0
395 Frist think You must Known the Subject Wise number of vacancy click here TN TRB list of vacancy. Candidates who want to download TN TRB Maths Syllabus PDF formate given below in this page links. Save the copies and refer the pdf during your exam preparation. We feel pleasure to provide TN TRB Maths Syllabus pdf on this page.

Syllabus: MATHS (Subject Code:
P03)

Unit-I – Algebra

Groups –
Examples – Cyclic Groups- Permulation Groups – Lagrange’s theorem- Cosets – Normal
groups – Homomorphism – Theorems – Cayley’s theorem – Cauchy’s Theorem – Sylow’s
theorem – Finitely Generated Abelian Groups – Rings- Euclidian Rings-
Polynomial Rings- U.F.D. – Quotient – Fields of integral domains- Ideals-
Maximal ideals – Vector Spaces – Linear independence and Bases – Dual spaces –
Inner product spaces – Linear transformation – rank – Characteristic roots of matrices
– Cayley Hamilton Theorem – Canonical form under equivalence – Fields –
Characteristics of a field – Algebraic extensions – Roots of Polynomials –
Splitting fields – Simple extensions – Elements of Galois theory- Finite
fields.

Unit-II – Real Analysis

Cardinal
numbers – Countable and uncountable cordinals – Cantor’s diagonal process –
Properties of real numbers – Order – Completeness of R-Lub property in R-Cauchy
sequence – Maximum and minimum limits of sequences – Topology of R.Heine Borel
– Bolzano Weierstrass – Compact if and only if closed and bounded – Connected
subset of R-Lindelof’s covering theorem – Continuous functions in relation to
compact subsets and connected subsets- Uniformly continuous function –
Derivatives – Left and right derivatives – Mean value theorem – Rolle’s
theorem- Taylor’s theorem- L’ Hospital’s Rule – Riemann integral – Fundamental
theorem of Calculus –Lebesgue measure and Lebesque integral on R’Lchesque
integral of Bounded Measurable function – other sets of finite measure –
Comparison of Riemann and Lebesque integrals – Monotone convergence theorem –
Repeated integrals.

Unit-III – Fourier series and Fourier Integrals

Integration
of Fourier series – Fejer’s theorem on (C.1) summability at a point –
Fejer’s-Lebsque theorem on (C.1) summability almost everywhere – Riesz-Fisher
theorem – Bessel’s inequality and Parseval’s theorem – Properties of Fourier
co-efficients – Fourier transform in L (-D, D) – Fourier Integral theorem –
Convolution theorem for Fourier transforms and Poisson summation formula.

Unit-IV – Differential Geometry

Curves in
spaces – Serret-Frenet formulas – Locus of centers of curvature – Spherical
curvature – Intrinsic equation – Helices – Spherical indicatrix surfaces –
Envelope – Edge of regression – Developable surfaces associated to a curve –
first and second fundamental forms – lines of curvature – Meusnieu’s theorem –
Gaussian curvature – Euler’s theorem – Duplin’s Indicatrix – Surface of
revolution conjugate systems – Asymptritic lines – Isolmetric lines –
Geodesics.

Unit-V – Operations Research

Linear
programming – Simplex Computational procedure – Geometric interpretation of the
simplex procedure – The revised simplex method – Duality problems – Degeneracy
procedure – Peturbation techniques – integer programming – Transportation
problem – Non-linear programming – The convex programming problem – Dyamic
programming – Approximation in function space, successive approximations – Game
theory – The maximum and minimum principle – Fundamental theory of games – queuing
theory / single server and multi server models (M/G/I), (G/M/I), (G/G1/I)
models, Erlang service distributions cost Model and optimization – Mathematical
theory of inventory control – Feed back control in inventory management –
Optional inventory policies in deterministic models – Storage models – Damtype
models – Dams with discrete input and continuous output – Replacement theory –
Deterministic Stochostic cases – Models for unbounded horizons and uncertain
case – Markovian decision models in replacement theory – Reliability – Failure
rates – System reliability – Reliability of growth models – Network analysis –
Directed net work – Max flowmin cut theorem – CPM-PERT – Probabilistic
condition and decisional network analysis.

Unit-VI – Functional Analysis

Banach
Spaces – Definition and example – continuous linear transformations – Banach
theorem – Natural embedding of X in X – Open mapping and closed graph theorem –
Properties of conjugate of an operator – Hilbert spaces – Orthonormal bases –
Conjugate space H – Adjoint of an operator – Projectionsl as a Hilbert space –
lp space – Holders and Minkowski inequalities – Matrices – Basic operations of matrices
– Determinant of a matrix – Determinant and spectrum of an operator – Spectral
theorem for operators on a finite dimensional Hilbert space – Regular and
singular elements in a Banach Algebra – Topological divisor of zero – Spectrum
of an element in a Branch algebra – the formula for the spectral radius radical
and semi simplicity.

Unit-VII – Complex Analysis

Introduction
to the concept of analytic function – limits and continuity – analytic
functions – Polynomials and rational functions elementary theory of power
series – Maclaurin’s series – uniform convergence power series and Abel’s limit
theorem – Analytic functions as mapping – conformality arcs and closed curves –
Analytical functions in regions – Conformal mapping – Linear transformations –
the linear group, the cross ratio and symmetry – Complex integration – Fundamental
theorems – line integrals – rectifiable arcs – line integrals as functions of
arcs – Cauchy’s theorem for a rectangle, Cauchy’s theorem in a Circular disc,
Cauchy’s integal formula – The index of a point with respect to a closed curve,
the integral formula – higher derivatives – Local properties of Analytic
functions and removable singularitiesTaylor’s theorem – Zeros and Poles – the
local mapping and the maximum modulus Principle.

Unit-VIII – Differential Equations

Linear
differential equation – constant co-efficients – Existence of solutions –
Wrongskian – independence of solutions – Initial value problems for second
order equations – Integration in series – Bessel’s equation – Legendre and
Hermite Polynomials – elementary properties – Total differential equations –
first order partial differential equation – Charpits method.

Unit-IX – Statistics – I

Statistical
Method – Concepts of Statistical population and random sample – Collections and
presentation of data – Measures of location and dispersion – Moments and
shepherd correction – cumulate – Measures of skewness and Kurtosis – Curve
fitting by least squares – Regression – Correlation and correlation ratio –
rank correlation – Partial correlation – Multiple correlation coefficient –
Probability Discrete – sample space, events – their union – intersection etc. –
Probability classical relative frequency and axiomatic approaches – Probability
in continuous probability space – conditional probability and independence –
Basic laws of probability of combination of events – Baye’s theorem –
probability functions – Probability density functions – Distribution function –
Mathematical Expectations – Marginal and conditional distribution – Conditional
expectations.

Unit-X – Statistics-II

Probability distributions – Binomial, Poisson, Normal, Gama, Beta, Cauchy, Multinomial Hypergeometric, Negative Binomial – Chehychev’s lemma (weak) law of large numbers – Central limittheorem for independent identical variates, Standard Errors – sampling distributions of t, F and Chi square – and their uses in tests of significance – Large sample tests for mean and proportions – Sample surveys – Sampling frame – sampling with equal probability with or without replacement – stratified sampling – Brief study of two stage systematic and cluster sampling methods – regression and ratio estimates – Design of experiments, principles of experimentation – Analysis of variance – Completely randomized block and latin square designs.