Doctoral Program and PhD Defense Procedure In Mathematical Sciences at NCST With
The Cooperation of A.Razmadze Mathematical InstituteAs Partner Organization
Degree offered : |
Doctor of Philosophy (PhD) in Mathematics |
Length of study : |
3 years |
Graduation requirements : |
54 course credits and a dissertation |
Language of instruction : |
English |
Our Doctoral program and PhD Defense Procedure is approved by the PhD Board of NCST consisting of well known experts of US and European Universities. So our PhD is recognized throughout the world.
Announcement
The National Centre for Science and Technology (NCST) (http://ncst.org.ge) announces the opening of the procedure for earning Doctoral (Ph.D.) Degree of NCST. At the beginning the degree will be granted only in Mathematical Sciences, especially in all sub-disciplines of Mathematics that are presented in the PhD Board of NCST and in cooperation with A.Razmadze Mathematical Institute.
To this aim NCST introduces a Doctoral Program and creates the Doctoral Committee.
The PhD Defense procedure will be of high level satisfying high standards and only candidates with Thesis of high merit will be granted by our Doctoral Degree. The Defense procedure will be transparent, provided by its live broadcasting in the net, and any interested person can observe it from our website.
The international PhD Board of NCST will be created consisting of well known experts in Mathematical Sciences.
All interested persons can consult our webpage for the details.
Dali Zangurashvili at NCST (dalizan@rmi.acnet.ge) is the coordinating person (Program Coordinator) for these activities which will begin in autumn 2007.
It is intended to realize this program at the newly founded Georgian – German University , IB Euro-Caucasian University.
Professors of NCST and A.Razmadze Mathematical Institute as well may participate in teaching courses, may be appointed as Thesis supervisor, as Doctoral Committee member, as Examination Committee member and as Thesis Committee member.
Doctoral Program
About the Program
This is an English language program introduced by the National Centre for Science and Technology, Tbilisi, Georgia, in cooperation with the A.Razmadze Mathematical Institute.
The Doctoral Program in Mathematics provides students of high ability and strong preparation with an opportunity to begin study for the doctoral degree upon graduation from universities.
The general aim of the doctoral program in mathematics is to prepare qualified graduate students to become productive workers in academic research scholars capable of communicating their knowledge to students and to the mathematical community. The program is planned to give students the background they will need to pursue careers as pure or applied mathematicians, to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of a major field of interest, the ability to formulate and recognize significant research problems, and the ability to analyze problems, reach solutions, and transmit ideas to others.
Scientific aspects
Doctor of Philosophy (PhD) in Mathematics can be earned by 54 course credits and a dissertation, normally in 3 years. In exceptional cases the Doctoral Committee may recommend one either one-year extension or one-year reduction. Courses are offered in various disciplines – while the NCST Mathematics Department's primary strength is in pure mathematics, there is a lot of opportunity to engage in pure and applied mathematical studies. In fact, one of the great aspects of our program is that students may take advantage of the math life provided by the universities and research institutions all based in Tbilisi. In addition, NCST encourages its doctoral students to spend at least one semester at another university during the research period (preferably abroad).
Admissions calendar
Entry requirements
1. Eligibility Requirements: Students from any country may apply. Applicants are expected to have earned a Master’s degree from a recognized university or institution of higher education, or provide documentation indicating that they will earn this degree from such an institution by the time of enrolling in our PhD program.
2. Statement of Purpose: Applicants are required to submit a one-page statement describing their interest in mathematics, achievements and future goals.
3. Mathematics Entrance Examination: In order to give evidence of proficiency in mathematics, applicants should take the NCST Mathematics Entrance Exam. This is free of charge. It is a written examination containing basic questions in algebra and analysis. The examination will be held on ? at the local office ?
Financial requirement
For admission to our Doctoral Program local students should pay to NCST 500 Euros for each year study and foreign students should pay to NCST 2500 Euros (or equivalent in US dollars) for each year study.
NCST creates the Doctoral Committee consisting of experts in the field who are members of NCST and A.Razmadze Mathematical Institute.
Areas of specialization:
Teaching program For Fall Semester and Winter SemesterDistinguished Invited Lecture Series Requirements
A total of 54 units are required. A student who is well prepared might expect to complete the PhD program in three years of full-time study or the equivalent.
Comprehensive Examination
Normally, students are required to take a comprehensive examination by the end of their first year of study. This exam, which may be written or oral, consists of two parts: Algebra and Analysis. They roughly cover the material in the four introductory courses: Algebra, Topology, Real Analysis and Function Theory. Students are expected to be able to handle examples as well as concepts and proofs. Failure to pass the comprehensive examination automatically terminates the student's acceptance in the Doctoral Program.
Students are advised to discuss with their supervisors the list of courses they are going to take. NCST offers courses in various parts of mathematics. Each of the regular courses has 3 credits. Students must take a total of 54 credits in introductory and advanced courses. Normally one takes at least 12 credits (4 three-credit courses) each semester. There are two semesters each year: Fall Semester and Winter Semester. They start in the end of September and the beginning of January, respectively, and each of them lasts 12 weeks. Sometimes we schedule special courses or invited lectures outside these two terms.
A student who already knows the material of a course can receive credit for it by the Doctoral Committee approving a course taken elsewhere. A maximum of 6 credits of courses can be waived in this way. Additional credits may be earned just by passing a special examination on the material. The key issue is if the student actually knows the material. Credits received are deducted from the required 54 credits.
Courses Offered
We offer courses in several fields, such as algebra, topology, mathematical analysis, functional analysis, geometry, mathematical logic, partial differential equations, probability theory and stochastic processes, statistics, etc. See Course List. We assume flexibility, especially in the case of advanced courses. Our offer exceeds the demand and not all the courses will be taken at a given moment. On the other hand, further courses may be added to the list, depending on the specific interests of the students. Also, we will take into account the fact that the interests of Mathematics itself may change. On occasion we will offer special courses on contemporary topics of mathematics.
It is possible to take reading courses (with the consent of the instructor).
Candidacy Examination (Qualifying Examination)
Before taking the qualifying examination, the student must have completed satisfactorily all parts of the preliminary examination and completed two years of full-time graduate study or the equivalent. The student may take the qualifying examination at any time thereafter, when prepared to demonstrate breadth of knowledge at an advanced level and some acquaintance with an area of research. The qualifying examination is usually a three-hour oral examination. The qualifying examination may not be attempted more than twice without the approval of the Examination Committee.
The Candidacy Examination is given in the area of mathematics in which the student has chosen to write the PhD Thesis. The exam covers the material of (at least) four courses taken in the area of the thesis subject. Of course, the list of these courses must not include any of the four introductory (mandatory) courses (i.e., Algebra, Topology, Real Analysis, Function Theory). Good general knowledge of the area is also expected. On this examination the student should demonstrate depth and breadth of knowledge as well as maturity and real mastery of basic material and the ability to apply it to specific examples. Students should meet with their prospective Thesis supervisor at least one semester before the Candidacy Exam to prepare a written list of topics to be covered on the exam. This list is then subject to approval by the Doctoral Committee and then distributed to the candidacy examiners.
The Doctoral Committee will select at least three examiners, including the student has tentatively designated as the Thesis supervisor. The head of this committee will be someone other than the prospective Thesis supervisor.
The next step, Admission to PhD Candidacy, is achieved by
The algebra and topology courses: Algebra, Topology and the analysis courses: Real Analysis, Function Theory.
After passing the Candidacy Examination each student submits a Research Proposal to the Doctoral Committee. Based on the Research Proposal, the Doctoral Committee appoints a Thesis supervisor who also acts as advisor. Usually, the candidate's choice is honoured, provided that the corresponding member is willing to serve as supervisor. This is the official start of the research period of the candidate. The supervisor must be research mathematician who is either a full- or part-time member of the faculty of the university or scientist of a research institute. Where it can be reasonably assumed that the supervisor may not be available for consultation for enough time or the studied field requires it, an associate supervisor should be appointed. Of course the candidate may also choose his/her associate supervisor and/or make suggestions to the Doctoral Committee. It may accept or reject the choice after consultation with the supervisor involved.
All students are strongly encouraged to get some teaching experience before completing their PhD. Usually, this will be obtained by teaching one or more occasional courses after passing the comprehensive and candidacy examinations.
In addition to mathematical advice, the Thesis supervisor will also make suggestions and recommendations for professional opportunities and career possibilities.
Students must take a total of 54 credits in courses.
In the first year, students are expected to earn at least 24 credits including the introductory courses in Algebra, Topology, Real Analysis, and Function Theory. The Comprehensive Examination is normally passed by the end of the first year.
The remainder of the required 54 course credits are normally taken by the end of the fifth semester. To assure mathematical breadth, among these 54 course credits the candidates must earn at least six credits in courses that are neither in the Thesis area nor are among the Algebra and Analysis mandatory courses (i.e., Algebra, Topology as well as Real Analysis, Function Theory).
Most students should complete Admission to Candidacy by the end of their second year,although in exceptional cases the Doctoral Committee may consider up to a further reduction. The actual doctoral candidature ceases upon the submission and depositing of the Thesis for examination. Students start their formal research period after Admission to Candidacy. In the research period, the student writes and defends the Thesis under close supervision and also completes all course work.
When the Thesis is written and approved by the supervisor (usually at the end of the third year study), the Doctoral Committee recommends the student to be awarded by a postgraduate certificate of NCST.
Under normal circumstances the formal research period of a candidate starts when the two comprehensive exam and the candidacy oral exam have been passed. However, all students are urged to start the research as soon as possible, preferably in the second year.
PhD Defense Procedure in Mathematical Sciences at NCST
Admission to the Ph.D. Defense procedure requires the candidate’s postgraduate certificate of NCST and a recommendation letter of the Doctoral Committee. The publication of Thesis’ results is not required.
The candidate must present the electronic copy of his/her Thesis written in English and a hardcopy (if requested) not exceeding 250 pages.
The PhD Defense procedure is performed in English.
The candidate should pay to NCST for the PhD Defense procedure 50 Euros (or equivalent in dollars).
Before the Defense:
a) Appointment of examiners
The candidate shall be invited to name individuals whom they do not wish appointed as examiners. The choice of examiners is made with regard to their knowledge and standing in the field, taking into account reputation and experience.
b) Criteria for the examination of the PhD Thesis
After the Thesis is submitted, it is forwarded to the examiners. This must be at least two weeks before the oral thesis examination. To satisfy the degree the Thesis must be an original contribution to the knowledge and understanding of the subject and must demonstrate the capacity of the candidate to carry out independent quality research. Each examiner is asked to indicate in writing whether:
The thesis makes an original contribution to the knowledge and to the understanding of the subject with it deals with.
The thesis demonstrates the candidates' capacity to carry out quality independent research.
The thesis contains material worthy of publication.
The knowledge of the state-of-the-art in the specific subject is demonstrated.
The format and literary presentation is satisfactory.
c) Examiners' Recommendations
The Thesis Committee, based on the majority voting principle, recommends the candidate to be awarded/not to be awarded the Doctor of Philosophy degree.
The recommendations are one of the following:
(i) Award the degree without further modification in the Thesis.
(ii) Award the degree subject to modifications in the Thesis:
to the examiners' satisfaction,
to the Thesis Committee's satisfaction.
(iii) Award the degree subject to answering the enclosed questions:
to the examiners' satisfaction,
to the Thesis Committee's satisfaction.
(iv) Do not award the degree but permit re-submission of the Thesis in a revised form within two years.
(v) Do not award the degree.
Note: If there are substantial differences in the examiners' recommendations, the Doctoral Committee must appoint an additional examiner.
For the Defense (these documents are taken by the Chair to the Defense):
1. The candidate submits “Thesis submission” form, “Ready to Defend” form, Statement of Originality.
2. The candidate submits his/her Supervisor’s letter confirming that the submitted Thesis has been performed by his/her guidance and is ready for the Defense.
3. The candidate prepares a copy of the official Thesis Title pages (one for signatures; one for without signatures) according to the Library’s specifications.
4. NCST prepares the Defense Report.
At the Defense:
After the Defense:
PhD Board of NCST in Mathematics