Applied Mathematics is a specific branch of mathematics that deals with practical methods as they are applied to specific fields. The M.Sc. in Applied Mathematics program will prepare the students to analyze realworld mathematical problems, consider assumptions, discover patterns, develop insights, construct mathematical models, and provide solutions that make sense. Students will explore various means of resolving reallife challenges by using statistics and highlevel mathematics. Through analyzing data, visualizing their results, and asserting their discoveries. Students will leave the program with the ability to critically contemplate and address problems that need solving using mathematical data.
Program Learning Outcomes Upon the successful completion of the program, student will be able to:
 Use mathematical concepts and techniques in practical and applied problems
 Communicate mathematical ideas, results, context, and background effectively and professionally in written and oral form.
 Apply relevant mathematical methods, further develop them and adapt them to new contexts
 Analyze complex problems of other fields of science and technology, plan strategies for their resolution, and apply notions and methods of mathematics to solve them
 Apply a wide repertoire of probabilistic concepts, computational science techniques and engineeringoriented methodologies of modern financial and industrial mathematics to reallife problems, and formulate suitable solutions
 Communicate and interact appropriately with different audiences
 Perform research in conjunction with a team as well as individually.
Special Admission Requirements
The Department of Graduate Studies Committee may grant regular or conditional enrollment for graduate study leading toward the Master degree to applicants who satisfy the following academic qualifications and criteria:
 The applicant must have a bachelor's degree from any math department (or a closelyrelated field) from a recognized college or university with an overall undergraduate grade point average of 3.00 (out of 4.0) or higher. These candidates are required to enroll in prerequisite courses, which they have not taken in their prior studies, as deemed necessary by the Department's “Graduate Studies Committee" and approved by the College and University. These prerequisite courses should be completed within no more than two semesters (FullTime) and will not be considered as part of the required credit load for the graduate degree.
 The undergraduate degree should be in a subject that will qualify students for the graduate specialization of their choice. Otherwise, students may be admitted upon the recommendation of the Department and after their study for required prerequisite courses assigned by the Department.
 The graduate admission committee may grant conditional admittance to an applicant whose GPA is 2.5 or higher and may require a GPA of at least 3.00 in the last 30 credit hours of their major courses, including courses that are related to their desired specialization. Conditionally accepted applicants must attain a grade point average of 3.00 or higher during their first semester with at least 9 credit hours before being fully admitted into the program.
 Applicants must provide certified transcripts from the institution where they received their B.Sc. degree, along with course descriptions, and must provide letter(s) of reference.
 Candidates are required to demonstrate English language proficiency by obtaining: A minimum of 550 on the Institutional TOEFL (administered at the University of Sharjah) or its equivalent on the iBT or CBT; or 6 on the academic IELTS for programs taught in English. Students may be admitted conditionally if they obtain 530 or higher on TOEFL provided that they enroll in an English language course and receive a TOFEL score of 550 by the end of their first semester of study. Students who do not meet these two conditions will be dismissed from the program.
 Applications will be reviewed and recommended for acceptance by the “Research and Graduate Studies Committee" by the Department and approved by the “Department Council".
Fulltime candidates of the Master degree must complete their requirements within a minimum of 3 semesters and a maximum of 8 semesters from the date they are admitted into the program. The admission requirements as cited above are almost similar to all of the Master programs at the University of Sharjah.
Program Structure & RequirementsThe Master program consists of 33 credit hours distributed as follows.
Requirements 
Compulsory 
Elective 
Total 

Courses 
Credit Hours 
Courses 
Credit Hours 
Courses 
Credit Hours 
Courses 
4

12 
4 
12 
8 
24 
Thesis 
1 
9 
 
 
1 
9 
Total Credit Hours 
21 

12 

33 

Study Plan Study Plan: Course List
 Compulsory courses (21 credit hours)
 Elective Courses (12 credit hours)
 Thesis (9 credit hours)
Compulsory Courses
Course Code

Course Title 
Course Title in Arabic 
Credit Hours 
Prerequisite 
Compulsory Courses

1440511 
Methods in Applied Partial Differential Equations 
طرق في تطبيقات المعادلات التفاضلية الجزئية 
3 
Undergraduate ODEs or PDEs. 
1440512 
Advanced Complex Analysis 
تحليل عقدي متقدم 
3 
1440332 or equivalent 
1440513 
Applied Linear Algebra 
تطبيقات الجبر الخطي 
3 
1440211 or equivalent 
1440514 
Advanced Real Analysis 
تحليل حقيقي متقدم 
3 
1440331 or equivalent 
1440599 
Thesis 
الأطروحة 
9 
After completing successfully 18 Credit hours 
Elective Courses
Course Code 
Course Title

Course Title in Arabic 
Credit Hours 
Prerequisite 
Elective Courses 
1440521 
Applied Functional Analysis 
التحليل الدالي التطبيقي 
3 
1440331 or equivalent 
1440522 
Advanced Methods for Partial Differential Equations 
طرق متقدمة للمعادلات التفاضلية الجزئية 
3 
1440341 or equivalent 
1440531 
Advanced Ordinary Differential Equations 
معادلات تفاضلية متقدمة 
3 
1440241 or equivalent 
1440532 
Selected Topics 
موضوعات مختارة 
3 
Consent of instructor 
1440542 
Optimization: Fundamentals and Applications

الأمثلة: أسس وتطبيقات

3 
1440221& 1440371 or equivalent 
1440582

Introduction to Bayesian Data Analysis 
مقدمة في تحليل البيانات باستخدام طرق بييزيان 
3 
1440381 or equivalent 
1440585

Applied Regression Analysis 
تحليل الانحدار التطبيقي 
3 
1440381 or equivalent 
1440584 
Applied Time Series Analysis 
تحليل المتسلسلات الزمنية التطبيقي 
3 
1440381 or equivalent 
1440591 
Numerical Solutions for Ordinary Differential Equations 
حلول عددية للمعادلات التفاضلية الخطية 
3 
1440371 or equivalent 
1440592 
Numerical Solutions for Partial Differential Equations 
حلول عددية للمعادلات التفاضلية الخطية الجزئية 
3 
1440371 or equivalent 
1440587

Generalized Linear Models 
النماذج الخطية العامة 
3 
1440381 or equivalent 
1440588 
Numerical Linear Algebra 
جبر خطي عددي 
3 
1440211, 1440371 or equivalent 
Study Plan: Course Distribution
First Year 
Fall Semester 
Spring Semester 
Course # 
Course Title 
Type 
Cr.Hrs 
Course # 
Course Title 
Type 
Cr.Hrs 
1440511 
Methods in Applied PDEs

CC 
3 
1440513 
Applied Linear Algebra 
CC 
3 
1440512 
Advanced Complex Analysis 
CC 
3 
1440514 
Applied Measure Theory 
CC 
3 
14405 
Elective Course 
EC 
3 
14405 
Elective Course 
EC 
3 
Total 


9 
Total 


9 
Second Year

Fall Semester 
Spring Semester 
Course # 
Course Title 
Type 
Cr.Hrs 
Course # 
Course Title 
Type 
Cr.Hrs 
1440599

Thesis 
CC 
3 
1440594 
Thesis 
CC 
6 
14405 
Elective Course 
EC 
3 




14405 
Elective Course 
EC 
3 




Total 


9 
Total 


6 
Course Description
: 1. Methods in Applied Partial Differential Equations (1440511)Introduction and derivation of reallife equations (vibration, diffusion, flows,…); solution methods for some linear and nonlinear PDE, separation of variables, Green's functions, Fourier and Laplace transforms.
2. Advanced Complex Analysis (1440512)Analytic functions, Cauchy's theorem and consequences, Mobius transformations, singularities and expansion theorems, maximum modulus principle, residue theorem, and its application, compactness and convergence in the space of analytic and meromorphic functions, elementary conformal mappings, Riemann mapping theorem, elliptic functions, analytic continuation, and Picard's theorem.
3. Applied Linear Algebra (1440513)Linear transformations. Change of basis, transition matrix, and similarity. Nilpotent linear transformations and matrices. The 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.
4. Advanced Real Analysis (1440514)Outer measure, measurable sets, measurable functions, Lebesgue integration, the Lebesgue dominated convergence theorem, Fatou's Lemma, Monotone convergence Theorem, Convergence in Measure, Continuity and differentiability of Monotone functions, The Lebesgue spaces, Duality, Riesz Representation theorem
5. Thesis (1440599)The student has to undertake and complete a research topic under the supervision of a faculty member. The thesis work should provide the student with an indepth perspective of a particular research problem in his chosen field of specialization. It is anticipated that the student is able to carry out his research fairly independently under the direction of his supervisor. The student is required to submit a final thesis documenting his research and defend his work in front of a committee.
6. Applied Functional Analysis (1440521)Metric and normed spaces. Convergence and completeness. Banach spaces. Linear operators. The dual space. Hilbert spaces and orthogonality. The Riesz representation theorem. Hilbertadjoint operator. Selfadjoint and compact operators. Fundamental Theorems of Banach spaces include the HahnBanach theorem, Uniform boundedness theorem, Open mapping theorem, and Closed graph theorem. Strong, weak, and weak* convergence. Banach fixed point theorem and applications. Basic properties of the spectrum of linear operators.
7. Advanced Methods for Partial Differential Equations (1440522)Sobolev spaces in R, Sobolev spaces in R^n, Lax Milgram Lemma, HilleYosida Theorem, linear and elliptic problems, Weak formulation, Existence, regularity, maximum principle Heat equation, Wave equation.
8. Advanced Ordinary Differential Equations (1440531)The course presents the advanced analysis of nonlinear systems, with an emphasis on the geometric interpretation of dynamical systems, including linearization, nonlinear feedback control tools, special attention to the averaging technic and the asymptotic tools of perturbation theory, tools for stability analysis of nonlinear systems like Poincare' Stability, Lyapunov's method, and Uniform stability.
9. Selected Topics (1440532)This course is designed for specialized topic areas in applied mathematics, which are not covered in the list of courses in the applied mathematics master program.
10. Optimization: Fundamentals and Applications (1440542)Convexity of sets and functions. Linear Programming: Theory of the Simplex method, Duality, and the dual Simplex method. Nonlinear Programming: Unconstrained optimization problems, Necessary and sufficient optimality conditions, Line search method, Steepest decent method, Newton's method, Optimization problems with equality and inequality constraints, Method of Lagrange multipliers, Necessary and sufficient KKT optimality conditions, Separable programming, Quadratic programming, Linear combinations method, Game Theory.
11. Introduction to Bayesian Data Analysis (1440582)Introduction to statistical sciences. Displaying and summarizing Data. Logic, probability, and uncertainty. Discrete random variables and their Bayesian Inference. Continuous random variables and their Bayesian inference. Comparing Bayesian and frequentist inferences for different statistics. Robust Bayesian methods. Bayesian inference for multivariate normal and multiple linear regression model. Computational Bayesian statistics.
12. Applied Regression Analysis (1440585)Simple linear regression. Residual Analysis, inference for model parameters. Multiple linear regressions with matrix approach Development of linear models. Inference about model parameters. Residuals Analysis. Analysis of variance approach. Model building and variable Selection of the best regression variables. Multicollinearity. Regression with qualitative variables. Using statistical packages to analyse real data sets. Case studies
13. Applied Time Series Analysis (1440584)This course considers statistical techniques to evaluate processes occurring through time. It introduces students to time series methods and the applications of these methods to different types of data in various contexts (such as actuarial studies, climatology, economics, finance, geography, meteorology, political science, risk management, and sociology). Time series modelling techniques will be considered with reference to their use in forecasting where suitable. While linear models will be examined in some detail, extensions to nonlinear models will also be considered. The topics will include: deterministic models; linear time series models, stationary models, homogeneous nonstationary models; the BoxJenkins approach; intervention models; nonlinear models; timeseries regression; timeseries smoothing; case studies. Statistical software R will be used throughout this course. Heavy emphasis will be given to fundamental concepts and applied work. Since this is a course on applying time series techniques, different examples will be considered whenever appropriate.
14. Numerical Solutions for Ordinary Differential Equations (1440591)Existence and Uniqueness of solutions for Initial Value Problems and BVP's, OneStep and multistep Methods for Nonstiff Initial Value Problems IVPs, Adaptive Control of OneStep Methods, OneStep Methods for Stiff Ordinary Differential Equations ODE, Multistep Methods for ODE and IVPs, Boundary Value Problems for ODEs, Error analysis and stability of methods, Numerical programming, and implementation.
15. Numerical Solutions for Partial Differential Equations (1440592)Finite Difference Method for Transport, Wave, Heat, and Poisson equations; Elliptic Partial Differential Equations; Sobolev Spaces; Weak Solutions; Finite Element Method.
16. Generalized Linear Models (1440587)The course introduces the genialized linear models that include categorical and discrete responses. It reviews the multiple linear regression models and covers the loglinear models, logistic regression for binary responses, and binomial and Poisson regression. It also includes mixed effects models, model selection and checking, and inference about model parameters of restricted and full data models. The R language, with many packages available that deal with the GLM, is used.
17. Numerical Linear Algebra (1440588)Topics include direct and iterative methods for solving linear systems; vector and matrix norms; condition numbers; leastsquares problems; orthogonalization, singular value decomposition; computation of eigenvalues and eigenvectors; conjugate gradients; preconditioners for linear systems; computational cost of algorithms. Topics will be supplemented with programming assignments.