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Master of Science in Mathematics

Master

Levels
4
Courses
16
Credits
39
Number of Alumni
41
Number of students
49
Overview

The Master of Science in Mathematics program provides a comprehensive curriculum consisting of 39 credit hours, including 26 credit hours for 11 required courses, 4 credit hours for two elective courses, and 9 credit hours for a thesis. The program aims to provide students with advanced mathematical knowledge and skills in specialized areas of mathematics, engaging them in recent scientific research developments to prepare them to work in advanced positions.

 

Program Mission
Providing the community with qualified cadres with advanced knowledge and skills that enhance their abilities to conduct research in mathematics through a stimulating research environment to achieve distinguished education, and community services.

Program Goals

  1. To provide students with advanced mathematical knowledge that enhances their skills in specialized areas of mathematics. 
  2. To develop and continuously improve the educational and research environment in the program.
  3. To prepare skilled and well-prepared cadres of mathematicians capable of carrying out scientific research in focused areas of mathematics and working in advanced positions.
  4. To engage students and faculty in community initiatives and partnerships.

 

Graduate Attributes
By the end of the program, students will have the following attributes:

  1. Problem-solving proficiency.
  2. Analysis, inference and conclusion proficiency.
  3. Technology and digital skills proficiency.
  4. Scientific research proficiency.  
  5. Communication proficiency.
  6. Self-learning and management.
  7. Ethical responsibilities commitment.
  8. Teamwork.

 

Program Learning Outcomes

By the end of the program, students will be able to:

  1. Demonstrate advanced and specialized knowledge of concepts and principles in mathematics at the graduate and specialized levels.
  2. Apply specialized theories, principles, and concepts to solve problems and prove statements in complex and advanced contexts.
  3. Analyze specialized theories and problems to draw inferences, generalizations, explanations, and reach conclusions in unanticipated situations.
  4. Evaluate solutions for problems in complex scenarios and challenges using analytical and computational techniques and digital technologies.
  5. Conduct independent and joint research projects in specific areas of mathematics.
  6. Communicate advanced mathematical ideas and research results effectively in written and oral forms.
  7. Plan for self-learning and professional development with the ability to monitor progress and take actions for adjustment.
  8. Commitment to professional and academic values when dealing with various issues.
  9. Work effectively on a team to establish goals, plan tasks, meet objectives and take responsibility as a team member and a leader.

Study Plan

Course Specification

Student Admission Requirements:
Admission to postgraduate studies: Admission to postgraduate studies requires the following:
  1. The applicant must be a Saudi or have an official scholarship for postgraduate studies if he is a non-Saudi. 
  2. The applicant must have a university degree from a Saudi university or another recognized university.
  3. To be of good conduct and medically fit.
  4. To submit two scientific recommendations from professors who have previously taught him.
  5. The student's average should not be less than good at the bachelor's level.
  6. Employer's consent to study if he is an employee.

Program levels

Level One
MATH 640 - Numerical Analysis - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"This course is a continuation of Numerical Analysis, in which postgraduate students will study advanced algorithms to obtain approximate numerical results for mathematical problems as mentioned below: 1. Numerical methods for solving nonlinear systems: Fixed-point method, Newton's method. 2. Numerical methods for solving initial value problems (single-step methods and multistep methods along with studying error, stability, and convergence of the algorithms). 3. Numerical methods for solving boundary value problems: Shooting method, method of finite differences along with studying error, stability, and convergence of the algorithms. 4. Programming of studied algorithms using MATLAB & Python."
MATH 630 - Theory of Differential Equations - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"The topics covered in this course include the existence and uniqueness of initial value problems, systems of linear differential equations with constant coefficients, matrix exponentials, the Laplace transform method for solving ODEs, stability analysis of linear and nonlinear systems of ODEs, and phase plane analysis."
MATH 620 - Functional Analysis - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"The main objectives are § To comprehend the properties and significance of reflexive spaces in functional analysis. § Exploring Weak Convergence and Weak Topology: To investigate weak convergence and its relation to the weak topology in functional analysis. § To grasp important theorems such as Mazur's lemma, the Banach-Alaoglu theorem in different cases, Tychonov's theorem, and the general Banach-Alaoglu theorem. § To delve into compact linear operators, their properties, as well as Fredholm and Hilbert- Schmidt operators. § To understand the concepts of spectrum and resolvent in the context of operators and the spectral mapping theorem. § To study spectral theory for various types of operators such as self-adjoint, compact, bounded, and self-adjoint operators. Including the spectral family of a bounded self-adjoint operator. § To explore the spectral representation of bounded self-adjoint operators. § To delve into Banach algebras, spectral theory within Banach algebras, and commutative algebra in the context of functional analysis."
MATH 610 - Abstract Algebra - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"Throughout this course, student will explore the algebraic structures of groups, rings, fields, and vector spaces, and develop the skills to apply abstract algebra techniques in solving both mathematical and practical problems. § Group theory: sub groups, cosets, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, permutation groups, simple groups. § Rings and fields: matrix rings, quaternions, ideals and homomorphisms, quotient rings, polynomial rings, principal ideal rings, Euclidean rings and unique factorization. § Fields and vector spaces: finite-dimensional vector spaces, algebraic field extensions, finite fields."
MATH 600 - Ethics and Editing Scientific Research - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"Within the Master of Science in Mathematics program, this course delves into the ethical dimensions and editing practices fundamental to scientific research within the realm of mathematics. It aims to equip students with a profound understanding of ethical challenges specific to mathematical research, ethical editing norms, and the integration of ethical considerations in mathematical inquiry."
Level Two
MATH 643 - Stochastic Processes - optional 1
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"Introduction to probability measure theory, Lp spaces, and Hilbert spaces. I'm almost sure, and LP convergence. Definition of stochastic processes, Gaussian processes, and Poisson processes. Brownian motion and its basic properties are conditional expectation and Martingales. Application of stochastic processes in financial economics."
MATH 632 - Mathematical Biology - optional 1
Credits
2
Theoretical
1
Pratical
2
Training
Total Content
3
Prerequisite
Course Description:
"Continuous Models for Two Interacting Populations: (Species in Competition, Predator–Prey Systems, Kolmogorov Models, Mutualism, Community Matrix, Nature of Interactions Between Species, Invading Species and Coexistence, Predator and Two Competing Prey, Two Predators Competing for Prey. Harvesting in Two-species Models: (Harvesting of Species in Competition, Harvesting of Predator–Prey Systems, Intermittent Harvesting of Predator–Prey Systems) Models for Populations with Age Structure: (Linear Discrete Models with Age Structure, Linear Continuous Models with Age Structure, Method of Characteristics, Nonlinear Continuous Models with age structure)."
MATH 642 - Optimization Methods - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"Convex optimization: Convex set, convex function, conjugate function, directional derivative, sub-gradient, duality theorem. Unconstrained optimization: One-dimensional search algorithms: Fibonacci and golden section search. Multidimensional search method: Steepest descent method, Newton's method, conjugate gradient method, quasi-Newton methods, and trust region method. Constrained optimization: Kuhn-Tucker condition for optimality, application to solution of simple nonlinear problems; quadratic programming and convex programming problems. Penalty and barrier functions. Sequential unconstrained minimization technique, multipliers method."
MATH 641 - Numerical Linear Algebra - mandatory
Credits
3
Theoretical
2
Pratical
2
Training
Total Content
4
Prerequisite
Course Description:
"Topics include § Vector and Matrix Norms § Conditioning of Problems and Stability of Algorithms § Gaussian Elimination and the LU Decomposition § Singular Value Decomposition. § Least-Squares Problems. § Symmetric Eigenvalue Problem."
MATH 631 - Partial Differential Equations 1 - mandatory
Credits
3
Theoretical
3
Pratical
Training
Total Content
3
Prerequisite
Course Description:
"Some fundamental topics of First and second-order PDEs, including Wave Equation, Diffusion Equation, Laplace Equation, Boundary-value Problems, Initial-boundary-value Problems, Well- pawedness, Maximum Principle, Energy Methods, Method of Separation Variables, Fourier Series, Green's Function, nonlinear PDE's and applications."
Level Three
MATH 646 - Stochastic Differential Equations - optional 1
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"The course treats basic theory of stochastic differential equations and its relation with partial differential equation. This course includes the following topics Ito integrals – construction of the Ito integral – Some properties of the Ito integral – Extension of the Ito integral - Ito formula – Martingale representation theorem - Stochastic differential equations – Examples and some solution methods - The existence and uniqueness of solutions – Weak and strong solutions - Linear Stochastic differential equations - The generator of an Ito diffusion – The Dynkin formula – The Kolmogorov’s Backward equation – The Feynman – Kac formula – The Characteristic Operator – The Martingale problem -The Girsanov theorem. Applications to boundary value problems “The Combined Dirichlet – Poisson problem, The Dirichlet problem, The Poisson problem."
MATH 636 - Partial Differential Equations 2 - optional 1
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"This course covers some topics of linear partial differential equations in Sobolev spaces. Second-order elliptic equations: definition, weak solutions and their existence, Regularity of solution, Weak and strong Maximum principles and Harnack's inequality, Eigen values of symmetric and non-symmetric elliptic operators Second-order Parabolic equations: definition, existence of weak solutions, regularity of solution, Maximum principles. Second-order Hyperbolic equations: definition, existence of weak solutions, regularity of solution. Hyperbolic systems of first order equations: definition, symmetric hyperbolic systems, systems with constant coefficients. Semigroup theory: definition, properties, generating contraction semi-group, applications."
MATH 697 - Selected Topics in Applied Mathematics - mandatory
Credits
2
Theoretical
2
Pratical
Training
Total Content
2
Prerequisite
Course Description:
"Science in the 21st century focuses on multiscale challenges, such as those arising from materials science, geoscience, life sciences, and social sciences, with the guidance of data-driven models, and interrogating these systems via large-scale computation. However, as information technologies continue to improve, we expect to see more advances in most fields of mathematics. As a result, the content of this course is determined by department members and then approved by the department council. The content of this course depends on current state to follow recent developments in a certain field of mathematics, such as recent advances in topics from real Analysis, probability theory, combinatorics, number theory and sets, logic, geometry, graph theory, integral equations, stochastic processes, functional analysis, etc."
MATH 645 - Advanced Scientific Computation - mandatory
Credits
3
Theoretical
2
Pratical
2
Training
Total Content
4
Prerequisite
Course Description:
"This course will focus on scientific computation methods for solving initial- and boundary-value problems for partial differential equations, with an emphasis on Finite Difference Methods and Finite Element Methods. Students will have the opportunity to improve their understanding of these methods through programming exercises and the use of simulation software with MATLAB and Python. Some class time will be dedicated to these hands-on activities. This course includes § Finite Difference Approximation for Initial Boundary-Value Problems, Stability of Finite Difference Approximations, Finite Difference Methods in Two Space, Limitations of Finite Difference Approximation, Algorithm Programming and Implementation (with MATLAB or Python). § Galerkin Method: Galerkin Finite Element Method for First and second-Order Equations, Finite-Difference Interpretation of the Galerkin Approximation, Galerkin Finite Element Approximations in Time, Algorithm Programming and Implementation (with MATLAB or Python) § Collocation Method: Collocation Method for First-Order Equations, Collocation Method for Second-Order Equations, Algorithm Programming and Implementation (with MATLAB or Python) § Finite Element Methods in Two Space: Finite Element Approximations over Rectangles, Finite Element A pproximations over Triangles, Algorithm Programming and Implementation (with MATLAB or Python)"
MATH 635 - Principles of Optimal Control - mandatory
Credits
3
Theoretical
2
Pratical
2
Training
Total Content
4
Prerequisite
Course Description:
"Introduction to optimal control (The basic problems - Some examples -. A geometric solution). Bang-bang principle (Optimal control of linear equation - Bang-bang principle). Linear time-optimal control (Existence of time-optimal controls - The Maximum Principle for linear time-optimal control) . The Pontryagin maximum principle (Calculus of variations - Hamiltonian dynamics - Statement of Pontryagin Maximum Principle - Maximum Principle with state constraints). Dynamic programming (Relationship with Pontryagin Maximum Principle). MATLAB Toolbox for Solving Optimal Control Problems (Recursive Integration Optimal Trajectory Solver: RIOTS)."
Level Four
MATH 699 - Thesis - mandatory
Credits
9
Theoretical
9
Pratical
Training
Total Content
9
Prerequisite
Course Description:
The course is designed to enhance the students’ knowledge and capabilities that are required to provide effective, comprehensive and high quality research needed for their design graduation thesis. The course will also enhance their thesis professional writing skills that are needed in their postgraduate studies. On successful completion this course student should be able to solve the advanced chemistry problems related to his topics. Prepare an academic thesis written in a clear, logical, concise and accurate professional style using standard referencing and citation conventions; and submit a thesis within a designated timeframe.
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