Ph.D. Mathematics is a Doctorate of Mathematics course. It is the study of structure, space, quantity, and change. It seeks out patterns and formulates new conjectures. On the completion of a doctorate, scholars should submit their ‘thesis’ and, then they deserve the respective degree they are pursuing.
The duration of the program is a minimum of 3 years and a maximum of 56 years. The minimum qualifications and other eligibility criteria for admission are M.Sc. Degree in Mathematical or Physical Sciences/ B. Tech Candidates from any discipline can also apply/ Some Institutes also offer direct admission for Graduate students with excellent academics performance. Ph.D. Mathematics is a broadbased course involving a minimum course credit requirement and a research thesis.
Key Points of Ph.D. Mathematics

This doctoral program propagates an opportunity for graduates to obtain highlevel research skills and substantially deepen their knowledge in the area of Mathematics. This Ph.D. in Mathematics program trains students to use theoretical and computational research methods to solve a wide range of problems from the most abstract to the very applied. The main focus of the program is on substantial research on core areas of mathematics leading to the Ph.D. dissertation which leads students to develop their skills in presenting and teaching mathematics and its applications.
The tabulation below is the list of Top Ph.D. Mathematics colleges in India according to NIRF:
NIRF Rank  College Name  City  Average Annual Fees  Average Placement Package 

1  Indian Institute of Science  Bangalore  INR 75,600  INR 7 Lakhs 
3  Banaras Hindu University  Varanasi  INR 22,268  INR 4 Lakhs 
11  Aligarh Muslim University  Coimbatore  INR 27,855  INR 4.50 Lakhs 
15  Ramakrishna Mission Vivekananda College  Kolkata  INR 21,000  INR 5 Lakhs 
40  Queen Mary’s College  Chennai  INR 5,805  INR 3 Lakhs 
After completion of this course, graduates may work in fields like Banks, Investment Firms, Commerce Industry, Business Industry, Colleges, Universities, Research and Development Firms, Indian Civil Services, Inventory Management, Insurance Agencies, Statistics, etc.
These professionals may work in positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Demographer, Researcher, Personal Banker, Cryptographer, Demographer, etc. The average salary for these professionals ranges between INR 3 to 9 Lakhs as per their experience and expertise in this field.
Ph.D. Mathematics: Admission Process
Most colleges and institutes offering Ph.D. Mathematics courses admit students based on the graduate degree level examination marks. Some institutes, however, do conduct entrance examinations to judge a candidate’s capability.
The following are the two major pathways through which Ph.D. Mathematics admissions takes place:
MeritBased Admission:
Most private universities such as Lovely Professional, AMU, and others that offer Ph.D. (Mathematics) courses usually admit students based on the marks secured at the master’s/ graduate degree. Apart from this, these colleges may conduct a Personal Interview or a small Written Test to further know the candidate and his/her skills.
Entrance Exam Based:
Top Ph.D. Colleges like Chandigarh University, RKMVCC, Stella Maris College, etc. offer admission in the Ph.D. (Mathematics) program through entrance examinations that usually consist of MCQ based questions related to Algebra, Analysis, Discrete Mathematics, etc. helping the college to screen the deserving candidates for admission.
After the result declaration of these Entrance Exams, colleges may further conduct a Personal Interview Round of the qualified candidates to know their interest in the course, skills, and career and might go through their Art Portfolio as well.
Ph.D. Mathematics: Eligibility
The common Ph.D. (Mathematics) eligibility criteria to be successfully admitted into a college offering this course is as follows:
 M.Sc./ Master’s Degree in Mathematical or Physical Sciences
 B. Tech Candidates from any discipline can also apply, it may vary by Institutes.
 Some Institutes also offer direct admission for Graduate Students with excellent academics records.
 Each college also further has a set minimum aggregate marks. Overall, it should be 55% (50% for SC / ST).
The abovestated eligibility criteria are the basic eligibility criteria. Each college will have its criterion on which prospective candidates are judged.
Ph.D. Mathematics: Entrance Exams
Some colleges that offer Ph.D. (Mathematics) programs require their candidates to sit for an entrance examination. This paper carries a total of 100 marks where candidates need to conclude writing the exam within a period of 3 hours.
Listed below are some of the popular Ph.D. Mathematics entrance exams.
 CSIRUGC NET for JRF Entrance Exam: CSIR UGC NET is a nationallevel exam conducted by the National Testing Agency (NTA) on behalf of Council of Scientific and Industrial Research (CSIR) to shortlist candidates for the award of Junior Research Fellowship (JRF) or lectureship in Indian universities and colleges.
 UGC NET Entrance Exam: The UGC NET for JRF, also known as National Eligibility Test (NET) or NTAUGCNET, is the test for determining the eligibility for the post of Junior Research Fellowship (JRF) or Asst. Professor award in Indian universities and colleges.
 NBHM Entrance Exam: National Board for Higher Mathematics is a board in India that conducts a national entrance exam intended to foster the development of higher mathematics, help in the establishment and development of mathematics centers, and give financial assistance to research projects and to doctoral and postdoctoral scholars.
There are few private colleges like Chandigarh University, LPU, etc. conducts their own entrance tests for this course.
Exam Name  Application Period  Exam Date  Exam Mode 

CSIRUGC NET for JRF  March 16 – June 30, 2020  To be notified soon  Online 
UGCNET for JRF  March 16 – June 30, 2020  To be notified soon  Online 
NBHM Entrance Exam 2021  November 26, 2020 January 5, 2021  January 25, 2021  Online 
How to Prepare for a Ph.D. Mathematics Entrance Exams?
The syllabus for Ph.D. Mathematics entrance exams will vary from institute to institute. However, most exams concentrate on mathematicsrelated subject knowledge and skills.
The paper shall have two different parts,
 Part I  Here 10 questions will be given. Out of these, 6 will have to be answered. This part will carry 40 marks.
 Part II  Here also 10 questions will be given, out of this 6 ought to be answered. This part will carry 60 marks.
The following sections are generally covered in Ph.D. Mathematics entrance exams syllabus:
 Abstract Algebra
 Complex Analysis
 Elements of Numerical Analysis
 Linear Algebra
 Ordinary Differential Equations
 Partial Differential Equations
 Real Analysis
Students should consider buying study material and practice material of Ph.D. Mathematics entrance exams so that they prepare well for the same. This paper carries a total of 100 marks where candidates will need to conclude writing the exam within a period of 3 hours.
How to get admission in a good Ph.D. Mathematics college?
To get admission in top Ph.D. Mathematics colleges, the following points must be kept in mind:
 The application process for most of the institutes starts in January every year and the classes begin in August.
 The Colleges shortlist candidates through respective entrance exams followed by an interview.
 The best way is to appear for CSIRNET and UGCNET exams to get a good college for Ph.D. and for some of the colleges’ GATE is also used as a prerequisite.
 For example, ISI Kolkata uses the GATE score for admission in its Ph.D. Mathematics program. Some institutes also take admission through the NBHM Screening test conducted for Ph.D. Scholarships.
Ph.D. Mathematics: What is it about?
Ph.D. Mathematics is the program of choice for students who wish to pursue a career in a mathematical research field.
 The minimum duration of this course is 2years, whereas you can complete this course in a maximum time span of 35 years.
 Ph.D. Mathematics is a fulltime doctoral degree.
 In Ph.D. Mathematics, students study statistical concepts relating to inspection, engineering design, and quality assurance.
 Ph.D. in Mathematics course involves research that uses various methods of mathematical types associated with the graph theory, asymptotic analysis, scientific computation, bifurcation theory, probability and statistics, ordinary and partial differential equations, stability theory, singular perturbations, and stochastic processes.
 In this course, major topics studied by the students are correlation, normality, probability, sampling, regression, and confidence intervals in reliability. This course is designed to enrich the applications like algebra and trigonometry, systems of linear equations, algebraic fractions, literal equations, quadratic equations, right triangles, vectors, word problems, and their solutions.
Ph.D. Mathematics: Course Highlights
Course Level  Doctorate Course 
FullForm  Doctor of Philosophy in Mathematics 
Duration  3 years 
Examination Type  Semesterbased 
Eligibility  M.Sc. Degree in Mathematical or Physical Sciences/ B. Tech Candidates from any discipline with a minimum of 55% score 
Admission process  Meritbased / Entrance Examination 
Course Fee  INR 20,000 – 3 Lakhs per annum 
Average Salary  INR 3 – 9 Lakhs per annum 
Top Recruiting Companies  Banks, Investment Firms, Commerce Industry, Business Industry, Colleges, Universities, Research and Development Firms, Indian Civil Services, Inventory Management, Insurance Agencies, Statistics (e.g. Ernst & Young, Tiger Analytics, TCS Innovation Lab, Weizmann Institute, etc.) 
Job Positions  Mathematician, Statistician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Cryptographer, Demographer, Professor, etc. 
Why study the Ph.D. Mathematics course?
Candidates who are inclined towards a research career, many positions are available in research institutions and universities for them. And who wish to pursue a teaching career, wellpaying teaching positions are available in plenty in private engineering colleges. Many research labs of multinational companies, financial services companies, and others are massively recruiting Indian mathematicians.
Some of the popular reasons why Ph.D. Mathematics must be pursued is as follows:
 This program prepares someone to keep momentum with the expanding frontiers of knowledge and provides research training relevant to the present social and economic objectives of the country.
 It comprehends to write a good research report and acquires the skill of presenting data in graphical form.
 They can also go for accountancy and business services, banking, investment and insurance, government, and public administration.
 They can become teachers and lecturers in schools and colleges/universities respectively; for becoming a lecturer in colleges they should pass the NET exam and the UGC guidelines.
Course Comparison
Ph.D. Mathematics Vs Ph.D. Economics
Both Ph.D. Mathematics and Ph.D. Economics have a bright future in the field of research with several aspects. There are many colleges in India who prefer both of the courses in their academic structure. Check the table below for more comparative details:
Parameters  Ph.D. Mathematics  Ph.D. Economics 

FullForm  Doctor of Philosophy in Mathematics  Doctor of Philosophy in Economics 
Duration  3 years  3 years 
Eligibility  M.Sc. Degree in Mathematical or Physical Sciences/ B. Tech Candidates from any discipline with a minimum of 55%  Postgraduation in Economics 
Exam Type  Semesterbased  Semesterbased 
Job Profiles  Mathematician, Statistician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Cryptographer, Demographer, Professor, etc.  Accounting, Auditor, Banking and Finance, Insurance Investment, Marketing, Stock Broker, Media Analyst, Management, Manufacturing, Advertising, Communication, etc. 
Average Fees  INR 20,0003 Lakhs  INR 80,000 6 Lakhs 
Average Salary  INR 3 – 9 Lakhs per annum  INR 2 – 8 Lakhs per annum 
Source: Official Surveys
The eligibility and admission criteria for both these degrees are the same. In terms of Career and Salary, both Ph.D. Mathematics and Ph.D. Economics almost have the same career prospects and job opportunities, and individuals can earn an average salary of around INR 29 Lakhs per annum or more in some cases depending upon candidate's skills, knowledge, and experience.
Ph.D. Mathematics: Top Colleges
The table below shows the best Ph.D. Mathematics colleges and universities that offer the course in a fulltime mode.
NIRF Rank  College Name  City  Average Annual Fees  Average Placement Package 

1  Indian Institute of Science  Bangalore  INR 75,600  INR 7 Lakhs 
3  Banaras Hindu University  Varanasi  INR 22,268  INR 4 Lakhs 
11  Aligarh Muslim University  Coimbatore  INR 27,855  INR 4.50 Lakhs 
15  Ramakrishna Mission Vivekananda College  Kolkata  INR 21,000  INR 5 Lakhs 
40  Queen Mary’s College  Chennai  INR 5,805  INR 3 Lakhs 
53  Sri Ramakrishna College of Arts and Science  Coimbatore  INR 60,000  INR 5.25 Lakhs 
58  Amity University  Noida  INR 3 Lakhs  INR 8.15 Lakhs 
58  Stella Maris College, Chennai  Chennai  INR 6,000  INR 3.50 Lakhs 
59  Birla Institute of Technology  Ranchi  INR 1.75 Lakhs  INR 6.25 Lakhs 
73  Kuvempu University  Shimoga  INR 1.62 Lakhs  INR 6 Lakhs 
View More Top Ph.D. Mathematics Colleges
College Comparison
The tabulation below shows the comparison made among the three top Ph.D. Mathematics colleges in India.
Parameter  Banaras Hindu University  Ramakrishna Mission Vivekananda College  Aligarh Muslim University 

Overview  Banaras Hindu University, a public university from Varanasi is one of the oldest universities in the country. It is one of the best colleges to pursue a Ph.D. program  RKMVCC College started functioning in 1963 with a view of remembering the first birth centenary of Swami Vivekananda. It offers UG, PG & PH.D. research programs in the field of science.  Established in 1875, the Aligarh Muslim University has students from around the world. Its Ph.D. program is highly ranked. 
Average Fees  INR 22,268  INR 21,000  INR 27,855 
Average Placement Offered  INR 4 Lakhs  INR 5 Lakhs  INR 4.5 Lakhs 
Courses Offered  Ph.D., B.Tech, MBBS, BBA, MBA, M.Tech, PG Program, MA, and BA (Hons)  B.Com, BBA, BCA, BSc, BA, M.Phil, MSc, Ph.D., and MSW.  Ph.D., B.Tech, MBBS, BBA, MBA, M.Tech, PG Program, MA, and BA (Hons) 
Top Companies Visited  Infosys, Coal India, ICICI Bank, IDBI Bank, Pantaloon, Visa Steel, FINO, Ansal API, etc.  Tata Consultancy Services, ACC Limited, etc.  IBM, TCS, ICICI Bank, ONGC, L&T, Kotak Securities, Genpact, etc. 
Source: Official Websites of Colleges and Universities
Ph.D. Mathematics: Syllabus
Although the Ph.D. Mathematics course curriculum varies from college to college, it mostly consists of some common foundation courses that students can select based on his/her interests.
The table below shows common subjects that are included in the structured Ph.D. Mathematics syllabus and subjects included in it:
1 Year  2 Year  3 Year 

Algebra  Differential Equation  Mathematical Finance 
Analysis  Differential Geometry  Mechanics 
Calculus  Discrete Mathematics  Metric Space 
Computational Techniques  English Literature  Number Theory 
Computer Science  Linear Programming  Probability Theory 
Ph.D. Mathematics: Books
Tabulated below are some of the Ph.D. Mathematics subject books that can help students to have a broader and better understanding of the course. The books mentioned below will also help the students in cracking various Ph.D. Mathematics exams.
Name of the Book  Author 

Calculus for Scientists and Engineers  K.D. Joshi 
Foundations of Discrete Mathematics  K.D. Joshi 
Introduction to Measure and Integration  Inder K Rana 
Fundamental Complex Analysis of One variable  Anant R Shastri 
Ordinary Differential Equations  Mohan C Joshi 
Ph.D. Mathematics: Job Prospects and Career Options
In India, Ph.D. Mathematics is one of the top career choices made by students. There are lots of job opportunities available in India as well as in foreign countries for Mathematical graduates.
 Ph.D. graduates may work in a wide range of mathematical areas like Numerical Analysis, Computational Complex Analysis Group, Biomathematics Group, Complexity and Networks, Dynamical Systems, Fluid Dynamics, Mathematical Physics, etc.
 Graduates who have the ability to handle customers and basic knowledge about the industry may also work in both private and government banks.
 They can also seek employment in various sectors such as in markets research, public accounting firms, government and private banks, government and private financial sectors, budget planning, consultancies, and corporations.
 Top companies that offer jobs for these professionals are Aquis, Airtel, ITC Infotech, IBM Global Services, ABC Consultants, NEXT Techno Enterprises, Brainfuse, etc.
The table below shows some of the most common Ph.D. Mathematics job profiles and career prospects after completing the course is as follows:
Job profile  Job Description  Average Annual Salary 

Cashier  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 
Insurance Manager  Insurance 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 
Finance Manager  Finance 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 opportunities.  INR 8 Lakhs 
Accountant  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 
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 
Professor/ Asst. Professor  They are much needed to provide basic education to the students who are interested to study art at doctoral level programs.  INR 5 Lakhs 
Source: Payscale
Ph.D. Mathematics: Future Scope
Students having a Ph.D. mathematics degree are importantly serving the education industry and due to the laws of UGC one position of Head of Department is always secured for Ph.D. holders only.
 Employment of mathematicians in India is expected to grow by 23% as the surging demand for knowledge and expertise in private sector analytics firms.
 The private sector offers better pay and opportunities. The package can also increase if they add advanced computing skills and statistical tools in their profile.
Ph.D. Mathematics: FAQs
Ques. What are the top colleges for Ph.D. Mathematics?
Ans. The top institutes and colleges for Ph.D. Mathematics are Banaras Hindu University, Aligarh Muslim University, Amity University Noida, Birla Institute of Technology Ranchi, Queen Mary’s College, among others.
Ques. What are the subjects in Ph.D. Mathematics?
Ans. Some of the subjects taught in Ph.D. Mathematics are Algebra, Calculus, Discrete Mathematics, Differential Equations, Computational Techniques, Differential Geometry, etc.
Ques. Which job profiles are available for a Ph.D. Mathematics?
Ans. Students of Ph.D. Mathematics can work as Mathematician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Demographer, Professor, etc.
Ques. What is the annual average tuition fee charged for a Ph.D. Mathematics program?
Ans. The annual average tuition fee at the top Ph.D. Mathematics colleges is between INR 2K to INR 3 Lakh.
Ques. What is the scope of the Ph.D. Mathematics course?
Ans. Students can choose for both private and public sector jobs in several sectors like the professor, loan counselor, Insurance Manager, etc.
Ques. What is the average salary in Ph.D. Mathematics?
Ans. The salary ranges from INR 39 Lakhs per annum as per the job profile.
Ques. What are the job positions in the Ph.D. Mathematics field?
Ans. Job positions like Mathematician, Statistician, Loan Officer, Accountant, Economist, Researcher, Personal Banker, Cryptographer, Demographer, Professor, etc. are available in the Ph.D. Mathematics field.