What Is the Scope of Mathematics?

Written by Coursera Staff • Updated on

Studying mathematics can provide a base to combat real-world problems. It is essential in many fields, from reaching Mars to flying planes, forecasting the weather, or interpreting data.

[Feature image] A girl is writing mathematical formulas on a blackboard.

Mathematics can be described as fun, creative, logical, analytical, rewarding, challenging, and mind-developing. Career and education-wise, mathematics has many specialisations and job opportunities. In this article, learn what mathematics specialisations are available and what career options you can choose if you study them. 

Specialisations in mathematics

Several universities offer associate, bachelor's, and master's degrees in mathematical sciences. You can also pursue a PhD in mathematics. Here are some of the important specialisations you can study.

Applied mathematics

This specialisation requires a solid command of mathematics and a foundational understanding of other courses, emphasising real-world issues and applying mathematical methods in various fields, such as medicine, computer science, finance, physics, engineering, biology, and business. 

Applied mathematics uses numerical and data analysis, modelling, algorithm creation, and simulations to investigate the relationships between mathematics, science, and our environment. Physicists, geologists, engineers, and technologists are among the top applicators of applied mathematics to solve complex problems concerning the planet.

Geometric analysis

Geometric analysis focuses on solving problems based on analytic and geometric concepts and has its foundations in calculus and differential equations involving curves. This specialisation includes concepts of Hodge theory, the Laplace equation on compact manifolds (existence, Sobolev spaces, Schauder estimates, uniqueness), elliptic equations (Fredholmness), Riemannian geometry (metrics, curvature, usual coordinates, Levi-Civita connection, Riemannian volume form, geodesics), and other concepts. 

The multiscale scope of mathematics of geometric analysis is in approximation theory, mathematical analysis, particle physics data analysis, statistical signal processing, computer vision, astronomical catalogues, medical imaging, and materials science.

Computational mathematics

Computational mathematics lets you learn the fundamentals behind running the internet, technologies, scientific theories, and their applications as it blends maths and computer science. Computer manufacturing, the creation of algorithms, and numerous other processes require mathematics. For instance, bioinformatics, a field of biology and technology, relies on computer and mathematical calculations to predict protein structures, create real-world simulations, and calculate flux operations. 

Discrete mathematics

Discrete mathematics teaches skills like formal proof combinatorial analysis, software engineering, and algorithmic analysis by practicing concepts like linear recurrence relations, mathematical induction, discrete probability, and counting principles. Learning this specialisation can equip you to make applications in many fields, including molecular biology, computer science, industrial technology, cryptography, and electrical engineering. 

In discrete mathematics, you need the accuracy of mathematical notation and procedures to devise the performance of a computer system, demonstrate its specifications, or figure out its efficiency. It combines computer science and mathematics to utilise sets, orders, functions, sequences, and other mathematical objects to decode problems, an essential step in solving them.

Careers in mathematics

Use the following list to explore the career options available when studying mathematics. 

Actuary

Average annual salary: ₹11,25,000 [1]

Primarily working on statistics, actuaries deal with risks by creating policies to combat and minimise problems. Involving finances, actuaries can have a variety of responsibilities.  Mathematics is a standard prerequisite to becoming an actuary.

Market researcher

Average annual salary: ₹8,60,000 [2]

Market research, which involves analysing data, interpreting statistics, and reporting results, requires multiple mathematical approaches for accurate prediction. In this role, you will gather data from customers and competitors through polls, interviews, research, and survey groups to help companies optimise their marketing strategies.

Accountant

Average annual salary: ₹15,96,000 [3]

Becoming an auditor or accountant is another profitable mathematics career opportunity. It requires financial reports for organisations and institutes in the government and private sectors. Becoming an accountant requires a passion for numbers and the ability to use them appropriately, and it requires a course on chartered accountancy or business. 

Cryptanalyst

Average annual salary: ₹12,39,794 [4]

Understanding computer processes requires a knowledge of mathematics. Both ethical and unethical hacking require mathematical expertise and knowledge. Becoming a cryptanalyst is a legal and moral way to apply mathematics. Hackers can be found in government and privately owned companies involving police, military, and IT companies. 

Insurance underwriter

Average annual salary: ₹6,30,000 [5]

An insurance underwriter’s responsibilities include evaluating, analysing, and assessing risk using statistics and probability. Working with risk and approximation, you would decide on acceptance and quantity of interest in this role.

Investment Analyst

Average annual salary: ₹13,40,979 [6]

An investment analyst monitors a company's stocks, financial data, trends, accounts, and other relevant data. In this role, you would research and analyse trends so that you can advise your employer or client on strategic investment opportunities.

Statistician

Average annual salary: ₹4,25,000 [7]

Statisticians are widely required in health care, agriculture, ecology, census boards, media, and insurance industries. Using statistics, they interpret data to produce approximate numbers, a base for applying and implementing organisational strategy. 

Learn mathematics with Coursera

Some students find mathematics fun and complex, while others find it challenging. However, many technical and non-technical fields rely on mathematical calculations to decide their following action. An online educational platform can be a perfect solution for students interested in maths. On Coursera, you can explore various courses and advance your knowledge. Stanford University’s Introduction to Mathematical Thinking course and others will help you acquire profound knowledge to expand your skill set. 

Article sources

1

Glassdoor. “ Salary: Actuary, https://www.glassdoor.co.in/Salaries/actuary-salary-SRCH_KO0,7.htm.”Accessed March 8, 2024.

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