BSc _Hons_ Mathematics v1.1.Jul 08 Doc

8/13/2019 BSc _Hons_ Mathematics v1.1.Jul 08 Doc

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School of Business Informatics and Software Engineering

BSc (Hons) Mathematics

PROGRAMME DOCUMENT

VERSION 1.1BM v1.1

July 2008

University of Technology, Mauritius

La Tour Koenig, Pointe aux Sables, Mauritius

Tel:(230) 234 7624 Fax: (230) 234 1747 Email: [email protected]

website: www.utm.ac.mu


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BM v 1.1/July 2008 Page 2 of 14

BSc (HONS) MATHEMATICS

A. Programme Info rmation

As well as being a discipline in its own right, Mathematics forms the basis of modern commercial, industrial and

technological activities. Mathematical models underpin engineering, sciences, computing and many aspects of

management today.

The B.Sc. (Hons.) Mathematics is a pure mathematics programme which provides the skills much in demand for

a wide range of careers today. According to how students interests and aptitudes develop, students may

specialise in progressively more depth or they may choose a broad range of modules from the major branches of

mathematics during the last year of study.

B. Programme Aims

The B.Sc. (Hons) Mathematics has been designed to provide the students with the skills and techniques needed

to develop a mathematical, computational and statistical knowledge and with an understanding of how these canbe applied to the formulation and solution of problems from scientific, technological, business, finance and other

areas. The Programme will give the students experience of mathematical activity and investigation, and develop

them to be resourceful in solving problems for which ready methods are not available. The Programme will also

provide the students with broad concepts of the principal branches of Mathematics.

C. Programme Objectives

After successful completion of the Programme, the graduates should

display a mastery of the principal skills required for work in mathematics,

have achieved broad understanding and knowledge, and have an interest in and appreciation of

mathematics,

be logical and analytical, and possess skills in information technology, communication, presentation

and problem-solving,

be skilled in the use, and appreciate the relevance, of mathematics in a variety of applications in

science, engineering and commerce.


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PART I

Regulations

D. General Entry Requirements

As per UTMS Admission Regulations.

E. Programme Entry Requirements

A Level in Mathematics.

F. Programme Mode and Duration

Full Time: 3 yearsPart Time: 4 years

G. Teaching and Learning Strategies

Lectures, Tutorials and Practicals

Class Tests and Assignments

Final year dissertation

H. Student Support and Guidance

Academic Tutoring: 3 hours per week per lecturer

Intensive tutoring conducted during Week 8 of the semester

I. Attendance Requirements

As per UTMs Regulations and Policy.

J. Credit System

Core module = 3 credits

Elective module = 6 credits

Final year project = 9 credits

K. Student Progress and Assessment

For the award of the Degree, all modules must be passed overall with passes in the examinations, courseworkand other forms of assessment.

All core modules will carry 100 marks and all electives will carry 200 marks. The modules will be assessed asfollows (unless otherwise specified) :


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Written examinations up to a maximum of 3-hours duration and continuous assessment carrying up to amaximum of 40% of total marks. Continuous assessment can be based on seminars and/or assignments orclass tests.

The project will carry 300 marks (9 credits)

Maximum marks attainable:

Level 1 1200Level 2 1200Level 3 1200

Grading

Grade Marks x(%)A x > 70A- 65 < x < 70B 60 < x < 65B- 55 < x < 60C 50 < x < 55C- 45 < x < 50D 40 < x < 45F x< 40

A-D PassF Fail

L. Evaluation of Performance

The % mark at Level 1 contributes a 20% weighting towards the degree classification.



M. Award Classification

Overall weighted mark y(%) Classificationy > 70 1st Class Honours60 < y < 70 2

ndClass 1st Division Honours

50 < y < 60 2nd

Class 2nd

Division Honours45 < y < 50 3rd Class Honours40 < y < 45 Pass Degreey < 40 No Award

N. Programme Organisation and Management

Programme Director and Coordinator: Dr Mohammad Sameer Sunhaloo

Contact Details:

Room: F 0.23

Telephone Number: 234 7624 (Ext. 150) Email: [email protected]


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PART II

O. Programme Structure Full Time

BSc (HONS) MATHEMATICS

YEAR 1 (Level 1)

Semester 1 Semester 2

Code Modules Hrs/Wk Credits Code Modules Hrs/Wk Credits

L P L P

ITE 1101 Computer Fundamentals 1+2 3 MATH 1122 Mechanics 3+0 3

MATH 1114Mathematics I 3+0 3 MATH 1115 Mathematics II 3+0 3

MATH 1116Real Analysis I 3+0 3 MATH 1117 Real Analysis II 3+0 3

MATH 1118 Probability and Statistics 3+0 3 MATH 1119 Mathematical Statistics 3+0 3

PROG 1101 Programming Essentials 2+2 3 MATH 1120 Algebra 3+0 3

COMM 1106Communication Workshop 3+0 3 MGMT 1101Organisation and

Management

3+0 3

YEAR 2 (Level 2)



L P L P

MATH 1121 Linear Algebra 3+0 3 MATH 2124 Abstract Algebra 3+0 3

MATH 2126 Complex Analysis 3+0 3 MATH 2127Applied MathematicalMethods

3+0 3

MATH 2128 Numerical Computing 2+2 3 MATH 2129 Matrix Computations 2+2 3

MATH 2130 Mathematical Programming 3+0 3 MATH 2131Numerical Methods for

ODEs2+2 3

MATH 1123 Discrete Mathematics Concepts 3+0 3 MATH 2133Decision Analysis andModelling

3+0 3

MATH 2132 Linear Statistical Models 3+0 3 PROG 1120Data Structures and

Algorithms2+2 3

YEAR 3 (Level 3)



L P L P

MATH 3138 Optimisation 3+0 3 MATH 3136 Probabilistic Models 3+0 3

MATH 3137 Fluid Dynamics 3+0 3 MATH 3135 Functional Analysis 3+0 3MATH 3125 Topology 3+0 3 1 elective 3+3 6

1 elective 3+3 6

PRJ 3105 Project 9


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List of Electives

Code Modules Hrs/WkL P

Credits

MATH 3139 Numerical Methods for PDEs 3+3 6

MATH 3140 Mathematics of Financial Derivatives 3+3 6

MATH 3141 Mathematics for Game Programming and ComputerGraphics

3+3 6

MATH 3142 Scientific Visualization and Graphics 3+3 6

MATH 3143 Statistical Analysis of Financial Data 3+3 6

MATH 3144 Computational Statistics 3+3 6


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YEAR 4

Start of Level 3



L P L P

MATH 3138 Optimisation 3+0 3 MATH 3125 Topology 3+0 3

MATH 3137 Fluid Dynamics 3+0 3 MATH 3136 Probabilistic Models 3+0 3

1 elective 3+3 6 MATH 3135 Functional Analysis 3+0 3

PROJ 3105 Project

YEAR 5

Semester 1

Code Modules Hrs/Wk Credits

L P

1 elective 3+3 6

PROJ 3105 Project 9

End of Level 3

List of Electives

Code Modules Hrs/Wk

L P

Credits

MATH 3139 Numerical Methods for PDEs 3+3 6

MATH 3140 Mathematics of Financial Derivatives 3+3 6

MATH 3141 Mathematics for Game Programming and ComputerGraphics 3+3 6

MATH 3142 Scientific Visualization and Graphics 3+3 6

MATH 3143 Statistical Analysis of Financial Data 3+3 6

MATH 3144 Computational Statistics 3+3 6

The University reserves the right not to offer any given elective if the critical number of s tudents is no tattained and/or for reasons of resource constraints.


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Q. Module Outline

ITE 1101: COMPUTER FUNDAMENTALS

A brief history of computing

Survey of various types/classes of hardware and software used in current ICT systems

Survey of main areas of application of ICT

Impact of ICT on individuals, business and society Forthcoming developments Areas of expertise, jobs and roles of professionals of the ICT sector

MATH 1114: MATHEMATICS I

Differentiation

Integration

Complex numbers Polar coordinates

Hyperbolic functions Limits

Partial derivatives First-order ordinary differential equations

Linear ordinary differential equations of second and higher order

MATH 1116: REAL ANALYSIS I

Real numbers Functions and graphs

Continuity and limit Differentiation Mean value theorem Maxima and minima

Indeterminate forms

MATH 1118: PROBABILITY AND STATISTICS

Probability theory

Bayes theorem

Random variables and distribution functions Mathematical expectation and generating functions

PROG 1101: PROGRAMMING ESSENTIALS

Single module code Basic I/O

Basic data types

Sequence, selection and iteration. Use of control graph Introduction to procedural programming. Use of call graph Implementation of simple algorithms

Elementary code inspection and testing

Fundamental quality attributes of code Introduction to professional programming conventions and protocols

COMM 1106: COMMUNICATION WORKSHOP

Development of key communication skills required by an IT professional

Techniques for presentation, interviewing, report-writing, meetings, negotiations, drafting of contracts andtender/marketing document

Quantitative appraisal of documentation: FOG index


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MATH 1122: MECHANICS

Coplanar forces in equilibrium Velocity and acceleration

Newtons laws of motion

Hookes law

Momemtum Projectiles Motion in a circle

General motion of a particle Simple harmonic motion

Resultant motion

MATH 1115: MATHEMATICS II

Matrices

Vectors Determinants Classical methods for solving linear systems of equations

Matrix eigenvalue problems Vector differential calculus

Vector integral calculus

MATH 1117: REAL ANALYSIS II

Real series

Convergence tests Riemann integration

Integral mean value theorem

Fundamental theorem of calculus Improper integrals

MATH 1119: MATHEMATICAL STATISTICS

Functions of random variables Sampling distibutions Estimation

Hypothesis testing

MATH 1120: ALGEBRA

Sets , relations and functions

Binary operations

Equivalence relation and equivalence class Groups and subgroups

MGMT1101: ORGANISATION & MANAGEMENT

Constitution and mission of organisations The core management role: lead, plan, organise, coordinate and control

A brief history on the evolution of management: from the mechancal to the political view of organisations

Standard management functions in organisations: finance & accounting, marketing, human resources,operations & quality, environment, social responsibility, contingency planning , strategic planning

Effectiveness of organisations


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MATH 1121: L INEAR ALGEBRA

Vector spaces and subspaces Linear transformations Orthogonality Inner-product spaces

Determinants

Eigenvalues and eigenvectors

MATH 2126: COMPLEX ANALYSIS

Complex numbers and functions

Complex integration Power series and Taylor series

Laurent series and residue integration

MATH 2128: NUMERICAL COMPUTING

Computer arithmetic Errors and error propagation

Solving nonlinear equations

Interpolation and approximation Numerical differentiation and numerical Integration

MATH 2130: MATHEMATICAL PROGRAMMING

Linear programming

The simplex method

Duality and sensitivity analysis Transportation model and its variants

Integer linear programming

Deterministic dynamic programming

MATH 1123: DISCRETE MATHEMATICS CONCEPTS

Basic counting rules Generating functions and their applications Recurrence relations The principle of inclusion and exclusion

The pigeonhole principle and itsgeneralizations

The Polya theory of counting Introduction to graph theory

Shortest path problems

MATH 2132: LINEAR STATISTICAL MODELS

Decision theory

Regression and correlation

Analysis of variance Nonparametric tests

MATH 2124: ABSTRACT ALGEBRA

Permutations, cosets and directed products Homomorphisms & factor groups

Rings and fields


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MATH 2127: APPLIED MATHEMATICAL METHODS

Formulation of ordinary and partial differential equations Mathematical techniques: Laplace transformation, Fourier analysis, Greens function

MATH 2129: MATRIX COMPUTATIONS

Matrix analysis Linear systems Orthogonalization and least squares

Matrix computations

Eigenvalue problems

MATH 2131: NUMERICAL METHODS FOR ODEs

Singlestep method

Multistep method

Predictor-Corrector methods Stability analysis

Stiff system

Boundary value problems Initial Value problems

Finite difference methods

MATH 2133: DECISION ANALYSIS AND MODELLING

Decision making under risk Decision making under uncertainty

Models of processes

Introduction to simulation

Planning and forecasting models

PROG 1120: DATA STRUCTURES AND ALGORITHMS

Object oriented programme using C++ Complexity analysis Linked lists

Stacks and queues

Recursion

Binary trees Graphs

Sorting

Hashing

MATH 3135: FUNCTIONAL ANALYSIS

Normed linear spaces

Banach spaces

Duality Bounded linear maps

Hilbert spaces

MATH 3137: FLUID DYNAMICS

Conservation laws Eulers and Bernoullis equations

Potential functions

Complex variable methods


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Irrotational flow in three dimensions

Viscosity Reynolds number

Boundary layers Navier-Stokes equation

MATH 3125: TOPOLOGY

Set Theory and the real number line Metric spaces

Topological spaces Convergence

Separation axioms

Countability axioms Compactness

MATH 3136: PROBABILISTIC MODELS

Random walk Stochastic dynamic programming

Stochastic inventory models Queueing systems

Finite markov chains Markovian birth-death processes

MATH 3138: OPTIMISATION

Unconstrained optimisation Steepest descent method,

Newton and quasi-Newton methods

Davidon-Fletcher-Powell method Fletcher-Reeves method

Constrained optimisation

MATH 3139: NUMERICAL METHODS FOR PDEs

Finite difference methods for elliptic, parabolic and hyperbolic differential equations Solution techniques for discretized systems

Finite element methods for elliptic problems

Multigrid and domain decomposition Methods

MATH 3140: MATHEMATICS OF FINANCIAL DERIVATIVES

European call and put options Payoff diagrams

Pricing an option Probability and stochastic background theory

The Black-Scholes formula Computing the implied volatility Monte-Carlo and binomial simulation

American options

MATH 3141: MATHEMATICS FOR GAME PROGRAMMING AND COMPUTER GRAPHICS

Transforms

Engine geometry

Ray tracing


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Illumination

Visibility determination Polygon techniques

Shadows

MATH 3142: SCIENTIFIC VISUALIZATION AND GRAPHICS

2D and 3D graphics GUI design

Data visualization techniques

Volume visualizations

MATH 3143: STATISTICAL ANALYSIS OF FINANCIAL DATA

Data exploration, estimation, and simulation

Regression

Local and parametric regression Time series and state space models

MATH 3144: COMPUTATIONAL STATISTICS

R open source software Objects: matrices, vectors, lists Input, output, data manipulation

Descriptive analysis

Graphical analysis Functions, logical operators, conditional expressions, loops

Pseudo-random numbers, Monte Carlo experiments, simulation based inference

Applied linear modelling: multiple regression, model selection, regression diagnostics, factors, analysis ofvariance, analysis of covariance, factorial designs

Applied time series analysis: time series objects, model identification, ARIMA modelling Applied multivariate analysis: principal component analysis, cluster analysis, factor analysis

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BSc _Hons_ Mathematics v1.1.Jul 08 Doc