Program OverviewEstablished in 2007, the Department of Mathematics provides students at the University of Sharjah with the opportunity to learn fundamental scientific and mathematical concepts in an atmosphere that is friendly, conducive to learning and encourages intellectual curiosity, exploration and independent thinking, and high ethics.
The Department offers a wide array of courses in pure and applied mathematics for all types of learners in addition to applications. More adventurous student can study advanced courses in mathematics and its applications.
Faculty members are active professionals in the fields they teach. All are graduates of prestigious universities and are active in research and self development. The faculty, through their dedication to teaching and guidance help students develop meaningful and lasting bonds with science and mathematics, while providing invaluable skills for leading a more interesting and productivelives.
A student undertaking the BS program in Mathematics should complete a total of 123 credit hours distributed as follows:
BS in Mathematics     
 UR  CR  PR  Total 
Mandatory Core Credits  12  15  45  72 
Mandatory Support Credits      12  12 
Elective Core Courses  12    21  33 
Elective Support Credits      6  6 
Total  24  15  84  123 
I. University RequirementsThe list of the University required courses and their descriptions are presented in the introductory pages of the College of Sciences section in this Bulletin.
II. College RequirementsThe list of the College required courses and their descriptions are presented in the introductory pages of the College of Sciences section in this Bulletin.
III. Program Requirements
A. Mandatory Core Courses
The Department of Mathematics core courses (45 credit hours) are listed below:
Course #  Course Title  CrHrs  Prerequisites 
1440132  Calculus II  3  1440131 
1440211  Linear Algebra I  3  1440131 
1440231  Calculus III  3  1440132 
1440232  Vector Calculus  3  1440231 
1440233  Foundations of Mathematics  3  1440131 
1440241  Ordinary Differential Equations I  3  1440132 
1440251  Geometry  3  1440233; 144033 
1440281  Introduction to Probability and Statistics  3  1440131 
1440381  Mathematical Statistics  3  1440281 
1440311  Abstract Algebra I  3  1440233 
1440331  Real Analysis I  3  1440132; 1440233 
1440332  Complex Analysis  3  1440231 
1440371  Numerical Analysis I  3  1440132; 1440211 
1440372  Operations Research I  3  1440211 
1440492  Graduation Project  3  Senior Standing 
B. Mandatory Support Courses
All Mathematics major students are required to take the following four courses (12 credits) of mandatory computer science courses.
Course #  Title  CrHrs  Prerequisites 
1411211  Programming II  3  1411116 
1411215  Data Structures  3  1411211 
1411246  Object Oriented Design with Java  3  1411211 
1411263  Introduction to Database Management Systems  3  1411116 
C. ElectiveCourses
The program includes 27 credit hours of elective courses chosen from various categories; 21 credits are Mathematics core electives and 6 credits of Computer Science courses.
Elective Core Courses
The following courses are offered by the Mathematics Department as electives although all may not be available in a particular semester. Additional courses may be developed in the future, based on changes in the discipline and demand.
Course #  Course Title  CrHrs  Prerequisites 
1440312  Linear Algebra II  3  1440211 
1440313  Number Theory  3  1440132; 1440233 
1440341  Partial Differential Equations  3  1440231, 1440241 
1440373  Graph Theory  3  1440211 
1440411  Abstract Algebra II  3  1440311 
1440431  Real Analysis II  3  1440331 
1440441  Ordinary Differential Equations II  3  1440341; 1440331 
1440451  Topology  3  1440331 
1440471  Numerical Analysis II  3  1440371 
1440472  Operations Research II  3  1440372 
1440481  Stochastic Processes  3  1440381 
1440491  Selected Topics in Mathematics  3  Department's Consent 
Elective Support Courses
The required sixcredit electives encompass two Computer Science courses selected from the following list:
Course #  Course Title  CrHrs  Prerequisites 
1411319  Programming Languages and Paradigms  3  1411215 
1411352  Operating Systems  3  1411215 
1411365  Database Design and Implementation  3  1411263 
1411366  Software Engineering  3  1411215 
1411440  Introduction to Computer Graphics  3  1411215 
Study Plan
The BS program in Mathematics encompasses 123 credits hours that are spread over eight semesters and could be completed in four years. The following distribution of courses by semester facilitates student's normal progression through the study plan.
Year I, Semester 1 (16 Credits)    
Course #  Title  CrHrs  Prerequisites 
0201102 or 0201105  Arabic Language  3  
1410100  Introduction to IT  3  
1430111  Physics I  3  
1430112  Physics ILAB  1  
1440131  Calculus I  3  
 University Elec. I  3  
Year 1, Semester 2 (17 Credits)    
Course #  Title  CrHrs  Prerequisites 
0202105  English for Academic Purposes  3  
1411116  Programming I  4  
1420101  Chemistry I  3  
1420102  Chemistry I LAB  1  
1440132  Calculus II  3  1440131 
1440211  Linear Algebra I  3  1440131 
Year 2, Semester 3 (15 Credits)    
Course  Title  CrHrs  Prerequisites 
0104100  Islamic Culture I  3  
1411211  Programming II  3  1411116 
1440231  Calculus III  3  1440132 
1440233  Found. of Mathematics  3  1440131 
1440281  Intro. To Prob.& Stat.  3  1440131 
Year 2, Semester 4 (15 Credits)    
Course #  Title  CrHrs  Prerequisites 
1411215  Data Structures  3  1411211 
1440232  Vector Calculus  3  1440231 
1440241  Ord. Diff. Equation  3  1440132 
1411xxx  Dept. Support Elect. I  3  
 UnivElec (2)  3  
Year 3, Semester 5 (16 Credits)    
Course #  Title  CrHrs  Prerequisites 
1411246  Object Oriented Design with Java  3  1411211 
1440251  Geometry  3  1440233 
1440311  Abstract Algebra I  3  1440233 
1440371  Numerical Analysis I  3  1440132; 1440211 
 University Elect. III  3  
Year 3, Semester 6 (15 Credits)    
Course #  Title  CrHrs  Prerequisites 
1440381  Mathematical Statistics  3  1440281 
1440332  Complex Analysis  3  1440231 
1411xxx  Dept. Support Elect. (2)  3  
1441xxx  Dept. Core Elect. I  3  
 University Elect. (4)  3  
1440461  Training Course  0  1440281 
Year 4, Semester 7 (12 Credits)    
Course #  Tile  CrHrs  Prerequisites 
1411263  Introduction to Database  3  1411211 
1440372  Operations Research I  3  1440211 
1441xxx  Dept. Core Elect. (2)  3  
1441xxx  Dept. Core Elect III  3  
 Depart. Core Elect. (4)  3  
Year 4, Semester 8 (15 Credits)    
Course #  Title  CrHrs  Prerequisites 
1440331  Real Analysis I  3  1440132; 1440233 
1440492  Graduation Project  3  Senior Standing 
1441xxx  Dept. Core Elect.(5)  3  
1441xxx  Dept. Core Elect. (6)  3  
1441xxx  Dept. Core Elect. (7)  3  
Course Description
Courses in the proposed program that are offered in the Department of Mathematics start with (1440). The program of study contains courses that are offered by other departments as well as from outside the College. Consistent with the University policies, mathematics courses in the program will be assigned numbers of the form (1440ABC) where:
A  Year (level)  
B  Areas (as follows): 1: Algebra 3: Calculus and Analysis 4: Differential Equations  5: Geometry 7: Applied Mathematics 8: Statistics 9: Projects and Selected Topics 
C  Course sequence in area  
1440131 
Functions, domain and range, examples of functions. Limits and continuity. Derivatives, applications of derivatives in optimization, linearization and graphing, the Mean Value Theorem. Integration, the Fundamental Theorem of Calculus, areas, volumes of solids of revolution, arc length. Conic sections.Prerequisite: None. 
1440132 
Functions, Inverse functions. Transcendental functions. L'Hopital's rule. Techniques of integration. Improper integrals. Sequence and infinite series of real numbers. Polar coordinates. Parametric curves in the plane.Prerequisite: 1440131. 
1440211 
Systems of linear equations, Gauss and GaussJordan elimination processes. Matrix algebra, determinants, Cramer's rule. Vector spaces, subspaces, basis and dimension, rank, change of basis. Characteristic polynomial, eigenvalues and eigenvectors of square matrices, diagonalization. Inner product spaces, orthogonal projections, GramSchmidt process. Computer applications. Introduction to linear transformation.Prerequisite: 1440131, 1440131. 
1440231 
Vectors and analytic geometry in space. Graphing surfaces in three dimensions. Vector–valued functions and motion in space. Functions of several variables. Extreme values and Lagrange multipliers. Multiple integrals. Areas and volumes.Prerequisite: 1440131, 1440132. 
1440232 
Integration in vector fields. Line integrals, circulation and flux, path independence and conservative fields. Green's Theorem in the plane. Surface area and surface integrals. Parameterized surfaces. Stocke's and Divergence Theorems. Curvilinear coordinates. Transformation of coordinates. Introduction to Cartesian tensors.Prerequisite: 1440231. 
1440233Foundations of Mathematics  30:3 

Logic, propositional logic, truth tables, propositional formulas, logical implication and equivalence, tautologies and contradictions, quantifiers. Methods of proof. Sets, applications of sets, Venn diagrams, Cartesian product, the power set. Cardinality. Mathematical Induction. Relations and partitions, functions. Zorn's Lemma and Axiom of Choice.Prerequisite: 1440131. 
1440241Ordinary Differential Equations I  30:3 

This course covers first and higher order ordinary differential equations (ODE) with applications in various fields. It contains: Basic concepts. First order ODE's, initial value problems, an existence and uniqueness theorem. Higher order ode's with constant coefficients. Laplace transform and inverse. Power series solutions, Frobenius theorem. Introduction to Linear systems of ODE's.Prerequisite:1440132. 
1440251 
The axiomatic Systems, Finite geometry. Finite Projective Plane, NonEuclidean geometry. Hyperbolic geometry (Sensed Parallels, Asymptotic Triangles. Saccheri Quadrilaterals, Area of Triangles, Ultraparallels, Transformation of the Euclidean Plane.Prerequisite:1440233. 
1440281Introduction to Probability and Statistics  30:3 

Descriptive statistics; Axiomatic probability; Random variables and their moments; Special discrete and continuous distributions; Sampling distributions; Estimation; Hypothesis testing; Linear regression; Analysis of variance. Prerequisite:1440131. 
1440381Mathematical Statistics  30:3 

Review of basic concepts of probability, random variables and distribution theory. Distribution of functions of random variables. Expectation and moment generating functions. Unbiased and Sufficient estimators. Point estimation, optimal properties of estimators. Interval estimation. Hypotheses testing.Prerequisite:1440281. 
1440311 
Groups. Subgroups. Quotient groups and homomorphisms. Introduction to rings and fields. Ideals. Ring homomorphisms and quotient rings. Applications. Prerequisite:144023. 
1440312 
Linear transformations. Change of basis, transition matrix and similarity. Nilpotent linear transformations and matrices. Canonical representation of matrices, Jordan canonical forms. Linear functionals and the dual space. Bilinear forms. Quadratic forms and real symmetric bilinear forms. Complex inner product spaces. Normal operators. Unitary operators. The spectral theorem.Prerequisites:1440211 and 1440233. 
1440313 
Divisibility. Prime numbers. Euclidean algorithm. Linear congruences. The Chinese remainder theorem. Fermat's little theorem. Wilson's theorem. Euler's theorem. Quadratic residues and reciprocity laws. Diophantine equations. Fermat's last theorem. Applications to cryptology and primality tests. Other possible applications.Prerequisites:1440132 and 1440233. 
1440331 
Sequences and Cauchy sequences of real numbers. Topology of the real line. The BolzanoWeierstrass theorem. The HeineBorel theorem. Limits, continuity, uniform continuity and differentiability of realvalued functions. The Mean Value Theorem. L'Hopital's rule. The Riemann integral.Prerequisites: 1440132 and 1440233. 
1440332 
Complex numbers; Analytic functions; Derivatives; Differentiation; CauchyRiemann equations; Polar coordinates; Harmonic functions; Elementary functions; Integrals; Complexvalued functions; Antiderivatives; CauchyGoursat theorem; Cauchy–integral formulas; Morera's theorem; Liouville's theorem; Fundamental Theorem of algebra; Series; Taylor and Laurent series; Power series, Integration and differentiation of power series; Residues and poles.Prerequisite:1440231. 
1440341Partial Differential Equations  30:3 

First order partial differential equations, the method of characteristics. Classification of second order pde's: parabolic, elliptic, and hyperbolic. The canonical form. Boundary value problems with applications to physical sciences and engineering. Detailed analysis of the wave, heat and Laplace equations; Separation of variables. Application of Fourier theory.Prerequisite: 1440241. 
1440371Numerical Analysis I  30:3 

Error analysis. Roots of nonlinear equations: bisection, fixed point, secant and Newton's methods. Systems of linear equations: direct methods, iterative methods. Systems of nonlinear equations: Newton's method. Interpolation: Lagrange, Newton's formulas, Gaussian quadrature. Approximation theory: orthogonal polynomials (Legendre, Laguerre, Chebychev, Hermite), GramSchmidt process, LS approximation. Numerical differentiation and integration: trapezoidal, Simpson, NewtonCotes formulas. Prerequisites: 1440132; 1440211. 
1440372Operations Research I  30:3 

Linear Programming. The simplex method, duality, sensitivity analysis, various versions of the simplex method. Transportation models. Network models. Nonlinear programming. Constrained and unconstrained optimization, KKT conditions.Prerequisites:1440211, 1440231. 
1440373 
Introduction to graphs. Representation of graphs. Graph isomorphism, connectivity. Euler and Hamilton paths. Shortest path problems. Planarity, graph coloring. Trees, tree traversal, sorting, spanning trees, matching. Networks, max flow.Prerequisite: 1440211. 
1440411 
Unique factorization domains. Modules and submodules. Field extensions. Finite Fields. Introduction to Galois theory. Applications.Prerequisite:1440311. 
1440431 
The RiemannStieltjes integral and functions of bounded variation. Metric spaces. Pointwise and uniform convergence of sequences of functions in metric spaces. Completeness of the space C(X,Y) of continuous functions. Pointwise and uniform convergence of infinite series of realvalued functions.Prerequisite:1440331. 
1440441Ordinary Differential Equations II  30:3 

Existence and uniqueness of solutions. Some fixed point theorems. Matrix analysis of differential equations. Second order differential equations in phase plane. Lyapunov functions. Stability of equilibria. Qualitative theory. Autonomous systems in one and two dimensions. Phase portraits, stability. SturmLiouville theory: eigenvalues and eigenfunctions.Prerequisites:1440241 and 1440331. 
1440451 
Topological spaces. Open and closed sets. Bases and subbases. Interior, exterior and boundary points. The closure of a set. Continuous functions. Homeomorphisms. Product spaces. Axioms of countability and separability. Compact spaces. Connected spaces. Metric spaces.Prerequisite:1440331. 
1440471Numerical Analysis II  30:3 

Numerical solution of ordinary differential equations. Onestep methods: Euler, Taylor, RungeKutta. Multistep methods.The eigenvalue problem: power and inverse power methods. Numerical solution of boundary value problems: finite difference and shooting methods. Numerical solution of partial differentialequations: Difference methods.Prerequisite:1440371. 
1440472Operations Research II  30:3 

Dynamic programming. Integer programming. Inventory models. Introduction to Game Theory. Queuing theory. Simulation models. Markov chains. Nonlinear programming algorithms: unconstrained optimization, constrained optimization. Prerequisite:1440372. 
1440481Stochastic Processes  30:3 

Revision of probability. Bernoulli processes and sum of independent random variables. Poisson processes. Markov chains and their application to queuing theory and branching process. Markov processes. Renewal process.Prerequisite: 1440381. 
1440491Selected Topics in Mathematics  30:3 

Senior standing; Consent of the department.Prerequisite: Senior standing; Consent of the department. 