Updated On : May 2, 2023

*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.

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 |

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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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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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.

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.

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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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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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.

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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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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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.

Frequently Asked Questions

What is the difference between pure mathematics and applied mathematics?

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

Is Applied Mathematics tough compare to Maths subject?

No. Applied mathematics is not tough if you are strong with engineering concepts. Try to learn all the basic formulas of pre maths to become strong in applied mathematics subject. Opting for online coaching will help students to learn applied mathematics easily by sitting at home.

What are the branches of applied mathematics?

Numerical analysis, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography are some of the branches of Applied Mathematics.

What are the topics included in CBSE Applied mathematics?

The following topics are included in CBSE Applied mathematics:

- Numbers, Quantification and Numerical Applications
- Algebra
- Mathematical Reasoning
- Calculus
- Probability
- Descriptive Statistics
- Basics of Financial Mathematics
- Coordinate Geometry