Suggested Strategy for Mathematics Mr.K. Venkanna

Mr.K. Venkanna
Director, IMS (Institute of Mathematical Sciences)
www.ims4maths.com
Email: ims4maths@gmail.com
Contact: 9999197625, 011-45629987

Suggested Strategy for Mathematics

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:

1. A subject of your interest.
2. Scoring pattern of that subject in past few years.
3. The availability of study material and
4. 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.

As IAS and IFoS exams are joined together, so there is an opportunity for the Mathematics optional students to write the IFoS exam along with the IAS exam simultaneously.

ROLE OF COACHING

The role of the coaching institute can never be underestimated in the preparation of CSE. Expert guidance is a very crucial aspect for the preparation. The mentor facilitates the process of preparation and enables the student to savour the success in a strategized manner. One can score 80%+ in Mathematics with the help of professionally well equipped and qualitatively upgraded teaching inputs based on most meticulously and scientifically designed comprehensive guidance programme which allows conceptual clarification of all topics. Moreover, coaching institute’s scientifically designed rigorous written tests and feedback mechanism will make the path of preparation easy and the hard work of sincere aspirants will bring the desired success. An academy with its experience and professional efficiency can prove to be a catalyst to ensure absolute proficiency and perfection in the subject. This is mandatory to ensure the updation of the student’s conceptual and analytical knowledge reservoir as per the requirements of the latest emerging trends of the civil services examination.

Mr.K. Venkanna
Director, IMS (Institute of Mathematical Sciences)
www.ims4maths.com
Email: ims4maths@gmail.com
Contact: 9999197625, 011-45629987

SYLLABUS

Paper I

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. Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues

Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

Analytic Geometry: Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties

Ordinary Differential Equations: Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution. Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters. Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.

Dynamics & Statics: Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler’s laws, orbits under central forces. Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

Vector Analysis: Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

Paper-II

Algebra: Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem.

Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields

Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series

Continuity and uniform continuity of functions, properties of continuous functions on compact sets.

Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.

Complex Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration.

Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems.

Partial Differential Equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions

Numerical Analysis and Computer Programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation.

Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods. Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers.

Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms.

Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers

Algorithms and flow charts for solving numerical analysis problems.

Mechanics and Fluid Dynamics: Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

From IMS (Institute of Mathematical Sciences), New Delhi