Ph. D. in Mathematics is a doctoral program offered by the School Physical Sciences, Amrita Vishwa Vidyapeetham, Amaravati, Amritapuri, Bengaluru, Coimbatore and Kochi campuses.
Contact Us:
Amaravati:
t_srinivasarao@av.amrita.edu
Amritapuri:
manjushar@am.amrita.edu
Bengaluru:
s_mullai11@blr.amrita.edu
Chennai:
d_khushbu@ch.amrita.edu
Coimbatore:
a_vinodkumar@cb.amrita.edu
A PhD program in mathematics is an advanced academic journey focused on deepening students’ understanding of mathematical theory, developing their research skills, and preparing them for careers in academia, industry, or government. Typically lasting around 4-6 years, these programs involve rigorous coursework in advanced mathematics topics such as algebra, analysis, geometry, and topology, along with specialized electives tailored to students’ research interests.
One of the central components of a PhD in mathematics is the dissertation, where students conduct original research under the guidance of a faculty advisor. This research contributes new knowledge to the field and demonstrates the student’s ability to think critically, formulate hypotheses, and solve complex mathematical problems.
Additionally, PhD students in mathematics often engage in teaching or assistantship duties, gaining valuable experience in communicating mathematical concepts and working collaboratively with peers and professors.
Successful completion of a PhD program in mathematics opens a range of career opportunities, including tenure-track positions at universities, research positions in industry or government agencies, or roles in fields such as finance, data science, and cryptography.
Ph.D. program in Mathematics aims to develop expertise in a specific mathematical area, fostering critical thinking, problem-solving skills, and the ability to contribute new knowledge to the field. Mathematics encompasses diverse areas, each with its own unique focus and application. Some broad categories are Stochastic Modelling and Analysis, Semi-group Theory, Number Theory, Machine and Deep learning, Graph Theory and Combinatorics, Inverse problems, ill-posed problems, and numerical analysis, Metric Fixed Point Theory, Genome Rearrangement Problems, Physics informed Neural Networks, Wavelet Analysis.
The main research interest is stochastic modelling and analysis with special reference to Queues, Queueing inventory systems, Reliability systems, Reliability Inventory Systems and Operations Research. In the Semigroups that arise in the context of transformations or mappings, the set is the domain of the transformations. Number theory has applications in various areas of mathematics and beyond, including computer science, cryptography, and physics.
Deep learning algorithms can segment and identify specific structures or abnormalities in medical images, aiding in treatment planning and precision medicine. The integration of deep learning and machine learning into the medical field has the potential to enhance diagnostic accuracy, treatment efficacy, and overall patient care.
Graph Theory and Applications deals with the study of various graph parameter bounds incorporated with other mathematical or fuzzy mathematical tools, analysing different aspects and applications of algebraic graph theory in other fields. The main interest comprises of discussions about certain combinatorial objects like magic squares, Kotzig arrays and magic rectangles and applications in design of experiments.
Fixed point theory provides a theoretical foundation for understanding and solving problems involving the stability and existence of solutions under various mathematical transformations. The main research interest is related to coupled fixed point theorems of different contractive type mappings.
Genome rearrangement problems such as reversals, transpositions, and translocations are mathematically formulated as permutations and studied as sorting problems. Physics informed Neural Networks (PINN) which is a recent technique for data-driven solutions of high dimensional PDEs using Deep Neural Networks and look forward to analysing various physical problems related to computational fluid dynamics using PINNs.
Banach spaces and concepts from functional analysis are essential tools in both formulating and addressing well-posed and ill-posed problems. The main interest is to study different numerical iterative methods to solve non-linear equations and their various types of convergences in Banach spaces and to work on several methods and try to improvise its order of convergence.
Wavelet analysis is a mathematical technique used for signal processing and analysis and it allows for a more flexible representation by using functions that are localized in both time and frequency.
Since its establishment in 2002, the Department of Mathematics at ASE, Bengaluru, has grown and evolved, focusing on providing research scholars with a strong mathematical foundation and analytical skills. It offers diverse research area, interdisciplinary collaborations, and experienced research guides. From 2007, the Department started offering Ph.D. programs and courses for Ph.D. scholars. Several scholars have already obtained the Doctor’s degree from the Department. Examination for the fundamental course in Mathematics that must be cleared by all research scholars and is conducted by the department in every six months. Currently, 44 research students are doing Ph.D. under the guidance of faculty members of the department. Moreover, our researchers have published numerous high-quality research articles in various international and national journals. In addition, our scholars published quality journal articles as well as reputed conference articles along with their guides.
The department has an ambitious plan to be the best Mathematics departments and to establish an international reputation as a centre for research in Mathematics.
The Department has a team of highly qualified faculty members with research interests in recent and advanced fields in Mathematics, Statistics and Computer Science, such as Analysis, Algebra, Differential Equations, Fluid Mechanics, Multivariate Statistics, Regression Analysis, Numerical Analysis, Number Theory, Artificial Intelligence, Machine Learning related, Data analytics etc. The Department has organized several International and National Conferences with paper presentations and invited talks of high quality and has a good number of research papers published in refereed International and National Journals. The Department’s research activities are supported through extramural funds for various government agencies like National Board of Higher Mathematics (NBHM), Department of Science and Technology DST, etc. Besides teaching and research activities, faculty spend quality time with the students in guiding them through their career prospects/job opportunities.
The vision and mission of the Department of Mathematics aligns with the overall theme of Amrita Vishwa Vidyapeetham, which is to provide education that is rooted in values and aimed at holistic development. Amrita Vishwa Vidyapeetham believes that education should go beyond academics and focus on the individual’s overall development.
This course offers a comprehensive and rigorous study in advanced mathematical theories and their applications. With a focus on both theoretical foundations and practical research, scholars engage in cutting-edge exploration across various domains such as algebra, analysis, geometry and applied mathematics. Under the guidance of esteemed faculty members, candidates delve into specialized areas of interest, contributing to the advancement of mathematical knowledge. The program fosters a collaborative and interdisciplinary environment, encouraging scholarly exchange and innovation. Graduates emerge equipped with the analytical prowess and research acumen to excel in academia, industry, and beyond, making significant contributions to the field of mathematics.
Amrita Vishwa Vidyapeetham has not appointed any agent or third-party representative within India for admissions to any programme. Students residing in India are advised not to make payments or seat reservation advances to any individual or organization claiming to offer admission assistance for Amrita campuses.
For international admissions, the University may work with authorized overseas representatives in select countries. International applicants are advised to verify the credentials of such representatives through official Amrita communication channels before proceeding with applications or payments.
– Issued in Public Interest by Directorate of Admissions and Academic Outreach
Computer Algebra
Numerical Analysis
Mathematical Modelling
Computational Finance
Differential Equation
Solid mechanics
Generalized thermoelasticity
Wave propagation
Numerical methods
Partial Differential Equations
Stochastic Modelling and Analysis
Number Theory
Semi-group Theory
Machine Learning and Deep learning
Physics informed Neural Networks
Graph Theory and Applications
Metric Fixed Point Theory
Stochastic modelling and distribution theory
Inverse problems, ill-posed problems, and numerical analysis
Graph Theory and Combinatorics
Wavelet analysis
Probability Theory and Stochastic modelling
Theoretical computer science
Numerical Functional Analysis
Numerical Methods
Finite Element Method
Computational Sciences
Optimization Techniques
Numerical Mathematical Logics
Graph Theory
Fluid Mechanics
Fluid Dynamics
Mathematical Modelling
Computational Mathematics
Real Analysis
Mathematical Logics
Heat and Mass transfer
Numerical technique
Pure Mathematics
Applied Mathematics
Computational Mathematics
Graph Colorings, Graph Indices and Graph Algorithms
Domination, Graph Indices
Graph Colorings and Graph Indices
Fem with Wavelets and B-splines
Hybrid numerical methods for Singularly Perturbed Problems
Inventory control
Singularly perturbed PDE
Numerical Methods on Singularly Perturbed Differential Equations
Statistical Inference and Six Sigma
Estimation in Robust Regression
Designing of control charts
Statistical inference based on lifetime probability distributions
Hematocrit depended on viscosity of blood and cardiovascular problems
B-splines Methods
Investigation of pulsatile blood flow behaviour in human large arteries
Mathematical models for heat transfer system
Fractional differential equations
Mathematical Models for semiconductor devices
Mathematical Modelling of disease transmission
Fractional nonlinear PDEs, Lie group analysis, Conservation laws, Non-linear PDEs and ODEs
Generalization of fuzzy numbers and multi-criteria decision models
Deciphering HIV infection models
Approximation of Fractal interpolation surfaces
Functional Analysis
Time series models, deep neural network models and hybrid models
Reservoir Computing
Fractal based image classification
Multi Criteria Decision Making, Medical Image Processing
Linear Algebra
Coding Theory
Coding Theory and Ring Theory
Graph based Deep learning models, Data Networks, Medical Image Processing
Fuzzy DEMATEL and Fuzzy VIKOR in health care
Pattern Classification and Clustering
Multi Criteria Decision Making, Medical Image Processing
Stability analysis and control system of differential equations
Dynamical Robustness in a network of oscillators.
Stability analysis of dynamical system
Prey-predator modelling by considering
Allee and fear effects
Number theory
Highly Composite Numbers
Mathematics
Statistics
Computer Science
Data Science
Climate Modelling
Queueing Theory
Non-linear Dynamical Systems and control
*Applicable Programs.
| Title of the Project | Funding Agency |
| Stochastic Modelling and Analysis of Connectivity Reliability in 6G IoT Networks using k –out-of- n systems | Amrita Vishwa Vidyapeetham (Internal Seed Grant) |
|
Title of the Project |
Funding Agency |
|
Finite Element Methods in Haemodynamic Applications |
NBHM |
| Title of the Project | Funding Agency |
| Studies on Qualitative Properties of Single and Multivalued Fractional Stochastic Differential Equations of Higher Order | NBHM |
| On Punctured Codes of Zq-Simplex Codes | NBHM |
| Extensions of Wavelet Packet transform to generalized functions | SERB CORE |
| Total Coloring for Certain Classes of Cayley Graphs | DST |
| Best proximity point iteration for various types of non-self-mappings | NBHM |
| Behzad – Vizing Conjecture on Graph Coloring for Product Graphs | DST-SERB |
| Stability and Stabilization of Random Impulsive Control systems | DST-SERB |
| Total Coloring Conjecture for Certain Classes of Graphs | NBHM |
| “Existence of best proximity points for the sum of two operators” | NBHM |
Amrita Vishwa Vidyapeetham, Amritapuri
Amrita Vishwa Vidyapeetham, Coimbatore.
High Performance Computing Platform:
Dr. Srinivasarao Thota
Associate Professor
Department of Mathematics
Amrita School of Physical Sciences
Amrita Vishwa Vidyapeetham, Amaravati
Andhra Pradesh-522503, India
Email: t_srinivasarao@av.amrita.edu
9182316071
Dr. Manjusha R,
Assistant Professor (Senior Grade),
Amrita School of Physical Sciences, Amritapuri
Amrita Vishwa Vidyapeetham, India.
manjushar@am.amrita.edu
Dr. Mullai Venthan SELVAM
Assistant Professor
s_mullai11@blr.amrita.edu
Dr. Khushbu Dash
Assistant Professor (Sl. Gd.),
Department of Science and Humanities,
School of Engineering, Chennai
d_khushbu@ch.amrita.edu
Dr. A. Vinodkumar
Associate Professor,
Amrita School of Physical Sciences, Coimbatore,
Amrita Vishwa Vidyapeetham, India.
Phone: 0422-2685601
a_vinodkumar@cb.amrita.edu
Dr. T. Senthil Kumar
Assistant Professor
tsenthilkumar@kh.amrita.edu
