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  • PhD in Mathematics

PhD in Mathematics

Programme Description

The PhD programme in Mathematics aims to introduce students to different areas of research in mathematics. Students of the PhD programme will be expected to contribute new results to their areas of study via original research undertaken.

A secondary aim of the PhD programme is also to create an environment that will enable research students to learn and immerse themselves into the pedagogical aspects of mathematics.

The PhD programme in Mathematics will train scholars in original research. It will enable the students to be able to think and do the research independently. The PhD scholars will also be encouraged to observe and participate in teaching of Mathematics at the undergraduate level to ensure familiarity with pedagogical aspects of Mathematics.

PhD scholars will also be encouraged to explore research methodology and areas of mathematics that intersect with and borrow from other disciplines, specially those available in AUD.

Programme Structure

Scholars admitted to the PhD programme in Mathematics, who are not MPhil degree holders in Mathematics will have to do the same course work prescribed for MPhil students. Even those PhD scholars who have an MPhil in Mathematics may be asked to do some course work if the Research Studies Committee (RSC) of the School of Liberal Studies (SLS) feels that his or her research topic requires course work of a particular kind. The nature of the course work to be carried out by such a scholar shall be determined by the RSC.

Once the coursework is completed a student admitted to the PhD programme will work on the dissertation which will be the student’s original work in the chosen area. A PhD scholar will also be encouraged to do the teaching practicum as prescribed for MPhil scholars.

See programme structure under MPhil in Mathematics

The broad research areas are Algebra, Analysis, Algebraic Number Theory and Mathematical Modelling and Simulation. Within these broad areas, research can be pursued in sub-areas such as Group Theory, Ring Theory, Linear Algebra, Complex Analysis, Summability theory, Approximation theory, Valuation Theory, Artificial Neural Networks and Mathematical Modelling.

PhD level courses



Course Name Core/Elective Credits


Group Theory




Commutative Algebra




Linear Algebra and Matrix Theory




Algebraic Number Theory




Module Theory




Functional Analysis




Differential and Integral Equations




Geometric Function Theory




Generalized Hypergeometric Functions and Fractional Calculus








Operator Theory




Representation Theory of Finite Groups




Advanced Group Theory




Generalized Inverses and Applications




Valuation Theory




Group Rings




Lie Algebras




Fractional Differential Equations




Mathematical Inequalities




Mathematical Modelling




Numerical Analysis



The list of Core and Elective Courses can be expanded depending on research interests of the Mathematics Faculty. Each year, four courses will be offered from the two categories listed below with the caveat that at least one course each will certainly be offered from each of the two categories listed below.

Category 1: core courses 1-5, Category 2: core Courses 6-11.



Candidates seeking admission in PhD programme must have completed MA/MSc from a recognised University/Institute in Mathematics or a related subject with 55% marks or an equivalent grade. A relaxation in marks of 5% or an equivalent relaxation of grade is allowed for those belonging to SC/ST/OBC (non creamy layer, Delhi)/ differently-abled categories (DOPT/UGC list).

Meeting the eligibility criteria alone will not ensure admission.


Geetha did her MA and DPhil (doctorate) in Mathematics at the University of Oxford.

Geetha did her MA and DPhil (doctorate) in Mathematics at the University of Oxford. Her area of research is finite group theory. She has published research in enumeration of finite groups, classification of finite groups using properties related to order of elements, conjugacy classes, subgroups etc. She is a coauthor of a research monograph titled Enumeration of finite groups, published by Cambridge University Press, UK in 2007. Sage Publications India has published her second co-authored book, titled, A Bridge to Mathematics, in 2017. She has also published several articles related to education, with an emphasis on undergraduate education. Apart from her interest in Group Theory and related areas she is deeply interested in popularising mathematics, mathematics education and issues related to women in mathematics. She has given several research talks and popular talks on mathematics in India and other countries to a varied audience ranging from middle and high school children, school teachers and mathematicians. For more details see:


Ramneek She did her MSc and PhD in Mathematics from Panjab University, Chandigarh. Her area of research is valuation theory. She has published research papers in her area of research, the details of which can be found on the link below:


Pranay completed his Doctoral degree from University of Rajasthan in 2011. His area of interest includes fractional differential and integral equations, univalent and multivalent functions, mathematical modelling. He has published several research papers in his areas of interests. Apart from that he is working as reviewer of several journals of national and international repute. For more details see:


Balchand Prajapati did his MSc in Mathematics from Banaras Hindu University, Varanasi and PhD in Mathematics (Algebra) from Indian Institute of Technology, Delhi. Before joining AUD Balchand was a Visiting Faculty at Birla Institute of Technology and Science, Goa Campus.His area of research is rings and group rings. His research focuses on finding the structure of rings and group rings with the help of derivations and automorphisms. He has published several papers in his area of research. Currently he has a research project entitled “Derivation On Group Algebra And Its Application” funded by Department of Science and Technology, Govt. of India. For more details see:


Kranti Kumar completed his Doctoral degree in Mathematics from Indian Institute of Technology Roorkee in 2013. His research interest includes noise pollution modeling, traffic flow modeling, differential equations and Artificial Neural Networks. Currently he is working on the UGC sponsored research project entitled “Modeling and simulation of vehicular traffic flow problems”. For more details see:


Mradul completed his Doctoral degree in Mathematics from Indian Institute of Technology Roorkee. Before joining AUD, he has served as an Assistant Professor at University of Petroleum and Energy Studies, Dehradun. His research interest includes Summability, Approximation theory and Wavelets. More details and research publications please go through following links:


Fee Structure

Rs. 1570 per credit for Course Work or Rs. 5950 per semester during Research/ Dissertation + Rs. 500 per semester for Student Welfare Fund + Rs. 5,000 as refundable Security Deposit.

SC/ST and Differently abled research scholars will be fully exempt from paying tuition fee. For others, partial/ full fee waivers are available based on income status.

Admission Procedure

Any candidate with a postgraduate degree in Mathematics or an allied subject from a recognised University can apply for admission and as per AUD rules. At the time of the application the candidate will be expected to submit a statement of purpose.

Statement of Purpose (SOP): It should include a well articulated argument as to why the candidate wishes to pursue research at AUD. It should also include details on the area/s in mathematics in which the candidate wishes to pursue research. The SOP should not exceed 500 words. Candidates’ proposed research areas should be aligned with the specialisations of SLS (Mathematics) faculty. Applicants are therefore encouraged to consult faculty profiles on the AUD website.

Entrance Test: SLS (Mathematics) will conduct two entrance exams. The first examination is common for candidates applying to both the MPhil programme and the PhD programme and will be based broadly on a Masters level curriculum in Mathematics. The second examination is meant only for candidates applying for the PhD programme. While the questions for this will also be based on a Masters curriculum, they will be exploratory in nature drawn from the areas of research in which supervision will be offered. Detailed syllabus, scheme of examination and past question paper for the entrance exam can be seen at http://aud.ac.in/admissions2018.

Interview: Only candidates qualifying in the written exam/s will be called for the interview. The interview shall be based broadly on a Master’s level curriculum, the written exam/s and the statement of purpose submitted.

A provisional admission to the PhD programme will then be offered to the candidates on the basis of combined merit in the written entrance exams and interview with 75% weightage for written exam and 25% in interview.

Admission Updates

On-line Application: Until 08 July 2018
Eligible Candidate List: 09 July 2018
Entrance Test: 10 July 2018
Interview List: 13 July 2018
Interview: 18-21 July 2018
First List: 23 July 2018

Detailed Admission Updates Click here

Online Application Form

Activities and Events


  • Mr. William Cocke, doctoral student, University of Wisconsin
    Topic: Another characterization of finite nilpotent groups

    Abstract: There are many characterizations of finite nilpotent groups. Most of these characterizations focus on subgroup series. We present a novel characterization involving the orders of the product of elements of prime power order.

    About the Speaker:
    William Cocke is a Ph.D. student at the University of Wisconsin. His main research interests are group theory and logic. He is an NSF Graduate Research Fellow at the University of Wisconsin and a FLAS Fellow for the academic year 2017-2018.

  • Dr. Pramod Kanwar, Professor of Mathematics at Ohio University Zanesville
    Topic: On idempotents and units in certain ring extensions

    Abstract: Idempotents and units in rings play critical role in the theory of rings and modules. Several classes of elements in rings (for example, clean elements, strongly clean elements, Lie regular elements, etc.) are defined in terms of idempotents and units. In the case of polynomial rings over fields (or even commutative domains), the polynomial ring has no nontrivial idempotents and the units in the polynomial rings are precisely the units in the base ring. Among other things, we will give conditions on the base ring under which the idempotents in the polynomial rings, Laurent polynomial rings, and power series rings are precisely the idempotents in the base ring or are conjugates to the idempotents of the base ring and also conditions under which the units in a polynomial ring are precisely the units in the base ring. We also give conditions for elements of polynomial rings over M2(Z2p) (p an odd prime) and M2(Z3p) (p a prime greater than 3) to be idempotents and conditions for elements of M2(Z2) and M2(Z3) to be units and observe that these unit groups do not have the same properties as the unit groups of the base rings M2(Z2) and M2(Z3) in the sense that unit groups of M2(Z2) and M2(Z3) are solvable and unit groups of polynomial rings over these rings are not solvable. In fact, we show that the unit group of a polynomial ring over an n x n matrix ring is never solvable.

    About the Speaker:
    Dr Kanwar is a Professor of Mathematics at Ohio University – Zanesville (USA). After obtaining his college education from University of Delhi, he was a senior lecturer at K. M. College (University of Delhi) before moving to USA for higher education. He also held visiting positions at Truman State University (USA) and University of Artois (France). He is the first mathematics faculty at Ohio University who is named Presidential Teacher for excellence in teaching and meritorious academic pursuits both inside and outside the classroom. He was also recognised by Ohio Magazine for contributions and dedication to achieving Excellence in Education. Dr Kanwar’s fields of interest are Theory of Rings and Modules and Algebraic Coding Theory. 

Advanced Instructional Schools (AIS)

Students of the MPhil and PhD Programme at AUD were selected for the AIS and the MPhil scholars attended the AIS in Algebraic Number Theory 2018 held at IIT Guwahati from 14th May - 2nd June 2018.



Students of the MPhil and PhD Programme at AUD have been selected for participation at the 2018 Annual conference of the Indian Women in Mathematics (IWM) to be held at Shiv Nadar University from 21-23 June 2018.