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Master of Science in Applied Mathematics

The Master of Science in Applied Mathematics program is designed to prepare students to analyze real-world mathematical problems, consider assumptions, discover patterns, develop insights, construct mathematical models, and provide solutions that make sense.

Introduction

Applied Mathematics is a specific branch of mathematics that deals with practical methods as they are applied to specific fields. The program will explore various means of resolving real-life challenges by using statistics and high-level mathematics.

Program Objectives

The goals of the program are to:

1. Acquire in-depth knowledge in advanced topics in Applied Mathematics.
2. Conduct advanced research and projects to serve the community.
3. Propose innovative solutions to real-world problems using mathematical background.

Program Learning Outcomes

Upon the successful completion of the program, students will be able to:

1. Use mathematical concepts and techniques in practical and applied problems.
2. Communicate mathematical ideas, results, context, and background effectively and professionally in written and oral form.
3. Apply relevant mathematical methods, further develop them, and adapt them to new contexts.
4. 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.
5. Apply a wide repertoire of probabilistic concepts, computational science techniques, and engineering-oriented methodologies of modern financial and industrial mathematics to real-life problems, and formulate suitable solutions.
6. Communicate and interact appropriately with different audiences.
7. 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:

1. The applicant must have a bachelor's degree from any math department (or a closely-related field) from a recognized college or university with an overall undergraduate grade point average of 3.00 (out of 4.0) or higher.
2. The undergraduate degree should be in a subject that will qualify students for the graduate specialization of their choice.
3. 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.
4. 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.
5. Candidates are required to demonstrate English language proficiency by obtaining a minimum of 550 on the Institutional TOEFL or its equivalent on the iBT or CBT; or 6 on the academic IELTS for programs taught in English.

Program Structure & Requirements

The Master program consists of 33 credit hours distributed as follows:

• Compulsory courses: 21 credit hours
• Elective courses: 12 credit hours
• Thesis: 9 credit hours

Compulsory Courses

1. Methods in Applied Partial Differential Equations
2. Advanced Complex Analysis
3. Applied Linear Algebra
4. Advanced Real Analysis
5. Thesis

Elective Courses

1. Applied Functional Analysis
2. Advanced Methods for Partial Differential Equations
3. Advanced Ordinary Differential Equations
4. Selected Topics
5. Optimization: Fundamentals and Applications
6. Introduction to Bayesian Data Analysis
7. Applied Regression Analysis
8. Applied Time Series Analysis
9. Numerical Solutions for Ordinary Differential Equations
10. Numerical Solutions for Partial Differential Equations
11. Generalized Linear Models
12. Numerical Linear Algebra

Course Description

Each course has a detailed description, including:

1. Methods in Applied Partial Differential Equations: Introduction and derivation of real-life equations, solution methods for some linear and nonlinear PDE.
2. Advanced Complex Analysis: Analytic functions, Cauchy's theorem and consequences, Mobius transformations, singularities and expansion theorems.
3. Applied Linear Algebra: Linear transformations, change of basis, transition matrix, and similarity.
4. Advanced Real Analysis: Outer measure, measurable sets, measurable functions, Lebesgue integration.
5. Thesis: The student has to undertake and complete a research topic under the supervision of a faculty member.
6. Applied Functional Analysis: Metric and normed spaces, convergence and completeness, Banach spaces.
7. Advanced Methods for Partial Differential Equations: Sobolev spaces, Lax Milgram Lemma, Hille-Yosida Theorem.
8. Advanced Ordinary Differential Equations: The course presents the advanced analysis of nonlinear systems.
9. Selected Topics: This course is designed for specialized topic areas in applied mathematics.
10. Optimization: Fundamentals and Applications: Convexity of sets and functions, linear programming, nonlinear programming.
11. Introduction to Bayesian Data Analysis: Introduction to statistical sciences, display and summary of data, logic, probability, and uncertainty.
12. Applied Regression Analysis: Simple linear regression, residual analysis, inference for model parameters.
13. Applied Time Series Analysis: Time series methods, applications of these methods to different types of data.
14. Numerical Solutions for Ordinary Differential Equations: Existence and uniqueness of solutions, one-step and multistep methods.
15. Numerical Solutions for Partial Differential Equations: Finite difference method, elliptic partial differential equations.
16. Generalized Linear Models: The course introduces generalized linear models, including categorical and discrete responses.
17. Numerical Linear Algebra: Direct and iterative methods for solving linear systems, vector and matrix norms.

Study Plan

The study plan includes a course list and distribution of courses over two years, with compulsory and elective courses, and a thesis.