Ph. D. in Applied Mathematics

Overview

The programme enables students to learn new methods in research to predict the observed, and unobserved phenomena and find solutions to real-world problems. In today’s world, new challenges and problems arising in all fields require solutions that are precise through numerical methods that involve differential equations, statistics, numerical methods, and analysis. With a close-knit community of learners working together diligently towards impactful research work, students get an opportunity to create new frontiers of knowledge in the fields of mathematics through quality research and a world-class framework.

Eligibility

A 1-year / 2-semester master's degree programme after a 4-year / 8-semester bachelor’s degree programme or a 2-year / 4-semester master’s degree programme after a 3-year bachelor’s degree programme or qualifications declared equivalent to the master’s degree with 55% marks in aggregate from a recognized University in "relevant discipline".
Candidate seeking admission after a 4-year / 8-semester bachelor’s degree programme should have a minimum of 75% marks in aggregate or its equivalent grade on a point scale wherever the grading system is followed in "related discipline".
A candidate with an M. Phil Degree with at least 55% marks in aggregate shall be eligible for admission to the Ph.D. programme.
A relaxation of 5% marks or its equivalent grade may be allowed for those belonging to SC / ST.

Areas of Research

General Topology
Fractional Calculus
Graph Theory
Applied Statistics
Fluid Dynamics
Numerical Methods

Distribution Theory
Machine Learning
Differential Equations
Combinatorics
Stochastic Processes
Artificial Intelligence

Nonlinear Dynamics
Discrete Mathematics
Reliability
Big Data Analytics

Salient Features

Research fellowship of Rs. 35,000 per month and a research allowance of Rs. 25,000 per year for full-time scholars.

Monetary support for attending national and international conferences for Full-Time Research Scholars.

University Journals for the publication of Research Articles.

Periodic similarity check of research papers and chapters.

Intense coursework prior to the commencement of the Research Study.

Facility for Transfer of Research Scholars from other Universities or Research Institutions to Alliance University and vice-versa.

Specific provisions and relaxations with respect to women Research Scholars and specially abled persons.

Extensive interaction with luminaries.

Course Work

Courses:

Research Methodology – Part A (General)
Linear Algebra
Specialisation-specific Paper
Research Methodology – Part B (Specialisation-specific)
Real Analysis/Measuring Theory
Specialisation-specific Assignment

Course Description

Sem I:

Research Methodology Part A: General (Common subject): This course introduces the students to the importance of systematic approach to research, research ethics, types of research design, research methods, data collection methods, data analysis techniques, and research report writing.
Linear algebra (Compulsory subject): This course introduces the students to the concepts and techniques of linear algebra, vector space theory, Banach space theory, and Lp space theory. These techniques are widely used in almost all fields of mathematics and statistics and are therefore important for developing a foundation for applied mathematics research.

Sem II:

Research Methodology Part B: Specialisation-specific (Compulsory subject): General (Common subject): This course introduces the students to research methods in their domain of specialisation.
Real analysis/Measure theory (Compulsory Subject): This course introduces the students to the concepts and techniques of real analysis, topological theory, measure theory, and differential equations. These techniques are widely used in almost all fields of mathematics and statistics and are therefore important for developing a foundation for applied mathematics research.

Specialisation-specific Assignment:The Specialisation-specific Research Methodology course contents, the Specialisation-specific Paper, and the Specialisation-specific Assignment are to be determined by the candidate’s Research Supervisor in consultation with the Research Advisory Committee.