# PhD in Computer Sciences _|_Grafiku i Kurseve

Any student who graduates with a PhD program in Computer Science must have 300 graduate credits, from which 180 must be in residence at UV. No more than 90 credits of research or reading courses can count towardthis requirement.

Course Requirements:

CN 508 - Advanced Data Structures

CSE 450 - Operating Systems

CSE 443 - Theory of Computation

CN 444 - Operations Research

CN 402

CN 408

CSE 443

CSE 450

CSE 550

MAT 553 - Probability and Statistics

Choose from the following:

CSE 551 - Interactive Computer Graphics

CSE 553 - Web Development and Programming

CSE 554 - Database Management Systems

CSE 555 - Data Mining

CSE 556 - Special Topics in Database Management Systems, Data Mining & Data Warehousing

CSE 557 - Network and Data Communications

CSE 558 - Individual Problems in Computer Science

CSE 559 - Knowledge Based Information Systems

CSE 444 | Computational Linguistics

CSE 550 | Programming Language Structures |

CSE 551 | Interactive Computer Graphics |

CSE 553 | Web Development and Programming |

CSE 554 | Database Management Systems |

CSE 555 | Data Mining

CSE 556 | Special Topics in Database Management Systems, Data Mining & Data Warehousing |

CSE 557 | Network and Data Communications

CSE 558 | Individual Problems in Computer Science |

CSE 559 | Knowledge Based Information Systems

Qualifying exams: There are two types of qualifying exams:

Qualifier of first level:

* Exam 1: Programming and Data Structures: CN 508, CN 444, CN 402, CN 408

* Exam 2: Theoretical Computer Science: CSE 443, CSE 450, CSE 550

The exams will be graded

* -Master pass/fail

* -PhD pass/fail

Students who indent to get a continue with the PhD program need to get a PhD pass. First level exams must be passed no later than student's third year of graduate study.

Qualifier of second level:

The student can choose under the supervision of his/her advisor two subjects in which he/she can take the second level qualifying exams.

Each graduate student will become a PhD candidate when he/she passes the PhD qualifying exams. The exams will be all written and have a duration of 5 hours.

Thesis Committee:This committee has 5 members who must be selected as follows:

* thesis advisor, who must be an active mathematician and have an international reputation. It is not necessary that the thesis advisor be from the faculty of UV

* two committee members must be from the subject area in which the student is writing the thesis

* one committee member must be from another department of the university which has a Phd program

* for the first 10 students who get PhD degrees it is required that a committee member is from a mathematics department outside Albania which has had a PhD program for at least 25 years. It is required that this member has supervised at least one PhD student and is an active researcher.

Oral Exam: This exam is taken when the student starts working on the PhD thesis. It is a preview of what the student intends to accomplish in the thesis.

PhD Thesis: The PhD thesis must satisfy all the requirements set by the Graduate school. The work must be original and publishable in a professional Computer Science journal.

* The PhD candidate must present his/her work to the open public for the first 60 minutes.

* The committee has the right to to ask questions to the candidate in private

* The committee must discuss the thesis and the work presented by the candidate without the candidate presence. After that the committee votes.

A unanimous vote is required for the candidate to pass.

For more information

univlora.edu.al/fsht/csee

## Formimi i pergjithshem: 40 kredite

Lendet Baze:
MAT 553,

Lendet me Zgjedhje: MAT 421, MAT 433, MAT 451, MAT 462, MAT 472, MAT 475, MAT 481, MAT 521, MAT 551, MAT 641, MAT 655, MAT 657, MAT 658, MAT 661, MAT 662,

Formimi baze: 60 kredite

Formimi special: 200 kredite

## Pershkrimet e Lendeve

CSE 001 - Programim - Provim Kualifikues MNP (0)

Konceptet baze te programimit.

MAT 421 - Real Analysis I (10)

Lebesgue measure, measurable functions and the Lebesgue integral; convergence theorems; monotone functions, bounded variation and absolute continuity.

MAT 433 - Numerical Methods (10)

Propagation of errors, approximation and interpolation, numerical integration, methods for the solution of equations,Runge- Kutta and predictor-corrector methods.

MAT 451 - Introduction to Algebra I (10)

This is an introduction to the graduate algebra. Groups, normal and simple groups, permutation groups, Abelian groups, Sylow theorem, Jordan-Holder theorem.

MAT 462 - Geometric Structures (10)

A study of topics from Euclidean geometry, projective geometry, non-Euclidean geometry and transformation geometry. Offered every fall.

MAT 472 - Number Theory (10)

Structure of the integers, prime factorization, congruences, multiplicative functions, primitive roots and quadratic reciprocity.

MAT 475 - Modelim dhe teknika te zgjidhjes se problemeve (10)

Math modeling

MAT 481 - Cryptography (10)

Elementary concepts in cryptography; classical cryptosystems; modern symmetric cryptography; public key cryptography; digital signatures, authentication schemes; modular arithmetic, primitive roots, primality testing. At least one mathematics course at or above the 3000 level and facility with either a programming language or a computer algebra system is required. 4176: Discrete logs; pseudoprime tests; Pollard rho factoring; groups; quadratic residues; elliptic curve cryptosystems and factoring; coding theory; quantum cryptography.

MAT 521 - Analysis I (10)

Lebesgue measure, measurable functions and the Lebesgue integral; convergence theorems; monotone functions, bounded variation and absolute continuity. The Lp spaces; product measures and Fubini's theorem; the Radon-Nikodym theorem.

MAT 551 - Algebra I (10)

Groups, Sylow theorems, solvable and simple groups, computation in permutation groups. GAP will be used to perform computations with groups. Free groups, finitely generated abelian groups, semi-direct products, extension of groups. Introduction to rings, Euclidean domains, PID's, UFD's, polynomial rings, irreducibility criteria for polynomials.

MAT 553 - Probability and Statistics (10)

The distribution of random variables, conditional probability and stochastic independence, special distributions, functions of random variables, interval estimation, sufficient statistics and completeness, point estimation, tests of hypothesis and analysis of variance.

MAT 641 - Computational Algebra I (10)

A study of the mathematics and algorithms which are used in symbolic algebraic manipulation packages.

MAT 655 - Computational Group Theory (10)

An introduction to computational group theory using computer algebra packages such as GAP.

MAT 657 - Coding Theory I (10)

We will be focusing on channel coding theory. In the first part of the course, a brief introduction will be given to information and coding theory in order to see what is the best one should expect from a good code. Then we will continue with the introduction to the basic algebra concepts needed in codding theory. Next we will follow will be more on the computational aspects of groups, finite fields, polynomials, etc other than the rigorous mathematical approach.

MAT 658 - Coding Theory II (10)

We will use software to do many computational problems (see below). These concepts will be utilized for the construction of polynomial and cyclic codes. BCH
codes and Reed-Solomon (RS) codes will be covered in detail.

MAT 661 - Mathematics of Communications I (10)

An introduction to mathematical concepts of digital communications. Random processes, Shanon's theorem, communication channels, antena theory, source coding, etc.

MAT 662 - Mathematics of Communications II (10)

A continuation of MAT 661, algebraic coding, turbo codes, LDPC codes, new developments in digital communications.

cse 002 - Informatike Teorike - Provim Kualifikues MNP (0)

Konceptet baze te informatikes.