PhD in Mathematics

• Providing the student with a broad knowledge of mathematics, particularly the in – depth knowledge of the chosen branch.
• Equipping the student with the ability to pursue independent research in an active area of mathematics.
• Meeting the requirements of higher educational institutions and research centers for highly qualified mathematicians.
• Satisfying the aspirations of a growing number of M.Sc. degree holders in mathematics to obtain a higher qualification locally.
• Promoting the quality of the Department’s performance and fostering its research activities.

• The applicant must hold a Bachelor’s degree (Full-time) in Mathematics from King Saud University or any other recognized institution, with a grade of at least “High Good” and a cumulative GPA of (3.25/5) or its equivalent, provided that the grade in specialized courses is no less than “Very Good” with a cumulative GPA of (3.75/5) or its equivalent.

• The applicant must hold a Master’s degree (Full-time) in Mathematics from King Saud University or any other recognized institution, with a grade of at least “Very Good” (if the university grants grades) and a cumulative GPA of (3.75/5) or its equivalent.

• The applicant must have a score of at least (5.5) in the IELTS ACADEMIC test or its equivalent.

• The applicant must obtain a score of at least (500) in the GRE-Math Subject test or pass the written exam conducted by the department.

First Year – First Semester

• TRACK COURSE 1 – Selected from Track List – 3 Credit Hours

• TRACK COURSE 2 – Selected from Track List – 3 Credit Hours

• TRACK/M.SC. COURSE – Selected from Track/M.Sc. Lists – 3 Credit Hours

First Year – Second Semester

• MATH 690 – Advanced Topics in Mathematics – 3 Credit Hours

• TRACK COURSE 3 – Selected from Track List – 3 Credit Hours

• TRACK COURSE 4 – Selected from Track List – 3 Credit Hours

Track List: Options by Specialization

Track A: Algebra

• MATH 641 – Group Theory (II) – 3 Credit Hours

• MATH 642 – Ring Theory (II) – 3 Credit Hours

• MATH 643 – Algebraic Geometry – 3 Credit Hours

• MATH 644 – Algebraic Number Theory – 3 Credit Hours

• MATH 645 – Universal Algebra – 3 Credit Hours

Track B: Geometry and Topology

• MATH 671 – Analysis on Complex Manifolds – 3 Credit Hours

• MATH 672 – Variational Theory and Minimal Submanifolds – 3 Credit Hours

• MATH 673 – Lie Groups and Symmetric Spaces – 3 Credit Hours

• MATH 674 – Geometric Topology – 3 Credit Hours

• MATH 675 – Algebraic Topology – 3 Credit Hours

• MATH 676 – Homotopy Theory – 3 Credit Hours

• MATH 677 – Topology of CW-Complexes – 3 Credit Hours

Track C: Analysis

• MATH 681 – Stochastic Differential Equations – 3 Credit Hours

• MATH 682 – Ergodic Theory – 3 Credit Hours

• MATH 683 – Complex Analysis (II) – 3 Credit Hours

• MATH 684 – The Theory of Distributions – 3 Credit Hours

• MATH 685 – Harmonic Analysis – 3 Credit Hours

• MATH 686 – Function Algebras – 3 Credit Hours

• MATH 687 – Geometric Function Theory – 3 Credit Hours

Track D: Computational and Discrete Mathematics

• MATH 631 – Lattice Theory – 3 Credit Hours

• MATH 632 – Coding Theory – 3 Credit Hours

• MATH 633 – Enumerative Combinatorics – 3 Credit Hours

• MATH 634 – Model Theory – 3 Credit Hours

• MATH 651 – Numerical Analysis (II) – 3 Credit Hours

• MATH 652 – Numerical Solutions of Partial Differential Equations – 3 Credit Hours

• MATH 653 – M Theory of Integer Programming – 3 Credit Hours

• MATH 654 – Dynamic Programming – 3 Credit Hours

• MATH 655 – Variational Inequalities – 3 Credit Hours

Track E: Applied Mathematics

• MATH 611 – Quantum Mechanics (II) – 3 Credit Hours

• MATH 612 – Methods in Fluid Dynamics – 3 Credit Hours

• MATH 613 – Topics in Deterministic and Non-deterministic Modeling – 3 Credit Hours

• MATH 652 – Numerical Solutions of Partial Differential Equations – 3 Credit Hours

• MATH 684 – The Theory of Distributions – 3 Credit Hours