. Advantages and disadvantages. Application. Systems and system environment. Discrete and continuous systems. Model of a system. Discrete-event system simulation. Random-number Generation: Properties. Generation of Pseudo-Random Numbers. Techniques for generating random numbers. Tests for random numbers. Statistical Models: Discrete distributions. Continuous distributions. Poisson process. Computer implementation. Queuing Models: Characteristics of queuing systems. Markovian single and multiple servers. Steady-state behavior of finite-population models. Networks of queues. Input Modeling: Data collection. Parameter estimation. Goodness-of-fit tests. Multivariate and time-series input models. Verification and Validation of Simulation Models: Model building. Verification and validation. Output analysis: Measures of performance using point estimation, interval estimation and confidence-interval estimation. Simulation of Manufacturing and Material Handling Systems: Manufacturing and material handling simulations. Network analysis.

Reference1. Banks, J., Carson, J. S., Nelson, B. L. & Nicol, D. M. (2005). Discrete-Event

System Simulations. 4th Ed. New Jersey: Prentice Hall Inc. 2. Fishman, G. S. (1978). Principles of Discrete Event Simulation. New York.

Wiley.3. Fishman, G. S. (2001). Discrete-Event Simulations: Modeling, Programming

and Analysis. New York. Springler-Verlag. 4. Leemis, L. M & Park, S. K. (2006). Discrete-Event Simulation: A first Course.

London: Pearson.5. Robinson, S. (2011). Conceptual Modeling for Discrete-Event Simulation.

Boca Raton: CRC.

BWA 31803 JAVA Programming

SynopsisGetting Started with Java: Introduction to Java. Expressions and Assignment Statements. The Class String. Program Style. Screen Output. Console Input Using the Scanner Class. Defining Classes & Arrays: Introduction to Arrays. Arrays and References. Programming with Arrays. Multidimensional Arrays. Flow of Control: Branching Mechanism. Boolean Expressions. Loops. Inheritance: Inheritance Basics. Derived Classes. Overriding a Method Definition. The super Constructor. The this Constructor. Encapsulation and Inheritance. Programming with Inheritance. Polymorphism and Abstract Classes: Late Binding. The final Modifier. Late Binding with to String. Downcasting and Upcasting. A First Look at the clone Method. Abstract Classes. Interfaces and Inner Classes: Interfaces.

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Simple Uses of Inner Classes. Exception Handling: Exception Handling Basics. Throwing Exceptions in Methods. More Programming Techniques for Exception Handling File I/O: Introduction to File I/O. Text Files. The File Class. Binary Files. Random Access to Binary Files. Applets: A Brief Introduction to HTML. Programming Applets. Applets in HTML Documents. Basic Graphical User Interfaces: Graphical Objects. Frames. Events and Listeners. Drawing Simple Objects.

Reference1. Savitch, W. J. (2005). Absolute Java Edition 2. USA: Pearson/Addison-Wesley.2. Flanagan, D. (2002). Java in a Nutshell. 4th Edition. USA: O'Reilly & Associates. 3. Deitel, H. M. et. al. (2002). Java How to Program 5th Edition. New Jersey, USA:

Prentice Hall.4. Garrido, J. M. (2003). Object-Oriented Programming: From Problem Solving to

Java. Canada: Charles River Media.5. Malik, D. S. & Burton, R. P. (2009). Java Programming: Guided Learning With

Early Objects. Boston, MA: Course Technology.

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BWA 31903 Mathematical Elements of Computer Graphics

SynopsisIntroduction to Computer Graphics:Description of some graphics devices. Two-Dimensional Transformations: Transformations, rotation, reflection and scaling. Three-Dmensional Transformations: Three-dimensional scaling, shearing, rotation, reflection and translation. Projections: orthographic, axonometric and oblique. Techniques for generating perspective views. Reconstruction of three-dimensional images. Plane Curves: Nonparametric and parametric curves. A procedure for using conic sections. Space Curves: Cubic splines, generalized parabolic blending, Bezier curves and B-spline curves. Surface Description and Generation: surfaces of revolution, sweep surfaces, ruled and developable surfaces, Bilinear surface, Coons surface, Bezier surfaces and B-spline surfaces.

Reference1. Rogers, D. F. & Adams, J. A. (1990). Mathematical Elements for Computer

Graphics. 2nd Ed. New York. McGraw-Hill. 2. Foley, J. D., Van Dam, A., Feiner, S. K. & Hughes, J. F. (1995). Computer

Graphics: Principles and Practice in C. 2nd Ed. Reading Mass: Addision-Wesley.3. Cooley, P. (2001). The Essence of Computer Graphics. Harlow, England:

Prentice Hall.4. Heiny, L. (1994). Power Graphics Using Turbo C++. 2nd. Ed. New York: John

Wiley and Sons.5. Mortenson, M. E. (1989). Computer Graphics: An Introduction to the

Mathematics and Geometry. Heinemann Newnes: Oxford.

BWA 41003 Number Theory And Cryptography

SynopsisThe Integers: Numbers and Sequences, Sums and Products, Mathematical Induction, The Fibonacci Numbers. Integer Representations and Operations: Representations of Integers, Computer Operations with Integers, Complexity of Integer Operations,Integer Representations and Operations. Primes and Greatest Common Divisors: Prime Numbers, The Distribution of Primes, Greatest Common Divisors, The Euclidean Algorithm, The Fundemental Theorem of Arithmetic, Factorization Methods and Fermat Numbers, Linear Diophantine Equations. Congruences: Introduction to Congruences, Linear Congrences, The Chinese Remainder Theorem, Solving Polynomial Congruences, Systems of Linear Congruences, Factoring Using the Pollard Rho Method, Applications of Congruences. Some Special Congruences : Wilson's Theorem and Fermat's Little Theorem, Pseudoprimes, Euler's Theorem. Multiplicative Functions: The Euler Phi-Function, The Sum and Number of Divisors, Perfect Numbers and Mersenne Primes, Mobius Inversion. Cryptology: Character Ciphers. Block and Stream Ciphers. Exponentiation Ciphers.Knapsack Ciphers.

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Cryptographic Protocols and Applications. Primitive Roots: The Order of an Integer and Primitive Roots, Primitive Roots for Primes, The Existence of Primitive Roots, Index Arithmetic, Primality Tests Using Orders of Integers and Primitive Roots, Universal Exponents. Application in Crytography.

Reference1. Rosen, K. H. (2000). Elementary Number Theory and Its Applications. Reading

Mass: Pearson Addison Wesley.2. Burton, D. M. (2007). Elementary Number Theory. London. Mc Graw Hill.3. Dudley, U. (1978). Elementary Number Theory. San Francisco, W.H. Freeman.4. Hardy, G. H. & Wright, E. M. (2008). An Introduction to the Theory of Numbers.

6th Ed. Oxford. Oxford University Press.5. Silverman, J. H. (2005). A Friendly Introduction to Number Theory. 3rd Ed.

London. Prentice Hall.

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BWA 41103 Metaheuristic Techniques in Mathematics

SynopsisThe aim of this module is to provide students with an understanding of the concept of some basic optimisation algorithms and evolutionary algorithms and the ways in which they can be applied to real world problems. The purpose of this course is to introduce the students to meta-heuristics techniques. A meta-heuristic technique is a top-level general strategy which guides other heuristics to search for feasible solutions in complex solution spaces.  Meta-heuristics have been generally applied to problems classified as NP-Hard or NP-Complete by the theory of computational complexity. However, meta-heuristics would also be applied to other combinatorial optimization problems for which it is known that a polynomial-time solution exists but is not practical. A number of meta-heuristics techniques using single solutions or sets of solutions will be described. The course will give emphasis to Swarm Intelligence (SI) techniques and their applications to combinatorial optimization problems in science and engineering. SI techniques are population based stochastic methods where the collective behavior of unsophisticated individuals interacts locally with their environment causing the emergence of coherent functional global patterns.

Reference1. Reeves, C. R. (1993). Modern Heuristic Techniques for Combinatorial

Problems. Blackwell. Scientific Publications. 2. Glover, F. & Kochenberger, G. A. (2003). Handbook of Metaheuristics. Boston:

Mass. Kluwer Academic Publishers.3. Russel, S. J. & Norvig, P. (1995). Artificial Intelligence – A Modern Approach.

Englewood Cliffs. Prentice Hall Publication. 4. Mitchell, M. (1999). An introduction to Genetic Algorithms. Cambridge. MIT

Press. 5. Paradalos, P. M. & Resende, M. G. C. (2002). Handbook of Applied

Optimization. Oxford. Oxford University Press.

Elective B: Optimization

BWA 30903 Advanced Linear Programming

SynopsisSimplex Method Fundamentals: From extreme points to basic solutions. Generalized simplex tableau in matrix form. Revised Simplex Method: Development of optimality and feasibility conditions. Revised simplex algorithm. Suboptimization. Bounded Variables Simplex Method: Checking for optimality. Determine the entering variables. Increasing a nonbasic variable from

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its lower bound. Decreasing a nonbasic variable from its upper bound. Decomposition. Decompose the model into smaller subproblem. Dantzig-Wolfe decomposition algorithm. Duality: Matrix definition of the dual problem. Optimal dual solution. Parametric Linear Programming: Systemic variation of the cost vector, C. Systemic variation of the right-hand-side-vector, b. Resource values and ranges. Objectives coefficients and ranges. Alternatives to the Simplex Method: Khachiyan’s Ellipsoid Method. Affine Scaling Method. Karmarkar Interior Point Method. Uncertain Linear Programming: Fuzzy linear programming. Stochastic linear programming.

Reference1. Dantzig, G. B. (2003). Linear Programming and Extensions. New York:

Springer. 2. Ignizio, J. P. & Cavalier, T. M. (1994). Linear Programming. Englewood Cliffs, NJ:

Prentice Hall International Editions.3. Vanderbei, R. J. (2001). Linear Programming: Foundations and Extensions.

Canada: Kluwer Academic.4. Christensen, R. (2001). Advanced Linear Modeling: Multivariate, Time Series

And Spatial Data;Nonparametric Regression And Response Surface Maximization. New York: Springer.

5. Vohra, R. V. (2011). Mechanism Design: a Linear Programming Approach. Cambridge, New York: Cambridge University Press.

BWA 31203 Variation of Calculus

SynopsisThe Classical Theory: Introduction to Calculus of Variation, Simple Variation Problems and Examples. Euler’s Condition : Euler-Lagrange Differential Equation, Weirstrass Necessary Condition, Erdmann Corner Condition, Lagendre Necessary Condition, Hamiltonian Formulation. Fields of Extremals : Hilbert’s Integral, Jacobi’s Necessary Condition, Conditions For an Extremum. Second Variation: Jacobi’s Differential Equation, Jacobi Necessary Condition, Sufficient Condition. Variation of a Functional: Types of Variational Problems, Variational Problems with Constraints. Direct Methods: Description of Problem and Its Solution, Lower Semicontinuity, Hilbert Spaces, Moreau-Yosida Approximation.

Reference1. Giusti, E. (2003). Direct Methods in Calculus of Variations, New Jersey: World

Scientific.2. Van Brunt, B. (2004). The Calculus of Variations. New York: Springer.3. Jost, J. & Li, X. Q. (1998). Calculus of Variations. New York: Cambridge

University Press.4. Dacorogna, B. (2008). Direct Methods In The Calculus Of Variations. 2nd ed.

New York: Springer. 5. Fonseca, I. & Leoni, G. (2007). Modern Methods In The Calculus Of Variations:

Lp Spaces. Berlin: Springer.38

BWA 31303 Optimal Control

SynopsisSystems and Control: Definition and Types of Systems, Laplace Transform, Composite Systems and Feedback. Control Systems: Controlled Systems, Stability of Linear Feedback Systems, State Space Equation, Linear Systems Solution, Transfer Matrix, Controllability and Observability. Optimal Control Problems: Necessary and Sufficient Condition, The Calculus of Variation Solution Approach, Pontryagin’s Theorem, Properties of Pontryagin’s Hamiltonian. Solution Approach Using Dynamic Programming: Introduction to Dynamic Programming, Bellman’s Optimality Principle, Bellman’s Optimality Principle, The Riccati Equation. Bellman-Hamilton-Jacobi Equation: Linear Quadratic Problems, Bounded Optimal Control Problem, Free End Point and Fixed End Point Problem, Free End Time Problem. Further Applications: Management, Economics, Engineering, Biology.

Reference1. Lewis, F. L. & Syrmos, V. L. (1995). Optimal Control. 2nd Edition, New York: John

Wiley & Sons.2. Kirk, D. E. (2004). Optimal Control Theory: An Introduction. New York: Dover

Publications.3. Brian, D., Anderson, O. & Moore, J. B. (1990). Optimal Control: Linear Quadratic

Methods. New Jersey: Prentice Hall.4. Hull, D. G. (2003). Optimal Control Theory for Applications, New York: Springer.5. Suresh, P. S. & Gerald, L. T. (2000). Optimal Control Theory: Applications to

Management Science and Economics. Boston: Kluwer Academic.6. Lenhart, S. & Workman, J. T. (2007). Optimal Control Applied to Biological Models.

Boca Raton: Chapman & Hall / CRC.

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BWA 40603 Technique of Optimization 1

SynopsisThis course covers some basic properties, basic descent methods, conjugate Direction Methods and Quasi – Newton Methods.

Reference1. Luenberger, D. G. and Ye, Yingyu. (2008). Linear and Non-Linear Programming,

3rd Ed. New York: Springer.2. Taha, H. A. (2006). Operations Research: An Introduction 8th Ed. Englewood

Cliffs, NJ: Prentice Hall.3. Nocedal, J. & Wright, S. (2006). Numerical Optimization. 2nd Ed. USA: Springer

Science and Business Media.4. Lange, K. (2004). Optimization. 1st Ed. USA: Springer Verlage.5. Fletcher, R. (2000). Practical Methods of Optimization. New York: John Wiley &

Sons, Limited.

BWA 40703 Technique of Optimization II (Constrained Optimization)

SynopsisConstrained Minimization Conditions: Constraints, Tangent Plane, First-Order Necessary, Conditions (Equality Constraints), Second-Order Conditions, Eigenvalues in Tangent Subspace, Inequality Constraints, Zero-Order Conditions and Lagrange Multipliers, Global Convergence of Descent Algorithms. Primal Methods: Advantage of Primal Methods, Feasible Direction Methods, Active Set Methods, The Gradient Projection Method, Convergence Rate of The Gradient Projection Method, The Reduce Gradient Method, Convergence Rate of The Reduce Gradient Method, Variations. Penalty and Barrier Methods: Penalty Methods, Barrier Methods, Properties of Penalty and Barrier Functions, Newton’s Method Penalty Functions, Conjugate Gradients and Penalty Methods, Normalization of Penalty Functions, Penalty Functions and Gradient Projection, Exact Penalty Functions. Dual and Cutting Plane Methods: Global Duality, Local Duality, Dual Canonical Convergence Rate, Separable Problems, Augmented Lagrangians, The Dual Viewpoint, Cutting Plane Methods, Kelly’s Convex Cutting Plane Algorithm, Modifications. Primal – Dual Methods: The Standard Problem, Strategies, A Simple Merit Functions, Basic Primal – Dual Methods, Modified Newton Methods, Descent Properties, Rate of Convergence, Interior Point Methods, Semi definite Programming.

Reference1. Luenberger, D. G. & Ye, Yingyu. (2008). Linear and Non-Linear Programming.

3rd Ed. New York: Springer.2. Taha, H. A. (2006). Operations Research: An Introduction. 8th Ed. Englewood

Cliffs, NJ: Prentice Hall.3. Nocedal, J. & Wright, S. (2006). Numerical Optimization. 2nd Ed. USA: Springer

Science and Business Media.40

4. Lange, K. (2004). Optimization. 1st Ed. USA: Springer Verlage.5. Fletcher, R. (2000). Practical Methods of Optimization. New York: John Wiley &

Sons, Limited.

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Elective C: Operational Research

BWA 30903 Advanced Linear Programming

SynopsisSimplex Method Fundamentals: From extreme points to basic solutions. Generalized simplex tableau in matrix form. Revised Simplex Method: Development of optimality and feasibility conditions. Revised simplex algorithm. Suboptimization. Bounded Variables Simplex Method: Checking for optimality. Determine the entering variables. Increasing a nonbasic variable from its lower bound. Decreasing a nonbasic variable from its upper bound. Decomposition. Decompose the model into smaller subproblem. Dantzig-Wolfe decomposition algorithm. Duality: Matrix definition of the dual problem. Optimal dual solution. Parametric Linear Programming: Systemic variation of the cost vector, C. Systemic variation of the right-hand-side-vector, b. Resource values and ranges. Objectives coefficients and ranges. Alternatives to the Simplex Method: Khachiyan’s Ellipsoid Method. Affine Scaling Method. Karmarkar Interior Point Method. Uncertain Linear Programming: Fuzzy linear programming. Stochastic linear programming.

Reference1. Dantzig, G. B. (2003). Linear Programming and Extensions. New York:

Springer.2. Ignizio, J. P. & Cavalier, T. M. (1994). Linear Programming, Englewood Cliffs, NJ:

Prentice Hall International Editions.3. Vanderbei, R. J. (2001). Linear Programming: Foundations and Extensions.

Canada: Kluwer Academic.4. Christensen, R. (2001). Advanced Linear Modeling: Multivariate, Time Series

and Spatial. Data; Nonparametric Regression and Response Surface Maximization. New York: Springer.

5. Vohra, R. V. (2011). Mechanism Design: A Linear Programming Approach. Cambridge, New York: Cambridge University Press.

BWA 31003 Network Flow

SynopsisIntroduction: Network Flow Problems, Network Notation, Representations and Transformations. Algorithm Design and Analysis: Developing Polynomial-Time Algorithms, Search Algorithms, Flow Decomposition Algorithms. Shortest Path: Label-Setting Algorithms: Tree of Shortest Paths, Shortest Path Problems in Acyclic Networks. Shortest Paths: Label-Correcting Algorithms: Generic Label-Correcting Algorithms, Special Modification of the Modified Label-Correcting Algorithm, Detecting Negative Cycles. Maximum Flows: Basic Ideas: Labeling Algorithm and the Max-Flow Min-Cut Theorem, Combinatorial Implementations of the Max-Flow Min-Cut Theorem. Maximum Flows: Polynomial Algorithms:

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Capacity Scaling Algorithm, Shortest Augmenting Path Algorithm, Distance Labels and Layered Networks. Minimum Cost Flows: Basic Algorithms: Minimum Cost Flow Duality, Relating Optimal Flows to Optimal Node Potential, Successive Shortest Path Algorithm, Primal-Dual Algorithm. Minimum Cost Flows: Polynomial Algorithms: Capacity, Cost and Double Scaling Algorithm, Repeated and Enhanced Capacity Scaling Algorithm. Minimum Cost Flows: Network Simplex Algorithms: Network Simplex Algorithm for the Maximum Flow Problem, Related Network Simplex Algorithms. Minimum Spanning Trees and Convex Cost Flows: Minimum Spanning Trees and Matroids, Minimum Spanning Trees and Linear Programming, Pseudopolynomial-Time Algorithms, Polynomial-Time Algorithm. Generalized Flows: Determining Potentials and Flows for an Augmented Forest Structure, Generalized Network Simplex Algorithm. Multicommodity Flows: Column Generation Approach, Dantzig-Wolfe Decomposition, Resource-Directive Decomposition, Basis Partitioning.

Reference1. Ahuja, R. K., Magnanti, T. L. & Orlin, J. B. (1993). Network Flows: Theory,

Algorithms and Applications. USA: Prentice Hall.2. Bazaraa, M. S., Jarvis, J. J. & Sherali, H. D. (1990). Linear programming and

Network Flows. New York: John Wiley.3. Chen, W. K. (2003). Net Theory and Its Applications: Flows In Networks.

London: Imperial College Press.4. Tanenbaum, A. S. & Wetherall, D. (2011). Computer Networks. Boston: Pearson

Prentice Hall.BWA 31103 Operation Research in Transportation System

SynopsisIntroduction to Transportation Problem : Definition, Basic Terminology: Origin, Destination, Unit Transportation Cost, Perturbation technique, Feasible Solution, Basic Feasible Solution, Optimal Solution, Transportation simplex method. Methods For Finding An Initial Basic Feasible Solution : North West Corner Rule, Matrix Minimum Method, Vogel Approximation Method. Methods For Finding An Optimal Solution : Stepping Stone Method, Modified Distribution Method( MODI), Degeneracy: At the Initial Solution, During the testing of the optimal solution. Unbalanced Transportation Problem : Maximization problem, Prohibited Routes, Time minimizing problem, Transshipment model. Assignment Problem : Introduction, Hungarian Method: Algorithm and Examples. Unbalanced Assignment Problem : Maximization problem, Multiple optimal solution. Application of Assignment Problem : Aircraft crew assignment problem, Travelling salesman problem.

Reference1. Thierauf, R. J. (1978). An Introductory Approach to Operations Research. New

York: John Wiley & Sons.2. Winston, W. L. (2004). Operations Research. Thomson Learning.3. Radrin, R. L. (1997). Optimization in Operations Research. London: Prentice

Hall.

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4. Taha, H. A. (2006). Operations Research: An Introduction. 8th Ed. London: Prentice Hall.

5. Hillier, S. & Lieberman, G. J. (2005). Introduction to Operations Research. 8th Ed. London: Mc Graw Hill.

BWA 40403 Inventory Control

SynopsisStocks and Inventories : Definition of inventory terms. Reasons for holding stocks. Classification of stocks. Inventory management and logistics. Strategic role of stock. Costs of holding stock. Approaches to inventory control. Economic Order Quantitiy : Defining the economic order quantity. Adjusting the economic order quantity. Uncertainty in demand and costs. Adding a finite lead time. Models for Known Demand : Price discount from suppliers. Finite replenishment rate. Planned shortages with back orders. Lost sales. Constraints on stock. Discrete, variable demand Models for Uncertain Demand : Uncertainty in stocks. Models for discrete demand. Order quantity with shortages. Service level. Uncertain lead time demand. Sources of Information : Inventory management information systems. Information from accounting. Information about supply and demand. Warehousing. Purchasing. Planning and Stocks: Levels of planning. Aggregate planning. Master schedules. Operational schedules. Simulation of stocks. Material Requirements Planning : Limitations of independent demands methods. Approach of material requirements planning. Benefits and problems with MRP. Adjusting the MRP schedules. Extension to MRP.

Reference1. Waters, D. (2003). Inventory Control and Management. 2nd Edition. England:

John Wiley & Sons Ltd. 2. Waters, C. D. J. (1999). Inventory Control and Management. England: John

Wiley & Sons Ltd. 3. Narasimhan, S. I., McLeavey, D. W. & Billington, P. J. (1995). Production

Planning and Inventory Control. 2nd Edition. New Jersey: Prentice-Hall, Inc. 4. Tersine, R. J. (1994). Principles of Inventory and Materials Management. 4th

Edition. New Jersey: PTR Prentice-hall, Inc. 5. Sharma, S. C. (2006). Operation Research: Inventory Control and Queuing

Theory. New Delhi: Discovery Publishing.

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BWA 40503 Queuing System

SynopsisIntroduction: Description and characteristics of Queuing Processes, Poisson Process and the Exponential Distribution, Markovian Property of the Exponential Distribution, Stochastic Processes and Markov Chains. Simple Markovian Birth-Death Queuing Models: Steady-State Solution for the M/M/1 Model, Methods of Solving Steady-State Difference Equations, Queue with Parallel Channels, Erlang’s Formula, Finite Source Queues, State-Dependent Service. Simple Markovian Queuing Models: Bulk Input, Bulk Service, Erlangian Models. Simple Markovian Queuing Models: Series Queues, Open and Closed Jackson Networks, Cyclic Queues, Non-Jackson Networks. Models with General Arrival or Service Patterns: Single-Server and Multiserver Queues with Poisson Input and General Service, General Input and Exponential Service. More General Models and Theoretical Topics: G/Ek/1, G[k]/M/1 and G/PHk/1, General Input, General Service ( G/G/1). Bounds, Approximations, Numerical Techniques and Simulation: Bounds and Inequalities, Approximations , Discrete-Event Stochastic Simulation.

Reference1. Gross, D. & Harris, C. M. (1998). Fundamentals of Queuing theory, Third

Edition. New York: John Wiley & Sons.2. Kleinrock, L, Gail, R. (1996). Queuing Systems: Problems and Solution. New

York: John Wiley & Sons.3. Papadopoulos, H. T., Heavey, C. & Browne, J. (1993). Queuing Theory In

Manufacturing Systems Analysis And Design. London: Chapman and Hall.4. Bose, S. K. (2002). An Introduction to Queuing Systems. New York: Kluwer Ademic.5. Stidham, S. (2009). Optimal Design of Queueing Systems. Boca Raton: CRC Press.

Elective D: Actuarial Science

BWA 31603 Mathematical Finance

SynopsisIntroduction to Mathematical Finance: What is finance, What is mathematical finance, Overview of some of the mathematical tools used in mathematical finance. Interest: simple interest, compound interest, Discount: simple discount, compound discount. Annuities: simple annuities, general annuities, perpetuities. Amortization: Amortization of a debt, outstanding principal, mortgages, refinancing a loan, sinking fund, comparison of amortization and sinking fund methods. Bonds: Types of bonds, callable bond. Capital Budgeting: net present value, internal rate of return, capitalized cost and capital budgeting, depreciation.

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Reference1. Zima, P. & Brown, R. L. (1996). Mathematics of Finance. 2nd Edition. London:

McGraw Hill.2. Parmenter, M. M. (1999). Theory of Interest and Life Contingencies, With

Pension Applications: A Problem-Solving Approach. 3rd Ed. Winsted, Conn.: ACTEX Publications.

3. Keynes, J. M. (1997). The General Theory Of Employment Interest And Money. 5th Ed. New York: Harcourt Brace Jovanovich.

4. Brigo, D. & Mercurio, F. (2001). Interest Rate Models: Theory And Practice, 3rd Ed. Berlin: Springer. Master level.

5. Qureshi, Anwar Iqbal. (2003). Islam and the theory of interes. 2nd Ed. New Delhi: Kitab Bhavan.

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BWA 31403 Actuarial Mathematics 1

SynopsisSurvival Distributions and Life Tables: Introduction, Probability for the Age-at-Death, Life Tables, The Deterministic Survivorship Group, Other Life Table Functions, Assumptions for Fractional Ages, Some Analytical Laws of Mortality, Select and Ultimate Tables. Life Insurance: Introduction, Insurances Payable, Relationships between Insurances Payable at the Moment of Death and the End of the Year of Death, Recursion Equations, Commutation Functions. Life Annuities: Introduction, Single Payment Contingent on Survival, Continuous Life Annuities, Discrete Life Annuities, Life Annuities with mthly Payments, Commutation Function Formulas for Annuities with Level Payments, Varying Annuities, Recursion Equations, Complete Annuities-Immediate and Apportionable Annuities-Due. Net Premiums: Introduction, Fully Continuous Premiums, Fully Discrete Premiums, True mthly Payment Premiums, Apportionable Premiums, Commutation Functions, Accumulation Type Benefits. Net Premium Reserves: Introduction, Fully Continuous Net Premium Reserves, Other Formulas for Fully Continuous Reserves, Fully Discrete Net Premium Reserves, Reserves on a Semicontinuous Basis, Reserve Formulas in Terms of Commutation Functions. Multiple Life Functions: Introduction, The Joint-Life Status, The Last-Survivor Status, Probabilities and Expectations, Insurance and Annuity Benefits, Evaluation – Special Mortality Laws, Evaluation – Uniform Distribution of Deaths, Simple Contingent Functions.

References1. Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. & Nesbit, C. J. (1997).

Actuarial Mathematics. 2nd Ed. Schaumburg: Society of Actuaries.2. Promislow, S. D. (2011). Fundamentals Of Actuarial Mathematics. Chichester:

Wiley.3. Dickson, D. C. M., Hardy, M. R. & Waters, H. R. (2009). Actuarial Mathematics

For Life Contingent Risks. Cambridge, UK; New York: Cambridge University Press.

4. Gupta, A. K & Varga, T. (2002). An Introduction to Actuarial Mathematics. Dordrecht: Kluwer Academic Publishers.

5. Rotar, V. I. (2006). Actuarial Models: The Mathematics Of Insurance. Boca Raton, FL: Chapman & Hall.

BWA 31503 Actuarial Mathematics II

SynopsisMultiple Decrement Models: Introduction, Two Random Variables, Random Survivorship Group, Deterministic Survivorship Group, Associated Single Decrement Tables, Construction of a Multiple Decrement Table, Net Single Premiums and their Numerical Evaluation. Valuation Theory for Pension Plans: Introduction, Basic Functions, Contributions, Age-Service Retirement Benefits, Disability Benefits, Withdrawal Benefits, Commutation Functions. Collective Risk Models for a Single Period: Introduction, The Distribution of

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Aggregate Claims, Selection of Basic Distributions, Properties of the Compound Poisson Distribution, Approximations to the Distribution of Aggregate Claims. Nonforfeiture Benefits and Dividends: Introduction, Cash Values, Insurance Options, Asset Shares, Experience Adjustment, Assumptions and Reserves. Special Annuities and Insurance: Introduction, Special Types of Annuity Benefits, Family Income Insurances, Retirement Income Policies, Variable Products, Flexible Plan Products, Disability Benefits for Individual Life Insurance. Advanced Multiple Life Theory: Introduction, More General Statuses, Compound Statuses, Contingent Probabilities and Insurance, Compound Contingent Functions, Reversionary Annuities, Net Premiums and Reserves. Population Theory: Introduction, The Lexis Diagram, A Continuous Model, Stationary and Stable Populations, Actuarial Applications, Population Dynamics.

Reference1. Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. & Nesbit, C.J. (1997).

Actuarial Mathematics. 2nd Ed. Schaumburg: Society of Actuaries.2. Menge, W. O. & Fischer, C. H. (1985). The Mathematics of Life Insurance. 3rd

Ed. New York: Ulrich. 3. Neill, A. (1977). Life Contingencies. 8th Ed. Oxford: Heinemann.4. Boland, Philip J. (2007). Statistical and Probabilistic Methods In Actuarial

Science. Boca Raton, FL: Chapman & Hall/CRC. 5. Wuthrich, M. V, Buhlmann, H. & Furrer, H. (2007). Market-Consistent Actuarial

Valuation. New York: Springer.

BWA 40803 Risk Theory

SynopsisThe Economics of Insurance: Introduction, Utility Theory, Insurance and Utility, Elements of Insurance, Optimal Insurance. Individual Risk Models for a Short Term: Introduction, Models for Individual Claim Random Variables, Sums of Independent Random Variables, Approximations for the Distribution of the Sum, Applications to Insurance. Collective Risk Models Over an Extended Period: Introduction, Claims Processes, The Adjustment Coefficient, Discrete Time Model, The First Surplus Below the Initial Level, The Maximal Aggregate Loss. Applications of Risk Theory: Introduction, Claim Amount Distributions, Approximating the Individual Model, Stop – Loss Reinsurance, The Effect of Reinsurance on the Probability of Ruin. Insurance Models Including Expenses: Introduction, General Expenses (Premium and Reserves, Accounting), Types of Expenses, Per Policy Expenses, Algebraic Foundations of Accounting, Modified Reserve Methods, Full Preliminary Term, Modified Full Preliminary Term, Canadian Standard.

Reference1. Kaas, R. (2009). Modern Actuarial Risk Theory: Using R. Berlin: Springer.2. Murphy, D. (2008). Understanding Risk: The Theory and Practice of Financial

Risk Management. Boca Raton, FL: Chapman & Hall.3. Martorell, S., Barnett, J. & Soares, C. G. (2009). Safety, Reliability and Risk

Analysis: Theory, Methods and Applications. Boca Raton: CRC.48

4. Bouchaud, J. P. & Potters, M. (2000). Theory of Financial Risks: From Statistical Physics to Risk Management. Cambridge: Cambridge University Press.

5. Menge, W.O. & Fischer, C.H. (1985). The Mathematics of Life Insurance. 3rd Ed. New York: Ulrich.

BWA 40903 Stochastic Process

SynopsisIntroduction. Introduction to Stochastic Processes and Modeling. Discrete Time Markov Chains. Chapman-Kolmogorov Equations. Classification Terminology. Long range behavior and invariant probability. Ergodic Markov Chains (Steady States). Absorbing Markov Chains (Transience). Continuous Time Processes. Kolmogorov Equation. Limiting Probabilities. Birth-Death Processes. Branching processes. Exponential RV’s. Poisson Processes. Markov Random Fields. Markov Chain Monte Carlo. Queuing Theory. Single Server Queues. Multiple Server. Finite Sources. Limited Queue Capasities. Non-Markovian and Special Queuing Models. Network of Queues. Deterministic Inventory. ABC Classification. Economic Order Quantity. Quantity Discounts. Finite Rate Production and Backorders. Probabilistic Inventory. Lot Size and Reorder Point Model.

Reference1. Goodman, R. (1988). Introduction to Stochastic Models. MenloPark, CA: The

Benjamin/Cummings Publishing Company, Inc.2. Taylor, H. M. and Karlin, S. (1998). An Introduction to Stochastic Modeling.

Third edition. Burlington, MA: Academic Press.3. Ross, S. M. (2007). Introduction to Probability Models. 9th Ed. Burlington. MA:

Academic Press.4. Guttorp, P. (1995). Stochastic Modeling of Scientific Data. USA: Chapman &

Hall.5. Buzacot, J. A. & Shanthikumar, J. G. (1993). Stochastic Models of Manufacturing

Systems. Englewood Cliffs. NJ: Prentice-Hall, Inc.

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