Math optional Books and syllabus for UPSC Exam

In India, for selecting the candidates to the various higher posts, students have been selected through the UPSC exam. Math Books and syllabus UPSC Exam is one of the prerogative exams of the nation that permit the candidates to select the optional subject according to their desire.

Maths optional for UPSC is selected by a lot of students for exam. Students with math and physics backgrounds prefer to choose math as an optional subject. Maths optional for UPSC is best suitable for people who are good with numbers. Maths optional syllabus is not so vast. This subject highlights the important facts and figures and there is a high chance that you can get higher marks by selecting it as an optional subject.

If an aspirant is willing to choose math as an optional subject, he needs to have studied math in graduation. Math to only class 12 is not suitable. If you have interest in math and have a strong grip in solving mathematical equations then you must choose math as an optional subject in the UPSC exam.

There are two papers of math in the UPSC Exam. Each paper contains 250 marks total of which comprises 500 marks. There are many fruitful advantages of appearing in the UPSC Exam. You can easily gain the seat of lecturer in college. You can become an IAS officer and many more achievements. So it’s important to choose the optional subject according to the background.

This short article is all about the complete maths optional syllabus for upsc and maths optional books for upsc exam which will surely help you in preparation. Completely go through this article and enhance your knowledge.

Books To Refer for Maths optional

There are a lot of books available in the market that you could refer for maths optional. Maths optional books for UPSC can be helpful in understanding various concepts and topics. These books can be very helpful for you in getting the desired result in the examination. Maths optional upsc books are a great way to enhance your knowledge about the maths optional for UPSC exam.

Books for Maths optional Paper 1

  • Calculus – Shanti Narayan Integral Calculus
  • Vector analysis – Shanti Narayan
  • Ordinary Differential EQs:- MD Raising Lumina, Golden series-NP Bali
  • Linear Algebra – K.C. Prasad, K B Datta
  • Dynamics, Statistics, and Hydrostatics – M.Ray
  • Linear Algebra – Schaum Series (Lipshutz) or Sharma and Vashisth

Books for Maths optional paper 2

  • Real Analysis – Shanti Narayan, Royden
  • Mechanics & Fluid dynamics – AP Mathur, Azaroff Leonid
  • Numerical analysis and Computer Prog. – V. Rajaraman, SS Shastri
  • Algebra – K C Prasad, KB Datta
  • Complex Analysis – GK Ranganath
  • Linear Programming – S D Sharma
  • Partial Diff.eqs. – Singhania

Other important books for Maths Optional

  • Matrices – Schaum Series (Frank Ayres) or Vashisth
  • Modern Algebra – A. R. Vashisth
  • Coordinate Geometry – R. L. Soni
  • Algebra – J. N. Sharma and S. N. Goyal
  • Complex Analysis – Schaum Series or J.N. Sharma
  • Analytical Solid Geometry – Shanti Narayanan
  • Calculus – I. A. Menon
  • Numerical Analysis – S.S. Sastry

Math Optional Syllabus   Paper- I

Here I have described section A for the math optional paper. It includes three main sections.

Linear algebra


Analytical geometry

1: Linear Algebra

This section of linear algebra includes linear dependence and independence, vector, space, dimensions, bases, finite dimensional vector spaces.

It also includes a theorem which is Cayley-Hamiliton theorem. Rest of the syllabus includes row and column reduction, matrices, matrix of linear transformation, reduction to canonical form, congruence, orthogonal, rank, symmetrical, skew symmetric unitary.

2: calculus:

The syllabus for calculus includes asymptotes, maxima and minima, limits, real numbers, indeterminate forms, differentiability, continuity, Taylor’s theorem with remainder, mean value theorem.

It also includes functions of several variables. The functions involve: maxima and minima, partial derivation, continuity, differentiability, Lagrange’s method of multipliers. 

It also includes Riemann’s definition of definite integrals, infinite and improper integral, indefinite integrals, beta and gamma functions.

For evaluation techniques there involves double and triple integrals.

Center of gravity, area, surface and volume are also included in the optional syllabus of math. 

3: analytical geometry:

The syllabus for analytical geometry includes second degree equations for two or three dimension, the minimum distance between two skew lines, sphere, cylinder, cone, pane, ellipsoid, paraboloid, and properties of hyperboloid, straight lines, and reduction to canonical forms.

Math Optional Syllabus   Paper- II

The section A of paper II includes 4 main sections:


Real analysis

Complex analysis

Linear programming

1: Algebra:

This section of algebra includes various groups and their subgroups. It also includes homomorphism of groups, normal subgroups, permutation groups, Sylow’s group, Cayley theorem, principal ideal domains, Euclidean domain and unique factorization domain, rings and ideals. Finite fields and field extensions are also included in it.

2: real analysis:

The syllabus for real analysis section includes ordered sets, ordered fields, real number system, real number system as an ordered field, bounds, real number system, completeness, Cauchy sequence, properties of continuous function on compact sets, continuity of functions, and uniform continuity of functions.

Improper integrals, Riemann integrals, series of  complex and real numbers, conditional and absolute convergence of series of complex and real numbers, rearrangement of series.

The syllabus also includes Continuity and uniform convergence, Integrability and differentiability for the series and sequence of function.

Change in the alternative of partial derivatives, differentiation of function of variables, maxima and minima, functional theorem, multiple integrals.

3: Complex analysis:

The syllabus for complex analysis includes Cauchy’s integral formula, Cauchy’s theorem, Cauchy Riemann equations, analytic function, Cauchy’s residue theorem, power series, Laurent’s series, Taylor’s series, and contour integration.

It also includes bilinear transformations, conformal mapping.

4: linear programming:

The syllabus for linear programming section includes basic solution of linear programming problems, optimal solution, basic feasible solution, simplex method for solution, graphical method for solution.


Assignment problem

Transportation problem

Travelling salesman problem


Maths is a subject that is considered tough by a lot of people. But for UPSC, many people choose upsc only because of their fondness for numbers and interesting topics. Passing maths optional for upsc is not a big deal. Maths is not a tough nut to crack. With the help of maths optional books for upsc you can study every single topic. With hard work and consistency everything is possible. All you need is a strategic plan and proper execution of those plans.

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