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Ph.D. Mathematics Course – Eligibility, Duration, Admission, Top Colleges, Syllabus, Scope

This programme is a doctorate degree designed for students interested in pursuing a career in applied mathematics research. Depending on the area of expertise, the programme provides an in-depth understanding of mathematical phenomena.

Applicants must have a master’s degree or an equivalent degree from a recognized college or university to be considered for the course. The admissions process, on the other hand, differs between colleges.

PhD in Mathematics- An Overview

Level of CourseDoctorate Degree Program
Also referred asDoctor of Philosophy in Mathematics
Duration3 years – 6 years
Type of ExaminationSemester Exams
Criteria for Eligibility A Master’s degree in Mathematical or Physical Sciences having minimum of 55% marks.
Students from engineering background are also eligible.
Admission processBoth Merit and Entrance Based
Course Fee20,000 – 3 Lakhs PA (Per Annum)
Average Salary3-9 Lakhs PA (Per Annum)
Top Recruiting CompaniesCommerce Industry, Business Industry, , Research and Development Firms, Indian Civil Services,Banks,TCS Innovation Lab, Inventory Management,Colleges, Universities, Insurance Agencies,Investment Firms, Statistics (e.g. Ernst & Young, Tiger Analytics,
Job PositionsLoan Officer, , Economist, Mathematician, Researcher, Professor, Personal Banker, Statistician, Cryptographer, Demographer, Accountant etc.

PhD Mathematics- Eligibility

  • To be admitted to a doctoral programme, you must have a master’s degree. In some fields, completing a Masters in Philosophy (M.Phil.) is required before beginning a PhD programme.
  • When M.Phil. candidates are admitted to PhD programmes, they will not be required to take an entrance examination or complete course work, and they will be considered to have met the UGC’s (Minimum standards and procedure for awarding M.Phil./PhD Degree) requirements.
  • In other cases, if a candidate has completed an M.Phil. at one university and then transfers to another for a PhD the new university may credit and exempt the previous university’s course work. However, such a candidate will be required to take the same entrance exam as a new candidate who is enrolling in a PhD programme for the first time. This procedure will be followed by candidates who have earned a PhD from a foreign university.
  • Some prestigious universities require candidates to pass an all-India level examination, such as the University Grants Commission’s ‘National Eligibility Test’ (NET) for Lectureship. Candidates who are in their final year of a bachelor’s degree are also eligible to take the NET Exam.

Admission Process- PhD Mathematics

The step-by-step procedure for entrance-based admission is as follows.

  • Step 1: Applicants must first create an account on the official website.
  • Step 2: Complete the application form with accurate information.
  • Step 3: Following the examination, the website will post a cutoff list. Candidates will then be assigned seats based on their entrance exam scores.
  • Step 4: For admission to this course, some colleges conduct personal interviews and group discussions.
  • Step 5: If a student meets all of the eligibility requirements, he or she will be offered admission to the course.

List of Entrance Exams for PhD in Mathematics

  2. IISc Entrance Test
  3. IISC PhD Mathematics Entrance Test
  4. Hyderabad University PhD Mathematics Entrance exam
  5. Joint Entrance Screening Test (JEST)
  6. UGC-NET for JRF
  7. National Board for Higher Mathematics PhD Fellowship Examination
  8. Tata Institute of Fundamental Research PhD entrance exam
  9. Graduate Aptitude Test in Engineering (GATE)

Examination Pattern of the PhD in Mathematics Exam

The question paper will be divided into two sections.

Part A will consist of ten questions. Six of these questions must be answered. This section will be worth 40 points.
Part B – There will be ten questions in this section, of which six must be answered. This section will be worth 60 points.
The questions will be based on a variety of topics, such as:

  1. Real Analysis
  2. Elements of Numerical Analysis
  3. Ordinary Differential Equations
  4. Linear Algebra
  5. Complex Analysis
  6. Partial Differential Equations
  7. Abstract Algebra

PhD Mathematics Syllabus

First YearSecond YearThird Year
AlgebraDifferential EquationMathematical Finance
AnalysisDifferential GeometryMechanics
CalculusDiscrete MathematicsMetric Space
Computational TechniquesEnglish LiteratureNumber Theory
Computer ScienceLinear ProgrammingProbability Theory

Top Institutes in India for PhD in Mathematics

NIRF RankCollege NameCityAverage Annual FeesAverage Placement Package
1Indian Institute of ScienceBangalore INR 75,600 INR 7 Lakhs
3Banaras Hindu UniversityVaranasi INR 22,268 INR 4 Lakhs
11Aligarh Muslim UniversityCoimbatore INR 27,855 INR 4.50 Lakhs
15Radhakrishna Mission Vivekananda CollegeKolkata INR 21,000 INR 5 Lakhs
40Queen Mary’s CollegeChennai INR 5,805 INR 3 Lakhs
53Sri Ramakrishna College of Arts and ScienceCoimbatore INR 60,000 INR 5.25 Lakhs
58Amity UniversityNoida INR 3 Lakhs INR 8.15 Lakhs
58Stella Maris CollegeChennai INR 6,000 INR 3.50 Lakhs
59Birla Institute of TechnologyRanchi INR 1.75 Lakhs INR 6.25 Lakhs
73Kuvempu UniversityShimoga INR 1.62 Lakhs INR 6 Lakhs

Important books for PhD Mathematics

Name of the BookAuthor
Ordinary Differential EquationsMohan C Joshi
Introduction to Measure and Integration Inder K Rana
Foundations of Discrete MathematicsK.D. Joshi
Fundamental Complex Analysis of One variableAnant R Shastri
Calculus for Scientists and EngineersK.D. Joshi

PhD in Mathematics Job Opportunities and Scope

Some of the areas of employment associated with Phd Mathematics are:

  • Computational Complex Analysis Group, Biomathematics Group, Mathematical Physics, Complexity and Networks, Dynamical Systems, Numerical Analysis, Fluid Dynamics, and other mathematical areas may employ Ph.D. graduates.
  • Graduates with customer service skills and a basic understanding of the industry can work in both private and government banks.
  • Market research, public accounting firms, government and private banks, government and private financial sectors, budget planning, consultancies, and corporations are all possible places for them to work.
  • Airtel, ITC Infotech, Aquis, IBM Global Services, Brainfuse ABC Consultants, NEXT Techno Enterprises, and others are among the top employers for these professionals.

In the table given below, you can have a look at some of top career options for PhD Mathematics holders:

Profile of Job Description of JobAverage Salary
Per Annum
Finance ManagerFinance Managers are responsible for monitoring accounts, reviewing financial reports, maintaining reports, and preparing activity reports and financial forecasts. They also examine the ways to raise profitability and analyze markets for business opportunitiesINR 8 Lakhs
Loan Counselor

Loan counselors are responsible for working with a financial institution, they process a client’s application materials, verify the information, and work with the client to come up with a financial plan.INR 4 Lakhs

Cashiers are responsible for selecting the right product, and also consider becoming a retail sales worker. They may also set up store displays and perform cashier duties. The training is generally offered by the employer. INR 3 Lakhs
Professor/ Asst. ProfessorThey are much needed to provide basic education to the students who are interested to study art at doctoral level programs.INR 5 Lakhs
Insurance ManagerInsurance Managers are responsible for researching which helps them forecast how likely it is for certain risk events to occur and how these events will impact their company with a potential loss.INR 6 Lakhs

These professionals are responsible for performing administrative duties such as the production of forms, and maintaining schedules. They prepare financial statements and tax returns, and accounting firms represent clients on matters pertaining to their financial affairs.INR 3.5 Lakhs

Some other job prospects associated with PhD. Mathematics:

  • Banking Sector
  • Academic Institutes
  • Trade & Transportation Centres
  • Maths Research Centres
  • Stock Exchanges
  • Military Schools
  • Defence Services

Benefits of enrolling in a PhD Mathematics Programme

  • A doctorate degree allows you to keep up with the expanding frontiers of knowledge and provides research training that is relevant to the country’s current social and economic goals.
  • It helps them learn how to write an effective research report and how to present data graphically.
  • Accountancy and business services, banking, investment and insurance, government and public administration are all options.
  • Individuals can work as teachers and lecturers in schools and colleges/universities; to work as a lecturer in colleges, they must pass the NET exam and follow the UGC guidelines.


Which job profiles are available for a Ph.D. in mathematics?

Mathematicians, loan officers, accountants, economists, researchers, personal bankers, demographers, professors, and other professionals can all benefit from a Ph.D. in mathematics.

What is the average salary for a Ph.D. in mathematics?

According to the job profile, the salary ranges from INR 3–9 lakhs per annum.

What are the subjects in Ph.D. mathematics?

In Ph.D. Mathematics, students learn about algebra, calculus, discrete mathematics, differential equations, computational techniques, differential geometry, and other topics.

Which topic is best for a PhD in mathematics?

Differential Geometry, Topology, and Analysis, Theoretical Computer Science, Algebra, Discrete Mathematics,
ODE, PDE, Fluid Mechanics, Numerical Analysis, and Scientific Computing, Probability and Statistics.

How hard is PhD in maths?

It all depends on your mathematical skills,  If it is high, it is not difficult; all that is required is a strong work ethic and the ability to devote 5–7 years to earn a degree. There is no step in your education that is more difficult than this one.

Can you finish a math PhD in 3 years?

Yes, a PhD can be completed in three years. In some cases, this is certainly possible, but only with a great deal of help, perseverance, and, most likely, some luck. A PhD degree will take an average student four to eight years to complete.

What are the jobs after PhD in mathematics?

Accountancy and finance are two professions that you can pursue. Math graduates with a bachelor’s degree in accounting have a variety of career options in a variety of industries.
Banking career, Actuarial career, Statistician career,Engineering, meteorology, and teaching are examples of academic and research careers.

What is the salary of PhD in mathematics?

The Indian market is friendly to mathematicians, with a median salary of 8.14 lakhs for a doctorate holder. Half of the Ph. D. holders receive more than 8.14 lakhs, while the other half receive less than 8.14 lakhs.

Is a maths PhD worth it?

A doctoral degree in mathematics demonstrates your dedication to lifelong learning while also providing you with strongly marketable skills. You’ll acquire many transferable skills that will be useful in almost any industry, in addition to subject-specific skills.

Which country is best for PhD in mathematics?

The United States of America is one of the best countries to study PhD in mathematics. Along with countries like – Lebanon, Sweden,  Fiji ,Germany, Hungary and Finland.

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