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