When it comes to selecting an optional subject, the situation is dicey; an aspirant has to look over certain aspects. An aspirant can be confused while trying to figure out what subject to choose and how to choose. Things like whether the subject is scoring, is it easy, is coaching available for the subject, can the subject be studied at home, and other such things have to be taken into consideration before opting for an optional subject.

So aspirants have started to follow the rule of thumb, which is that the aspirant should have background knowledge of the subject they are opting for. If an aspirant has graduated with mathematics and has a keen interest in it, then they should opt for it. Without prior knowledge of mathematics, if one opts for it as optional, they might face many difficulties. So a graduate-level knowledge of an optional subject in the UPSC civil service exam is a must.

### Mathematics as Optional Subject

Mathematics is one of the optional subjects that aspirants can choose. The optional subject is mandatory for the UPSC mains after an individual clears the prelims. Mathematics optional consists of 500 marks, which is divided into 250 marks each for Mathematics Paper-Ⅰ and Mathematics Paper-Ⅱ. So we are going to discuss the source material for mathematics for UPSC, and some strategies to study the mathematics syllabus.

#### Mathematics Paper-Ⅰ Syllabus

**#.** Linear Algebra

**#.** Calculus

**#. **Analytic Geometry

**#.** Ordinary Differential Equations

**#.** Dynamics and Statics

**#.** Vector Analysis

#### Mathematics Paper-Ⅱ Syllabus

**#.** Algebra

**#.** Real Analysis

**#.** Complex Analysis

**#.** Linear Programming

**#.** Partial Differential Equations

**#.** Numerical Analysis and Computer Programming

**#.** Mechanics and Fluid Dynamics

### Book List for UPSC Mathematics Optional

Listed below are some of the best reference books available for mathematics optional. Some books in the list are recommended for both Paper-Ⅰ and Paper-Ⅱ.

#### Books for Mathematics Paper-Ⅰ

**#1.** Linear Algebra

**#.** *Schaum Series* – Seymour Lipschutz

**#.** *Linear Algebra* – K. C. Prasad, K. B. Datta

**#2.** Calculus

**#.** *Mathematical Analysis* – S. C. Malik and Savita Arora

**#.** *Differential Calculus* – Shanti Narayan

**#3.** Analytic Geometry

**#.** *Analytic Geometry* – Shanti Narayan and P. K. Mittal

**#.*** 3-D Geometry* – P. N. Chatterjee

**#4.** Ordinary Differential Equations

**#. ***Differential Equations – Golden Series* – N. P. Bali

**#. ***Ordinary and Partial Differential Equations* – M. D. Raisinghania

**#5.** Dynamics and Statics

**#. ***Dynamics, Statics and Hydrostatics* – M. Ray

**#. ***Dynamics and Statics *– Krishna Series

**#6.** Vector Analysis

**#. ***Schaum Series* – Murray R. Spiegel

**#.** *Vector Analysis* – Shanti Narayan, P. K. Mittal

#### Books for Mathematics Paper-Ⅱ

**#1. **Algebra

**#. ***Contemporary Abstract Algebra* – Joseph Gallian

**#. ***Abstract Algebra (Group and Ring Theory) *– R. Kumar

**#2. **Real Analysis

**#. ***Real Analysis* – H. L. Royden

**#. ***Mathematical Analysis* – S. C. Malik and Savita Arora

**#3. **Complex Analysis

**#. ***Complex Analysis* – G. K. Ranganath

**#. ***Schaum Series* – Spiegel, Lipschutz, Schiller and Spellman

**#4. **Linear Programming

**#. ***Linear Programming & Theory of Games *– S. D. Sharma

**#. ***Operations Research* – J. K. Sharma or Kanti Swarup

**#5. **Partial Differential Equations

**#. ***Ordinary and Partial Differential Equations *– M. D. Raisinghania

**#.** *Advanced Differential Equations* – M. D. Raisinghania

**#6. **Numerical Analysis and Computer Programming

**#. ***Introductory Methods of Numerical Analysis* – S. S. Sastry

**#. ***Numerical Methods* – Jain, Iyengar and Jain

**#.** *Digital Logic and Computer Design* – M. Morris Mano

**#7. **Mechanics and Fluid Dynamics

**#. ***Fluid Dynamics* – M. D. Raisinghania

**#. ***Mechanics and Fluid Dynamics* – Azaroff Leonid, A. P. Mathur

**H3 Strategy for Mathematics Optional Subject**

#### #1. Know Your Mathematics Syllabus

Before you start the mathematics optional UPSC preparation, ensure you go through the whole syllabus and check the topics and chapters. Understand what the topics and what will be asked in the examination are. Once you are familiar with the syllabus, you would know what will be asked, and you would know which topics you have studied in the previous classes, and what more you need to study. You will also be able to jot down the important topics.

#### #2. Practise and Practise the Formulas

Formulas are an integral part of mathematics; many inventions, discoveries, and equations are based on formulas. And there is not one, but many formulas one has to understand while studying maths. To excel at any formula, you should solve the problems of one particular concept, and practice every different kind of problem-related to the concept.

This practice will make the formula and the concept more clear for you. You can also try to solve every problem and concept with different possible solutions that could solve it. And never go on without clearing any doubt regarding a formula.

#### #3. Avoid Silly Mistakes

When aspirants are practising the math problems, they get a lot invested in it, and they might note down the wrong number of the sum. Then they would go on to commit the same silly mistake of writing the wrong number in the examination. Even though their whole sum would be right, one wrong number can lead them to lose marks. Or even writing a wrong formula, but attempting the rest of the sum correctly would be wrong. So read carefully, and be attentive while studying.

#### #4. Practice Previous Years’ Question Papers

This is the most crucial step in the preparation for any UPSC examination. Practising the question papers from previous years gives an insight into what has been asked all these years. By solving multiple papers, you will get a hold of which topics are important and which will be asked in the final examination.

You will be able to identify from which topic or chapter most of the questions have been asked. Hence, practising question papers and mock tests are one of the ways for UPSC preparations.

#### #5. Manage Your Time

Time is a vital characteristic for examinations, especially in mathematics. You have to solve the whole mathematics question paper, and you have to solve all the problems in the given time. Sometimes students think a lot about answering a particular problem, which is a total wastage of time. Likewise, many students are not able to manage their time in the examination.

So the way out is to practice the question papers from previous years, but it should be done as if you are writing the examination. Keep the time limit of 3 hours for every question paper you practice. It will help you to increase your speed and also you will be able to solve the problems in a stipulated time. Doing so will help you to complete your UPSC exam in the given time.

#### #6. Make Notes for Revision

You would be required to take short notes while studying, because for revision before the day of the examination, you won’t be able to go through all the books. It will be helpful if you take down short notes of the steps involved in solving a math problem. Also, ensure you write down formulas so you can memorise them for the examination. The solving method of a problem is important, but also writing the right formula is essential. Making short notes is going to save you a lot of time during examinations.

##### Conclusion

These book references are some of the best study materials that you can pick out to study for UPSC preparations. These strategies are the best route for you to be well-prepared for the examination. Ensure you follow these book references and the tips. To aid your preparations, you can join the online UPSC classes of UPSC Pathshala. UPSC Pathshala provides the best learning experience and best source material. Attend their free demo session to decide for yourself.

Mathematics is considered a tough subject but this article has made it easy for all the candidates by providing everything wrapped in one format. Do you guys want to ask anything related to the optional subject of UPSC?