Have you started your UPSC IAS exam preparation yet? Are you apprehensive about UPSC maths optional syllabus? Have you found the right resources that can give you the right materials to study for the IAS exam? Can’t decide which sources to believe when it’s coming about choosing the right kind of material? Well, calm down! We have got your back here.

Here in this article, you are going to get a complete list of UPSC maths optional books that too as per the UPSC maths optional syllabus. Read the article till the end to find important web links that will definitely help you prepare for the upcoming IAS exam.

Maths as an UPSC Optional Subject

Selecting the correct optional subject for UPSC Mains is a critical decision for all UPSC candidates. A good rule of thumb is to choose a subject in which you have some academic experience and a true interest. Other considerations to consider in picking the Optional Topic include the subject’s prior performance in UPSC, the time needed to prepare the subject, the subject’s input to the General Studies syllabus, and the tutoring available in the subject.

First and foremost, a candidate must have studied mathematics during his or her undergraduate studies. Even if one has done well in mathematics up to 12th grade, it is insufficient for UPSC Mains.

Second, an applicant must have a real interest in the subject, as the curriculum will appear overwhelming to someone who lacks enthusiasm for it. A student with a passion for Maths, on the other hand, will not find creating concepts and practising them difficult at all.

UPSC Maths Optional Books List

Let’s take a look at the recommended UPSC maths optional books. Below is the list divided into Paper 1 and Paper 2 as per the UPSC maths optional syllabus and also divided topic-wise.

Linear Algebra – A.R.Vasishtha

Calculus and Real Analysis – S.C Malik and Savita Arora Shanti Narayana

3-D Geometry – P.N. Chatterjee

Ordinary Differential Equations – M.D. Raisinghania, Ian Sneddon

Vector Analysis – A.R. Vasista

Algebra – Joseph A. Gallian, Shramik Sen Upadhayay

Complex Analysis, Schaum Series – J.N. Sharma, Ponnu Swami

Linear Programming – Shanti Swarup, Kanti Swarup

Numerical Analysis – Jain and Iyenger, K. Shankar Rao, S.S. Sastry

Computer Programming – Raja Raman

Dynamics & Statics – A.R. Vasista

Mechanics and Fluid Dynamics – M.D. Raisinghania, R.K. Gupta, J.K. Goyal and K.P. Gupta

Also Read: Check-out the Complete UPSC Mathematics Optional Syllabus

UPSC Maths Optional Syllabus

Let’s have a look at the UPSC maths optional syllabus before going through the booklist divided into Paper-I and Paper-II.


Linear Algebra


Analytic Geometry

Ordinary Differential Equations

Dynamics & Statics

Vector Analysis



Real Analysis

Complex Analysis

Linear Programming

Partial differential equations

Numerical Analysis and Computer programming

Mechanics and Fluid Dynamics

Books for Mathematics Paper I

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

Calculus – Shanti Narayan Integral Calculus

Differential Calculus

Vector Calculus

Analytic Geometry – Shanti Narayan, HC Sinha, DK Jha and Sharma

Ordinary Differential EQs:- MD Raising Lumina, Golden series-NP Bali

Dynamics, Statistics, and Hydrostatics – M.Ray

Vector analysis – Shanti Narayan

Also Read: Here’s Another List of Books for Mathematics

Books for UPSC Maths Optional Syllabus Paper II

Algebra – K C Prasad, KB Datta

Real Analysis – Shanti Narayan, Royden

Complex Analysis – GK Ranganath

Linear Programming – SD Sharma

Partial Diff.eqs. – Singhania

Numerical analysis and Computer Prog. – V. Rajaraman, SS Shastri

Mechanics & Fluid dynamics – AP Mathur, Azaroff Leonid

Other Important Books for IAS Exam

Modern Algebra – A. R. Vashisth

Algebra – J. N. Sharma and S. N. Goyal

Linear Algebra – Schaum Series (Lipshutz) or Sharma and Vashisth

Matrices – Schaum Series (Frank Ayres) or Vashisth

Calculus – I. A. Menon

Coordinate Geometry – R. L. Soni

Solid Mechanism – Kazmioo

Mathematics Dictionary – James

Differential Equations – Schaum Series (Frank Ayres) or N.M. Kapur or Raisinghania

Numerical Analysis – S.S. Sastry

Complex Analysis – Schaum Series or J.N. Sharma

Operations Research – Kanti Swaroop or Manmohan

Differential Calculus – Gorakh Prasad

Analytical Solid Geometry – Shanti Narayanan

Text Book of Coordinate Geometry – Rai Ballabh

Mechanism – D. S. Mathur

Statistical Mechanism – Carson Horg

Also Read: Here’s The Important UPSC Maths Optional Question Papers

Why Choose UPSC Maths Optional for UPSC IAS Exam?

There are certain factors that work in your favour if you take Maths as your optional subject for the IAS exam. Let’s look at the general advantages one can have by taking maths as his/ her optional subject.


Mathematics is one of the most scoring subjects in the school level, graduation or even the UPSC IAS exam. If one is prepared enough and has written the right answer, there is no scope of getting marks deducted in this subject.

Direct Questions

UPSC maths optional questions are direct type. Most of those are given from the textbooks. Anybody who is prepared well will find those questions to be easy to medium on the difficulty level.


UPSC maths optional syllabus is static. It is not related to current affairs or news thus does not need frequent updating. One just needs to finish the syllabus and prepare that very well.

Preparation Tips for UPSC Maths

If your professors in high school and college advised you that the best way to get good grades was to practise math problems a lot and avoid making dumb mistakes, they were perfectly correct. These are the fundamentals for excelling in mathematics. We’ve put up a list of recommendations to help you do well in the UPSC Mains Maths Optional subject.

Increase Your Practise Time

Practicing gets you faster at fixing issues and improves your speed and efficiency, which will help you perform well on tests.

Avoid Silly Mistakes

Even one erroneous sign or number might cost you a lot of money. To prevent making such foolish blunders, keep cool and concentrated while answering questions. However, a lot of practise will help you prevent such errors. Also, immediately before the exam ends, set aside some time for revision so you may double-check your answers and make any necessary revisions.

Be Systematic

Along with the appropriate solution, presentation is quite important. As a result, write the answer in a neat and orderly manner. Do not rush through any key steps or write the solution clumsily.

Do Not Cram Maths

Maths is a logical topic, therefore don’t try to cram answers or theorems into your head. Simply grasp the logical flow and solidify your notions; this will aid you in solving all types of questions because you will be able to use logic in tests and will not miss any critical steps in the solution.


This is something that any applicant who has Maths as a secondary subject should remember. Mathematical formulae are the foundation of the subject. Prepare a formula page with all of the formulae on it so that you can revise it at any time and from anywhere.


Hopefully, this list of UPSC maths optional books will help you prepare better for the UPSC maths optional syllabus. For more informative posts on this and UPSC maths optional question papers and other UPSC IAS exam-related informative posts, keep an eye on this page. Do share your feedback by commenting in the below box.

Check out the options subject courses on UPSC Pathshala to learn how to tackle a paper.

Also Read : Power of an IAS Officer: What does an IAS Officer Do? Check-out Everything in Detail

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UPSC Maths Optional Books: Expert Suggested Books for UPSC Maths Optional Syllabus
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UPSC Maths Optional Books: Expert Suggested Books for UPSC Maths Optional Syllabus
Are you planning to choose Maths as your UPSC optional subject? If yes, read this post. Here you will find the best books and tips to tackle this optional. Click here to learn more.
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Shilpa is a professional web content writer and is in deep love with travelling. She completed her mass communication degree and is now dedicatedly playing with words to guide her readers to get the best for themselves. Developing educational content for UPSC, IELTS aspirants from breakthrough research work is her forte. Strongly driven by her zodiac sign Sagittarius, Shilpa loves to live her life on her own notes and completely agrees with the idea of ‘live and let live. Apart from writing and travelling, most of the time she can be seen in the avatar of 'hooman' mom to her pets and street dogs or else you can also catch her wearing the toque blanche and creating magic in the kitchen on weekends.

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