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Course Synopses
M1330 Essential Mathematics
Decimals, fractions, and operations involving them. Estimation, signed numbers, Discount, interest. Ratios and percentages, including percentage rates of growth, Metric Units, Scale reading, Coordinates, scales, Drawing and interpretation of different types of graphs: continuous, discontinuous, discrete, linear, non-linear etc., Scale drawing. Drawing and reading of plans and maps (including drawing of sketch maps) Algebraic expressions. Solutions of equations.
M1431 Algebra I for Non-Mathematics Majors
Revision of decimals, fractions, powers, roots, ratios, percentages, etc. Approximations, errors and significant figures. Idea of a set. Set notation. Idea of a variable. Relations between variables. Rules for dealing with variables. Equations of straight lines. Idea of a function. Graphs of functions, including drawing and interpretation of non-algebraic graphs. Slope of straight line and curve. The binomial theorem. Solutions of linear, quadratic, cubic and simultaneous equations (graphically and algebraically). Arithmetic and geometric progressions, with applications.
M1432 Calculus I for Non-Mathematics Majors
Concept of derivative as slope of curve. Differentiation of simple functions, including sums, products, quotients, chain rule, implicit differentiation: to include maxima and minima, curve sketching, rate problems. Exponential and logarithmic functions and their applications. Concept of integral as area under a curve and anti-derivative. Integration of simple functions by substitution and by parts.
Applications of integration including area under and between curves, simple differential equations (variables separable), and simple growth models.
M1501 Algebra, Trigonometry and Analytic Geometry
Set notation. Permutations, combinations and binomial theorem. Real number system. Radicals, inequalities and values. Coordinate geometry; equations of a straight line and circle. Introduction to Conics. Relations, functions and their rational zeros. Mathematical induction. Introduction to the arithmetic of complex numbers. Power functions. De Moivre's theorem. Rational functions, inverse functions, exponential and logarithmic functions. The circular functions, identities and their graphs. Arithmetic and geometric series.
M1502 Calculus I
Limits: Notation of a limit of function, Computation of limits, limits with infinity, notation of continuous function. Derivatives of elementary functions: Derivative as limit, rules of differentiation, higher order derivatives, implicit differentiation. Partial derivative. Applications of derivatives to curve sketching and rates of change and extremum problems. Integration: Simple rules of integration, integration by substitution and by parts. Partial Fractions Definite integrals and their applications.
M2451 Algebra II for Non-Mathematics Majors
Revision of algebraic manipulation. Matrix algebra: Definition of matrix; basic operations; identity and inverse matrices. Determinants; Cramer's Rule. Solution of simultaneous equations by matrix inversion.
Solution of matrix equations. Linear programming: Linear inequalities and regions. Solution of problems by graphical and algebraic method.
M2452 Calculus II for Non-Mathematics Majors
Revision of differentiation and integration; integration by partial fractions and by parts. Maclaurin's series. Partial differentiation; meaning of partial derivative; maxima and minima problems including those subject to constraints; growth models; differential equations; difference equations; introduction to double integrals.
M2401 Logic, Set Theory and Algebraic Structures
Logic: statements/propositions, logical connectives, equivalence, alternative statement forms, open statements and quantifiers, methods of proofs; Naïve Set Theory: sets, methods of describing sets, subsets, set operations, Cartesian product, counting and cardinality, arbitrary union and intersection, relations and functions, equivalence and order relations with lattice diagrams; Algebraic Structures: definition and examples of sets with one or more operations, basic terminologies in groups, rings and fields with contrasting examples, review of the ring of integers.
M2402 Linear Algebra
Euclidean n-spaces: addition of n-tuple of real numbers (vectors), multiplication by scalars, dot product of n-tuple vectors, parametric equation of line and planes; Vector Spaces over arbitrary fields: definition of vector spaces with examples, subspaces, linear independence, bases, dimension, coordinates of vectors; Matrices over arbitrary fields: definition of matrices and matrix operations with examples, types of matrices, invertible matrices, determinant’s of matrices; System of Linear Equations: matrix representation of system of linear equations, Cramer’s rule in solving equations; Linear Transformations: definition with examples, kernel and images space of linear maps, basic homomorphism theorems, change of bases, matrix representation of linear maps, eigenvalue and eigenvector.
M2403 Calculus II A
Infinite Series: Sequences, limit of a sequence. Series: Convergence and Divergence of a numerical series, Tests for convergence of a series, Power series; convergence and divergence of power series, Taylor’s and Maclaurin’s series, Successive Differentiation. Expansion of functions in Maclaurin’s and in
M2404 Calculus II B
Functions of two real variables, Limits and Continuity, Partial derivatives, differentiability and chain rules, Euler’s Theorem on homogeneous functions, Partial derivatives with constrained variables, Total differential coefficient, Gradients and directional derivatives, Tangent planes and Normal lines, Higher order derivatives, Functions of n real variables, The Jacobian Matrix. Relative Maxima and Minima, Linear Approximations and Increment estimates, Lagrange multipliers. Multiple Integrals, Double integrals, Areas, Moments and Centre of mass, Double integrals in polar form, Triple integrals, Change of variables in double and in triple integrals. Ordinary differential equations of the first order.
M2405 Vectors and Mechanics
Vectors: Vector algebra in, Scalar and vector products and their applications. Equations of straight lines and planes. Distances of points from lines and planes. Establishing the sine and cosine rules. The internal division theorem and its applications. Establishing vector identities using the Kronecker delta and the Levi-Civita symbols or any other technique/method. Statics: Forces acting at a point, like and unlike parallel forces, moments and the principle of moments, couples, the resultant of a force and a couple. Lami's theorem and its applications. Laws of friction and the general conditions equilibrium. Centre of gravity: Determination by integration, centre of gravity of compound bodies and of the remainder. Dynamics: Velocity, uniform and variable acceleration, space-time and velocity-time graphs, rectilinear motion, Plane kinematics and projectile motion. Use of plane polar co-ordinates: radial and transverse components of velocity and acceleration. Newton's laws of motion and their applications. Potential and kinetic energy and the principle of conservation of energy. Constrained motion on a circle with constant and variable angular velocity. Simple harmonic motion.
M2406 Numerical Analysis I
The Calculus of Finite Differences: basic properties of finite difference theory, notations of finite difference Calculus, method of constructing a difference table, nth , (n+1)th and higher order polynomial’s differences. Interpolation with equal intervals: meaning of interpolation, assumptions for interpolation, various methods of interpolation. The various methods of curve fitting, the use of the Calculus of finite differences, interpolation with equal intervals, Newton Gregory formula for Backward Interpolation. Interpolation with unequal intervals: notations for divides differences, simple method to write divided differences, theorems on divided differences, Sheppard’s rule, Lagrange’s formula for interpolation. Central Differences: Gauss central formulae, Stirling’s formula, Bessel’s formula, Everett’s formula , Sheppard’s notations for central differences. Numerical Differentiation and Integration: Method of operators, general quadrature formula, Trapezoidal rule, Simpson’s one third rule, Weddle’s rule, Cote’s-method. The Euler-Maclaurin’s summation formula.
M3401 Vector Calculus
Vector-valued functions, limit of a vector function, Continuity and Derivability of a vector function, vector functions of several variables, Partial derivatives, Differential operators, Curvilinear coordinates, Integral transformations. Line, surface and Volume integrals. Green's Gauss's and Stoke's theorems. Curves and Surfaces: Fundamental triads of lines and planes associated with any point on a curve, Frenet's formulae, Expressions for curvature and torsion.
M3402 Real Analysis I
The Real Number System: R as a complete ordered commutative field. Absolute value, Archimedean property and nestled interval theorem. Neighbourhood. Bolzano-Weistrass Theorem. Sequences: Convergent and divergent sequences. Uniqueness of limit.
M3403 Differential Equations
1. 1st and higher order differential equations: elementary properties of solutions, techniques of solving equations with constant and variable coefficients (such as reduction of order variation of parameters, undetermined coefficients, inverse operators, Total differential equations.
2. Partial Differential equations: Partial differential equations of the first order, Lagrange's linear partial differential equation; nonlinear first order partial differential equations, Charpit's method, nonlinear first order in more than two independent variables, Jacobi's method; higher order linear partial differential equations.
M3404 Mechanics
Particle Dynamics: Constrained motion, in 2-D, Central orbits, Planetary motion, Motion in resisting medium, variable mass problems. Rigid Body Dynamics: moments and products of inertia, D'Alembert's principle, principle of conservation of linear and angular momentum, principle of conservation of energy, Rigid body motion about a fixed axis, Plane motion of rigid body.
M3405 Introduction to Abstract Algebra
Group Theory: algebraic structure with one operation, properties of a binary operation, examples of Abelian and non-Abelian groups, subgroups and cosets, special subgroups, homomorphism theorems and quotient groups, Permutation (symmetric) groups, alternating subgroup and some applications; Ring Theory: definition with examples, types of rings with models, integral domain, sub-rings, ideals, quotient rings, ring homomorphism, unique factorization domain, Euclidean domain, fields with examples.
M3406 Tensor Analysis
Some preliminaries. Tensor Algebra. Tensor Calculus. Riemannian metric, Christoffel symbols, Covariant differentiation, Intrinsic derivation of tensors, Law of covariant differentiation of tensors, Ricci Theorem, Curvature of a curve, Geodesics, First Curvature Principal normal, Parallelism, Generalized covariant differentiation Riemann's symbols and curvature tensor.
M3407 Numerical Analysis II
Interpolation and Quadrature Formulae: Error classification, Remainder terms in Lagrange’s and
M3408 Introduction to Elementary Number Theory
The System of Integers: the axioms of ordered rings, the integers as an ordered integral domain, the equivalence of well ordering axiom and the Principle of Mathematical Induction; Basic Divisibility theory: definition, example and related questions on factor/divisor, prime number, multiple, greatest common factor, least common factor, Fundamental Theorem of Arithmetic, prime factorization and application, contrasting questions on prime numbers; Some Number Theoretic Functions: number of factors, sum of factors, application to certain types of (perfect, abundant, deficient, Mersene, Fermat) numbers; Diophantine Equation: definition with examples, motivating questions on linear and higher order Diophantine equations, Euclidean Algorithm and Euler’s Method in solving linear Diophantine equations, Fermat equation and related problems; Theory of Congruence and Modulo Arithmetic: definition and ring of integers (mod m), basic properties of the ring of integers and finite prime fields, equations over the ring of integers, polynomials over finite rings, congruence theory in solving higher order Diophantine equations; Algebraic Numbers: definition of algebraic and transcendental numbers, examples of algebraic extension of rational numbers (number fields), constructing intermediate fields and related some related questions.
M4401 Ordinary Differential Equations
1. Power series about ordinary and singular points including a point at infinity. Conversion from nth order differential equation to system of first order equations; Initial Value Problem (IVP), statement of existence and Uniqueness theorem, Integral representation of (IVP), successive approximation (Picatti) method.
2. Systems of linear equations: Vector space of solutions of homogeneous system, fundamental matrix, eigenvalue method of solution of homogeneous system; nonhomogeneous system, general solution; periodic linear system, computation of characteristics multipliers (exponents) Boundedness of solutions.. Solution of differential equations by Numerical method.
M4402 Introduction To Metric Spaces
Definition of a metric. Examples of metric spaces, metric spaces generated by a norm. Balls and spheres in metric spaces, diameter, distances between sets. Convergence and completeness, uniform convergence, equivalent metrics, Closed sets, closure, density, separability, the boundary of a set. (Completeness: Applications to fixed point theorems). Continuity-characterisations of, Isomertries and homomorphisms; uniform continuity. Compactness; continuous functions on compact metric spaces; equi-continuity-The Ascoli-Arzela's Theorem.
M4403 Real Analysis II
Normed Spaces: Inner product spaces, normed space associated to an inner product space and the Cauchy-Schwarz inequality. Open and closed balls related to a norm. Equivalent norms and their common neighbourliness. Norms on Rn : The Euclidean norm. Two more equivalent norms with corresponding balls in R2 are squares and rhombus respectively. Equivalence of the three norms. Geometrical interpretations of common neighbourliness of the three norms in R2 and R3.Limits, Continuity and Derivatives: Elementary (vector) real functions of several variables. Limits, uniqueness of limit. Proofs of rules for calculating limits. Limits in various directions. Continuity and Uniform continuity of elementary functions (at least up to rational functions). Explicit use of the three norms in specific examples. Differentiability and directional derivatives. Partial derivatives. Introduction to Riemann Integral: Partitions, mesh and refinement of a partition of a rectangular n-box. Lower sum and upper sum of a function relative to a partition. Riemann sums of a function over an n-box relative to a partition. Riemann integrable functions.
M4404 Introduction to Functions of a Complex Variable
Review of elementary notions of limits and continuity on R . Differentiation: Holomorphic Functions. Cauchy-Riemann equations. Harmonic functions. Elementary functions. Integration: Line integrals, change of Variables and contours. Green's Theorem. Cauchy's Theorem and the Cauchy's integral formulas. Series: sequences, power series and the circle of convergence. Taylor's and Laurent's series. Singularities: The residue theorem and some applications.
M4405 Topics in Algebra I
Group Theory: models of Abelian and non-Abelian groups, cyclic groups, types of subgroups, cosets and Lagrange’s theorem for finite groups, standard homomorphism theorems, permutation group and related notions, Cayley’s theorem, product of groups, Sylow subgroups and Sylow Theorems; Ring Theory: definition with models, types of rings with contrasting examples, subrings, ideals, ring homomorphism and quotient rings, characteristic of rings and integral domain, divisibility notions on commutative rings, unique factorization domains and application, polynomial rings over fields, irreducibility, Eisenstein criterion of irreducibility, factorization and application over finite fields.
M4406 Topics in Algebra II
Quotient Rings and Fields: properties of commutative rings, prime ideals, and maximal ideals and quotient fields; Modules: definition and examples, submodules, quotient modules and homomorphism, vector spaces over general fields with contrasting models; Field Theory: definition with examples, subfields, field extensions, algebraic and transcendental elements, types of field extensions with examples, finite field extensions, algebraically closed fields, elementary idea of Galois’s Extension.
M4407 Mathematical Methods
Orthogonal sets of functions, Sturm-Liouville problem, Fourier series: Euler's formulae, sectionally continuous functions, functions having arbitrary period, even and odd functions, half range expansions, Parseval's theorem. Fourier integrals and Fourier transforms. Bessel's functions, orthogonality of Bessel's functions, generating function for Bessel's functions. Legendre's polynomials, Rodrigue's formula, orthogonality of Legendre's polynomials. Boundary Value Problems.
M4408 Classical Mechanics
Coordinate systems, transformation equations, generalized coordinates, degrees of freedoms, degree of constraints, equation of constraints, velocity, kinetic energy, acceleration in generalized coordinates, virtual displacements and Virtual works. Lagrange's equations of motion for a system of particles, conservative systems, Lagrange's equations for conservative systems, Lagrangian treatment of Rigi Body Dynamics, The Euler's method of Rigid Body Dynamics, small oscillations, Hamilton's form of the equations of motion, physical significance of the Hamiltonian, passage from the Hamiltonian to Lagrangian, Variational methods, Hamilton's principle, principle of least action.
M4409 Topology
Set theory; basic definitions and relations, maps, countable and uncountable sets. Basic properties of topological spaces; definitions and examples of topological spaces; metric spaces; Hausdorff spaces. Continuous maps; sequences: limit points; neighbourhood; T-spaces. Compact and countably compact sets; finite intersection property. Subspaces; homeomorphic spaces; connected and separated sets; closure of a set. First and second countable spaces; normal spaces, completely normal spaces.
M4410 Fluid Mechanics
Kinematics, Equation of continuity. The general equation of motion of an inviscid fluid. Motion in two dimensions of an incompressible fluid. General theory of irrotational motion. Motion of cylinders in two dimensions.
M4411 Mathematical Modeling
Mathematical modelling is mathematics applied to solving real world problems. Because of the many, and diverse, fields to which mathematics is applied, it would not be prudent to have a rigid outline for this course. Also, the course content, and its presentation, will be determined by the particular areas of interest of the lecturer concerned. However, this course will (in general) cover topics from: Single compartment models, Stochastic models, shortest path and MST problems, heat conduction in a rod, perturbation (including singular perturbation) methods.
M4412 Graph Theory
Definition of a graph, sub graphs, binary relations (singular and non-singular block), incidence matrices; connected graphs; Euler paths, labyrinths and Hamiltonian circuits; trees, arbitrarily traceable graphs.
PM5601 Abstract Algebra
1. Ordered sets: Example from mathematics, computer science and social science. Diagrams, Maps between ordered sets. The Duality principle. Maximal and minimal elements; top and bottom. Building new ordered sets.
2. Lattices and complete lattices: Lattices as ordered sets. Complete lattices chain condition and completeness. Completions (Dedekind-MacNeille completion).
3. CPOS. Algebraic lattices and domains: Directed joins and algebraic closure operators. CPOS (complete partial ordered sets) Finiteness, algebraic lattices and domains. Information systems.
4. Ideals and filters: Ideals and filters. Prime ideals, maximal ideal and ultrafilters. The existence of prime ideals, maximal ideals and ultrafilters.
5. Representation theory: Representation by lattices of sets. The prime ideal space (Stone’s representation theorem for Boolean algebra). Priestley’s representation theorem for distributive lattice.
PM5602 Measure Theory and Integration
Sigma algebras of subsets and measures. Extension of a measure and completion. Lebesgue measure. Properties of Lebesgue measure. Measurable space. Measurable function. Simple measurable function. Approximation of a non-negative measurable function by an increasing sequence of non-negative simple measurable function. Measure space. Definition of the Integral with respect to a measure. Integrable functions. Properties of the Integral. Monotone convergence theorem. Fatous’s Lemma. Dominated convergence Theorem. Integration with respect to Lebesgue measure versus Riemann Integration.
PM5603 General Topology
Metric Spaces. Examples (to include Euclidean spaces and examples of normed linear spaces). Open ball; open set, topology of a metric. Definition of a topological space. Interior of a set. Closed sets. Closure, Boundary; Cluster point; Convergence of sequence. Cauchy sequence; Completeness. Completeness and Closure. Cantor’s intersection Theorem. Baire’s Theorem. Continuous mapping characterization by sequences. homomorphisms. Compactness: Survey of equivalent definitions (Sequential compactness. Finite intersection property theorem. Bolzano-Weiersstress property). Heine-Borel Theorem. Continuous functions in compact spaces. Uniform Continuity. Ascoli’s Theorem. Definition of connectedness. Countability. Separable spaces, Product spaces. Separation axioms. Hausdorff spaces. Regular and
PM5604 Functional Analysis
i) Finite dimensional inner Product Spaces: Structure theorems, linear transformations; normal self adjoint, Unitary, positive linear transformation; projections and Spectral Theorem.
ii) Normed Linear Spaces : Banach space. Example; Quotient space; linear functionals; Hahn-Banach theorem; Bounded linear functionals; conjugate (or dual) space; Consequences of Hahn-Banach theorem; Second conjugate; space-reflexivity.
iii) Hilbert Spaces: Definition. Examples: Hilbert space as a Banach space; Geometric structure; Riesz representation theorem-reflexivity; orthonormal sets and bases; Bessel’s inequality and Fourier transform.
PM5605 Complex Analysis
Meromorphic functions. Argument principle. Rouche’s theorem. Fundamental theorem of algebra. Infinite products. Integral functions. Weierstrass’s theorem. Hadamards factorisation theorem. Analytic continuation. Expansion of meromorphic and integral functions and summation of series by the method of residues. More about functions. Winding numbers.
PM5606 Differential Geometry
Space Curves. Arc length. Tangent, normal and binormal. Curvature and torsion of a curve. Involutes and evolutes. Local and intrinsic properties of a surface. Curves on a surface. Isometric correspondence. Geodesics. Gauss-Bonnet theorem. The second fundamental form. Principal Curvature. Lines of curvature. The Sphere map and the Weingarten map. The Gauss equation.
PM5607 Set Theory and Logic
1. Introduction: The basis of intuitive Set Theory. Operations for Sets. The Algebra of Sets. Equivalence Relations. Functions. Operations for Collections of Sets. Ordinary Relations.
2. Logic: Connectives. Valid arguments and consequences. Symbolising everyday languages. Formulation of predicate and propositional Calculus. The concept of an axiomatic theory. Informal theories.
3. Set Theory: Axioms of extension, pairing, union and power set. Axiom of infinity. Axiom schema of replacement and restriction. Ordinal numbers. Ordinal arithmetic. Cardinal numbers and their arithmetic. Axiom of Choice and their equivalence.
4. First-Order Theories: Formal axiomatic theories. Propositional Calculus and Predicate Calculus as formal theories. First-Order axiomatics theories. Consistency and satisfiability of Sets formula. Consistency, Completeness and Categoricity of First-Order theories.
AM5601 Numerical Solution of Differential Equations)
Solutions of algebraic equations and convergence rate of iterative methods. Approximating functions; Taylor Series, Truncated Fourier series. Runge-Kutta methods. Theory of spline functions. Interpolation and Extrapolation; Quadrature. Finite difference methods of o.d.e’s, and their accuracy and stability; Euler’s method, Linear multi-step methods, leap frog Method. Predictor-Corrector methods, Hybrid methods. Systems of o.d.e’s. Initial and boundary value problems; accuracy and stability, shooting methods, central differences, extensions to non-linear equations. Classification of p.d.e’s. Finite difference methods for p.d.e’s. Method of characteristics. Finite element methods; time marching; Boundary-integral methods; Initial and boundary value problems;
AM5602 Partial Differential Equations
Surfaces and curves in three dimensions. Simultaneous differential equations of the first order. Methods of solution of dx/P=dy/Q =dz/R. Orthogonal trajectories of systems of curves on a surface. Pfaffian differential equations. Linear, semi-linear, quasi linear equations of the first order. Integral surfaces passing through a given curve. Use of the methods of Cauchy, Charpit and Jacobi in solving non-linear partial differential equations of the first order. Characteristics of the linear and semi-linear partial differential equations of the second order. Boundary value and initial value problems. Equations of the hyperbolic type. Riemann’s method. The equation of wave motion. Equations of elliptic type. The heat equations.
AM5603 Mathematical Modeling
The concept of a mathematical model; fundamental steps in mathematical modelling. Input-output models and compartmental analysis. Framework for modelling word problems.
Differential equation models:
AM5604 `Introduction to Continuum Mechanics
Cartesian Tensors. Operations with tensors. Quotient rule. Symmetric and antisymmetric tensors. Isotropic tensors. Preliminary definitions of continuum. Convective derivatives. Displacements and velocity gradients. Polar decomposition. Rate of deformation. Vorticity. Superposed rigid body motions. Continuity. Surface forces and stresses. Cauchy’s equation of motion. Thermodynamics: Preliminaries. Energy equation. Entropy inequality. Constitutive equations. Reiner-Revlin fluid. Classical linear theory as a special case of R-R Fluid. The Navier-Stokes equation of motion. Basic equations of motion of a Newtonian Fluid.
AM5605 Advanced Mathematical Methods
Existence and uniqueness of solutions of Lx = a, where L is a linear operator and a is a given function. Methods of solution of this equation: eigenvalue methods; perturbation methods, approximate solutions. Green’s function Method. Application to Sturm-Liouville systems and to second order partial operators of the elliptic, parabolic and hyperbolic type.
AM5606 Fluid Mechanics
Physical properties of fluids; body and surface forces. Inviscid Incompressible fluids: Euler equations of motion, Bernoulli’s equation; applications of dimensional analysis. Fluid statics. Irrotational flows, circulation and Kelvin’s theorem. Two dimensional flows, Complex velocity potential and the stream function. Axisymmetric flows and the Stokes stream function. Unsteady flows and flows with vorticity. Viscous Fluids: Elementary cartesian tensors; stress; rate of strain; Navier-Stokes equations and exact solutions. Dynamical similarity and flows with low Reynolds number. Stokes approximation. Lubrication theory. Thermodynamics. Inviscid compressible flow.
AM5607 Calculus of Variations and Optimization
Functions and functionals. Extrema of functionals: the absolute and the relative minima of a functional. Method of variation in problems with fixed boundaries. The method of lagrenges multipliers. The Euler-Lagrange equation. Drocken extremels. Jocobies necessary conditions for a minimum. Variational problems with variable end points. Isotronic problems. Direct methods: Euler method of finite-difference. Ritz’s method.
Classical methods for functions of one or two variables: quick revision of Linear programming, dynamic programming and calculus of variations. Unconstrained and Constrained Optimization.
COMPUTER SCIENCSES COURSES
CS1301 Computer Appreciation, Awareness and Skills
The course introduces the student to the elementary concepts of Computer organisation (i.e computer logical organisation and operating systems), Computer Applications (i.e wordprocessors, spreadsheets, databases etc), Internet and e-mail(i.e e-mail clients, web browsers, web sites and elements of e-commerce).
CS1401 Introduction to Computing and Information Technology I
[Elementary Algorithms and Applications]
This course introduces a range of algorithmic concepts and constructs, independent of any particular programming language, together with a wide range of application softwares. The course also covers an introduction to the historical and social context of computing and overview of computing as a discipline. Practical exercises may include executing pseudocode using a type‑less language such as Python and using office productivity software.
Topics include: Computing applications, Algorithms and problem‑solving, Introduction to recursion, Fundamental programming constructs, Fundamental computing algorithms, Basic algorithmic analysis, Introduction to net‑centric computing, Social context of computing.
CS1402 Introduction to Computing and Information Technology II
[Fundamentals of Information Systems]
This course provides an introduction to systems and development concepts, information technology, and application software. It explains how information is used in organizations and how IT enables improvement in quality, timeliness, and competitive advantage. The course also cover an introduction to the historical and social context of computing and overview of computing as a discipline.
Topics include: Systems concepts; system components and relationships; cost/value and quality of information; competitive advantage of information; specification, design, and re‑engineering of information systems; application versus system software; package software solutions; procedural versus non‑procedural programming languages; database features, functions, and architecture; networks and telecommunication systems and applications; characteristics of IS professionals and IS career paths; information security, crime, and ethics. Practical exercises may include developing macros, designing and implementing user interfaces and reports; developing a solution using database software.
CS 2301 Introduction to Computing Applications for Science Majors
1. Introduction to the historical development of computers. Introduction to logical and physical organization of a general purpose digital Computer system.
2. Introduction to Windows operating systems (e.g Windows 95, 98, NT etc).
3. Data management techniques (in a windows environment):
- Word processing (choose a suitable window based word processor)
- Spread sheets (choose a suitable window based spread)
- Data bases (choose a suitable window based DBMS)
4. The Internet:
- email
- news groups
- The world wide web
5. Introduction to Programming (object oriented programming).
(Choose a suitable OO language e.g Visual Basic).
CS2431 Programming Fundamentals:
Introduces the fundamental concepts of procedural programming.
Topics include: Computing applications: Word processing; spreadsheets; editors; files and directories, Fundamental programming constructs: Syntax and semantics of a higher‑level language; variables, types, expressions, and assignment; simple I/O; conditional and iterative control structures; functions and parameter passing; structured decomposition, Fundamental data structures: Primitive types; arrays; records; strings and string processing Overview of operating systems: The role and purpose of operating systems; simple file management
CS2432 Introduction to Object‑Oriented Programming:
Introduces the fundamental concepts programming from an object‑oriented perspective. Through the study of object design, this course also introduces the basics of human computer interfaces and graphics, along with significant coverage of software engineering.
Topics include: Introduction to object‑oriented programming: Using an object‑oriented language; classes and objects; syntax of class definitions; methods; members, Message passing: Simple methods; parameter passing , Subclassing and inheritance, Simple data structures: Arrays; strings, Collection classes and iteration protocols, Using APIs: Class libraries; packages for graphics and GUI applications, Object‑oriented design: Fundamental design concepts and principles; introduction to design patterns; object‑oriented analysis and design; design for reuse, Software engineering issues: Tools; processes; requirements; design and testing; risks and liabilities of computer‑based systems.
CS2410 Introduction to Discrete Mathematics
The course aims at introducing introductory concepts in discrete mathematics.
Topics include: Sets, Functions and Relations, Propositional Calculus, Combinatorics, Finite State Machines, Probability and Base R Arithmetic
CS2420 Introduction to Digital logic design
This course introduces student to digital circuit designs at the gate level. This course includes a laboratory in which students will use a CAD tool to design primitive computer components. The students will be introduced to schematic editors as well as simple hardware description languages.
Topics include: Introduction to Logic gates, truth tables and logic equations, Combinatorial logic, Clocks, Flip-flops and Sequential logic.
CS3240 Practicals in Networking: Basic Routing
Students will take a set of practicals that would lead to completion of CCNA 2.
CS3400 Data Structures and Algorithms
The purpose of this course is to introduce the student to the fundamental data structures and algorithms that underline much of today's computer programming.
Topics:‑ The traditional list, stack, and queue structures, tree structures including binary and 2‑3 trees, hashing techniques, and some important sorting algorithms including quicksort, heapsort, and binsort.
CS3410 Theory Of Computation
The course discusses theoretical foundations of computers and their algorithms.
Topics include: Introductory Computability: countable sets, primitive recursion, partial recursive functions and Turing machines. Introductory formal language theory : formal grammars and Chomsky classifications, regular expressions, FSM, PDA, Parsing. Introductory formal logic: introductory formal language proportional calculus (axiomatic ‑ Hilbert system L), introductory formal predicate calculus (axiomatic ‑ Hilbert system K)
CS3420 Computer Architecture I
Introduction to computer design. This course provides a comprehensive view of computer design. It covers the overall design of computers, their architecture and their details. General introduction to instruction set architecture and examples e.g. Intel 80x86, MIPS etc. Overview of advanced features of computer architectures.
Topics:- Design Methodology, Processor organization and design, Data path and control design, Memory organization, System organization, Performance issues.
CS3421 Operating Systems I
Introduction to computer operating systems. This course includes a laboratory in which students enhance a miniature version of UNIX operating systems.
Topics:- History, concepts and Operating system structure, Process Management, Memory Management, File Systems, An introduction to distributed operating systems.
CS3430 Systems Analysis and Design
This course is designed to introduce the student to the process of the analysis and design in computer systems development. Systems are analyzed and designed in relation to input and output, processing, control, presentation to management, and evaluation.
Topics Include: Information-gathering techniques, Process analysis and modeling techniques, Data Design, Interface Design, System Implementation.
CS3432 Principles of Database Design and Data Management
This course aims at introducing the student to the design and management of DBMS
Topics Include: Database Systems Concepts & Architecture, Data Modeling, Normalisation & Functional Dependencies, Database Languages.
CS3431 Artificial Intelligence
Introduction to ProLog programming language and resolution refutation technique; Knowledge Representation: The Frame problem, Predicate Logic, Production Rule Systems, Semantic Nets, Frames and Scripts, Object oriented representation. Heuristic Control Strategies and Search Techniques: Bactracking, Backward and Forward reasoning, Generate and Test, Hill Climbing, A class algorithms, depth first, breadth first, best first search strategies, constraint satisfaction and means ends analysis. Planning: Components of a planner, Goal stack planning, Non‑linear and hierarchical Planning, real time and reactive systems. Learning: Rote learning, Learning by taking advice, Learning from examples (induction), Discovery and Analogy, ID3 Algorithm
CS3433 Programming Languages Workshop
This course will give students an insight into different types of programming languages and hence allow them to make an informed choice about a suitable language for a given programming task.
In the course different languages from differing programming paradigms ,such as procedural, functional and logic programming, are studied and compared with regards to their syntax, data abstraction and typing, compilation/interpretation and their run time environments.
CS3434 Information Systems Theory and Practice
Students who have constructed personal information systems will be exposed to the theory of the Information Systems discipline. Application of these theories to the success of organizations and to the roles of management, users and IS professionals are presented.
Topics:
Systems Theory and Concepts; Information Systems and Organisational Systems; Decision Support Systems; Level of Systems: Strategic, tactical and operational; System components and relationships; Information systems strategies; Role of information and information technology; role of people using, developing and managing systems; IS planning and change management; human computer interface; IS development process; evaluation of system performance; societal and ethical issues related to information systems design and use.
CS3441 Computer Communications and Networks
Introduction to concepts of transport connections and sessions; design issues in network layers and protocols; terminal and file handling protocols; Message handling and remote procedure calls; Network security and privacy; algorithms for deadlock detection; routing algorithms; applications of the internet; concurrency control and distributed communication; networking facilities and resource control and management methods in network and distributed operating systems; Micro-kernels and object-oriented operating systems
CS4401 IT Project Planning and Management
This course covers the factors necessary for successful management of information systems development or enhancement projects. Both technical and behavioural aspects of project management are applied within the context of an information systems development project. Topics include: Managing the system life cycle: requirements determination, design, implementation; system and database integration issues; network management; project tracking, metrics, and system performance evaluation; managing expectations of managers, clients, team members, and others; determining skill requirements and staffing; cost‑effectiveness analysis; reporting and presentation techniques; management of behavioural and technical aspects of the project; change management. Software tools for project tracking and monitoring. Team collaboration techniques and tools.
CS4402 Information Systems Project
Project course for Information systems majors.
Each project is carried out under the direction of a departmental supervisor, but the content will depend upon the particular interests of the individual student. The project is assessed by means of written reports and an oral presentation, which takes the place of a final examination.
CS4403 Computer Science Project
Project course for Computer science majors. Students will typically develop an application that can readily be implemented without major modifications.
Each project is carried out under the direction of a departmental supervisor, but the content will depend upon the particular interests of the individual student. The project is assessed by means of written reports and an oral presentation, which takes the place of a final examination.
CS4411 Algorithm Analysis and Design
Introduces formal techniques to support the design and analysis of algorithms, focussing on both the underlying mathematical theory and practical considerations of efficiency. Topics include: Asymptotic analysis of upper and average complexity bounds; best, average, and worst case behaviours; standard complexity classes; empirical measurements of performance; time and space tradeoffs in algorithms; using recurrence relations to analyse recursive algorithms Fundamental algorithmic strategies, Implementation strategies for graphs and trees; performance issues for data structures Graph and tree algorithms: Depth‑ and breadth‑first traversals; shortest‑path algorithms (Dijkstra’s and Floyd’s algorithms); transitive closure (Floyd’s algorithm); minimum spanning tree (Prim’s and Kruskal’s algorithms);
CS4410 Compiler Construction and Design
Recapitulation of formal grammars; Introduction to Compiling: Source code, Target code and the structure of a typical compiler; Comparative compiling techniques; Lexical analysis: Role, Specification and Finite Automata - NFA and DFA; Syntax analysis: Simple precedence, Operator precedence and LR(k) parsers; Semantics: Type checking, Overloading of functions and Polymorphic functions; Run-Time storage allocation; Code generation and Code Optimization; Compiler-compilers; Pragmatics of compiler writing and Translator writing; Error recovery.
CS4412 Formal Program Verification and Specification
Formal program specification and the Z notation; Basic semantics of computer programs; Proof rules for programming constructs; Transfundamental programming constructs; analysis and verification of programs.
CS4420 Advanced topics in Computer Systems Architecture
This will be a follow‑up to a computer architecture course, CS3420. Lectures will be on advanced topics in computer systems design, they will typically concentrate on performance‑enhancing techniques. These may include: Cache Memory design, Pipelining and superscalar techniques, Symmetric‑Multiprocessing, On‑chip multiprocessing and emerging technologies such as Redundant Arrays of Independent Disks, Clustering and Server farms and Grid computing.
This course will introduce students to the latest technology in the industry and expose students to some latest research areas.
CS4430 Distributed Database Systems
Distributed databases - various contemporary issues including data model partitioning, fragmentation, replication issues, query optimisation, concurrency control, restart and recovery, distributed database design, client-server and distributed database applications. Building distributed systems with Oracle DBMS. Particular attention will be paid to detailed consideration of distributed database management issues, e.g. GIS.
CS4431 Human Computer Interaction
This course aims to introduce the student to human factors in computing with a particular emphasis on the interaction between man and machine.
Topics Include: Human factors of Interactive Systems, Windowing Systems (GUI), Multimedia Systems, HCI Design-Implementation-Evaluation, CSCW and Social Issues.
CS4432 Management Information Systems
This course is designed to equip the students with fundamental concepts and techniques of Management Information Systems.
Topics Include: The Role of IS in organisations, Business Information Systems, Business Reengineering, Managing & Controlling IS, Ethical & Global Issues of IS, Trends in IS.
CS4433 Software Engineering
Follows the life cycle from the requirement, specification, and design phases through the construction of actual software. Topics include programming teams, programming methodologies, debugging aids, documentation, evaluation and measurement of software, verification and testing, and the problems of maintenance, modification, and portability.
CS4434 Expert Systems
Knowledge Acquisition and Representation; Building an Expert System: A recapitulation of Knowledge Representation and Heuristic Search, Reasoning about Incomplete Knowledge. Tools for Building Expert Systems: Expert Systems Shells, High-Level Programming Languages, blackboard architecture and multi-paradigm programming environments. Inferences and Explanations: Techniques in building explanation programs. Uncertainty handling: Sources of uncertainty, Expert Systems and Probability Theory, Vagueness and Possibility, Uncertainty in AI Systems.
CS4435 Electronic Business Strategy, Architecture and Design
The course focuses on the linkage between organizational strategy and networked information technologies to implement a rich variety of business models in the national and global contexts connecting individuals, businesses, governments and other organizations to each other. The course provides an introduction to e-business strategy and the development and architecture of e-business solutions and their components.
Topics:
Electronic commerce economics; Business models; Value chain analysis; Technology architectures for electronic business; Supply chain management; Consumer behaviour within electronic environments; Legal and ethical issues; Information privacy and security; Trans-border data flows; Information accuracy and error handling; Disaster planning and recovery: Solution planning, implementation and rollout, site design; Internet standards and methods; Design of solutions for the Internet; Intranets and extranets: EDI, payment systems, support for inbound and outbound logistics.
CS4440 Practicals in Networking: Advanced Routing and Network Design:
Students will take a set of practicals that would lead to completion of CCNA 3 and 4.
CS4442 Cryptography and Network Security
The course aims to introduce students to the mathematical foundations of cryptographic algorithms of both a symmetric and public key nature to meet the growing security demands over the Internet.
Topics studied include: Conventional Cryptography (Symmetric‑Key Cryptography), Public Key Cryptography, Authentication Protocols, Digital Signatures, Electronic Mail Security, Web Security.
CS5000 Industrial Attachment (18 c.h)
In this course students will be found industrial placements for at least 3 months. The student will be placed under some overseer (from the industry) and a supervisor. At the end of the attachment the student will submit a report of his/ her industrial experience. Together with the overseer report, the student’s report will be assessed as pass or fail.
CS5401 Special Topics In Computer Science
This course will introduce students to the latest technology in the industry and expose students to some latest research areas.
CS5402 Computer Networking Project:
Project course for BEng students. Students will typically design or analyse a computer network architecture or protocols and build a prototype network.
Each project is carried out under the direction of a departmental supervisor, but the content will depend upon the particular interests of the individual student. The project is assessed by means of written reports and an oral presentation, which takes the place of a final examination.
CS5430 Multimedia Systems
This course is designed to introduce the student to techniques of multimedia production. Practical, hands-on experience with the various media used in computer-based multimedia including: text, still graphics, motion graphics, animation, sound, hyperlinking. Includes stand alone computer- and Web-based applications. Introduction to basic principles of communication via multimedia.
Topics Include: The definition of multimedia; the history of multimedia; basic hardware for multimedia; basic software for multimedia; various techniques for multimedia production; the development cycle for multimedia; current resources for the production of multimedia presentations; guidelines for evaluation of multimedia materials.
CS5431 Computer Graphics and Visualisation
This course discusses current computer graphics hardware and software systems, techniques and applications. The course will also explore algorithms for creating and manipulating graphic displays and techniques for implementation.
Topics Include: Overview of Computer Graphics, Graphics Hardware, 2D and 3D transformation and viewing, Image Manipulation and Storage, Colour models and Colour applications, Animation.
CS5440 Network Management
This course builds on material taught in both Computer Communications and Networks I and II to give students practical experience with popular commercial networks like UNIX, NT and Novell. Students will configure, trouble shoot, and integrate this networks. After the course, the students are expected to perform at the same (or better) levels as CNE and MCSE certified network managers. This course is aimed at producing industry-ready graduates.
Post Graduate Diploma in Information Systems
DCS9400 Information Systems Project
The project area will be in Information Systems with a heavy lineage towards computerized business solutions.
Each project is carried out under the direction of a departmental supervisor, but the content will depend upon the particular interests of the individual student. The project is assessed by means of written reports and an oral presentation, which takes the place of a final examination.
DCS9401 Computer Organization
The course aims at introducing the fundamentals of computer organization and operating systems from the user’s perspective. It is not meant for programmers. The course strives to strike a balance between theory and hands-on experience with modern computer systems.
Topics include: Introduction and historical development of computer systems, Processor organization, Memory organization, Backplane buses and storage organization, Operating systems interfaces, files and directories.
DCS9402 Programming Basics
The course aims at introducing a student to the fundamentals of computer programming with an inclination towards object oriented programming.
Topics include: Elements of abstract data types and data structures - arrays, lists, queues etc. Programming concepts and constructs (a suitable programming language will be used for practical purposes).
DCS9404 Principles of Database Design & Data Management
The course is designed to equip students with the techniques of design , management as well as transactions associated with databases in business systems.
Topics Include: Database Systems Concepts & Architecture, Data Modelling, Normalisation & Functional Dependencies, Database Languages
DCS9405 Management Information Systems
This course is designed to equip the students with fundamental concepts and techniques of Management Information Systems.
Topics Include: The Role of IS in organisations, Business Information Systems, Business Re-engineering, Managing & Controlling IS, Ethical & Global Issues of IS, Trends in IS.
DCS9406 Systems Analysis and Design
This course aims at introducing the students to the latest methods used in the industry. The idea of structured methodology is highlighted.
Topics covered will include: Data Flow Diagrams, Logical Data Modelling, Normalization, Entity Life Histories, Effect, Correspondence Diagrams, Process Specification, Physical Design Methods, SSADM, Yourdon and JSD.
DCS9407 Human Computer Interaction
This course aims to introduce the student to human factors in computing with a particular emphasis on the interaction between man and machine.
Topics Include: Human factors of Interactive Systems, Windowing Systems (GUI), Multimedia Systems, HCI Design-Implementation-Evaluation, CSCW and Social Issues.
DCS9409 Entrepreneurship and E-Business Development
This course examines the nature and role of entrepreneurship, small businesses, the environment with which small business operates, and the techniques for effective management of small businesses in the Internet and Information age. The course also covers Internet programming, website design and authoring for computer business solutions.
DCS9410 Networks and Telecommunications Management
This course provides an in-depth knowledge of data communications and networking requirements including networking and telecommunications technologies, hardware, and software. Emphasis is upon the analysis and design of networking applications in organizations. Management of telecommunications networks, cost-benefit analysis, and evaluation of connectivity options are covered. Students learn to evaluate, select, and implement different communication options within an organization.