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UPSC Maths Optional Books – All aspirants of the UPSC Civil Services examination need to study Mathematics first for UPSC Prelims General Studies (CSAT) Paper 2. However, the subject gets more advanced only in the optional papers. The difference between the two stages is the medium of the exam and the difficulty level of questions. In the CSAT paper, objective-type Maths MCQs will be asked while in Optional Papers 1 and 2, descriptive problems will need to be answered. Thus, candidates must refer to the entire UPSC Maths optional booklist only after going through the type of topics present in the latest UPSC Mains Syllabus. Another reason why Maths is one of the popular UPSC Mains optional subjects is that it has high-scoring trends of around 300-350 marks on average for both papers.

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List of Maths Optional Books for UPSC

In the UPSC IAS Mains optional subject of Maths, candidates will need to attempt a total of 5 out of 8 questions from both papers. To do that without doubts and confusion, you need to properly understand the official Maths Syllabus for UPSC optional first. Then, go through the list of Best UPSC Maths optional books as recommended by toppers and experts below.

Maths Book For UPSC (Optional Paper-I)

Candidates will need to appear for two papers for UPSC Optional Maths subject. In Paper-I, questions will be asked from topics including Linear Algebra, Calculus, Dynamics and Statics, Vector Analysis, etc. Let’s go through all the topic-wise Maths books for UPSC Mains Optional Paper 1 below.

Best Maths Optional Books For UPSC (Optional Paper 1) 
Maths Optional Paper-I Topics Book Name Author/Publication Book Description
Linear Algebra Linear Algebra Hoffman and Kunze This book features intuitive introductions and examples to motivate important ideas and to illustrate the use of results of linear algebra theorems.
Schaum’s Outline of Linear Algebra Lipson and Lipschutz This book covers revised chapters and problems on linear equations with applications on computer science, engineering, mathematics , physics, and quantitative analysis.
Calculus Differential Calculus Shanti Narayan, PK Mittal It covers chapter-wise problems on calculus topics with question papers for practice.
Mathematical Analysis SC Malik and Savita Arora A large number of solved examples to illustrate various types of Mathematical Analysis theorems have been included in this book, essential for fundamental concept-clearing.
Analytic Geometry Analytical Solid Geometry Shanti Narayan, PK Mittal This book covers basic to advanced level 2D and 3D geometry concepts with analytical problems for practice.
Ordinary Differential Equations Ordinary and Partial Differential Equations M D Raisinghania It contains chapter-wise practice questions and differential equations of both types for UPSC Maths optional Paper-1, section B.
Dynamics and Statics A Textbook On Dynamics S. Chand This text covers detailed highlights on types of motion, Kepler’s laws, work and equilibrium with solved chapter-wise examples.
Vector Analysis Schaum’s Outline of Vector Analysis Spiegel & Lipschutz It is an expert take on vector analysis with crisp theories, concepts and 450+ fully solved problems for revision.
A Text Book Of Vector Analysis Shanti Narayan, PK Mittal Concepts related to multiplication of vectors by scalars, and both vector algebra and calculus concepts are covered in this book.
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Maths Books For UPSC (Optional Paper-II)

In the UPSC Mains Maths optional paper 2, numerical related to a mix of Mathematical and computational problems. Let’s check out all topic-wise Maths books for UPSC Mains Optional Paper 2 below.

Best Maths Optional Books For UPSC (Optional Paper 2) 
Maths Optional Paper-II Topics Book Name Author/Publication Book Description
Algebra Contemporary Abstract Algebra Joseph Gallian The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings on traditional Abstract Algebra concepts.
Schaum’s Outline of Linear Algebra Lipschutz & Lipson It covers new problems and revised chapters on linear algebra with computer science and quantitative analysis.
Real Analysis Elements Of Real Analysis Shanti Narayan, M D Raisinghania It is one of the best books for Real Analysis concepts with detailed examples and chapter-wise questions.
Real Analysis Halsey Royden It’s a classic text with highlights on theory of functions of a real variable, measure and integration theory and some of the more important and elementary topics in general topology and normed linear space theory
Complex Analysis Complex Variable (Schaum’s Outlines) Spiegel, Schiller, Spellman and Lipschutz It’s a crisp text with expert takes on every complex mathematical and algebra concepts with equation-based problems on Cauchy-Riemann, Taylor and Laurent’s series.
Linear Programming Topics in Linear Programming & Game Theory Lakshmishree Bandopadhyay It’s a research-driven book with chapter-wise explanations and problems on linear programming, transportation & assignment problems.
Partial Differential Equations Advanced Differential Equations M.D. Raisinghania It covers both ordinary and partial differential equations with explanations of each technique and solutions.
Numerical Analysis & Computer Programming Introductory Methods of Numerical Analysis SS Sastry It contains answers to all chapter-end exercises. illustrate algorithms, computational steps or flow charts for many numerical methods.
Mechanics & Fluid dynamics Fluid Dynamics M.D. Raisinghania This text illustrates concepts on fluid dynamics with complete hydrodynamics and boundary layer theory.

Check all the official UPSC Maths Optional Previous Year Papers for practising the most asked questions here!

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List Of Maths Books For UPSC – Download PDF

As you can see above. we have covered an exhaustive list of recommended Maths books for UPSC. You can either bookmark this page or print a copy of the Maths optional UPSC books to remember the names and authors. This list will assist you in keeping track of all the Math books required for UPSC preparation. You can also get some of the best Maths books for UPSC optional in PDF format from the internet.

Download Maths Optional Books for UPSC in PDF!

Tips to Prepare with Maths Optional UPSC Books

Mathematics can be a high-scoring subject if it is prepared structurally and strategically. That is why we have highlighted some key tips that will assist you in covering the Maths optional UPSC books in a more efficient manner, allowing you to utilize most of your preparation time. These strategies can be applied to other books for UPSC as well.

  • Before referring to the UPSC Maths optional books directly, try to have a clear understanding of Maths formulas, shortcuts, and other calculation techniques to use the book materials much more efficiently.
  • Choose all the Maths optional books for UPSC IAS Mains preparation as per your level of comfort and preparation degree. It also means sticking to one book for a topic if you are proficient in it.
  • Go for books that will help you clear the basic fundamentals of each topic with solved examples and practice sets. For instance, refer to Shanti Narayan’s books on Calculus for good example-wise explanations.
  • Linear Algebra, Calculus, Analytic Geometry, and Vector Analysis are some of the basic UPSC Maths optional topics. Choose books that provide detailed solutions on these topics first.
  • Make short handwritten notes of each concept and that formula you grasp during reading a book. Try to practice from that later and apply it in problem-solving.
  • Do not burden yourself with too many books and other external study materials for UPSC Maths. Practice basic concepts first and then solve previous questions from model papers to clear the UPSC IAS Cut Off easily.

We hope that this article could provide you with detailed study information and preparation tips using the best UPSC Maths optional books for Papers 1 and 2. If you want to access such subject-oriented study materials and resources for UPSC or equivalent administrative exams, download the Testbook App now or enroll in our UPSC Online Coaching program for an extra edge of confidence in learning and solving.

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UPSC Maths Books – FAQs

Which book is best for UPSC Maths optional?

You can check out this article for the entire list of best Maths optional books for UPSC IAS exam. Some of the best names are -Linear Algebra by Hoffman and Kunze, Differential Calculus by Shanti Narayan, PK Mittal, Analytical Solid Geometry by Shanti Narayan, Ordinary and Partial Differential Equations by M D Raisinghania, Real Analysis by Halsey Royden.

How should I prepare for Maths optional in UPSC?

First go through the complete paper-wise UPSC Maths optional syllabus. Then, refer to all the Maths optional books provided here for each topic and revise them thoroughly. Once done, solve as many problems and questions as you can from mock paper, PYPs, and practice sets for good preparation.

What level of Maths is required for UPSC optional?

You need to be proficient in undergraduate or advanced level Maths to answer questions on GATE or JEE-level Mathematical Algebra and Calculus concepts. Thus, you can choose Maths if you have an educational background in B.Sc Maths or B.Tech.

Is Vajiram and Ravi good for UPSC Maths optional?

Yes, the study materials on Maths optional from Vajiram & Ravi are trusted by aspirants for conceptual clarity. Testbook Supercoaching on UPSC Optional subject coaching also provides an exclusive Vajiram & Ravi live course on Maths.

What are some of the Maths optional books for UPSC recommended by toppers?

Some of the best topper-recommended UPSC Maths optional books are as follows:Schaum's Outline of Linear Algebra by Lipschutz & Lipson, Linear Algebra by Hoffman and Kunze, Contemporary Abstract Algebra by Joseph Gallian, Analytical Solid Geometry by Shanti Narayan & PK Mittal, Statistical Mechanism by Carson Horg.
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