Level – 1
Course units effective from academic year 2016/2017 to date
Course Code  PMM101G3 
Course Title  Foundations of Mathematics 
Academic Credits  03 (45 hours of lectures and tutorials) 
Objectives:  


Intended Learning Outcomes:  


Syllabus Outline  
Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM102G2 
Course Title  Limit Process 
Academic Credits  02 (30 hours of lectures and tutorials) 
Objectives:  


Intended Learning Outcomes:  


Syllabus Outline  
Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM103G3 
Course Title  Algebra and Number Theory 
Academic Credits  03 (45 hours of lectures and tutorials) 
Objectives:  


Intended Learning Outcomes:  


Syllabus Outline  
Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM104G2 
Course Title  Calculus 
Academic Credits  02 (30 hours of lectures and tutorials) 
Objectives:  


Intended Learning Outcomes:  


Syllabus Outline  
Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Level – 2
Course units effective from academic year 2016/2017 to date
Course Code  PMM201G3  
Course Title  Linear Algebra  
Credit Value  03  
Hourly Breakdown 
Theory  Practical  Independent Learning 
45  —  105  
Objectives:  


Intended Learning Outcomes:  


Course Contents:  
Vector spaces: vector space, linear independence, linearly dependence, subspace, spanning set, basis, dimension, the Steinitz replacement theorem and its corollaries, quotient space.
Linear transformations: linear transformation, image and kernel of a linear transformation, the ranknullity theorem, algebra of linear transformations, matrix representation of a linear transformation, isomorphism. Matrices: matrix addition , matrix multiplication ,elementary row operations, echelon matrices, row reduced echelon matrices, transpose, trace and diagonal of a matrix, special kinds of matrices , row space and column space of a matrix, row rank and column rank of a matrix, elementary matrices, normal form of a matrix, invertible matrices. System of linear equations: homogeneous and nonhomogeneous systems, conditions for consistency, Gaussian elimination method. 

Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM202G2  
Course Title  Advanced Calculus  
Credit Value  02  
Prerequisites  PMM102G2, PMM104G2  
Hourly Breakdown 
Theory  Practical  Independent Learning 
30  —  70  
Objectives:  


Intended Learning Outcomes:  


Course Contents:  
Limits and Continuity of functions of several variables: Limits, Sequence characterization of limits, Algebraic properties of limits, Repeated limits, Nonexistence of limit, Continuity, Properties of continuous functions, Continuity and composite functions, Uniformly continuous functions, Lipchitz continuity and applications
Differentiation of functions of several variables: Partial derivatives, Directional derivatives, Total derivative, Elementary properties of derivatives, Relation between directional derivative and total derivative, Derivative matrix, Jacobian, Chain rule and applications, Mean value theorem, Partial derivatives and differentiability, Power series, Radius of convergence, Taylor’s expansion and applications Extremum Problems: Local maximum and minimum, Global maximum and minimum, Hessian matrix, Second derivative test for local extremum, Extreme problems with constraints. 

Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM203G3  
Course Title  Analysis  
Credit Value  03  
Prerequisite  PMM102G2 and PMM104G2  
Hourly Breakdown 
Theory  Practical  Independent Learning 
45  —  105  
Objectives:  


Intended Learning Outcomes:  


Course Contents:  
Metric space: Motivation and Definition, Examples, Equivalence Metrics, Distances between Sets, Diameter, Inequalities for Distances, Isolated Points, Nearest Points, Open and Closed Balls, Dense Subset, Interior, Closure and Frontier, Derived Set, Examples and Relationships, Open Sets, Closed Sets, Characterization and Properties, Convergence and Completeness, Bounded Sets, Totally Bounded Sets, Continuity, Uniform Continuity, Lipschitz Functionsand Continuity.
Riemann integration: Riemann Sums, Riemann Integrals, Criterion of Integrability, Properties of Riemann Integral, Indefinite Integral, Fundamental Theorem of Calculus and Mean Value Theorems. Uniform convergence of sequences and series of functions: Pointwise and Uniform Convergence of sequence of functions, Cauchy Criterion for Uniform convergence, Test, Uniform Convergence and Continuity, Uniform Convergence of series of functions, Uniform Convergence and Integration, Uniform Convergence and Differentiation, Weierstrass MTest, Dirichlet’s Test, and Abel’s Test. Improper Integrals: Three kinds of Improper Integrals, Evaluation of Integrals, Absolute and Conditionally Convergence, Tests for Absolutely Convergence, Cauchy Criterion for Integrals, Dirichlet’s Test,Test, Abel’s Test and Uniform Convergence and Integrals. 

Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM204G2  
Course Title  Linear Algebra and Analytic Geometry  
Credit Value  02  
Hourly Breakdown 
Theory  Practical  Independent Learning 
30  —  70  
Objectives:  


Intended Learning Outcomes:  


Course Contents:  
Determinants: determinant, properties of determinants, adjoint of a matrix, Laplace’s expansion. the Cramer’s rule, determinant rank.
Diagonalizability: eigenvalues and eigenvectors, characteristic polynomial, geometric and algebraic multiplicities of eigenvalues, test for diagonalizability, the CayleyHamilton theorem, minimum polynomial, quadratic forms and change of variables. Analytic geometry in two dimension: transformation of coordinates, pair of straight lines, circle, conic sections; parabola, ellipse, hyperbola, tangents, normals, pole and polar, classification of conics. 

Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Level – 3
Course units effective from academic year 2016/2017 to date
Course Code  PMM301G3  
Course Title  Abstract Algebra  
Credit Value  03  
Hourly Breakdown 
Theory 
Practical 
Independent Learning 
45 
— 
105 

Objectives:  


Intended Learning Outcomes:  


Course Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM302G3  
Course Title  Complex Analysis  
Credit Value  03  
Hourly Breakdown 
Theory 
Practical 
Independent Learning 
45 
— 
105 

Objectives:  


Intended Learning Outcomes:  


Course Contents:  
Complex Numbers:
Algebraic Aspects: Definition of Complex Numbers, Cartesian form and polar form, Euler’s formulae, de Moivre’s theorem, Relation between trigonometric functions and hyperbolic functions, Complex Logarithms. Geometric Aspects: The Argand diagram, representation, locus, straight lines in terms of complex numbers, circles in terms of complex numbers, joint family of circles and straight lines, two families of circles, representation of complex numbers by points of a sphere Complex Power Series: Radius of Convergence, Properties of Power Series,Hadamard’s formula Differentiation: Function of a complexvariable, Limits, Continuity, Derivatives, Cauchy Riemann equations, Sufficientconditions, Analytic functions: Entire functions, Harmonic functions, and Harmonic conjugate. Contour Integrals : Smooth and piecewise smooth paths, Integration of continuous functions along smooth contours, Estimation Lemma, Fundamental theorem of Calculus, Cauchy’s theorem, Cauchy Goursat’s theorem, Deformation theorem, Cauchy’s integral formula, Morera’s theorem, Cauchy’s estimates, Liouville’s theorem, fundamental theorem of algebra, Taylor’s expansion, Laurent’s expansion. Residue Theorem: Zeros and singularities of complex variable functions, Residue theorem, Evaluation of the certain real integrals, Argument principle, Rouche’s theorem, Application of the definite integrals. 

Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  

Course Code  PMM303G3  
Course Title  Discrete and Combinatorial Mathematics  
Academic Credits  03  
Hourly Breakdown 
Theory 
Practical 
Independent Learning 
45 
– 
105 

Objectives :  


Intended Learning Outcomes :  


Course Contents:  


Teaching Methods :  


Assessment / Evaluation Details :  




Recommended Readings :  

Course Code  PMM304G3  
Course Title  Geometry  
Credit Value  03  
Prerequisites  PMM204G2  
Hourly Breakdown  Theory  Practical  Independent Learning 
45 hours  —  105 hours  
Objectives:  


Intended Learning Outcomes:  


Course Contents:  


Teaching Methods:  


Assessment/ Evaluation Details:  


Recommended Readings:  
