## MP SLET Maths Syllabus | MP SET MPPSC Maths Syllabus Assistant Professor | MP PSC Syllabus Maths Asst Professor गणित

As per the MPPSC recruitment 2016 for
Assistant professor in various subjects; similarly maths is also one of the subjects
which is under the MPPSC Assistant professor recruitment 2016. Here is the
MPPSC Maths Syllabus for Assistant professor post. For more clarification please
also refer official website of MPPSC.

*Click to >> Download MP SET First paper Syllabus*

MATHEMATICAL SCIENCES [CODE No. – 12]

Syllabus

Note:-

There will be two question papers, Paper-II and Paper – III

The Paper – II will cover 50 Objective Type Questions & all compulsory. Each question will carry two marks. Total marks of Paper – II will be 100.

The Paper – III will cover 75 Multiple Type Questions (Multiple Choice, Matching Type, True/False, Assertion-Reasoning Type) and all compulsory. Each question will carry two marks. Total marks of Paper – III will be 150.

#### MPPSC Maths Syllabus UNIT – 1

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.

Bolzano Weierstrass theorem, Heine Borel 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 transformation, inverse and implicit function theorems.

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

#### MPPSC Maths Syllabus UNIT – 2

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 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, Galois Theory.

Topology: basis, dense sets, subspace and product topology, separation axioms, connectedness and

compactness.

#### MPPSC Maths Syllabus UNIT – 3

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 of 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.

#### MPPSC Maths Syllabus UNIT – 4

Descriptive statistics, exploratory data analysisSample space, discrete probability, independent events, Bayes theorem. Random variables and

distribution functions (univariate and multivariate); expectation and moments. Independent random

variables, marginal and conditional 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, Poisson and birth-and-death processes.

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, confidence intervals,

tests for linear hypotheses. 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 designs, randomized block designs and Latin-square designs. Connectedness and

orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction.

Hazard function and failure rates, censoring and life testing, series and parallel systems.

Linear programming problem, simplex methods, duality. Elementary queuing and inventory models.

Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C,

M/M/C with limited waiting space, M/G/1.

All students are expected to answer questions from Unit I. Students in mathematics

are expected to answer additional question from Unit II and III. Students with in

statistics are expected to answer additional question from Unit IV.

All the topics of UGC NET and CSIR NET regarding topics which is also prefer by MPPSC exam board. If any discripancy we are not responsible; So we are request you please also refer MPPSc official website and get all authentic informations. www.mppsc.nic.in www.mppscdemo.in

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