SCHOOLS OF STUDY SCHOOL OF MATHEMATICS & STATISTICS The School offers facilities for intensive training and research in the basic areas of Mathematics, Statistics and Operations Research. Prof. C. Raghavendra Rao is the Dean I/c of the School. The School aims to train people who are oriented towards research and teaching in advanced areas of Mathematics, Statistics and Operations Research. Special attention is given to foundational topics. The School offers research facilities in the following areas: Algebraic Groups, Hopf Algebras, Lie Algebras, Algebraic Geometry, Combinatorial Number Theory, Analytic Number Theory, Dynamical Systems, Topological Dynamics, Many valued logic. Fluid Dynamics, Ordinary Differential Equations, Partial Differential Equations, Numerical PDE. Modelling and Analysis of large data, Bayesian Modelling, Modelling of Spatio-Temporal data, Bioinformatics/Genomics, Reliability, Survival Analysis, Statistical Inference, Extreme Value Theory. The School has good computing facilities. There are three labs. A Statistics lab with 25 PCs and 2 UGC (SAP) labs with 25 and 15 PCs respectively. The University Library has been recognized as a Regional Library by the National Board for Higher Mathematics (NBHM). Programmes of study The School offers I.M.Sc., M.Sc. and Ph.D. Programmes. The M.Sc. Programme is offered in three streams namely, Mathematics, Applied Mathematics and Statistics-Operations Research. This programme is spread over a period of four semesters. For each stream, there are separate core courses and electives. The School offers Ph.D. programmes in Mathematics, Applied Mathematics and Statistics. Students admitted to this programme are required to satisfactorily complete their course work prescribed by the School in the first two semesters in order to continue their Ph.D. They are also expected to take part in the weekly Colloquium / Seminar of the School. The School also participates in the 5-Year Integrated M.Sc. Programme in Mathematical Sciences, which is administered through College for Integrated Studies. Entrance Examination MSc in Mathematics/Applied Mathematics/Statistics-OR The written test in objective type will have questions on Sets, Sequences, Series, Limits, Continuity, Differentiation, Integration, Graphs of Functions, Coordinate Geometry of two and three dimensions, Group Theory, Ring Theory, Vector Spaces, Matrices, Determinants, Linear Transformations, Rank, Nullity, Eigenvalues, System of Linear Equations, Elementary Probability and Logical reasoning. Page 50 :: PROSPECTUS: 2020-21// UNIVERSITY OF HYDERABAD: INDIA’S INSTITUTION OF EMINENCE M.Sc. in Statistics-OR The written test in objective type will have questions on Sets, Sequences, Series, Limits, Continuity, Differentiation, Integration, Graphs of Functions, Vector Spaces, Matrices, Determinants, Linear Transformations. Elementary Probability - Events, Independent Events, Conditional Events, Bayes’ Theorem, Chebyshev’s Inequality. Random Variables and their Distributions – Binomial, Poisson, Geometric, Negative Binomial, Uniform, Normal, Exponential, Gamma, Beta. Inference – Methods of Moments and ML Estimation, Test for Mean and Variance of the normal distribution, Contingency Tables, Simple Linear Regression. Linear Programming Problem- Graphical Solution. Important notes ● Two separate tests will be held for M.Sc Mathematics (including Mathematics and Applied Mathematics) and M.Sc Statistics ● At the end of the first year, students can choose between Mathematics and Applied Mathematics ● Students cannot change between Mathematics and Statistics ● Topics listed above is only indicative Ph.D in Mathematics/ Applied Mathematics/ Statistics-OR Entrance to the programme is based on a written test. Candidates clearing the entrance test will be called for an interview as per merit list. The written test consists of two parts. PART A will have questions related to Research Methodology. PART B will have questions on Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Partial Differential Equations, Functional Analysis, Measure & Integration, Algebra, Number Theory and Numerical Analysis (Mathematics/ Applied Mathematics); Probability & Measure Theory, Real Analysis, Linear Algebra & Matrix Theory, Inference, Linear Models, Design & Analysis of Experiments, Sampling (Statistics-OR). Important notes ● *The Ph.D. interview will be for 30 marks for all candidates who are called for interview, i.e., without making any distinction between those who qualify in the National level Fellowship awarding tests or the Entrance Examination. ● Candidates qualifying in National level tests awarding Fellowships (i.e., JRF's who qualify in CSIR/UGC Tests and NBHM-Ph.D. Test) will be exempted from writing the Ph.D. Entrance Examination and will be invited to appear for the interview directly. ● List of topics above is not exhaustive Vacancy position with the faculty and their broad areas or research. Vacancy for the Sl. Name of the Broad Area of Position Specialization Academic year No. Faculty specialization. 2020-21 Prof. B.S. 1 Professor 0 ----- Padmavati 2 Prof. R. Radha Professor 0 Page 51 :: PROSPECTUS: 2020-21// UNIVERSITY OF HYDERABAD: INDIA’S INSTITUTION OF EMINENCE 1) Big data: Modelling and analysis of biological and environmental data, 2) Bayesian Integrated modelling: 1) Inference for high- “Omics”-data, dimensional data, 3) Modelling and analysis of 2) Variable Selection in Prof. M. 3 Professor heterogeneous data: 2 High-Dimensional Bhattacharjee bioinformatics, statistical genetics, Random Matrices environmental data, reliability & 3) Predictive modelling in survival analysis, econometrics, Bayesian framework 4) Parametric and Non-Parametric Statistical Inference for Stochastic Processes. Ordinary Differential Ordinary Differential Equations, Equations, functional Prof. Saroj functional differential equations, differential equations, 4 Professor 4 Panigrahi dynamic equations on time scale, dynamic equations on integral equations. time scale, integral equations. Prof. Analytic and elementary number 5. 2 number theory Sankarnarayanan theory Associate 6 Dr. B.Shobha 0 Professor Associate 7. Dr. M.S Datt Algebra/Representation Theory 0 Professor Dr. T.K.S. Associate Dynamical Systems and operator 8. 1 Operatory Theory Moothathu Professor theory Associate 9 Dr S. Illangovan Professor Dr. T. Suman Associate Population Dynamics, 10 Applications of PDE 1 Kumar Professor PDE Combinatorial Number Theory, Dr. Mohan N. Assistant 11 additative Combinatrix, 0 Chintamani Professor Cryptography and Number Theory Dr Archana Assistant Algebraic Geometry, Vector 12 0 Subhash Morye Professor Bundles Extreme Value Analysis- Generalized Multivariate Pareto Dr. B.G. Assistant Distribution, Distribution Theory, 13 0 Manjunath Professor conditional specification, Pseudo- Distributions, Statistical Inference and Multivariate analysis Dr. P. Assistant 14 Dynamical Systems 1 Cnhiranjeevi Professor Dr. Nageswara Assistant 15 Fuzzy Logic 0 Rao Vemuri Professor Dr. Biswajyothi Assistant 16. Number Theory 0 Saha Professor Assistant Survival Analysis, Nonparametric 17. Dr. Anjana .S. 1 Survival Analysis Professor Inference Dr. S. Abhay 18. Asst. Prof. Algebra 1 Division Algebras Anant Analysis, Dynamical Dr. S.B. Associate Delay differential 19. Systems and Fractional 0 Bhalekar Professor equations Differential Equations Assistant 20. Dr. Sandipan De -- Prof. 13 Breakup of weightages The Ph.D. interview will be for 30 marks for all candidates who are called for interview, i.e., without making any distinction between those who qualify in the National level Fellowship awarding tests or the Entrance Examination. Page 52 :: PROSPECTUS: 2020-21// UNIVERSITY OF HYDERABAD: INDIA’S INSTITUTION OF EMINENCE Faculty Professors B. Sri Padmavati Ph.D. (Univ. of Hyderabad) Fluid Dynamics R. Radha Ph.D. (IIT, Bombay) Fluid Dynamics M. Bhattacharjee Ph.D. (Pune University) Modelling and Analysis of large data, Bayesian Modelling, Modelling of Spatio-Temporal data, Bioinformatics/Genomics, Reliability, Survival Analysis S. Panigrahi Ph.D. (Berhampur) Differential Equations Associate Professors B. Shobha Ph.D. (IIT, Delhi) Statistical Inference and Reliability M. Sumanth Datt Ph.D. (Univ. of Hyderabad) Hopf Algebras, Algebraic Groups T.K.S. Moothathu Ph.D. (Univ. of Hyderabad) Topological Dynamics S. Ilangovan Ph.D. (TIFR, Mumbai) Lie Algebras and Representation Theory T. Suman Kumar Ph.D. (Universite Pierre et. Marie Nonlinear population dynamics, Curie, France) Hyperbolic PDE Assistant Professors M. C. Namdev Ph.D. (HRI, Allahabad) Combinatorial Number Theory A. S. Morye Ph.D. (HRI, Allahabad) Algebraic Geometry B.G. Manjunath Ph.D. (Univ. of Siegen, Germany) Extreme Value Theory P. Chiranjeevi Ph.D. (Univ. of Hyderabad) Dynamical Systems Nageswara R. V. Ph.D. (IIT Hyderabad) Many Valued Logic B. Saha Ph.D. (IMSc. Chennai) Analytic Number Theory Page 53 :: PROSPECTUS: 2020-21// UNIVERSITY OF HYDERABAD: INDIA’S INSTITUTION OF EMINENCE SCHOOL OF COMPUTER INFORMATION SCIENCES The School of Computer and Information Sciences (SCIS) epitomizes excellence in all the major functions associated with higher learning such as teaching, research, student development and curriculum planning. The strengths of the School are its quality faculty, innovative and flexible curricula with their unique focus on post-graduate education, state-of-the-art research with a remarkably high number of PhD scholars – both ongoing and recently graduated, and highly open and transparent