Syllabus Dips Academy-Csir mathematics

distributions. Characteristic functions. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case). Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution. Standard discrete and continuous univariate distributions. Sampling distributions. Standard errors and asymptotic distributions, distribution of order statistics and range. Methods of estimation. Properties of estimators. Confidence intervals. Tests of hypotheses: most powerful and uniformly most powerful tests, Likelihood ratio tests. Analysis of discrete data and chi-square test of goodness of fit. Large sample tests. Simple nonparametric tests for one and two sample problems, rank correlation and test for independence. Elementary Bayesian inference. Gauss-Markov models, estimability of parameters, Best linear unbiased estimators, tests for linear hypotheses and confidence intervals. Analysis of variance and covariance. Fixed, random and mixed effects models. Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression. Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic forms. Inference for parameters, partial and multiple correlation coefficients and related tests. Data reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation. Simple random sampling, stratified sampling and systematic sampling. Probability proportional to size sampling. Ratio and regression methods. Completely randomized, randomized blocks and Latin-square designs. Connected, complete and orthogonal block designs, BIBD. 2K factorial experiments: confounding and construction. Series and parallel systems, hazard function and failure rates, censoring and life testing.
Operation Research (O.R)
Linear programming problem. Simplex methods, duality. Elementary queuing and inventory models. Steady-state solutions of Markovian queuing models: M/M/1, M/M/l with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.
GATE
Linear Algebra : Finite dimensional vector spaces. Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton theorem, diagonalisa-tion, Hermitian, Skew –Hermitian and unitary matrices. Finite dimensional inner product spaces, selfadjoint and Normal linear operators, spectral theorem, Quadratic forms.
Complex Analysis : Analytic functions, conformal mappings, bilinear transformations, complex integration; Cauchy’s integral theorem and formula, Liouville’s theorem, maximum modulus principle, Taylor and Laurent’s series, residue theorem and applications for evaluating real integrals. Real Analysis : Sequences and series of functions , uniform convergence, power series, Fourier series, functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, theorems of green, Stokes and Gauss; metric spaces, completeness, Weiestrass approxi-mation theorem, compactness, Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem. Ordinary Differential equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients, method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality, Sturm Liouville system, Green’s functions. Algebra: Normal subgroups and homomorphisms theorems, automorphisms. Group actions, sylow’s theorems and their applications groups of order less than or equal to 20, Finite p-groups. Euclidean domains, principal, Principal ideal domains and unique factorizations domains. Prime ideals and maximal ideals in commutative rings. Functional Analysis: Banach spaces, Hahn-Banach theorems, open mapping and closed graph theorems, principle uniform boundedness; Hilbert spaces, orthonormal sets, Riesz representation theorem, self-adjoint, unitary and normal linear operators on Hilbert Spaces. Numerical Analysis: Numerical solution of algebraic and transcendental equations; bisection, secant method, Newton-Raphson method, fixed point iteration, interpolation: existence and error of polynomial interpolation. Lagrange, Newton, Hermite (osculatory) interpolations; numerical differenti-ation and integration, Trapezoidal and Simpson rules; Gaussian quadrature; (Gauss-Legendre and Gauss- Chebyshev), method of undetermined parameters, least square and orthonormal polynomial approximation; numerical solution of systems If you miss an opportunity, do not cloud your eyes with tears; keep your vision clear so that you will not miss the next one DIPS Academy /11
ISI Kolkata
of linear equations; direct and itervative methods, (Jacobi Gauss- Seidel and SOR) with convergence; matrix eigenvalue problems; Jacobi and Given’s methods, numerical solution of ordinary differential equations; initial value problems. Taylor series method, Runge-Kutta methods, predictorcorrector methods; convergence and stability. Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification: Cauchy, Dirichlet and Neumann problems, Green’s function of Laplace, wave and diffusion equations in two variables Fourier series and transform methods of solutions of the above equations and applications to physical problems. Mechanics: Forces in three dimensions, Poinsot central axis, virtual work, Lagrange’s equations for holonomic systems, theory of small oscillations, Hamiltonian equations. Topology : Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma, Tietze extension theorem, metrization theorems, Tychonoff theorem on compactness of product spaces. Probability and Statistics : Probability space, conditional probability, Baye’s theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, condition expectation, moments. Weak and strong law of large numbers, central limit theorem. Sampling distributions, UMVU estimators, sufficiency and consistency, maximum likelihood estimtors. Testing of hypothesis, Neymann-Pearson tests, monotone likelihood ratio, likelihood ratio tests, standard parametric tests based on normal, X2, t, F-distributions. Linear regression and test for linearity of regression, Interval estimation. Linear Programming: Linear programming problem and its formulation, convex sets their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods, infeasible and unbounded LPP’s alternate optima. Dual problem and duality theorems, dual simplex method and its application in post optimality analysis, interpretation of dual variables. Balanced and unbalanced transport-ation problems, unimodular property and u-v method for solving transportation problems. Hungarian method for solving assignment problems. Calculus of Variations and Integral Equations : Variational problems with fixed boundaries; sufficient conditions for extrremum, linear integral equations of Fredholm and Volterra type, their iterative solutions, Fredholm alternative.
TIFR
The screening test is mainly based on mathematics covered in a reasonable B.Sc. course. The interview need not be confined to this. Algebra : Definitions and examples of groups (finite and infinite, commutative and non-commutative), cyclic groups, subgroups , homomorphisms, quotients. Definitions and examples of rings and fields. Basic facts about finite dimensional vector spaces, matrices, determinants, and ranks of linear transformations. Integers and their basic properties. Polynomials with real or complex coefficients in 1 variable. Analysis: Basic facts about real and complex numbers, convergence of sequences and series of real and complex numbers, continuity, differentiability and Riemann integration of real valued functions defined on an interval (finite or infinite), elementary functions (Polynomial functions, rational functions, exponential and log, trigonometric functions). Geometry / Topology: Elementary geometric properties of common shapes and figures in 2 and 3 dimensional Euclidean spaces (e.g. triangles, circles, discs, spheres, etc.), Plane analytic geometry (= coordinate geometry) and trigonometry. Definition and basic properties of metric spaces, examples of subsets of Euclidean spaces (of any dimension), connectedness, compactness. Convergence in metric spaces, continuity of functions between metric spaces. General : Pigeon-hole principle (box principle), induction, elementary properties of divisibility, elementary combinatorics (permutations and combanitions, binomial coefficients), elementary reasoning with graphs.
DRDO
Linear Algebra: Finite dimensional vector spaces. Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton theorem, diagonalization, Hermitian, Skew–Hermitian and unitary matrices. Finite dimensional inner product spaces, self – adjoint and Normal linear operators, spectral theorem, When the mind is tired, every single action requires great effort DIPS Academy /12
Quadratic forms. Complex Analysis : Analytic functions, conformal mappings, bilinear transformations, complex integration: Cauchy’s integral theorem and formula, Liouville’s theorem, maximum modulus principle, Taylor and Laurent’s series, residue theorem and applications for evaluating real integrals. Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, theorem of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness. Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem. Ordinary Differential Equations : First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients, method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality, Sturm Liovullie system, Green’s functions. Algebra: Normal subgroups and homomorphisms theorems, automorphisms. Group actions, sylow’s theorems and their applications groups of order less than or equal to 20, Finite p-groups. Euclidean domains, Principal ideal domains and unique factorizations domains. Prime ideals and maximal ideals in commutative rings. Functional Analysis: Banach spaces, Hahn-Banach theorems , open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal sets, Riesz representation theorem, self–adjoint, unitary and normal linear operators on Hilbert Spaces. Numerical Analysis: Numerical solution of algebraic and transcendental equations ; bisection, secant method, Newton-Raphson method, fixed point iteration, interpolation: existence and error of polynomial interpolation, Lagrange , Newton , Hermite (oscutatory) interpolations; numerical differentiation and integration. Trapezoidal and Simpson rules: Gaussian quadrature; (Gauss- Legendre and Gauss- Chebyshev), method of undetermined parameters, least square and orthonormal polynomial approximation; numerical solution of systems of linear equations; direct and iterative methods, (Jacobi, Gauss- Seidel and SOR) with convergence; matrix eigenvalue problems; Jacobi and Given’s methods, numerical solution of ordinary differential equations; initial value problems, Taylor series method , Runge-Kutta methods, predictor – corrector methods; convergence and stability. Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy Dirichilet and Neumann problems, Green’s functions; solutions of Laplace, wave and diffusion equations in two variables Fourier series and transform methods of solutions of the above equations and applications to physical problems. Mechanics: Forces in three dimensions, Poinsot central axis, virtual work, Lagrange’s equations for holonomic systems, theory of small oscillations, Hamiltonian equations. Topology: Basic concepts of topology , product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma, Tietze extension theorem, metrization theorems, Tychnoff theorem on compactness of product spaces. Probability and Statistics : Probability space, conditional probability , Baye’s theorem, independence , Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments. Weak and strong law of large numbers, central limit theorem, Sampling distributions, UMVU estimators, sufficiency and consistency , maximum likelihood estimators. Testing of hypotheses, Neyman-Pearson tests, monotone likelihood ratio, likelihood ratio tests, standard parametric tests based on normal X2, t, F-distributions. Linear regression and test for linearity of regression. Interval estimation. Calculus of Variation and Integral Equaitons: Variational problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and volterra type, their iterative solutions. Fredholm alternative.
ISI (JRF)
ISI Bangalore
General Topology: Topological spaces, Continuous functions, Connectednes, compactness, Separation Axioms. Product spaces. Complete metric spaces. Uniform continuity. Functional Analysis: Normed linear spaces, Banach spaces, Hilbert spaces, Compact operators. Knowledge of some standard examples like C[0, 1] LP[0, 1]. Continuous linear maps (linear operators). Hahn-Banach Theorem, Open mapping theorem, Open mapping theorem, closed graph theorem and the uniform boundedness principle. Real Analysis: Sequences and series, Continuity and differentiability of real valued functions of one and two real variables and applications, uniform convergence, Riemann integration. Give a lot of time to the improvement of yourself, then there is no time to criticise others DIPS Academy /13
Linear Algebra: Vector spaces, linear transformations, characteristic roots and characteristic vectors, systems of linear equations, inner product spaces, diagonalization of symmetric and Hermitian matrices, quadratic forms. Elementary number theory : Divisibility, congruence, standard arithmetic functions, permutations and combinations. Lebesgure integration: Lebesgue measure on the line, measurable functions, Lebesgue integral, convergence almost everywhere, monotone and dominated convergence theorems. Complex Analysis : Analytic functions, Cauchy’s theorem and Cauchy integral formula, maximum modulus principle, Laurent series, Singularities, Theory of residues, contour integration. Abstract Algebra : Groups, Symmetric and Alternating groups, Direct product and finite abelian groups, Sylow theorems; Rings, Polynomial rings, integral domains, Euclidean rings, fields, extension fields, roots of polynomials, finite fields. Ordinary differential Equations: First order ODE and their solutions, singular solutions, initial problems for first order ODE, general theory of homogeneous and nonhomogeneous linear differential equations.
I.I.Sc. Banglore
Real Analysis : Real valued functions of a real variable: Continuity and differentiability, sequences and series of real numbers and functions, uniform convergence, Riemann integration, fundamental theorem of integral calculus. Topology if Rn, Compactnes and connectedness. Complex Analysis: Continuity and differentiability, analytic functions, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Maclaurin expansions, Laurent’s series, singularities, theory of residues and contour integral, conformal mappings. Linear Algebra: Vector Spaces: Linear independence, basis, dimension, linear transformations, matrices, systems of linear equations, rank and nullity, characteristic values and characteristic vectors, Cayley-Hamilton characteristic and minimal
IISc
polynomials, diagonalizability, Jordan canonical form. Abstract Algebra : Groups: subgroups, Lagrange’s theorem, normal subgroup, quotient group, homomorphism, permutation groups, Cayley’s theorem, Sylow theorems, Rings, Ideals Fields. Ordinary Differential Equations : First order ODEs and their solutions, singular solutions, experience and uniqueness of initial value problems for first order ODE. Gewneral theory of homogeneous and homomor-geneous linear differential
equations. Variation of parameters. Types of singular points in the phase plane of an autonomous system of two equations. Partial Differential Equations: Elements of first order PDE. Second order linear PDE: Classification, wave Laplace and Heat equations. Basic properties and important solutions of classical initial and boundary value problems. Elements of Numerical Analysis: Interpolation : Lagrange and Newton’s forms, error in interpolation. Solution of nonlinear equations by iteration, various iterative methods including Newton. Raphson method, fixed point iteration. Convergence, integration: trapezoidal rule, Simpson’s rule, Gaussian rule, expressions for the error terms. Solution of ordinary differential equations: simple difference equations, series method, Euler’s method, Runge Kutta methods, predictor- corrector methods, error estimates.
MCA Entrance Exam
Algebra:
Fundamental operations in Algebra, Expansions, Factorization, simultaneous linear and quadratic equations, indices, logarithms, arithmetic, geometric and harmonic progressions, binomial theorem, permutations and combinations, surds, determinants, matrices and application to solution of simultaneous linear equations, Set Theory, Group Theory. Coordinate Geometry: Rectangular Cartesian coordinates, equations of a line, midpoint, intersections etc., equations of a circle, distance formulae, pair of straight lines, parabola, ellipse and hyperbola, simple geometric transformations such as translation, rotation, scaling. Calculus: Limit of functions, continuous functions, differentiation of functions tangents and normals, simple examples of maxima and minima, Integration of function by parts, by substitution and by partial fraction, definite integrals, and applications of Definite Integrals to areas. Differential Equations: Differential equations of first order and their solutions, linear differential
equations with constant coefficients, homogenous
linear differential equations.
Vector: Position Vector,
additions and subtraction of
vectors, scalar and vector
products and their
applications to simple
geometrical problems and
mechanics.
Trigonometry: Simple identities, trigonometric equations, properties of triangles, solution of triangles, height and distance, inverse function, Inverse Trigonometric functions, General solutions of trigonometric equations, Complex numbers. Real Analysis: Sequence of real numbers, Convergent Sequences, Cauchy’s Sequences, Monotonic Sequences, Infinite series and their different tests of convergence, The only way to gain respect is, firstly to give it DIPS Academy /14
JNU
Absolute convergence, Uniform convergence, properties of continuous functions, Rolle’s theorem, Mean value theorem, Taylor’s and Maclaurian’s series, Maxima and Minima, Indeterminate forms.
Statistics & Linear Programming: Frequency distribution and measure of dispersion, skewness and Kurtosis, Permutations and Combinations, Probability, Random variables and distribution function, Mathematical expectation and generating function, Binomial, Poisson normal distribution curve fitting and principle of least squares, Correlation and Regression, Sampling and large sample tests, Test of significance base on t, x2 and f distribution, Formulation of simple linear programming problems, basic concepts of graphical and simple methods.
Analytical Ability and Logical Reasoning
The questions in this section will cover logical reasoning, quantitative reasoning.
ComputerAwareness
Computer Basics: Organization of a Computer, Central Processing Unit (CPU), Structure of instructions in CPU, input/output devices, computer memory, memory organization, back- up devices.
Data Representation: Representation of characters, integers and fractions, binary and hexadecimal representations, Binary Arithmetic: Addition, subtraction, division, multiplication, single arithmetic and two’s complement arithmetic, floating point representation of numbers, normalized floating point representation, Boolean algebra, truth tables, Venn diagrams.
Elements of Data Structures Computer Organization C Language

Dips Academy Mathematics-Syllabus for Various exams

CSIR-NET
Analysis:
Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Boizano Weierstrass theorem, Heine Bore! theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transfonnation. Metric spaces, compactness, connectedness. Normed Linear Spaces. Spaces of Continuous functions as examples.
Linear Algebra:
Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification of quadratic forms.

Complex Analysis:
Algebra of complex numbers, the complex plane, polynomials, Power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’ s theorem, Cauchy’ s integral formula, Liouville’ s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.
Algebra:
Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s ? function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings,
unique factorization domain, principal ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions.

Ordinary Differential Equations (ODEs):
Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODEs, system of first order ODEs. General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green’s function.
Partial Differential Equations (PDEs):
Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. Classification o f second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations.
Numerical Analysis:
Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods.
Calculus of Variations:
Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations.
Linear Integral Equations:
Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel.
Classical Mechanics:
Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, theory of small oscillations.

Descriptive statistics, exploratory data analysis:
Sample space, discrete probability, independent evcnts, Bayes theorem. Random variables and distribution functions (univariate and multivariate); expectation and moments. Independent random variables, marginal and conditional If I keep the weaknesses of others in my mind, they soon become a part of me

Dips Academy Scholarship

SCHOLARSHIP
Rank in Entrance-Cum-Scholarship Scholarship Examination
1 100% Tuition Fee Waiver 2 70% Tuition Fee Waiver 3 50% Tuition Fee Waiver 4 35% Tuition Fee Waiver 5 20% Tuition Fee Waiver
Note: In the case when the students do not score the minimum eligibility marks (30%), then the scholarship percentage will be altered accordingly.
TERMS & CONDITIONS
The final discretion of scholarship award will remain with DIPS as the decision will be final and binding on the candidate.
One student can not carry his rank for next or any further batch.
The scholarship award can be withdrawn by the DIPS management if any in disciplinary behavior found against the student.
The registered office of DIPS Pvt. Ltd. is at New Delhi. In case of any dispute, students/parents are subject to the exclusive jurisdiction of appropriate courts in Delhi/New Delhi only.

Admission Procedure In Dips Academy

ADMISSION PROCEDURES
You can take admission in different batches directly at the DIPS office. But admission in the ENB and EGB is on entrance cum-scholarship test basis. In this test DIPS provides fabulous scholarship to the top 5 student also, for the test students must have to register himself.
Test Date : 10th Jan & 10th July Every Year.
Test Schedule : 11:30 AM – 01:00 PM.
Test Pattern & Syllabi : Test paper consists 50 questions from different sections of mathematics. Each question carries three marks and there is a suitable negative marking for each wrong answer. Syllabi of test are very similar to CSIR-NET syllabi.
How to Register : Fill in your complete details in the prescribed form, which is given to you along with this booklet or take it from DIPS office along with the photocopy of M.Sc mark sheet (if available) and a recent photograph.
Last Date of Registration : 9th Jan for the test on 10th Jan 9th July for the test on 10th July
Fee for test : There is no fee for the test.
Result Declaration : 11th Jan and 11th July (result will be announced at 6:00 PM)

DIPS ACADEMY-BEST TEAM FOR MATHEMATICS

6. DIPS–India’s best team
Mathematics
(i) Mr. Rajendra Dubey (Director)
An IITian who deals in pure mathematics having a long experience of more than 28 batches and have produced so far more than 250 JRF/ NET. His name is a milestone in the field of training in Mathematics.
(ii) Prof. S. C. Gupta (Retd. from Hindu College, DU)
One of the most famous author in the field of statistics. He co-authored the bible in statistics named "Fundamentals of Mathematical Statistics" with Dr. Kapoor.
(iii)Mr. Arbind Kumar (NET Qualified)
A young, dynamic and one of the most popular faculty in OR and appilied mathematics and a faculty who is always surrounded by his students.
(iv) Mr. Abhishek Agrawal (JRF Qualified)
The most energetic and young faculty. His enovative and alligant proves and tricks are very popular among the students.
(v) Mr. Narayan Singh (JRF Qualified)
General Sciences : DIPS Academy calls experts in their own field for even in general science section.
(i) Gaurav Rajput (M.Tech)
(ii) Mr. Pradeep Singh (JRF Qualified)
(iii) Dr. Devesh (JRF Qualified)
(iv) Mr. Prakash Pandey
(v) Mr. P. V. Jain
THE RESULTS
Why Students Consider DIPS the Best in Higher Mathematics Training?
THE VALUE SYSTEM
DIPS value system revolves around truth, transparency & commitment. Whatever we think, we say & whatever we say, we do. We present to you what we actually are.
THE QUALITY
We never compromise on quality. Our penchants & pursuit of quality is evident in our every activity in all our action, at all time everywhere. Best Faculty: We are the only institute that follows a very strong, systematic & objective selection and training process before a teachers becomes a DIPS faculty. We provide the best faculty panel in India for mathematics as well as general science.
Every Growing Pool of Questions:
DIPS has a unique and India’s elite team of experts which is continously engaged in fabricating and compiling new questions as per the requirement. The construction of the problems are classified on various issues as question on definition or on theorem or application of theorem. DIPS has the best question bank in India covering the objective question on application part of pure mathematics as well as theoretical questions on applied mathematics. This is the rarest combination which dipsite avail. Regular Doubt Sessions: DIPS provides the regular doubt sessions for students after completion of each topics. We provide two or three extra classes on each topics for doubts only. More than this, the student can ask their personal doubts to the concerning faculty at any time.
Student Self Assessment Program:
DIPS organise weekly test as well as test series for its students. These tests help students in time management & accuracy as well as in self improvement. According to the performance of the students DIPS provides suggestions for their further improvements.
* Our test series is ever best in India and it is conducted for other students also. Each test of our test series based on previous exams. So it is very useful for the aspirants. Description of Test Series Course Month No. of Test NET June & Dec. 4 IAS (mains) September 10 IAS (Prelims) March-April 10 G.S. (IAS-Pre.) March –April 5 MCA Jan 5
RESEARCH & DEVELOPMENT
Our research and development team work round the clock to ensure that our teaching methodology, study material and course structure etc. is updated. The committed teams keeps a knee eye on the latest development and changes in the IAS/NET/GATE or other higher level exams and swiftly incorporates them in our course curriculum.
DIPS is the India’s one of the largest result producer institute in the field of higher mathematics. Its our glory that not a single university of India can produce more results than DIPS in the higher level examination of mathematics.
CSIR-NET/JRF: DIPS has produced more than 350 JRF/ NET.
IAS/PCS:DIPS has produced more than 50 selections in IAS and different state PCS exams.
GATE: More than 250 students of DIPS has qualified the GATE and each and every year there is 15 to 20 students in Top 100.
JNU:In this reputed institute, DIPS has a notable presence in MCA/M.Tech. More than 10 selections are from DIPS Academy (including two toppers).
Other Exams:Apart from that in all other entrance exams for ISI, TIFR, DRDO, NBHM, JEST, MCA the "Dipsites" achieved good results.
Now, it is our proud that in each esteemed institute like IIT, JNU, ISI, IISc, IMSc. etc. the "Dipsites" has notable presence in the field of research.
DIPS PERFORMANCE INDICES IN 2008-2009 IAS-07
: 7 Selections IAS-08
: 2 Selections CSIR-NET (June 08)
: 36* Selections GATE-08
: 41* Selections (18 in Top 100) CSIR-NET (Dec. 08)
: 32* Selections GATE-09
: 46* Selection (15 in Top 100)

DIPS ACADEMY’S STRUCTURE

1. DIPS Classroom Program Cell
Exclusive NET Batch (ENB): These commence on 15th of January & 10th February for June NET and 15th July, 28th July & 10th August for December NET. These batches are sharply focused on CSIR-JRF/NET. Admission in the 1st batch for both June NET and Dec. NET is on entrance exam basis.
Exclusive GATE Batch (EGB): The exclusive GATE batch commence on 15th July, first week of August & September every year and ends just five day before the day of examiniation. In this batch we try to develop among our students, the skill of solving objective type questions and provide shortcut tricks. Admission in the 1st batch of GATE is also on entrance exam basis.
Quick Review GATE Batch (QRGB): This is especially designed for GATE. It is fast track 100 hours Batch and runs in the month of January only. Commencing on 5th of January.
IAS-Main Batches: Batches for IAS mains run throughout
the year and commence on 10th of every month. IAS-Pre. Batches: These batches starts in the Mid of January & 1st week of February every year.
IAS-Foundation Batches: These batches are designed for fresh graduates or early beginner of UPSC exams and covers everything of the syllabus starting from scratch. These batches commence in the month of June & January every year.
MCA / JAM Batch: These batches starts in the 25th of July
and 1st of every subsequent months upto October. JNU M.Tech Batch: This Batch is designed only for JNU M.Tech entrance exams and commencing on 10th February, every year.
DLP /Part Time Program for NET :
DLP is a distance learning program which is recently launched to cater the working aspirants. In this program there is weekend (Saturday & sunday) class, doubt session & test for enhancement & betterment of the students. As well as study material and assignment of each topic in which more than thousand of question will be provided.
2. DIPS Counseling and Information Cell:
This cell provides all the information regarding the various
higher level exams related to MATHEMATICS and provide a platform, where DIPS students can discuss any of their issues regarding their preparation and provides various books and prototype question papers.
3. DIPS Correspondence Program Cell:
There are many people preparing for exams but due to their own reasons they are unable to join the regular DIPS Batches. They can also avail the benefits of our high quality study material designed by experience Mathemati-cians of DIPS group. Study material package consists of more than thousand questions for Paper I whereas selective topics for Paper II covering atmost 25 popular questions and guidlines for preparation and choosing topics.
4. DIPS Library:
DIPS library has a versatile collection of books on pure as well as on applied Mathematics. These books help students enhance their knowledge beyond their regular books. It has also some classic collection on literature, personality development and General studies due to keen interest of Director Mr. Rajendra Dubey in these areas.

5. Fee Structure:
(i) ENB : 20,225/
(ii) EGB : 20,225/
(iii) ENB & EGB (Combined) : 22,475/
(iv) IAS (Pre-Cum-Mains) : 28,100/
(v) IAS (Pre.) : 11,235/
(vi) IAS (Mains) : 22,475/
(vii) MCA/JAM : 19,100/
(viii) DLP (NET) : 11,235/
(ix) Crosspondence Course (NET) : 7,000/
Mode of Payment is through cash / cheque /demand draft in favour of Dubey’s Information Pool & Solution Pvt. Ltd. payable at New Delhi.

(To give happiness to others is a great act of charity )

ABOUT DIPS ACADEMY-INDIA'S PIONEER INSTITUTE OF MATHEMATICS

DIPS ACADEMY is an educational wing of Dubey’s Information Pool and Solutions (DIPS) Pvt. Ltd. It is India’s first and only organization focused exclusively on MATHEMATICS for all Higher level competitive examinations like CSIRNET, GATE, Civil Services, MCA etc. DIPS ACADEMY has been founded by Mr. Rajendra Dubey, member of Board of Directors DIPS Pvt. Ltd. Along with a team of expert Mathematician from various IIT’s and other reputed Universities. Ever since it was founded, DIPS has been growing at a breath taking pace. Over the last 7 years DIPS students are achieving a new height in all kind of research institutes and other high profile jobs. It is the India’s largest result producer training centre in the higher level exam like NET and GATE. Also apart from this, DIPS Academy has good results in the very high profile job IAS.

dipsacademy-HIGH PROFILE JOBS FOR GRADUATE STUDENTS

DIPS ACADEMY

Your under graduate subjects can be utilized in these high profile exams like Civil Services Exam. popularly known as IAS. CIVIL SERVICES EXAMINATION (IAS ) UPSC conducts examination for civil services (IAS / IPS) at all India basis. There are three levels of CSE. (i) Prelims (ii) Mains (iii) Interview (Personality test) PRELIMS: There will be two papers. (1) General Studies: Consisting 150 objective questions, one mark each. (2) Optional: You can choose Mathematics in this paper which consists 100 objective questions of 3 marks each. This examiniation is meant to serve as a screening test only; the marks obtained in the Preliminary Examination by the candidates who are declared qualified for admission to the Main Examination will not be counted for determining their final order of merit. There will be four alternatives for the answers to every question. For each question for which a wrong answer has been given by the candidate, one third (0.33) of the marks assigned to that question will be deducted as penalty.
After getting success in prelims. You will be eligible for the main examination MAINS : In this exam; there will be 9 papers. First two papers are of general study of 300 marks each. You have to choose two optional subjects in which you can choose one as Mathematics, there will be two papers for each optional subjects of 300 marks each. In addition to these paper’s there is one paper of essay writing of 200 marks and; Two qualifying papers one of General English, other of Regional Language. After qualifying main examination you will be called for interview/personality test. INTERVIEW : Interview has 300 marks and the final merit is declared by combining of the marks of mains & interview. IFS (INDIAN FOREST SERVICES) This exam is also conducted by UPSC and it is very much similar as CSE. In this exam there are two levels–Written and Interview. In written exam there are seven papers. General Science and English each is of 300 marks whereas two optional papers contains 800 marks. Interview is of 300 marks

AVENUES FOR UNDER GRADUATE STUDENTS-DIPS ACADEMY

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MCA

Master of Computer Application (MCA) is the most fascinating avenue for students aspiring for computer Science and information Technology students having maths at graduation level may persue MCA from high steamed Institute like JNU, Trichurapalli, symbiosis, Pune University , DU and through other state level exams. Entrance exam of objective type comprises of maths, general computer aptitude & reasoning.

JAM

Jam is conducted by IIT to take admission in all IITs for M.Sc. & MCA (IIT Roorkee only) Questions paper is set from various topics of pure & applied mathematics at graduation level. Integrated Ph.D.Programs IISc Bangalore offers exciting opportunities to well motivated and talented Bachelor’s degree holders with a level case of scientific enquiry for pursuing advanced research in frontier areas of Biological, chemical, physical and Mathematical Sciences leading to the Ph.D degree of the institute. Eligibility for this program is Bachelor’s degree in any branchof Biology/chemistry/ physics / Mathematics under 10+2+3 system. Candidates with M.Sc. qualifications are not eligible for admission to this program. Following institutes provide integrated Ph. D. program:

(i) TIFR, (ii) HRI, (iii) IMSc, (iv) IISc. M. MATHS A three-year B.Sc., Or a B.E./B. Tech. with Mathematics with an exceptionally strong background in Analysis and Abstract Algebra, or , a B. Stat./B.Math of the Indian Statistical Institute, is eligible for admission to the M.Math. The total duration of the M.Math. programme is two years (four semesters). An academic year usually starts in July-Agust and continues till May, consisting of two semesters with a recess. M. STAT Students having the B.Stat. Degree of ISI, B.A./B.Sc. (Statistics), B.Math. degree of ISI, or B.A./B.Sc. (Mathematics) with Statistics as a full subject are eligible for the M.Stat. selection test. Students with B.Stat.(Hons.) degree of ISI are eligible for direct admission to the M.Stat. Programme.

NET-GATE MATHEMATICS -DIRECT JOBS FOR P. G. STUDENTS OF MATHEMATICS

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There are some government organizations which seek students having master degree in Mathematics like-
DRDO (Defence Research & Development Organization): It recruits Scientist B and conducts written test (SET) in the
month of September followed by interview. Student should remember that posts are filled every year but candidates from Mathematics stream may get their chance every alternate year in general, so they should not miss the opportunity whenever it strikes. The best way to do so is be prepared with main topics of Mathematics. The syllabus of GATE covers most of the topics asked in this exam. The level of questions is almost same as NET/GATE. Also questions from general
mental ability section is asked. For more details log on www.rec.drdo.gov.in
AAI (Airport Authority of India): It contingently invites PG students of Mathematics for the post of ATC or system
analyst. The pattern of examination is same as of DRDO but the level of questions is somewhat low. For more details log
on www.airportsindia.org.in, www.ai.aero
IMAGERY ANALYST: This is also a very attractive post filled by the government of India through cabinet secretariat
and it is a Gazetted post. In this exam knowledge of English is necessary. As far as Mathematics is concerned pattern,
syllabus and level of questions is exactly same as of GATE and solving last ten years GATE papers can help a lot. Infact
objective questions from the same year GATE paper may repeat.

(Relationships based on falsehood are like houses built with their foundations of mud)

JEST - MATHEMATICS

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Being Sciene Graduate or Post Graduate, are you really aware of avenues open for you? Remember this is the era ofinformation, “more information you have, more mighty you are.”Now here we introduce the avenues open for you i.e. the places where you can make your dreams come true.Believe in yourself and be sure that no financial or social background bars you studying in the following Institutes theonly things which matters is your potential.

CSIR-JRF/NETCSIR-UGC hold a national eligibilitytest twice a year in the month of Juneand December for JRF and Lectureship(LS).Approximately 12000 students appearfrom Maths stream and among themapproximately two hundred studentsawarded eligibility certificate fromCSIR/UGC, which make them eligiblefor teaching in various degreeinstitutions all over India. Meritoriousstudents get JRF in which they enjoyscholarship of about 12,000/-permonth better among them may getinterview/written call from CSIR forSPM (Shyama Prasad Mukherjee)fellowship and successful candidatesget about 25,000/- per month asscholarship.The minimum qualification requiredis MA/MSc. with atleast 55% marks(For SC/ST 50% required) where as agelimit for JRF is 28 yrs. for malecandidates and 33 yrs. for femalecandidates. There is no bar on age toqualify NET for Lectureship (LS) andthere is some relaxation in age limitfor JRF for SC/ST.For more details log onhttp://www.csirhrdg.res.in/GATE (Graduate AptitudeTest In Engineering)MHRD holds Graduate Aptitude Testin the Engineering every year. For theeligibility for admission to postgraduate programs with MHRD andother Government Scholarship inEngineering/ Technology /Architecture/ Pharmacy/ Science.The post graduate students ofMathematics can pursue M. Tech inComputer Science/ IndustrialM a t h e m a t i c s / I n f o r m a t i o nTechnology/ Hydrology from I.I.T’s and also research in Mathematics(Ph.D) having a valid GATE Score.

JEST

It invites Applications from motivatedstudents, with consistently goodacademic record, for enrolment in a Ph.D. Programme in Mathematics /Theoretical Computer Science, at anyof the following institutes:(i) Aryabhatta Research Institute ofObservational Sciences.(ARIES), Nainital, for Astronomy.(ii) Harish-Chandra Research Institute(HRI), Allahabad, for TheoreticalPhysics, Mathematics & Astrophysics.(iii) The Institute of MathematicalSciences (IMSc), Chennai, forTheoretical Physics, Mathematics andTheoretical Computer Science.(iv) Jawaharlal Nehru Centre forAdvanced Scientific Research(JNCASR), Bangalore, forExperimental and TheoreticalCondensed Matter Physics, StatisticalMechanics and Materials Science.(v) National Centre for RadioAstrophysics (NCRA), Tata Institute of Fundamental Research, Pune, forAstronomy and Astrophysics.

The minimum qualification forResearch is M.A./ M. Sc. inMathematics in related disciplines orthe students who expect to completetheir final examination by August ofthis year are also eligible to apply.Candidates applying for Ph. D.Programmes in all disciplines willhave to appear for the JEST (writtenexamination) in the relevant disciplineUsing the JEST score each institute willcall a limited number of candidates forits further selection proceduredepending on its requirements.For Mathematics at HRI/ IMSc,application forms can be obtained bywriting to : The Registrar, Harish-Chandra Research Institute (HRI), OffG. T. Road, Chhatnag Road, Jhunsi,Allahabad - 211 019. Alternatively forMathematics the application form canbe downloaded fromhttp://www.mri.ernet.in/.At HRI, candidates with a Bachelor’sdegree will also be considered for the Integrated M. Sc. - Ph. D. programmein Mathematics/Physics.At IMSc, graduates with B. Sc./B. E./B. Tech. degree will also beconsidered for admission to theM.Sc. (by Research) programme inMathematics/Theoretical ComputerScience/Physics, as part of anintegrated Ph.D. these disciplinesThere are several other Institute whichconduct their own entrance exams forthe eligibility for M. Tech andResearches like-

I.I.Sc. BangloreI.I.Sc. conducts its entrance test inmonth of May every year foradmissions to Integrated Ph.D/Ph.D./M.Tech. Entrance examinations consistobjective and short answer typequestions. Successful candidates haveto clear interview at Banglorecampus.Students having high GATEscore(above 90 percentile) or JRF areeligible for direct interview. For moredetails log on http://www.iisc.ernet.in/I.S.I. Kolkata/Delhi/BangloreUnique institution devoted to theresearch, teaching and application ofstatistics, natural sciences and socialsciences It conducts its entrance test inthe month of May for M. Tech andPh.D. ISI offers various avenues forstudents of Mathematics fromGraduation to Doctoral level. They offers courses like B.STAT(HONS), JRFin computer and communicationsciences & JRF in Physics, in AppliedMathematics, M. STAT, M. Tech incomputer Science, M.Tech in Quality,Reliability and Operations Research,M. Math, B. Math. For more details logon http://www.isical.ac.in/,ww.isibang.ac.in, http://www.isid.ac.in/

JNU

It conducts its entrance exam for M.Tech in the month of May. Eligibilityis M.Sc. with minimum 55%marks.Students having High GATE score orJRF are eligible for direct interview.For more details log onhttp://www.jnu.ac.in/

TIFR

The School of Mathematics at TataInstitute of Fundamental Research(TIFR) have interests in areas likeAlgebra, Algebraic Geometry, LieGroups, Lie Algebras, AlgebraicGroups, Representation Theory andQuantum Groups, Theory of Numbers,Combinatorics, Differ-entialGeometry and Topology, Real andComplex Analysis, Ergodic Theory,Probability Theory on Groups andMathematical Physics.The School of Mathematics has aCentre in Bangalore dedicated to thestudy of Applied Mathematics wheremathematicians work in the fields ofDifferential Equations, Harmonic Analysis, Numerical Analysis andProbability Theory. For more detailslog on http://www.tifr.res.in/There are some other places alsowilling to give you admission forhigher studies provided you areambitious enough and having gutsNBHMThe National Board for HigherMathematics (NBHM) was formed bythe Department of Atomic Energy tofoster the development of highermathematics in the country, help in theestablishment and development ofmathematics centres and give financialassitance to research projects and todoctoral and post-doctoral scholars.For more details log onhttp://www.nbhm.dae.gov.in/HRIHarish-Chandra Research Institute(HRI)( formerly known as MehtaResearch Institute(MRI)) is aninstitution dedicated to research inmathematics, and in theoreticalphysics. It is located in Allahabad,India, and is funded by the Departmentof Atomic Energy, Government ofIndia. For more details log onhttp://www.mri.ernet.in/.

CSIR-UGC NET GATE AND IAS ACADEMY FOR MATHEMATICS - DIPS ACADEMY

Through this booklet I get anopportunity to share my viewswith young and energeticmathematicians, seeking their careerin mathematics. I feel pride whenrealize that very few teachers &professors of maths get a chance to talkto such a large number of students ofvarious universities. Though ithappens through pen but I’m luckyenough. Thanks to my readers!!It is seen that amateurmathematicians—in fact, Lawyers,Philosophers, and priests by professionbut mathematicians by chance hadgreat contribution to the developmentof mathematics as a subject we studytoday. Have you ever given a thoughtthat why is it so? How they are able tothink on the typical mathematicalpattern?It seems that they areconditioned to think upon thePROBLEM in totality. They might haveunderstood the word “PROBLEM”perfectly and therefore whileattacking the problem, they attackedevery part of the ‘PROBLEM’. For them,the word ‘PROBLEM’ is first to findanswer or at least something from it.It is only after that the subject of theproblem is concerned. This might bethe reason that they had used theideology, concept & thoughts ofdifferent subjects while providing thesolutions for “the then existingproblems”—whether correct orincorrect. And therefore, theirinnovative approach in the quest ofsolutions had given them a visionwhich often came out as a ‘theorem’though they themselves might nothave been able to proved it at that timeor the proof given by them is incorrecttoday. But their theorem is beyonddoubt remarkable. Fermat’s lasttheorem is a remarkable example.This brings us to the point thatwhile learning something, the understanding of the word PROBLEMshould be in priority, because whilelearning, delivering something orexamining ourselves, we come acrossthis word invariably. So let’s startthinking about the word“PROBLEM”—Before I define the wordPROBLEM, Let me clear that this wordis not stick to one subject—Mathematics. We are concerned withthe word PROBLEM in totality—wherever it may appear, let it be. e.g.financial matters, family matters,national or international affairs or itcan even be ‘Love affair’ or any thingyou may think of. Here I try to defineof the word PROBLEM. —“A problem is set ofinformation (implicit or explicit orboth) with one or more questions”Seems interesting!!Now, if we adopt thisdefinition of the word ‘PROBLEM’ it isnot difficult to define the wordSOLUTION; Here it comes as a naturalconsequence:“The ‘SOLUTION’ is to find the ‘rightsequence’ of the informations given inthe PROBLEM, which leads us to theanswer of the questions raised in theproblem”.Let us start analysis of thedefinition of ‘solution’. This definitioninvolves two important parametersone is “information” and the other is“the right sequence”. It varies fromperson-to-person that how he or sheextracts information from the givenproblem because it's not always thatall the useful information in anyproblem are in explicit form. Whereasthe implicit information comes out onlyafter a reasonable investment of timein the problem. As for the 'rightsequence' is concerned it is not thenumber of information but theperspective from which a person sees the information which decides that how& when it (the right sequence) will beobtained. Obviously a good commandover the technicality of subjects relatedto the problem may help the studenthandle the information and getting theright sequence.Here is an observation whichwill give a strong support to my logicsclaiming importance of right sequenceof information for solutions—Have you ever noticed, thatwhy in most of the examinations likebanks, railway recruitments, SSC, evencivil services (IAS) or any other exam,mathematical and verbal/non-verbalreasoning based questions are asked.Even in these questions, you are askedto find the missing numbers in the seriesor sequence (the right sequencerequired!). Sometimes, you are givencertain figures and then asked to findthe unknown figure? Here also you areasked to catch a pattern (rightsequence!!).Now, you might have realizedwhy the pattern of most of theexaminations, right from Macaulay tothe present time, still persists.So dear students, you mighthave got some ideas regardingproblems and their related aspects.Hope you will start thinking over theword PROBLEM and try to attack andfind solutions in your own innovativeways. Now you might have chain ofthoughts in your mind regardingproblems and solutions. Feel free towrite to me at rajendra@dipsindia.com.Or you can send me through letters atthe address of DIPS Academy. I’ll bereally happy and thankful to you if youshare your views regarding this articleor the points I have raised here.

Rajendra Dubey
(The author is a mentor of Higher
Mathematics and CEO of DIPS Pvt. Ltd.)

(Freedom starts in the mind, not by cutting ropes)