DIPS ACADEMY has truly been one of the most profound learning experience where I gained the confidence to move ahead in my carrer with the opportunity to put myself on the forefront in dealing mathematics. DIPS programme is very well designed with very helpful test series. Dubey Sir and other faculty are superb. The lectures of Dubey Sir are the most intersting and inspiring.
I am very contented with the dips family specially dubey sir, he's an excellent mentor with amazing teaching skills.The mathematical atmosphere along with one to one interaction, dips material and doubt clearing sessions provided by DIPS ACADEMY were very helpful throughout the journey.
" The guidance of Dubey Sir, a teacher with immense knowledge and wonderful teaching skills, was of great help for me. His approach towards tackling problems, in particular, is pecular and worth emulating I thank him for his invaluable guidance and continuous motivation. "
I'm Mamta Kumari and I secured AIR 47 in IIT - JAM Mathematics. I am very thankful to Dubey Sir, Amit Sir and all the other faculty members for their teachings and guidance. The classes used to be very interactive and environment was very positive for learning. I have learned a lot from Dips academy and I'm very thankful to all the faculties for teaching us the actual meaning of Mathematics in the best possible way.
TEST SERIES SCHEDULE (CSIR-NET/JRF June-2024 ONLINE) |
|||
Date | TEST TYPE | Modules | Syllabus |
MWT-01 | Real Analysis I + Metric Space | 10-May-24 | 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. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity,monotonic functions, types of discontinuity, uniform continuity, Metric spaces, compactness, connectedness.s. |
MWT-02 | ODE + Markov chain | 12-May-24 | Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, differential equation with constant and variable coefficient, 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, Markov Chain |
MWT-03 | Linear Algebra -1 | 15-05-24 | system of linear equations,Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations, matrix representation of linear transformation, Algebra of matrices, rank and determinant of matrices, |
MWT-04 | PDE+LPP | 18-May-24 | Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations. LPP |
MWT-05 | Real Analysis II +TOPOLOGY | 21-May-24 | differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Topology, |
MWT-06 | I.E. +COV+NA | 24-May-24 | Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel, 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, Mathematical Preliminaries and Errors , Solution of Algebraic and Transcendental Equation , Interpolation and Approximation, Ordinary Differntial equaiton -initial value problem , Differenation and integration, system of linar algebraic Equations and Eigenvalue Problems |
MWT-07 | Linear Algebra II | 27-May-24 | Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification of quadratic forms |
MWT-08 | COMPLEX ANALYSIS | 30-May-24 | 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. |
MWT-09 | MA + RT | 02-Jun-24 | Permutations, combinations, Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- 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, |
MWT-10 | Pure | 05-Jun-24 | RA+MA+LA+RT+CA+Functional analysis +Topology +Metric space |
MWT-11 | Applied mathematics | 08-jun-24 | ODE+PDE+COV+I.E+NA+MARKOV CHAIN +LPP |
FLT-01 | Full Length Test | 11-Jun-24 | As per Exam Pattern |
FLT-02 | Full Length Test | 14-Jun-24 | As per Exam Pattern |
FLT-03 | Full Length Test | 17-Jun-24 | As per Exam Pattern |
FLT-04 | Full Length Test | 20-Jun-24 | As per Exam Pattern |
IIT-JAM MATH TEST SERIES SCHEDULE 2024 (ONLINE) |
||||||
TEST TYPE | Modules | DATE | Syllabus | |||
---|---|---|---|---|---|---|
MWT-01 | Real Analysis: I | 02-Jan-24 | Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series. : limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, | |||
MWT-02 | Real Analysis: II | 05-Jan-24 | "Taylor's theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus. Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima. radius and interval of convergence, term-wise differentiation and integration of power series. Multivariable Calculus & Differential Equations: Functions of Two or Three Real Variabels: Limit, continuity, partial derivatives, maxima and minma." | |||
MWT-03 | Group Theory | 08-Jan-24 | "Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms. " | |||
MWT-04 | Linear Algebra | 11-Jan-24 | "Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. " | |||
MWT-05 | ODE | 14-Jan-24 | " Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation. " | |||
MWT-06 | Group Theory + Linear Algebra | 17-Jan-24 | "Matrices: systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors. Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms. " | |||
MWT-07 | Integral Calculus | 20-Jan-24 | "fundamental theorem of calculus.double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. " | |||
MWT-08 | Real Analysis+IC+ODE | 23-Jan-24 | "Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series. Functions of One Real Variable: limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus. Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima.; Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation. ; fundamental theorem of calculus.double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals. " | |||
FLT-01 | Full Length Test | 27-Jan-24 | As per Exam Pattern | |||
FLT-02 | Full Length Test | 30-Jan-24 | As per Exam Pattern | |||
FLT-03 | Full Length Test | 03-Feb-24 | As per Exam Pattern | |||
FLT-04 | Full Length Test | 06-Feb-20 | As per Exam Pattern |
GATE MATHS TEST SERIES SCHEDULE 2024 |
||||||
TEST TYPE | Modules | DATE | Syllabus | |||
---|---|---|---|---|---|---|
MWT-01 | Real Analysis | 03-Jan-24 | Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem; Weierstrass approximation theorem; contraction mapping principle, Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem. Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; | |||
MWT-02 | PDE | 05-Jan-24 | Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable; Wave equation: Cauchy problem and d'Alembert formula, domains of dependence and influence, nonhomogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods. | |||
MWT-03 | Mordern Algebra | 07-Jan-24 | Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group action, Sylow’s theorems and their applications; | |||
MWT-04 | Linear Agebra | 09-Jan-24 | Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms. | |||
MWT-05 | Complex Analysis | 11-Jan-24 | Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations. | |||
MWT-06 | Ring Theory | 13-Jan-24 | Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions, algebraic extensions, algebraically closed fields | |||
MWT-07 | ODE | 15-Jan-24 | First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations, Sturm's oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions. | |||
MWT-08 | Integra Calculus | 17-Jan-24 | Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; | |||
MWT-09 | LPP | 19-Jan-24 | Linear programming models, convex sets, extreme points; Basic feasible solution, graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method. | |||
MWT-10 | Topology + Functional+ Metric Space | 21-Jan-24 | "Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators. Basic concepts of topology, bases, subbases, subspace topology, order topology,product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma. | |||
MWT-11 | Vector Calculus | 23-Jan-24 | Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem. | |||
MWT-12 | Numerical Analysis | 25-Jan-24 | Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation: Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error, Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2 | |||
FLT-01 | Full Length Test | 28-Jan-24 | As per Exam Pattern | |||
FLT-02 | Full Length Test | 30-Jan-24 | As per Exam Pattern | |||
FLT-03 | Full Length Test | 01-Feb-24 | As per Exam Pattern |
IIT-JAM STATISTICS TEST SERIES SCHEDULE 2024 (ONLINE) |
|||
Date | TEST TYPE | Modules | Syllabus |
MWT-01 | Probability Theory | 02-Jan-24 | Random experiments, sample space and algebra of events, relative frequency and Axiomatic definitions of probability, properties of probability function, addition theorem of probability function (Inclusion –exclusion principle), Geometric probability, Bools and Bonferroni’s inequalities, conditional probability and multiplication rule, theorem of total probability and Baye’s theorem, Pairwise and mutual independent of events. |
MWT-02 | Integral Calculus | 05-Jan-24 | Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes. |
MWT-03 | Univariate and standard Distribuion | 08-Jan-24 | "Definition of random variable cumulative distribution function, discrete & conditions random variables, probability mass function, probability density function, distribution of a function of a random variable using transformation and Jacobian method, mathematical expectation and moments, mean, median mode, variance, standard deviation coefficient of variatioin, Quartiles, measure of skewness and kurtosis of probability distribution. Moment generating function, its properties and uniquess, markov and chebyshev’s inequalities and their application Degerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeomtric, uniform Experimential double exponential, Gamma, Beta ( I & II type) , normal and Cauchy distributions, their properties, interrelations and limiting (approximation) cases. " |
MWT-04 | Multivariate Distribution | 11-Jan-24 | Marginal c.d.fs of random vector, joint and marginal pmf, joint and marginal pdf, conditional c.d.f., conditional pmf and conditional pdf, independenc of random variables. Distribution of functions of random vector using transformation of variables and Jacobian method, mathematical expectation of functions of random vectors, joint moments, covariance and correlation. Joint moment generating functions and its properties uniquess of joint m.g.f. and its application, conditional moments, condition of expectation and conditional variance, additive properties of binomial, poisson, negative binomial, gamma and normal distribution using their m.g.f.. |
MWT-05 | Real Analysis | 14-Jan-24 | "Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers. Differential Calculus: Limits, continuity and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables." |
MWT-06 | Standard Multivaitae Limit Theorem and samplimg distrbution | 16-Jan-24 | Mutlinomial distribution and its properties (moments, correlation, marginal distributions, additive property), Bivariate normal distribution its marginal and conditional distribution and related properties, convergence in probability , convergence in distribution and their interrelations, weak law of large numbers and central limit theorem (iid case) and their applications .Sampling distribution of statistic, definition and distribution of rth order statistic and pdf of iid case for continuous distribution. Distribution of smallest and largest order statistic, Central -distribution , Central student’s t-distribution: Snedecor’s central F-distribution, Relationship between , and distribution. |
MWT-07 | Estimation | 19-Jan-24 | Unbiasedness , sufficiency of a statistic, Factorization theorem, complete statistic, consistency and relative efficiency of estimators, uniformly minimum variance unbiased estimator, Rao-Blackwell and Lehmann scheffe theorem and their applications, crammer –Rao lower bound, method of moment of maximum likelihood estimator, Invariance of maximum likelihood, estimator least square estimator and its application in simple linear regression modules, confidence intervals and confidence coefficient confidence intervals for the parameters of univariate normal, two independent normal, and exponential distribution. |
MWT-08 | Linear Algebra | 22-Jan-24 | Vector spaces with real field, subspaces and sum of subspaces, span of a set. Linear dependence and independence, dimension and basis. Matrices: Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices. |
MWT-09 | Testing of Hypothesis | 25-Jan-24 | Null and alternative hypothesis (simple and composite), Type-I and Type –II errors, critical region, level of significance, size and power of the test, P-value. Most powerful critical region and tests, Neyman pearson lemma and its application to construction of MP and UMP tests for parameters of single parameter families. Likelihood ratio test for parameters of univariate normal distribution. |
FLT-01 | Full Length Test | 28-Jan-24 | As per Exam Pattern |
FLT-02 | Full Length Test | 31-Jan-24 | As per Exam Pattern |
FLT-03 | Full Length Test | 04-Feb-24 | As per Exam Pattern |
DIPS ACADEMY has truly been one of the most profound learning experience where I gained the confidence to move ahead in my carrer with the opportunity to put myself on the forefront in dealing mathematics. DIPS programme is very well designed with very helpful test series. Dubey Sir and other faculty are superb. The lectures of Dubey Sir are the most intersting and inspiring.
I am very contented with the dips family specially dubey sir, he's an excellent mentor with amazing teaching skills.The mathematical atmosphere along with one to one interaction, dips material and doubt clearing sessions provided by DIPS ACADEMY were very helpful throughout the journey.
" The guidance of Dubey Sir, a teacher with immense knowledge and wonderful teaching skills, was of great help for me. His approach towards tackling problems, in particular, is pecular and worth emulating I thank him for his invaluable guidance and continuous motivation. "
I'm Mamta Kumari and I secured AIR 47 in IIT - JAM Mathematics. I am very thankful to Dubey Sir, Amit Sir and all the other faculty members for their teachings and guidance. The classes used to be very interactive and environment was very positive for learning. I have learned a lot from Dips academy and I'm very thankful to all the faculties for teaching us the actual meaning of Mathematics in the best possible way.