Scope of Research in Mathematics

Mathematics is undoubtedly the hardest and the most beautiful discipline, which has always propelled humanity to the inquiry of the unknown. Galileo Galilei said, “Mathematics is the language in which God has written the universe”. Maths isn’t regarded as the favourite subject of many because of its abstractness, complexities and lack of scope for cramming. Moreover, the core mathematics becomes so abstract even in the first year of college that many students drop it as a course in the second or third year. But if you want to pursue it as a career, this blog will be helpful to you.

In this blog, we will discuss:

• Mathematics and Research
• Best Institutes for Mathematics
• What are the Important Exams ?
• Career Opportunities

Mathematics and Research

Mathematics is a broad subject that applies to practically every area. Everything is “glued” by the most important element- Mathematics, whether it be physics, chemistry, biology, geology, economics, history, environmental science, data analysis and management, military research, or computing. Some of the branches of mathematics are: 

• Number Theory: It is the study of numbers, primarily integers, and their relationships.
• Statistics: It is the collection and analysis of data.
• Probability: It is the study of random events and subsequently assigning a value to every event.
• Geometry: It is the study of shape, size, relative positions, and properties of space.
• Logic: It deals with exploration of formal logic in mathematics.
• Combinatorics: It is the study of discrete, countable structures and their properties.
• Calculus: In simple terms, it is the study of continuous change.

Statistics, a branch of mathematics, is the backbone of stock markets, which in turn are the backbones of a country’s economy. Mathematical models assess and manage financial risks in various investment portfolios. Using statistical tools and probability theory aids in predicting market fluctuations and mitigating potential losses. You can’t even imagine the existence of bridges and unique architecture without the mathematical help to the engineers and architects.

Cryptographic algorithms, based on number theory and discrete mathematics, secure digital communications and protect sensitive information from unauthorized access. For example, the RSA encryption and elliptic curve cryptography rely completely on complex mathematical concepts for data protection. Without continuous research and updates to algorithms, you can’t guarantee the proper working of the model.

The MRI (Magnetic Resonance Imaging) and CT (Computed Tomography) scans, which you might have seen in hospitals, also rely on complex mathematical models to give accurate 3-D images of internal body structures. 

These are only a few examples of how extensively mathematical research is used. People devote their whole lives to just proving a single theorem or constructing a statistical model for some predictions. With this vastness, there is a great demand for research in every domain of mathematics. 

Best Institutes for Mathematics

India has been a great hub for mathematical education from ancient times. There has been many great mathematicians from Aryabhatta and Shree Dharacharya to Ramanujan and C.R. Rao. To keep their honor, there are many great institutions that are doing marvelous research in mathematics and providing excellent undergraduate, graduate, and post-graduate education along the way. A few of them are mentioned below:

• Indian Institute of Science, Bangalore
• Indian Statistical Institute (ISI), Kolkata
• Institute of Mathematical Sciences (IMSc)
• Chennai Mathematical Institute (CMI)
• Indian Institute of Technology, Bombay
• Indian Institute of Technology, Kanpur
• Indian Institute of Technology, Madras
• Tata Institute of Fundamental Research (TIFR)
• Indian Institute of Technology, Kharagpur
• Indian Institute of Technology, Delhi

A bachelor’s or master’s degree in mathematics or a related discipline from one of these institutions offers several prospects for students. Doing a PhD is required if you are interested in research. Hence, most graduates apply for PhDs at these institutions or overseas universities. 

What are the Important Exams?

Maths is about the practice and application of abstract concepts in real-world scenarios. There are many examinations at various levels, ranging from Olympiads to the most challenging exam, the Putnam Mathematical Competition. A few of the most important exams are mentioned below:

• IMO (International Mathematics Olympiad): 

It is conducted by the Science Olympiad Foundation (SOF) for students of class I-XII. There are various levels of exams – within the school, then at the city-state level, and then at the international level.

• International Olympiad of Mathematics (iOM):

SilverZone Olympiad organises it for students in classes I to XII.

• National Talent Search Examination (NTSE): 

It is for class X students only. If you qualify for the state-level exam, you get to write at the national level.

• Maths Talent Search Examination (MTSE):

Conducted by the Indian Institute for Studies in Mathematics (IISMA). Mental ability, mathematical reasoning, accuracy, and speed are the main focus of this examination. It’s for students in classes III to IX.

• Mathematics Olympiad (MO) by Homi Bhabha Centre for Science Education (HBCSE):

It has various levels, such as Pre-Regional Mathematics Olympiad (PRMO), Regional Mathematics Olympiad (RMO), Indian National Mathematics Olympiad (INMO), and finally International Mathematics Olympiad (IMO). It is for classes VIII and higher.

• JEE- Mains & Advanced:

These are essential exams to get into the top institutes in India- the IISc and IITs. The mathematics section is usually the toughest among Physics, Chemistry and Mathematics.

• IISER Aptitude Test (IAT):

IAT is similar to JEE Mains and is vital if you want to enter IISERs or IISc. 

• ISI Screening Test:

This is the admission test by the Indian Statistical Institute (ISI). 

• CMI Entrance Exam:

This is the Chennai Mathematical Institute (CMI) admission test. 

There are many other important examinations at various levels. Giving competitive exams strengthens the application of concepts and improves critical thinking skills. Olympiads are generally more challenging than standard school exams, which enhances students’ analytical skills and critical thinking, thus preparing them for higher-level mathematics in colleges and universities.

Career Opportunities

A career in mathematics gives a diverse range of opportunities. Studying mathematics from top-tier institutes in India, such as the Indian Statistical Institute (ISI), Chennai Mathematical Institute (CMI), and the Indian Institute of Science (IISc), can open up a myriad of rewarding career opportunities in research. Graduates from these esteemed institutions possess a strong theoretical foundation and analytical skills, making them well-equipped for various roles in the field of mathematical research. Some promising career paths for mathematics graduates from these institutes include:

• Academic Research and Teaching

You can pursue a career in academia, conducting advanced research in pure and applied mathematics. You can aspire to become a professor or researcher at universities and research institutions, contributing to advancing mathematical knowledge and nurturing the next generation of mathematicians. Mathematics professors are usually in high demand and are paid well in most government institutions.

• Statistical Analysis and Data Science 

With a strong statistics and data analysis background, you can find opportunities in industries such as finance, healthcare, and technology. You can work as a data scientist, statistician, or analyst, utilising your mathematical expertise to extract meaningful insights from complex datasets and contribute to data-driven decision-making processes.

This is an important part of every company or research institution. Hence, you have plenty of job opportunities. Around 50% of graduates from institutes like ISI get placed in this sector with an average salary of Rs.20 LPA

• Operations Research and Optimization

You can pursue careers in operations research, working on complex optimisation problems in industries such as logistics, manufacturing, and supply chain management. Companies like Amazon, DHL, FedEx, Toyota, and others recruit students from the institutes mentioned above. You can apply mathematical modelling and analytical techniques to streamline processes, improve efficiency, and make data-driven decisions that enhance the overall performance of organisations. 

• Scientific Research and Development:

You can pursue research opportunities in interdisciplinary fields such as computational biology, theoretical physics, and engineering. You can collaborate with experts from various domains, contributing your mathematical expertise to solve complex scientific problems and develop advanced technologies that profoundly impact society. Mathematicians are often called upon by research organizations to assist them in resolving problems in their studies. As a result, there are many possibilities to collaborate with various areas while doing your own study.

Conclusion

Mathematics is an exciting subject and if you are interested and passionate about it, it will reward you with beautiful opportunities in both research and industries. Though mathematical research requires more time and mental talent than other types of study, the applications of the research are widespread. But nothing is impossible if you are passionate about something and determined to work hard for it. And who knows, one day you might also get the ‘Nobel Prize in Mathematics’- The Fields Medal.

If you want to know about Biotechnology and how to do research in it, check out this blog.

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