UPSC Mathematics Optional Paper

The optional subject for the UPSC exam is something candidates must elect, which makes it crucial. Usually, an optional paper pertaining to a subject should be chosen based on the candidate’s experience and interest.

So, when it comes to the specific subject of mathematics for the UPSC mathematics optional paper, candidates should have sufficient knowledge about the subject and its syllabus since there are certain advantages of choosing this subject for the optional paper. The optional paper contributes a lot to the overall marks.

Criteria for Choosing UPSC Optional Subjects Mathematics Paper

There are certain criteria that candidates must fulfill for choosing mathematics as the optional paper. These include:

• The candidate should have studied mathematics up to their 12th-grade education and during their graduation.
• The candidate must have sufficient knowledge and interest in the subject and should be well accustomed to the syllabus.

The Last 10 years of Maths optional papers reveals that the examination consists of two papers. Each paper has a weightage of 250 marks, totalling 500 marks on aggregate. The two papers- I and II, focus on different areas of mathematical study.

Question Paper Pattern of Mathematics Optional UPSC

The two papers, Paper I and Paper II, are structured differently from one another as they focus on different areas of focus. Paper-I contains questions related to-

• Calculus
• Linear Algebra
• Analytic Geometry
• Ordinary Differential Equations
• Dynamics & Statistics
• Vector Analysis

Paper-II contains questions pertaining to-

• Algebra
• Real Analysis
• Complex Analysis
• Linear Programming
• Partial Differential Equations
• Numerical Analysis and Computer Programming
• Mechanics and Fluid Dynamics

Therefore, candidates for the upcoming IAS exam should prepare for the examination keeping these many chapters and topics in mind for their optional Mathematics paper.

Also, refer to the following links:

Syllabus for UPSC Mathematics Optional Paper

The syllabus for Paper I contains:

• In the topic for Linear Algebra, vector spaces, linear dependence and independence, dimensions, transformations, Algebra of Matrices, Rank of a Matrix, Symmetric- skew-symmetric matrices, etc., are important.
• For Calculus, real numbers, real variables, limits, continuity, differentiability, mean-value, Curve tracing, definite integrals and so on are required.
• For Analytic geometry, cartesian and polar coordinates in 3D, second-degree equations, reduction, paraboloid, hyperboloid, ellipsoid, etc.
• In ordinary differential equations, formulation of differential equations, first order and first-degree equations, orthogonal trajectory, Laplace and inverse Laplace, 2nd order linear equations, etc., are generally asked.
• In Dynamics and Statistics, rectilinear motion, harmonic motion, constrained motion, catenary, etc., are asked.
• Finally, in vector analysis, scalar and vector fields, differentiation, gradient, curves in space, Gauss and Stoke’s theorems and so on are important.

The syllabus for Paper-II contains:

• In Algebra, Groups, subgroups, cyclic groups, Cayley’s theorem, subrings and ideals, integral domains, quotient fields, principal ideal domains, etc.
• Real and complex analysis, real number analysis, sequences, limits, uniform convergence, partial derivatives of functions, maxima and minima, Taylor’s series, Analytic function, contour integration, singularities, Laurent’s series, etc., are important.
• In linear programming, basic, optimal, duality, transportation, etc., are crucial.
• In partial Differential equations, the family of surfaces in 3D, Cauchy’s method of characteristics, the equation of a vibrating string, the Laplace equation, etc., are important.
• In numerical analysis and computer programming, numerical methods of algebraic and transcendental equations, Regula-Falsi, Newton-Raphson methods, interpolation, Lagrange’s interpolation, etc., are required.
• Finally, in mechanics and fluid dynamics, generalised coordinates, Hamilton equations, the moment of inertia and so on are important.

For detailed IAS Maths Syllabus, candidates can visit the linked article.

Is Mathematics a good optional for UPSC?

Of course, it is! There are certain unique advantages to choosing Mathematics as an optional UPSC question paper. These include:

• A more or less static syllabus
• Objective questions
• Generally easy and logic based questions
• Less competition

So, these were some highly important information pieces about the optional Mathematics paper in the UPSC exam. Start practising, and all the best!

Take inspiration from the preparation strategy of IAS Toppers from the past and prepare for the upcoming UPSC CSE.

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