Program Overview
Established 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	15	15	45	75
Mandatory Support Credits	-	-	12	12
Elective Core Courses	9	-	21	30
Elective Support Credits	-	-	6	6
Total	24	15	84	123

I. University Requirements
The list of the University required courses and their descriptions are presented in the introductory pages of the College of Sciences section.


II. College Requirements
The list of the College required courses and their descriptions are presented in the introductory pages of the College of Sciences section.

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 six-credit 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 Calculus I 3-0:3

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 Calculus II 3-0:3

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 Linear Algebra I 3-0:3

Systems of linear equations, Gauss and Gauss-Jordan 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, Gram-Schmidt process. Computer applications. Introduction to linear transformation.Prerequisite: 1440131, 1440131.

 

1440231 Calculus III 3-0:3

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 Vector Calculus 3-0:3

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.

 

1440233 Foundations of Mathematics 3-0:3

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.

 

1440235 Mathematical Software 3-0:3

This course is an introduction to the necessary software used for scientific programming such as MATLAB and MATHEMATICA or Maple. It is designed for science and engineering students. The main concern is the learning of advanced techniques for solving and graphing basic problems of Calculus and Linear algebra. Moreover, this course focuses on advanced scientific writing using LATEX packages.  Prerequisite:  1440131 and 1440211.

1440241 Ordinary Differential Equations I 3-0:3

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 Geometry 3-0:3

The axiomatic Systems, Finite geometry. Finite Projective Plane, Non-Euclidean geometry. Hyperbolic geometry (Sensed Parallels, Asymptotic Triangles. Saccheri Quadrilaterals, Area of Triangles, Ultraparallels, Transformation of the Euclidean Plane.Prerequisite:1440233.

 

1440281 Introduction to Probability and Statistics 3-0:3

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.

 

1440381 Mathematical Statistics                                   3-0:3

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 Abstract Algebra I 3-0:3

Groups. Subgroups. Quotient groups and homomorphisms. Introduction to rings and fields. Ideals. Ring homomorphisms and quotient rings. Applications. Prerequisite:144023.

 

1440312 Linear Algebra II 3-0:3

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 Number Theory 3-0:3

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 Real Analysis I 3-0:3

Sequences and Cauchy sequences of real numbers. Topology of the real line. The Bolzano-Weierstrass theorem. The Heine-Borel theorem. Limits, continuity, uniform continuity and differentiability of real-valued functions. The Mean Value Theorem. L'Hopital's rule. The Riemann integral.Prerequisites: 1440132 and 1440233.

 

1440332 Complex Analysis 3-0:3

Complex numbers; Analytic functions; Derivatives; Differentiation; Cauchy-Riemann equations; Polar coordinates; Harmonic functions; Elementary functions; Integrals; Complex-valued functions; Antiderivatives; Cauchy-Goursat 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.

 

1440341 Partial Differential Equations 3-0:3

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.

 

1440371 Numerical Analysis I 3-0:3

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), Gram-Schmidt process, LS approximation. Numerical differentiation and integration: trapezoidal, Simpson, Newton-Cotes formulas. Prerequisites: 1440132; 1440211.

 

1440372 Operations Research I 3-0:3

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 Graph Theory 3-0:3

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 Abstract Algebra II 3-0:3

Unique factorization domains. Modules and sub-modules. Field extensions. Finite Fields.  Introduction to Galois theory. Applications.Prerequisite:1440311.

 

1440431 Real Analysis II 3-0:3

The Riemann-Stieltjes 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 real-valued functions.Prerequisite:1440331.

 

1440441 Ordinary Differential Equations II 3-0:3

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. Sturm-Liouville theory: eigenvalues and eigenfunctions.Prerequisites:1440241 and 1440331.

 

1440451 Topology 3-0:3

Topological spaces. Open and closed sets. Bases and sub-bases. 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.

 

1440471 Numerical Analysis II 3-0:3

Numerical solution of ordinary differential equations. One-step methods: Euler, Taylor, Runge-Kutta. 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.

 

1440472 Operations Research II 3-0:3

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.

 

1440481 Stochastic Processes 3-0:3

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.

 

1440374 Mathematical Modelling 3-0:3

Application of a mathematical techniques arising in physics, Biology, Econometrics. The study of discrete and continuous models, theoretical and empirical models, deterministic and probabilistic models, and analytic and simulation of interesting models will be considered. Prerequisite: none.

 

1440461 Internship 3-0:3

This course aims to provide students with practical training. Training Program provides students with knowledge, skills, abilities, and opportunities required for success in their studies and workplace. Prerequisite: 1440281 and at least 70 Credit Hours

1440492 Graduation Project 3-0:3

Students are supervised during their formulation of research proposals. Instructors direct their students in carrying out different tasks leading to the execution of the projects. Students are required to give presentations regarding their achievements, and written final reports are to be submitted for evaluation. Prerequisite: Senior standing; Consent of the department.​

1440491 Selected Topics in Mathematics 3-0:3

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