Mathematics Graduate Programs

Master’s Degree

The master's program in Mathematics is structured as follows:

  • MAT 533 Real Analysis I (3 credits),
  • MAT 535 Algebra I (3 credits),
  • MAT 523 Differential Equations I (3 credits),
  • 4 courses to be selected from among graduate courses (12 credits),
  • MAT 597 Seminar (no credit)
  • MAT 599 Dissertation (no credit)
  • Master's Thesis
  • FBE 600 Scientific Research Techniques and Publication Ethics (no credit - must)

List of Master's Courses:

Course Code

Course Title

Credits

MAT 501

Introduction to Difference Equations I

3 Credits

MAT 502

Introduction to Difference Equations II

3 Credits

MAT 503

Introduction to Optimal Control Theory I

3 Credits

MAT 504

Introduction to Optimal Control Theory II

3 Credits

MAT 505

Mathematics of Finance I

3 Credits

MAT 506

Mathematics of Finance II

3 Credits

MAT 507

Complex Dynamics and Newton Method

3 Credits

MAT 508

Normal Families

3 Credits

MAT 509

Partial Differential Equations I

3 Credits

MAT 510

Partial Differential Equations II

3 Credits

MAT 511

Numerical Solutions to Partial Differential Equations I

3 Credits

MAT 512

Numerical Solutions to Partial Differential Equations II

3 Credits

MAT 513

Linear Difference Equations and Stability Theory I

3 Credits

MAT 514

Linear Difference Equations and Stability Theory II

3 Credits

MAT 515

Cryptology I

3 Credits

MAT 516

Cryptology II

3 Credits

MAT 517

Coding Theory I

3 Credits

MAT 518

Coding Theory II

3 Credits

MAT 519

Approximation Properties of Linear Positive Operators I

3 Credits

MAT 520

Approximation Properties of Linear Positive Operators II

3 Credits

MAT 521

Numerical Analysis I

3 Credits

MAT 522

Numerical Analysis II

3 Credits

MAT 523

Differential Equations I

3 Credits

MAT 524

Differential Equations II

3 Credits

MAT 525

Applied Mathematics I

3 Credits

MAT 526

Applied Mathematics II

3 Credits

MAT 527

Topology I

3 Credits

MAT 528

Topology II

3 Credits

MAT 529

Functional Analysis I

3 Credits

MAT 530

Functional Analysis II

3 Credits

MAT 531

Spectral Analysis of Differential Operators I

3 Credits

MAT 532

Spectral Analysis of Differential Operators II

3 Credits

MAT 533

Real Analysis I

3 Credits

MAT 534

Real Analysis II

3 Credits

MAT 535

Algebra I

3 Credits

MAT 536

Algebra II

3 Credits

MAT 537

Functions Theory I

3 Credits

MAT 538

Functions Theory II

3 Credits

MAT 539

Differential Geometry I

3 Credits

MAT 540

Differential Geometry II

3 Credits

MAT 541

Complex Analysis I

3 Credits

MAT 542

Complex Analysis II

3 Credits

MAT 543

Summability Theory I

3 Credits

MAT 544

Summability Theory II

3 Credits

MAT 545

Selected Topics in Analysis

3 Credits

MAT 550

Fuzzy Differential Equations

3 Credits

MAT 551

Mathematical Biology

3 Credits

MAT 555

Selected Topics in Differential Equations

3 Credits

MAT 556

Probability Theory I

3 Credits

MAT 557

Probability Theory II

3 Credits

MAT 558

Mathematical Statistics I

3 Credits

MAT 559

Mathematical Statistics II

3 Credits

MAT 560

Selected Topics in Applied Mathematics

3 Credits

MAT 561

Differentiable Manifolds

3 Credits

MAT 562

Differential Topology

3 Credits

MAT 563

Variational Analysis

3 Credits

MAT 564

Elliptical Curves

3 Credits

MAT 565

Selected Topics in Topology and Geometry

3 Credits

MAT 566

Combinetorial Mathematics I

3 Credits

MAT 567

Combinetorial Mathematics II

3 Credits

MAT 568

Numbers Theory

3 Credits

MAT 569

Modular Functions

3 Credits

MAT 570

Advanced Linear Algebra

3 Credits

MAT 571

Reductive Sequences

3 Credits

MAT 572

Finite Objects

3 Credits

MAT 573

Finite Groups

3 Credits

MAT 574

Selected Topics in Algebra

3 Credits

MAT 597

Seminar

3 Credits

MAT 599

Master's Thesis

3 Credits

 

Doctorate
  • FBE 600 Scientific Research Techniques and Publication Ethics (no credit - must)

Ph.D. Programs in Mathematics:

  • Analysis and Functions Theory
  • Algebra and its Applications
  • Applied Mathematics

are the three areas where Ph.D. in Mathematics are awarded. For students who already hold a master's degree, the Ph.D. program is composed of at least 7 courses (21 credits), the qualification exam, and the Ph.D. thesis. Students who study for a Ph.D. in Analysis and Functions Theory, Algebra and its Applications, or Applied Mathematics should take at least two courses from outside their areas. The area a selected course pertains to shall be subject to the decision of the department chair, on the basis of the relevant advisor’s recommendation.

The list of courses in the Ph.D. in Mathematics program:

Course Code

Course Title

Credits

MAT 641

Functional Analysis I

3 Credits

MAT 651 Applied Mathematics
MAT 652 Numerical Solutions of Common Differential Equations
MAT 653 Numerical Solutions of Partial Differential Equations
MAT 654 Dynamics Systems
MAT 660 665 Selected Topics in Differential Equations
MAT 666 670 Selected Topics Applied Mathematics
MAT 671 Algebraic Topology I
MAT 672 Algebraic Topology II
MAT 673 Differential Geometry I
MAT 674 Differential Geometry II
MAT 675-680 Selected Topics in Topology and Geometry

MAT 642

Functional Analysis II

3 Credits

Compact linear operators defined in norm spaces, and their spectrums; spectral theory of limited self-adjoint linear operators; positive operators; projection operators; spectral family; spectral theory of unlimited linear operators in Hilbert space.

MAT 643

Approximation Theory I

3 Credits

Function spaces; positive linear operators; Korovkin-type approximation theories for algebraic and trigonometric cases; miscellaneous applications; continuity module; approximation rates.

MAT 644

Approximation Theory II

3 Credits

Latest developments in Korovkin theory; statistical approximation; statistical approximation rates; Korovkin theorems in fuzzy logic theory; miscellaneous applications; approximation to functions using various non-positive linear operators.

MAT 645

Topological Vector Spaces I

3 Credits

A course offered to allow the students get specialized in any of the special topics and theories of Classical Analysis.

MAT 646

Topological Vector Spaces II

3 Credits

MAT 647

Selected Topics in Analysis

3 Credits

MAT 651

Applied Mathematics

3 Credits

Banach, Hilbert and Sobolev spaces; Fourier transforms and orthogonal functions; weak solutions; variational forms; Galerkin approximation; linear, elliptical limit and eigenvalue problems; Sturm-Liouville problems. Variational methods; their application of non-linear integral and elliptical differential equations; semigroup theory.

MAT 652

Numerical Solutions of Common Differential Equations

3 Credits

Introduction to numerical methods; linear single- and multi-step methods. Runge-Kutta method. Convergence; Stiff differential equations; stability analysis and absolute stability. Numerical methods for two point boundary value problems: Shooting method.

MAT 653

Numerical Solutions to Partial Differential Equations

3 Credits

MAT 654 Dynamic Systems (3-0) 3

MAT 654

Dynamic Systems

3 Credits

MAT 660

Selected Topics in Differential Equations

3 Credits

MAT 666

Selected Topics in Applied Mathematics

3 Credits

A course offered to allow the students get specialized in any of the special topics and theories of Applied Mathematics.

MAT 670

Algebraic Geometry

3 Credits

MAT 671

Algebraic Topology I

3 Credits

Main group. Van Kampen theorem, covering spaces. Singular homology, homology long-complete sequence, Mayer Vietoris sequence. Cellular homology, simpicial homology. Axioms of homology; main groups and homology; applications of homology.

MAT 672

Algebraic Topology II

3 Credits

Co-homology groups; universal factor theorem; co-homology of spaces. Multiplications in co-homology, Künneth formula. Poincare duality. Universal factor theorem for homology. Homotophy groups.

MAT 673

Differential Geometry I

3 Credits

Differentiable manifolds, straight mapping, tangential and co-tangential beams, differential of a mapping, vector areas, tensor areas, differential forms, the concept of direction with manifolds, integration with manifolds, Stokes theorem.

MAT 674

Differential Geometry II

3 Credits

Lie differential of tensor areas. Connections, covariant differentials of tensor areas, parallel shift, holonomy, bevel, twist. Levi-Civita (or Riemann) connection, geodesics, normal coordinates. sectional, Ricci and scaler bevels.

MAT 675

Global Analysis

3 Credits

A course offered to allow the students get specialized in any of the special topics and theories of Topology and Geometry.

MAT 676

Selected Topics in Topology and Geometry

3 Credits

MAT 681

Lie Groups and Lie Algebra

3 Credits

Definition and basic characteristics of Lie Groups and Lie Algebra; classical matrix Lie groups; Lie sub-algebra related with Lie sub-groups; masking groups; exponential mapping; association between Lie algebra and simple connection Lie groups; expression theory.

MAT 682

Object Expansion and Galois Theory

3 Credits

Object expansion, object to serve for factorization of a polynom, multiple roots, Galois groups, criteria for solubility by radicals, Galois group as the permutational groups of the roots of n-degree polynoms; finite objects.MAT 683 Algebraic Numbers Theory (3-0) 3

MAT 683

Algebraic Numbers Theory

3 Credits

MAT 684

Analytical Numbers Theory

3 Credits

A course offered to allow the students get specialized in the special topics and theories of Numbers Theory.

MAT 685

Applicable Analysis and computational Numbers Theory

3 Credits

MAT 686

Matrix Theory

3 Credits

A course offered to allow the students get specialized in any of the special topics and theories of Algebra.

MAT 687

Ring Theory

3 Credits

MAT 688

Selected Topics in Numbers Theory

3 Credits

MAT 689

Selected Topics in Algebra

3 Credits

MAT 697

Seminar

3 Credits

MAT 699

Ph.D. Thesis

3 Credits

 

Scientific Preparation

The students who do not hold a bachelor’s degree in mathematics, but wish to have graduate studies in Mathematics are required to take the following courses, and achieve a grade point average of at least 2.5 in the courses, within the framework of the scientific preparation program.

Course code

Course Title

MAT 209

Advanced Analysis I

MAT 210

Advanced Analysis II

MAT 211

Linear Algebra I

MAT 215

Differential Equations

MAT 309

Algebra

MAT 311

Complex Functions Theory