11-12-2023

# Mathematics in PU: Pure Math vs. Applied Math

Pre-university Course (PUC), quite often addressed as PU is a senior secondary education in the state of Karnataka is the same and ranks equivalent to 11th and 12th of CBSE, DP1, and DP2 of the International Baccalaureate Programme. Your first ever chance to opt for the subject comes after your 10th and this very concept is fruitfully efficient for streamlining your preferred career path at a considerably young age. However, selecting a stream out of all the options can sometimes turn up to you as a hurdle too, if your interests are still unidentified and scattered. Mathematics is an integral subject for many careers as well as higher studies and in PU (only in Karnataka), students are left with two choices in the same subject, pure math and applied math respectively. Let us understand both subject divisions and their subject structure in detail.

**Pure Math vs. Applied Math**

Pure math is that stream of mathematics that exclusively focuses on abstract concepts, complex theories, and derivations of universally accepted formulas and equations. An ideal example to make the subject index clear would be the research and study behind graphs, quadratics, arithmetic theories, trigonometry, and so on. In short, pure math aims at solving problems based on mathematical formulas and not on problems based on real-life problems. Additionally, pure math is extensively used in the research field and can lack spontaneous practical-solving problems.

Applied Mathematics is a vast field majorly focused on the application of various mathematical equations and theorems to solve real-world problems in different fields. The applicative nature of the subjects makes it highly integrative and collaborative and this ranks among the top reasons for math being an unavoidable factor in subjects like physics, chemistry, biology, accounting, finance, medicine, business, and so on. Applied math is always high in demand for its problem-solving nature and for the practicality and logical reasoning it brings alone. Your PU course stream provides an option to choose applied math, and the topics listed below will be your course structure for 1st and 2nd PUC Applied Math.

**Pure Math vs. Applied Math: Course Duration and Eligibility**

Both the courses of Pure Math and Applied Math for PU have been designed for 2 years (4 Semesters). These two years are inclusive of theoretical and practical subject coaching and assessments.

**Eligibility criteria for Pure Math: **10th Grade completion with a percentage falling under the cut-offs as listed by the University.

**Eligibility criteria for Applied Math**: 10th Grade completion with a percentage falling under the cut-offs as listed by the University.

**Pure Math Vs Applied Math: Course Curriculum**

The course curriculum of both streams of math covers a wide range of topics and they are as follows:

**Topics included in Pure Math for Pre-University**

Sets, Sets- Relations and Functions, Trigonometric Functions, Principle of Mathematical, Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequence and Series, Straight Lines, Conic Section, Introduction to Three-dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vectors, Three Dimensional Geometry, Linear Programming, Probability.

**Topics included in Applied Math for Pre-University**

Numbers, Quantification, and Numerical Applications, Algebra, Mathematical Reasoning, Calculus, Probability, Descriptive Statistics, Basics Financial, Mathematics, Coordinate, Geometry, Algebra, Calculus, Probability, Distributions, Inferential Statistics, Index Numbers and Time-based data, Financial Mathematics and Linear Programming.

**Pure Math vs. Applied Math: Career Opportunities**

**Pure mathematics:**

**Mathematician:**Uses mathematical principles and formulas to find out new derivations and solve world-concerning problems in different industries**Statistician:**Understands and analyses large sets of data to draw meaningful predictions and analysis- Actuary: Understands and analyses the financial risk by making use of previously learned mathematical principles and theories
**Data scientist:**Uses data and analyses it with the help of statistical principles to research the future market and world conditions**Software engineer**: Engages in using engineering principles and mathematical knowledge in building user-helping software and applications

**Applied mathematics:**

**Engineer:**Uses the principles of physics and mathematics to understand real-world problems and provide solutions to the same**Physicist:**Specialises in the field of physics and makes use of mathematical formulas to solve problems**Economist:**Applies theories of economics and mathematics to study the relationship between society’s resources and production capacities**Financial analyst:**Analyses and performs metric ratios to make and overlook to make investments to yield revenue**Data scientist:**Analyses and evaluates data to formulate valuable insights

**Which course might be the perfect fit for you?**

Now, having understood the differences, similarities, and also the varied topics that are being covered under each subject, it must give you a clearer understanding of which subject aligns more with your passion and interest.

Your choice of stream in PUC should always be based on your career preference and interests. Opting for subjects in this manner has two benefits, one is that you get deeply educated in the field which further helps you with a good foundation for your chosen career field. Second, you will be clear as to how this subject might not be working for you, which in effect lets you think more and explore other areas.

In case you are worried about the career scopes of each field (Pure Math and Applied Math), then here are some career options that you can consider giving a try or where these subjects are incorporated.

**In Short**

To conclude, both Pure Math and Applied Math are very rewarding and full of scopes in terms of career aspects. However, it is vital to know that choosing a subject of your interest and passion is necessary to succeed in the prospective field. It is recommended to have an engaging conversation with a career counsellor or the respective teacher of the subject if you are feeling stuck and clueless about opting for the subject for your PUC.