Guru Nanak Dev University Dr. Poonam Kumar Sharma Conferred with Honorary DSc in Mathematics

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DSc (Honoris Causa)

Dr. Poonam Kumar Sharma

Doctrin de Science Award Honoris Causa

The Pride of Bharat (India)

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Dr. Poonam Kumar Sharma

Fellow, Directorate of Mathematics

Associate Professor

Post Graduate Dept. of Mathematics,

D.A.V. College ,

Jalandhar Under

Guru Nanak Dev University

Exclusive Interview with Dr. Poonam Kumar Sharma

Question: What inspired you to enter into Mathematics?

Answer: Mathematics gives me a different approach to understand the universe which also motivates me to study the subject, with a hope of understanding the universe in more scientific and detailed matter. That happiness after solving a problem which trapped me for hours motivates me to do more mathematics.

Question: Since how long, you have been into this scientific field and in which cities you have been associated for administration, entrepreneurship, teaching, research, commercial and training programs?

Answer: I am working in this field of teaching since 1993 and contributing in research and training programs from 1999 for teaching and relevant research activities. I am associated with D.A.V. College, Jalandhar, Punjab as professor in Mathematics, Jamia Millia Islamia, University, New Delhi as a research scholar for Ph.D., Punjab Technical University, Jalandhar and Lovely Professional University, Phagwara for guiding Ph.D. scholars.

Question: What are your future plans for administration, entrepreneurship, teaching, research and training programs in Mathematics?

Answer: Digital technologies have emerged as an essential tool in education. These technologies have shown a powerful impact on the education system. The recent COVID-19 pandemic has further institutionalised the applications of digital technologies in education. These digital technologies have made a paradigm shift in the entire education system. It is not only a knowledge provider but also a co-creator of information, a mentor, and an assessor. Technological improvements in education have made life easier for students. Instead of using pen and paper, students nowadays use various software and tools to create presentations and projects. When compared to a stack of notebooks, an iPad is relatively light. When opposed to a weighty book, surfing an E-book is easier. These methods aid in increasing interest in research. So, my future plan is to work in the direction of creating environments for online learning. Whatever is needed to enhance the use of technologies must be worked out.

Question: Please introduce yourself and how do you want to be remembered / known in world?

Answer: My name is Dr Poonam Kumar Sharma, and I have 30 years of teaching experience in D.A.V. College, Jalandhar. I am an author of ten books on mathematics out of which one book is a research book published from Lambert Academic Publication, Germany and eight books for M.Sc. (mathematics) and one book for B.A/BSc (Mathematics) with ISBN number, published by Sharma publications, Jalandhar. I published 160 research articles in national and international journals and delivered 35 invited talks in national and international conferences. I also completed one major research project sponsored by UGC amounting to Rs. 10 lakhs. My name was nominated in Who’s Who in the world 2015. I had visited USA and Bulgaria to present my research papers under UGC travel grant scheme. On being a Dean, Alumni Association of DAVC Jalandhar I organized three alumni meets, one in 2013, second in 2015 and third in 2018 successfully. I remained an active member of various administrative committees during my tenure at D.A.V. College, Jalandhar. I have guided 25 students for their M. Phil dissertation and 6 students have pursued Ph.D. under my supervision, out of which four students has been awarded their Ph.D. degrees one in 2017, second in 2019, third in 2020 and fourth in 2023. One student about to submit her Ph.D. thesis in 2024. My hobbies are teaching, writing, listening to music and surfing on the internet.

Question: What kind of businesses can be started in Mathematics? What minimum infrastructure would it need?

Answer: The following business can be stated with having the knowledge of Mathematics

1. Coaching institute can be started up with least infrastructure of black boards, chairs.

2. Guidance to various kind of investments cum sale and purchase of stocks can be started up with least infrastructure of computer and charts to display important market trend of some important companies.

3. Statistical data presentation cum analysis centre can be started up with least infrastructure of computer and statistical softwares.

4. Technical guidance in programming/software development/ quizzes development can be provided with least infrastructure of computer.

Question: What are your recommendations to improve the standards of journals publishing research articles on Mathematics?

Answer: The journals publishing research articles on Mathematics are expected to publish genuine research work without plagiarism.

Question: What are your recommendations to improve syllabus of Mathematics for more creativity, applications and opportunities?

Answer: The following steps must be taken to make the syllabus of mathematics far more creative and applications oriented: Collaboration and creativity are essential skills for mathematics learning and problem-solving. It helps the students to develop deeper understanding, communicate their ideas, and apply their knowledge to new situations. This also foster a sense of curiosity, motivation, and confidence in mathematics. Technology can facilitate collaboration and creativity by providing tools and platforms for students and teachers to share, discuss, and co-create mathematical products, such as models, simulations, games, or presentations.

Question: What is Mathematics? What are the major branches in Mathematics?

Answer: Mathematics can be summarized as the art and science of discovering patterns and explaining them. As such, Mathematics is both ubiquitous and universal. It is all around us, in nature, in technology, and in the motion of the earth, sun, moon, and stars above. There is mathematics in everything that we do and see, from shopping and cooking, to throwing a ball and playing games, to solar eclipses and climate patterns. Mathematics and numeracy thus give us the fundamental ideas and tools required to think about the world around us and the world beyond us. Some of the important branches of Mathematics are: Pure mathematics, Arithmetic, Algebra, Geometry, Topology, Probability and Statistics, Calculus, Logic, Number theory etc.

Question: What are your recommendations to frame guidelines on funding of research projects on Mathematics?

Answer: DST and UGC are the funding agencies that provide maximum funds for research projects. It will be better to enhance funds for reference books so that more reference books can be purchased.

Question: How can universities produce revolutionary PhD and Post Doc thesis and dissertations on Mathematics? What are your recommendations to improve the academic standards?

Answer: The academic standards can be improved by conducting central entrance examination for admission to Ph.D. There should be open defence viva for Ph.D.

Question: What are your views and suggestions on India’s Moon Mission Chandrayaan-3 and ISRO's Aditya-L1 Solar Mission?

Answer: Now, as ISRO has successfully landed the Chandrayaan-3 on the south pole of the moon, there are several lessons that can be learned.

Embrace Failure as a Stepping Stone, not a Stumbling Block.
Rigorous Testing.
Openness to Collaboration.
Clear Communication with The Public.
Robust Redundancy Planning.
Calculating Decisions.

Aditya L1 payloads are expected to provide the most crucial information to understand our knowledge of the Sun, and how its radiation work, heat, flow of particles, and magnetic fields affect us. Below is the list of other objectives that the mission should embark upon:

To study the upper atmospheric layers of the Sun called chromosphere and corona. While the corona is the outermost layer, the chromosphere is just below it.
To examine coronal mass ejections (CMEs), which are large expulsions of plasma and magnetic fields from the Sun’s corona.
To analyse the corona’s magnetic field and the driver of the space weather.
To understand why the Sun’s not-so-bright corona is a million degrees Celsius hot when the temperature on the surface of the Sun is just about 5,500 degrees Celsius.
To help scientists know the reasons behind the acceleration of particles on the Sun, which leads to the solar wind the constant flow of particles from the Sun.
To diagnose the temperature, velocity and density of corona and coronal loops plasma.
To understand the sequence and process of eruptive events at solar.

Question: How can students seek job and career opportunities in Mathematics?

Answer: The logical thinking, problem-solving and decision-making skills you learn while studying a mathematics degree can lead to careers in Information Technology, Statistician, Actuarial Analyst, Data Analyst, Investment analyst, Software Engineer and professor in college (university) etc.

Question: What job titles are available in Mathematics?

Answer: Some of the common job titles available in Mathematics are: Mathematics teacher, Inventory manager, Accountant, Purchasing specialist, Research analyst, Budget analyst, financial analyst, Cost estimator, Business analyst, Market researcher, Statistician, Database administrator, Economist, Actuary, Software engineer, Data Scientist etc.

Question: Which are Typical employers in Mathematics?

Answer: Careers in mathematics are not limited to teaching in schools or colleges anymore. People with a career in mathematics conduct research, or use Mathematical modelling and frameworks to solve business problems or help an individual make critical investment decisions which can be useful throughout one's life.

Question: Which are the courses available in Mathematics?

Answer: Some of the core courses available in Mathematics are the following

· Arithmetic, Trigonometry, Geometry

· Real (Complex) analysis

· (Advanced) Calculus

· Numerical Analysis

· Linear (Abstract) Algebra

· Topology

· Nonlinear Dynamics

· Information Theory

· Probability

· Computational mathematics

· Optimisation Theory

· Computer Science

· Applied (Theoretical / Computing) Statistics

· Combinatorics /Discrete Mathematics

· (Spectral) Graph Theory

· Modelling

· Mathematics for machine learning and data science

· Mathematical Logic (Fuzzy Logic)

Question: What are your recommendations to write a world class research article in Mathematics? What essential components and factors must be there?

Answer Today the field of research has become more advanced. To write world class research article in Mathematics, copy paste method should be avoided and inferences and outcomes of genuine research should only the incorporated in research article. Basic and the applied research method be used. A critical requirement of a publication is to present the paper in enough detail so that a reader can follow the reasoning and confirm the resulting conclusions. Moreover, an author should be willing to defend the paper against criticism, therefore he/she should have available for later review the data used and key detail about the experimental method. Nowadays the vast majority of papers published in scientific journals today follow a simple structure. With some variations, they use an “Introduction, Material and Methods, Results and Discussion” format. This format seems to be durable. This format seems to faithfully reflect scientific work and, if necessary, to verify its approach and conclusion.

Question: What are your recommendations to write a world class case report in Mathematics? What essential components and factors must be there?

Answer First the author should present a complete aspect of the already known facts of the case study. Then he should write his work with originality. Even if an author is confident in his own aptitude, he needs to consult experts for checking. The author should provide enough details on the case. Because it is the details that mark the specificity of the reported study.

Question: What are your recommendations to write a world class review in Mathematics? What essential components and factors must be there?

Answer An important requirement is to master widely the subject in the time. The next step is to present the paper in sufficient detail so that a reader can follow the reasoning presented and validate the resulting conclusions. Moreover, an author should be willing to protect the paper against criticism, therefore he should have available for later review the presented material used and the methodology used.

Question: What are your recommendations to establish a world class research institute for Mathematics?

Answer: The following points should be taken care of while establishing a world class research institute for mathematics:

· The research institute for mathematics should be located in an environment close to nature so that mathematicians can hike or walk or whatever light group outdoor activity suits them--lots of math gets done during such interludes.

· The building should be designed so that lots of serendipitous hallway encounters take place as people move around the building; apparently this was one of the reasons for MIT's success in its early days--people ran into each other in the hall and started chatting casually about stuff.

· Do not skimp on the administrative and support staff as they are crucial to creating an environment conducive to mathematical activity.

· A good math department secretary is worth his/her weight in gold. The mathematicians should not have to spend an inordinate amount of time going through red tape to get the services and items they need.

· A good library is nice. People still like to thumb through physical math books and journals.

· Also, the quiet surroundings are conducive to solitary mathematical contemplation

Question: What are your recommendations to improve employment and scope in Mathematics?

Answer: With the proper learning of Mathematics (steam wise). One can have tremendous opportunities to use it in almost every field. There is a large basket of professions for a maths graduate/post-graduate. Some of professions are the following:

· Scope in IT Industry (If you are fond of constructing computer algorithms, you can choose the Information and Communication Technology industry. This industry can provide you with the perfect opportunity to harness your Maths honours degree.)

· Scope in Accountancy and Management (If you have got a fervour for business, a career in Management, Mathematics, Accountancy and professional service is an implausible way of using the skills you’ve gathered during your degree. The industry offers great career prospects for a mathematics graduate.)

· Scope in Actuarial Sciences (If you like to play with numbers, and have interest in probability and statistics, then you can think of a profession in Actuarial Sciences. Actuaries use mathematical and statistical modelling to envisage future events that helps to appraise financial impact on an organisation. The actuarial profession offers great opportunities in a rapidly expanding province.)

· Scope in Investment and Banking (If you want to become a banker, then you can be an investment banker or a retail banker after completing your B.Sc. in Mathematics. Investment banking offers financial advice and services to large industries, governments and high-net-worth individuals. A career in investment banking can be highly lucrative and fast-paced. Retail banking covers the events of the many high street banks, providing financial services and products to individuals and businesses. There are a huge number of jobs in retail banking, many of which are customer handling and allow you to utilise your maths degree. If you are a natural leader, then you should have a knack for management and organising resources, then you should consider a career in management.)

· Scope in Operational Research Analyst (If you want to be an operations research analyst: Operations research is the science of improving efficiency and making best decisions. As an operational research analyst, you will be able to use your mathematical and statistical knowledge to improve the strategies of organisations. Applying your mathematical skills to solve real-world problems is incredibly rewarding.)

· Scope in teaching and Research Institutes (If you aspire to be a teacher. Going for a Master’s degree programme and acquiring a PhD will help you to fulfil your desire. This will enhance your knowledge in a particular field. You may gain professional qualifications or change your field of study as well. Achieving a PhD in mathematics proposes an incredible opportunity to make an original contribution to mathematics.)

Question: What are your recommendations to authors, who are writing Books on Mathematics for more creativity and understanding of the subject?

Answer: The language used in writing the books must be very apt and precise. Elaborate descriptions be given where ever necessary so that the topic can be well understood by the reader. The topic must be in some sense me related to real life problems and how it can be solved must be provided.

Question: What according to you are the Top 5 major challenges (research problems) which need to be resolved urgently by world’s scientists in the area of Mathematics?

Answer: Top five major challenges (research problems) which need to be resolved may be as follows,

1) Basic and Fundamental research is lost.

2) To avoid plagiarism,

3) Utility and usefulness of research to society.

4) To avoid repetition in research problem.

5) Today to avoid cut paste method in research.

Question: What are your recommendations to improve standards of Conferences in Mathematics? How can they be brainstorming and more creative?

Answer: The resource persons should deal the topic in more innovative and participative in manner. The latest development in the field of particular topic along with proper references be dealt with by the speaker. The concepts of topic can be made effective by using appropriate techniques and tools.

Question: Which major challenges do you see to establish India as world leader in Mathematics?

Answer: The scene in India continues, as always, to be uneven. In spite of its size, India’s presence in the world of Mathematics, Science and Technology is still small. The investment required to break into the world knowledge system is huge, and it appears both India and China will find it difficult to afford this for quite some time to come. In rough numbers, India accounts for about one-half percent of the total expenditure in the world on research and development, and about two percent of the resulting publications. Today the major problem in further development of India lies in learning to manage the extraordinary talent that the country possesses. India is often said to be home to one of the largest scientific communities in the world, but only a small percentage of those graduating in the mathematics, sciences are doing research. Indian society has traditionally reserved its deepest respect only for persons of moral authority. The current challenge is to encourage respect for those distinguished in mathematics and sciences as well.

Question: Any other thing, you would like to share with World?

Answer: The study of Mathematics should be made compulsory up to 12th stranded for all. But the curriculum for mathematics subject must be revised taking care of to relate the mathematics syllabus with real life problems. Also, the teacher’s must be taught how to teach in an effect manner so as to make it interesting to everyone.

Website Link Information

‪P. K. Sharma - ‪Google Scholar

‪

https://orcid.org/0000-0001-5463-8665

https://www.researchgate.net/profile/Poonam-Kumar-Sharma

http://livedna.org/91.4966

https://loop.frontiersin.org/people/1401922/bio

https://ssrn.com/author=4776870

https://davjalandhar.academia.edu/DrPOONAMKUMARSHARMA

https://drpoonamkumarsharma.academia.edu/

Poonam Kumar Kumar Sharma (sciprofiles.com)

Editor/ Referee / Reviewer of Journals

1. Member of the Editorial Board of “International Journal of Fuzzy Mathematics and Systems”, of Research India Publication, New-Delhi.

2. Member of the Editorial Board of “International Journal of Engineering Research & Management Technology, Published by : Advances Research Educational Society

3. Referee of Journal of Intelligent and Fuzzy System, STM Publishing House, IOS Press.

4. Referee of Neural Computing and Application, Springer Link

5. Referee of Journal of the Egyptian Mathematical Society

6. Referee of Annals of Fuzzy Mathematics and Informatics (AFMI).

7. Referee of Asian Journal of Mathematics and Computer Research

8. Referee of Boletim da Sociedade Paranaense de Matemática, Universidade Estadual de Maringa, Website of State University of Maringa’s Journal.

9. Referee of Journal of universal Mathematics, ISSN: 2618-5660. http://dergipark.org.tr/en/pub/jum/board

10. https://loop.frontiersin.org/people/1401922/bio

Courses Taught :

Topology, Modern Algebra, Real Analysis, Theory of Numbers, Dynamics and Statics Linear Algebra and Calculus, Discrete Mathematics.

Research Project Completed

1. “The Relation modules of finite groups” Submitted to Kurukshetra university, Kurukshetra by Bijoy Kumar Shill in 1999

2. “ Higher Relative relation modules” Submitted to Kurukshetra university , Kurukshetra, by Vikram Verma in 1999

3. “The Relative relation modules of finite groups” Submitted to Kurukshetra university by Poonam Sharma in Kurukshetra , 2000

4. “ Generalized semi-closed sets in topological spaces” Submitted to Periyar University by Arti Sharma in April 2007

5. “Semi-generalized Regular spaces and semi-generalized Normal spaces” Submitted to Periyar University by Rohit Sharma in April 2007

6. “ Decomposition of fuzzy topological spaces” Submitted to Periyar University by Poonam Bhardwaj in May 2007

7. “ Strongly connected spaces” Submitted to Alagappa University by Shallu, in May 2007

8. “Semi-connectedness and semi-locally connectedness in Biotopological spaces” Submitted to Periyar University by Shobik Soni in June 2007

9. “ Certain Common Fixed Point Theorems” Submitted to Periyar Universityby Pooja Anand in July 2007

10. “ Connectedness in Biotopological spaces” Submitted to Periyar University by Geetanjali in July 2007

11. “ Quasi-metric space and Biotopological spaces” Submitted to Periyar University by Pushpinder in october, 2007

12. “ Fuzzy a - connecedness and Fuzzy a - disconnectedness in Fuzzy topological

spaces.” Submitted to Chawdary Devi Lal University, Hisar, Harayana by Harinder Pal in 2008

13. “Compactness in Fuzzy topological spaces” Submitted to Vinayka Mission Research Foundation–Deemed University, Saleem ( Tamil-Nadu) by Divya Kakkar in 2008

14. “ Finistic spaces in L-topology” Submitted to Vinayka Mission Research Foundation–Deemed University, Saleem ( Tamil-Nadu) by Naveen Kumar in 2008

15. “Semi-continuity and Semi-homeomorphism in topological spaces” Submitted to SRI Venkateswara University, Tirupati by Paramjeet Singh in 2008.

16. “ Some weak form of continuity in Topological spaces” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Raman deep in 2009

17. “ Fixed point Theorems in Generalized metric spaces” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Gagandeep Kaur in, 2009

18. “ Minimal Presentation of Groups” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Najar Singh in 2009

19. “ On Fuzzy Bitopological Spaces” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Kannu Kochhar in 2009

20. “ Some Relation modules of Finite Groups” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Rajni Goyal in 2009

21. “ Compactness in Bitopological spaces” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Gaurav Jindal in 2009

22. “ Projective and Injective Modules “Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Sumit Garg in 2009

23. “ On Semi-homeomorphism in Topological spaces” Submitted to Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Sushma Sharma in 2009

24. “ Relative Relation modules of Finite groups” Submitted for Maharishi Markandeshwar University (Mullana), Ambala, Harayana, by Bharti Thakur, June,2010

25. Some Common Fixed point Theorems in Metric Spaces” Submitted for Maharishi Markandeshwar University (Mullana), Ambala, Harayana by Rualjit Kaur in June, 2010

Abroad Visit:

1) Visited Bulgaria on September, 2016 to present research paper in the international conference at Sofia, Bulgaria from 2-3, September 2016 under UGC travel grant scheme.

2) Visited U.S.A. on July, 2013 to present research paper in the international conference at Las Vegas from 22-25, July 2013 under UGC travel grant scheme.

Extra Responsibilities

Member of Board of Studies in Mathematics (UG) of Guru Nanak Dev University, Amritsar for the period 01-07-2020 to 30-06-2022.
As a Dean Alumni Association of D.A.V. College, Jalandhar Organizes three Alumni meets one in December 14, 2013 second in December 5, 2015 and third in 8th December, 2018.
Completed Major Research Project titled” A Study of intuitionistic fuzzy G-modules” sponsored by University Grant Commission New Delhi. February, 2017.
Supervised Mr. Amit Seghal for Ph.D., on the topic “Study of numbers of different types of subgroups in an Abelian group and generalized Dihedral group”, from NIILM University, Kaithal, Haryana, Degree awarded on 26th November, 2017.
Supervised Ms. Vandana Bansal for Ph.D., on the topic “A study on some aspects of intuitionistic fuzzy Graph Structures, from IKG PTU Jalandhar, final Ph.D. viva voce completed on 2nd December, 2019 and Notification for Ph.D award made on 19th December, 2019.
Supervised Ms Gagandeep Kaur for Ph.D., on the topic “ A study on intuitionistic fuzzy aspects of Rings, Modules and Associated Algebraic structures, from IKG PTU Jalandhar, final Ph.D. viva voce completed on 11th June, 2020 and Notification for Ph.D. award made on 23rd July, 2020.
Supervised Ms. Kanchan for Ph.D., on the topic “A study on intuitionistic L-fuzzy modules, from IKG PTU Jalandhar, final Ph.D. viva voce completed on 12th June, 2023 and Provisional Notification for Ph.D. was made on 13th June, 2023.
Had been a Convener of the Teacher’s Enrichment Workshop (TEW) 2014 on Rings and Modules sponsored by National Centre for Mathematics (NCM) (A joint center of IIT Bombay and TIFR, Mumbai) from 15-21st April, 2014 at D.A.V. College, Jalandhar.
Had been Organizing Secretary of U.G.C. Sponsored National Conference “Recent Trends in Discrete and Fuzzy Mathematics” held at D.A.V. College, from 2th Feb. to 4th Feb., 2013.
Had been Organizing Secretary of U.G.C. Sponsored National Conference “Emerging Trends in Mathematics and Its Applications” held at D.A.V. College , from 4th Feb. to 6th Feb., 2012.
Had been Organizing Secretary of U.G.C. Sponsored National Conference “Recent Trends in Algebra and Analysis” held at D.A.V. College, from 4th Feb. to 6th Feb., 2011.
Had been an expert in Mathematics and Science fair organized by Punjab Govt.

Presently working as Associate Professor at Post Graduate Dept. of Mathematics, D.A.V. College , Jalandhar Under Guru Nanak Dev University since 1994.
Worked as Lecturer in Mathematics in D.A.V. College, Chandigarh under Punjab University from 1993-1994

Area of interest Modern Algebra, General Topology, Discrete Mathematics, Fuzzy topology, Fuzzy Algebra, Intuitionistic fuzzy Mathematics.

Academic Record

Ph.D. (Jamia Millia Islamia University, New Delhi) Thesis Supervisor: Dr. Mohammad Yamin. Thesis synopsis: "Some Relative Relation Modules Of Finite Groups", 1993.

M.Sc. (Mathematics, 1988) (D.A.V. College, Jalandhar, under Guru Nanak Dev University) (First Division)

B.Sc. (Non-Medical, 1986) (D.A.V. College, Jalandhar, under Guru Nanak Dev University) (First Division)