Difference Between Applied Mathematics and Mathematics

Summary: Mathematics is an important subject across all boards of education in India. CBSE and other board students are required to know the difference between applied Mathematics and Mathematics explained in this article! 

The Central Board of Secondary Education introduced applied mathematics as one of the optional subjects in the CBSE class 11 and class 12 curriculum.

To keep studying maths, you must choose between applied mathematics and mathematics. 

This post provides detailed information about the difference between Applied Mathematics and Mathematics.

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Difference Between Applied Mathematics and Mathematics

Check the difference between Applied Mathematics and Mathematics:

Parameters	Applied mathematics	Mathematics
Definition	It is the application of mathematical methods by various fields such as Physics, Engineering, Medicine, Business, Computer Science, etc	It is the study of topics like quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis)
Applications	Algebra, geometry, number theory, differential or integral calculus	Physics, biology, business, economics
Career Options	Accountant, Computer programmer, Engineer, Investment manager, Lawyer, Theoretical mathematician, Numerical analyst	Academic institutions and research institutes, aerospace and transportation equipment manufacturers or service providers, Analytics and forecasting organizations, Chemical or pharmaceutical manufacturers, Communications services providers, Computer information and software firms, Consumer products companies, Energy systems firms
Difficulty Level	Easy	Moderate

Difference Between Applied Mathematics and Mathematics

Mathematics helps students to explore future career options after graduating from school. It has been observed that the syllabus of mathematics, which is meant for science students, is not much helpful for students pursuing Commerce or Humanities. Hence, CBSE has added applied mathematics to the academic syllabus as an elective subject.

Mathematics helps you to acquire knowledge and critical understanding and to develop a positive attitude to think, analyze, and lucidly logically. In contrast, Applied mathematics helps you understand basic mathematical and statistical tools and their applications in the field of Commerce and social sciences. 

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Topic-Based Difference Between Mathematics & Applied Mathematics

The mathematics syllabus is aligned very well to help you with the science stream. In contrast, the applied mathematics syllabus is aligned for those who choose the commerce, science, or humanities stream.

You can compare Mathematics & Applied Mathematics topics from the table below to better understand their differences.

Mathematics	Applied Mathematics
Sets and Functions	Numbers, Quantification and Numerical Applications
Algebra	Algebra
Coordinate Geometry	Mathematical Reasoning
Calculus	Calculus
Mathematical Reasoning	Probability
Statistics and Probability	Descriptive Statistics
Relations and Functions	Basics of Financial Mathematics
Vectors	Coordinate Geometry
Three Dimensional Geometry	Inferential Statistics
Linear programming	Index Numbers and Time-based data
	Linear Programming
	Financial Mathematics

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Application-Based Difference Between Pure Mathematics & Applied Mathematics

Pure mathematics is used to solve problems related to mathematics, and applied mathematics is used to answer questions related to various fields like physics, biology, economics, etc.

The problems and theorems that directly challenge pure mathematics can appear in fields such as algebra, geometry, number theory, differential or integral calculus, etc. In contrast, applied mathematics adopts problem solutions or proven theorems to apply them in other fields such as physics, biology, business, etc.

It is known that without mathematics, neither physics nor engineering would be possible. The application of applied mathematics includes numerical analysis, the mathematics of engineering, information theory, continuous modelling, information theory, game theory, and cryptography.

Pure mathematics involves using pure numbers, while applied mathematics involves quantities such as numerical values and units of measurement. Applied mathematics is used in practical applications in day-to-day life, while pure mathematics is the study of principles without much practical application.

Career Difference Between Applied Math and Mathematics

Let us look at the detailed career options for pure and applied mathematics and choose the one per your interest in the CBSE classes 11 and 12.

Mathematics

You can pursue graduation, business, science, etc. if you opt for mathematics in your secondary education school. You can enter into the following fields with mathematics.

• Accountant
• Computer programmer
• Engineer
• Investment manager
• Lawyer
• Theoretical mathematician
• Numerical analyst
• Teacher
• Market Researcher
• System Analyst
• Statistician
• Government

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Applied Mathematics

Let us look at the organizations that offer jobs in applied mathematics.

• Academic institutions and research institutes
• Aerospace and transportation equipment manufacturers or service providers
• Analytics and forecasting organizations
• Chemical or pharmaceutical manufacturers
• Communications services providers
• Computer information and software firms; established or start-ups
• Consumer products companies
• Energy systems firms
• Electronics and computer manufacturers
• Engineering research organizations
• Financial service and investment management firms
• Government labs, research offices and agencies
• Insurance companies
• Medical device companies
• Producers of petroleum and petroleum products

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Which is tough, Mathematics or Applied Mathematics?

Generally, depending on the area of individual interest, the easiness of the mathematics and applied mathematics subjects depends. Knowing the difference between pure maths and applied maths will let you better understand which is the hard subject.

Mathematics

Pure mathematics is abstract and theoretical. It is used to solve problems, find facts and answer questions that do not depend on the world around us but on the rules of mathematics itself. If you are an arts or science graduate, then pure mathematics is easy to learn.

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Applied Mathematics

The activity of applied mathematics is intimately connected with research in pure mathematics. It is better than pure mathematics because it uses the formulas of pure maths and applies them in real life. Applied maths tries to model, predict, and explain things in the real world. 

Applied maths is easy for students who are strong with engineering concepts. You can learn applied mathematics just as easily if you can learn new words and use them daily.

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Conclusion

In conclusion, Applied Mathematics and Mathematics are two distinct yet complementary disciplines. Applied Mathematics is the application of mathematical principles and theories to solve real-world problems, while Mathematics is the study of the underlying principles and theories of mathematics. Both fields are essential to understanding the world and important components of a well-rounded education.