UPSC Maths Optional strategy by Manan Agarwal (AIR 46)

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UPSC Maths Optional strategy Manan Agarwal (AIR 46)

Topic-wise Source and Strategy for Maths Optional

For the theory part, I referred to standard textbooks and did not use any coaching notes. The textbooks have adequate solved questions for practice as well. For test series simulation, I joined IMS (2020) and Pariksha Ganga (2022). I will also share my topic-wise short notes, Learning Diary and test series copies on Telegram channel. Paper-I




Important Areas

Linear Algebra

Schaum’s Outlines Linear Algebra 4/e

a.Made short notes of each sub-topic

b.Very important to keep revising the short notes

c.Solve a variety of Qs from test series to get a hang of it

a.Orthogonal and

Unitary Matrices

b.Row Echelon Form

c.Change of Basis



Mathematical Analysis by SC Malik and Savita


a.Has very extensive set of Qs to practice

b.Nicely written book with explanations

c.Use Internet videos to help in surface and volume integrals

a.Euler’s theorem for

homogenous functions

b.Taylor Series expansion

c.Beta and Gamma function


Krishna Series Book (2D & 3D)

a.Need to memorise method of solving various types of locus Qs

b.Keep short notes handy

c.Once you get the feel of solving Qs, different shapes will feel repititive

a.Finding asymptotes

b.Radical plane

c.Director sphere

d.Enveloping cone

e.Normal to a conicoid

f.Reduction to std

form algorithm


MD Raisinghania

a.Solve diverse Qs from the book; the book is an ocean, do not get lost in it, avoid solving same type of Qs it will give you fake confidence

b.Also look for old UPSC PYQs in the book, solve all of them

c.I also learnt : In choice-based questions in the exam (Q6,7,8), opt for ODE only after solving entirely in rough because looks may be deceptive!

a.Reduction of order of ODE

b.Reduction to normal form

c.Laplace transform

Statics and


Krishna Series

a.Physics topics can be very easy if you can visualise the


b.Less need to memorise here, it is mostly conceptual

c.Solve recent PYQs as they are getting trickier



Krishna Series

a.Has some overlap with Calculus

b.Mostly logical

c.Memorise the S-F formulae with proof

d.Green’s Theorem and Stokes Theorem Qs can be tricky, need a lot of coneptual clarity regarding surface of integration, etc

a.Curvature and torsion calculations

b.Surface and volume integral

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Important Areas

Modern Algebra

R Kumar books:

a.Group Theory

b.Ring Theory

They have excellent bank of solved questions

a.Here my idea was to master the easier concepts from 10M point of view

b.It is an iterative process : read the theory try to solve the Q – look at the solution repeat

c.Do not waste a lot of preparation time on this; can prioritise other topics but must have enough grasp over easy to moderate questions; keep referring notes to memorise definitions of ring, field, ideals, etc


Real Analysis

Mathematical Analysis by SC Malik and Savita Arora

a.Has very good Q bank

b.Multiple revisions to familiarise with proof methods

a.Memorise all the convergence tests

b.Keep revising the questions and how to solve them

a.Different tests for convergence and where to apply them

Complex Analysis

Krishna Series

a.Simple topic but needs a lot of conceptual clarity

b.Can get lost in the book; keep referring PYQs and Syllabus to filter relevant content

a.Polar form of

Cauchy-Reimann equation


Integral Formula




Krishna Series book

a.Practice and memorise methods of solving

a.Simplex, Dual

Primal and 2Phase Method

(simplified in my

Learning Diary)


MD Raisinghania

a.Solve diverse Qs to get a hang of it

b.BVP problems need to be understood properly; develop your short method of solving in exam, since there is also time

and space constraint

a.Practice is the key

a.Origin of PDE





d.Boundary Value



Analysis and



Higher Engineering Mathematics by Dr BS Grewal, 42nd edition

a.Each method mentioned in syllabus is important

b.Errors are also important


Mechanics and Fluid


MD Raisinghania

a.From Syllabus and PYQ perspective

b.One must know at least basics of every topic

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Manan Agarwal

AIR-46, UPSC CSE 2022