The Civil Services Examination, the creme de la creme of all examinations, is also known as the toughest and the longest examination of India. Therefore, I consider it quite important to share my view points of the bright future of the aspiring candidates.

Though the CSE is a hard nut to crack but one could sail through this 'hurdle race' via strategic planning, consistent efforts, diligence, a patient and calm approach and most importantly with the belief in one's own potential.

The right selection of the optional is the pre requisite of a good rank in CSE. One must choose the optional keeping the following points in mind:

- A subject of your interest.
- Scoring pattern of that subject in past few years.
- The availability of study material and
- Expert guidance.

Ideally, the students should choose their subject of graduation or post graduation as their optional but then one must check their subject for its viability in the civil services examination keeping in consideration the aforementioned 4 points namely Criterion of interest, scoring pattern, availability of study material and expert guidance

As per the above mentioned criteria of choosing optional, Mathematics is one of the safest and most scoring optional in the Civil Services Examination. This is the only subject which allows the students a scope to score as high as 350+ marks in a new pattern of examination with one optional subject. The popular trends show that out of every 20 students, at least one student has Mathematics as one of his or her optional subject. Data shows that before the year 2000, The maximum number of students in the Civil services examination were the students who had taken Mathematics as their optional. However, with the change in the CSE pattern, students have started facing difficulty with mathematics as an optional due to the lack of availability of quality guidance and the confusion created by the labyrinth of false propagandist and mercantile, inefficient and inexperienced teachers.

However since the last few years, the popularity of the subject has increased as expert guidance keeping in view the need of the CSE is available now.

**WHO CAN OPT IT ?**

The students who have studied B.Sc Mathematics/ B. Tech. can take Mathematics as the optional in this examination. In fact, Mathematics is one such optional which gives you the advantage of a much higher score than what one could manage with other humanities subjects and thus, the chances of getting the best ranks are much better. However, there is a certain phobia about choosing Mathematics as an optional amongst the students. Let us examine this problem through an observational analysis of the situation.

We can broadly categorize the science students, especially the ones from the Mathematics background who are aspiring for the CSE, into two categories. The first category is of those students who opt for Mathematics as an optional in this prestigious examination. The second category is obviously those students. who do not opt for it. Talking about the former category, it is a group of self motivated, diligent students who already have a penchant for this subject. This category usually consists of those students who seem to eat, sleep and drink Mathematics. They are highly passionate about this subject and extremely devoted to it. However, It is the latter category of students who encourage me to delve into their mind set and explore the reasons for their decision. What I have discovered about the same is a disappointing fact of these students being beguiled and demotivated by the ''opinion givers of the society. Even the illogical CSE theories created by the mercantile propagandists affects the psychology of these students by enticing them to select inconsequential and irrelevant optionals. Either they are discouraged enough to take the plunge with a safe subject which ultimately results in their sad failure despite rigorous hard work, or else they achieve the results only after investing insurmountable energies and irreversible time on a wrong decision.

I have a message for these students – 'Unleash your potential'; Go for something that channels your expertise in its best direction rather than going for something that has not been your area of excellence and interest. Choose the 'stepping stone' not the 'stumbling block'. Overcome your irrational fears and anxieties and make a prudent decision.

Mathematics is the most advantageous and the highest scoring optional. You have been solving Mathematics questions since elementary school. Think about it; After spending more than 15 years in the field of Mathematics, if you are being manipulated to change your path for an irrelevant option with just 6 months or one year of preparation, you are actually leaving your area of proficiency and are indirectly trying to take up the challenge of competing with the masters of their respective fields.

**Mr.K. Venkanna**

Director, IMS (Institute of Mathematical Sciences)

www.ims4maths.com

**Email:** ims4ims2010@gmail.com

**Contact:** 9999197625, 011-45629987

Section A

**Linear Algebra:** Vector, space, linear dependance and independance, subspaces, bases, dimensions. Finite dimensional vector spaces. Eigenvalues and eigenvectors, eqivalence, congruences and similarity, reduction to canonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skew-hermitian formstheir eigenvalues.

**Calculus:** Lagrange's method of multipliers, Jacobian. Riemann's definition of definite integrals, indefinite integrals, infinite and improper integrals, beta and gamma functions. Double and triple integrals (evaluation techniques only). Areas, surface and volumes and centre of gravity.

**Analytic Geometry:** Sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

**Ordinary Differential Equations:** Clariaut's equation, singular solution.
Higher order linear equations, with constant coefficients, complementary function and particular integral, general solution, Euler-Cauchy equation. Second order linear equations with variable coefficients, determination of complete solution when one solution is known, method of variation of parameters.

**Dynamics, Statics and Hydrostatics:** You can skip this entire section, if you have prepared other sections well.

**Vector Analysis:** Triple products, vector identities and vector equations. Application to Geometry: Curves in space, curvature and torision. Serret-Frenet's formulae, Gauss and Stokes' theorems, Green's identities.

Section A

**Algebra:** Normal subgroups, homomorphism of groups quotient groups basic isomorophism theorems, Sylow's group, principal ideal domains, unique factorisation domains and Euclidean domains. Field extensions, finite fields.

**Real Analysis:** Riemann integral, improper integrals, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions. Differentiation of functions of several variables, change in the order of partial derivatives, implicit function theorem, maxima and minima. Multiple integrals.

**Complex Analysis:** You can skip this entire section, if you have prepared other sections well.

**Linear Programming: **
Basic solution, basic feasible solution and optimal solution, Simplex method of solutions. Duality. Transportation and assignment problems. Travelling salesman problems.

**Partial differential equations:** Solutions of equations of type dx/p=dy/q=dz/r; orthogonal trajectories, pfaffian differential equations; partial differential equations of the first order, solution by Cauchy's method of characteristics; Char-pit's method of solutions, linear partial differential equations of the second order with constant coefficients, equations of vibrating string, heat equation, laplace equation.

Mains Syllabus of Mathematics | Question Papers of Mathematics | Civil Service Exam Book for Mathematics