Difference Between Applied Mathematics and Mathematics for Class 11th and 12th CBSE

Summary: Mathematics is an essential subject across all boards of education in India. CBSE and other board students must know the difference between applied mathematics and mathematics, which is crucial in selecting either one for their CBSE class 11th and 12th! 

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

Mathematics helps students to explore future career options after graduating from school. It has been observed that the mathematics syllabus, which is meant for science students, is not very helpful for students pursuing commerce or humanities streams. 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 think logically. In contrast, Applied mathematics enables you to understand essential mathematical and statistical tools and their applications in the Commerce and social sciences field. 

Check the difference between Applied Mathematics and Mathematics:

Feature	Applied Mathematics	Mathematics
Focus	Solves real-world problems across various fields	Develops and explores underlying mathematical principles and theories
Applications	Physics, Engineering, Finance, Computer Science, Biology, Economics	Abstract problems within mathematics itself
Skills Used	Strong foundation in core mathematics, computational skills, and ability to model real-world phenomena	Problem-solving, logical reasoning, proof construction
Courses	Numerical Analysis, Statistics, Operations Research, Mathematical Modelling	Abstract Algebra, Topology, Real Analysis, Number Theory
Outcome	Practical solutions to real-world problems	Deeper understanding of mathematical structures and relationships

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Difference Between Applied Mathematics and Mathematics Topics

The mathematics syllabus is aligned very well to help you with the science stream. In contrast, the applied mathematics syllabus aligns with 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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Difference Between Applied Mathematics and Pure Mathematics Applications

Pure mathematics is used to solve mathematics-related problems, and applied mathematics is used to answer questions related to various fields, such as 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.

Mathematics is crucial in understanding and exploring physics and engineering concepts. Applied mathematics includes numerical analysis, information theory, continuous modelling, 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 has practical applications in day-to-day life, while pure mathematics is the study of principles without much practical application.

Difference Between Applied Mathematics and Mathematics Career Options

Let's look at the detailed career options for pure and applied mathematics and choose the one that best suits your interests in CBSE classes 11 and 12.

Applied Mathematics

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

Career	Average Fresher Salary
Accountant	₹1.2 Lakhs
Computer programmer	₹1.0 Lakhs
Engineer	₹4.3 Lakhs
Investment manager	₹2.8 Lakhs
Lawyer	₹1.2 Lakhs
Theoretical mathematician	₹ 7 Lakhs
Numerical analyst	₹ 2.1 Lakhs
Teacher	₹ 3.3 Lakhs
Market Researcher	₹ 4.2 Lakhs
System Analyst	₹ 3 Lakhs
Statistician	₹2.0 Lakhs
Government Jobs	₹3.2 Lakhs

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Mathematics

If you opt for mathematics in your secondary education, you can pursue a graduation in the scientific field. Below are some of the top career options for a mathematics student -

Career	Average Fresher Salary
Professor	₹2 Lakhs
Statistician	₹2 Lakhs
Mathematician	₹8 Lakhs
Data Analyst / Business Analyst	₹2.1 Lakhs
Chartered Accountant	₹10 Lakhs
Investment Banker	₹3 Lakhs
Data Scientist	₹4 Lakhs
Astronomer	₹7 Lakhs
Programmer/ Software Engineer/ Blockchain Developer	₹2 Lakhs
Economist	₹2.5 Lakhs

Let us look at the organizations that offer jobs in 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 Easy, Applied Mathematics or Mathematics?

Generally, depending on the area of individual interest, the easiness of the mathematics and applied mathematics subjects depends. Knowing the difference between mathematics and applied mathematics can help you better understand which is the most challenging 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 a science graduate, 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, the differences between Applied Mathematics and Mathematics are distinct yet complementary. Applied Mathematics involves applying mathematical principles and theories to solve real-world problems, while Pure Mathematics studies the underlying principles and theories of mathematics. Both fields are essential to understanding the world and are important components of a well-rounded education.