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Old 8th June 2017, 04:56 PM
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Default Tezpur University Statistics

My sister is pursuing Integrated M.Sc. in Mathematics Program from Tezpur University. She has passed 3rd Semester and taken admission in 4th. She wants syllabus of Introductory Statistics Subject of 4th Semester of this Program. So willyou give link to get detailed syllabus of Introductory Statistics subject of Integrated M.Sc. in Mathematics Program of Tezpur University?
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Old 8th June 2017, 05:02 PM
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Default Re: Tezpur University Statistics

As you want syllabus of Introductory Statistics subject of 4th Semester of Integrated M.Sc. in Mathematics Program of Tezpur University, so here I am giving detailed syllabus:

Tezpur University Integrated M.Sc. in Mathematics Program ‘Introductory Statisticsn’ Syllabus

MI 201 Introductory Statistics

Unit-1
Collection of data, methods of collections of primary data, presentation and classification of data.

Unit-2
Discrete and continuous variables, Frequency distributions, Graphical representation, cumulative frequency distribution and ogives.

Unit-3
Measures of location, the arithmetic mean of group data, properties of arithmetic mean, median and mode; other measures of location: quartiles, deciles and percentiles.

Unit-4
Measures of dispersion,Variance and standard deviation of ungrouped and grouped data, properties of standard deviation.

Unit-5
Elements of probability theory, classical definition of probability, axiomatic approach to probability, probability of a simple event, probability of composite event, addition rule, multiplication rule: conditional probability.

Unit-6
Probability Distributions: Binomial distribution, Properties of Binomial Distribution, Stirling approximation, Poisson Distribution, Properties of Poisson distribution. Moments of higher order, relation between mr and mr′, skewness and Kurtosis.

Unit-7
Correlation and regression: scatter diagram, coefficients of correlation, linear regression, fitting of regression line, the method of least squares, explained and unexplained variation, coefficient of variation, correlation and regression for grouped data.

Unit-8
Tests of significance, Null hypothesis and hypothesis testing; Chi-square distribution and tests related. Non parametric tests, ‘t’ tests – paired and student ‘t’ tests, ‘F’ test, critical difference at 0.01 and at 0.05.

Textbook(s)
1. Medhi, J. Statistical Methods: An introductory Text, (New Age International (P) Ltd,, 2000).
2. Gupta, S.C. and Kapoor, V. K. Fundamentals of Mathematical Statistics, (S. Chand & Co., 2007).

Reference book(s)
1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. I,
(Wiley, 2005).
2. Uspensky, J.V. Introduction to Mathematical Probability, (McGraw Hill, 2005).
Here I am providing syllabus of other subjects of 4th Semester:

MI 202 Probability and Mathematical Statistics (L3 -T1 -P0 -CH4 -CR 4)

Unit-1
Discrete sample space, Bayes’ formula, Discrete random variable, expected value of a random variable.
Unit-2
Standard probability distribution: Bernoulli, Binomial, Hypergeometric, Geometric, Poisson and Normal distribution.
Unit-3
Elements of Sampling theory: sampling with and without replacement.
Unit-4
Sampling distribution of the sample mean, sampling distribution of proportion, standard error.
Textbook(s)
1. Medhi, J. Statistical Methods: An introductory Text (New Age International (P) Ltd, 2000).
Reference book(s)
1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, 2005).

MI 203 Linear Spaces and Complex Numbers (L2 -T1 -P0 -CH3 -CR 3)

Unit-1
Algebra of matrices; symmetric, skew symmetric, Hermitian and skew Hermitian matrices; elementary transforms, reduction to echelon and normal form.
Unit-2
System of linear equations, existence and uniqueness of solutions, rank of a matrix.
Unit-3
Definitions and examples of vector spaces, elementary properties of and as vector spaces, subspaces, operations on subspaces.
Unit-4
linear dependence and independence of vectors, basis and dimension of vector spaces.
Unit-5
linear mappings and their algebraic properties; eigenvalues and eigenvectors, characteristic equation, statement of Cayley-Hamilton theorem and its use in finding the inverse of a matrix.
Unit-6
Algebraic properties of complex numbers, geometrical interpretation of complex numbers, modulus and argument of complex numbers; exponential and trigonometric functions of a complex variable.
Unit-7
Theorems on limit and continuity of a function of complex variable, differentiability, analytic function, Cauchy-Riemann equations, Harmonic functions.
Unit-8
derivatives of elementary functions; contour integration, Cauchy’s integral theorem, Cauchy’s integral formula.

Textbook(s)
1. Churchill R. V. and Brown, J. W. Complex variables and applications, (McGraw-Hill International edition, 2006).
2. Hoffman K. and Kunze, R. Linear Algebra, 2nd edition, (Prentice Hall, 2008).

Reference book(s)
1. Dutta K. B. Matrix and Linear Algebra, (Prentice Hall of India, 2008).
2. Lang S. Linear Algebra, (Springer-Verlag, 2006).
3. Spiegel M. R. Theory and Problems of Complex Variables, Schum’s Outline Series,
(McGraw-Hill, 2000).
MI 204 Mathematical Methods and Partial Differential Equations (L2-T1 -P0 -CH3 -CR 3)
Unit -1
Partial differential equations: What are partial differential equations (PDEs), and where do they come from? Flows, vibrations and diffusions. Solutions of first order PDEs: Charpits method, Jacobi method.
Unit -2
Second-order linear equations and their classification. Initial and boundary conditions, with an informal description of well-posed problems. D'Alembert's solution of the wave equation. Duhamel's principle for one dimensional wave equation. Separation of variables: application of the method to simple problems in Cartesian coordinates for one dimensional wave and heat equations.
Unit -3
Calculus of variation: Variational problems with fixed boundaries-Euler’s equation for functionals containing first order derivative and one independent variable. Extremals. Functionals dependent on higher order derivatives. Functionals dependent on more than one independent variable. Variational problems in parametric form. Invariance of Euler’s equation under co-ordinate transformation. Variational problems with Moving boundaries-Functionals dependent on one and two functions. One sided vatiations. Sufficient conditions for an extremum - Jacobi and Legendre conditions.
Unit -4
Special Functions: Series solution of differential equations. Power series method. Bessel and Legendre equations. Bessel and Legendre functions and their properties. Convergence. Recurrence and generating functions.

Textbook(s)
1. Rao, K. S. Introduction to Partial Differential Equations, 2nd Edition (Prentice Hall of India, 2007).
2. Gupta, A. S. Calculus of Variation with Applications, (Prentice Hall of India, 1997).
3. Gelfand, I. M. and Fomin, S. V. Calculus of Variation, (Dover Publications, 2000).

Reference book(s)
1. Andrews, G.E., Askey, R. A. and Roy, R. Special Functions, (Cambridge University Press, 1999).
2. Sneddon, I. N. Elements of Partial Differential Equations, 4th ed., (Dover, 2006).
MI 205 Algebra (L2 -T1 -P0 -CH3 -CR 3)

Unit-1
Relations, Equivalence relations, Mapping and binary operations
Unit-2
Groups, subgroups, cosets, Lagrange’s theorem, Subgroup generated by a set, cyclic groups permutation groups, normal subgroups, quotient groups.
Unit-3
Polynomials, Euclid’s Algorithm, greatest common divisor, unique factorization of polynomials over a field F of numbers (statement only), Fundamental theorem of Algebra (statement only), roots and their multiplicity, Irreducible polynomials over Q, R, C.
Unit-4
Relationship between roots and the coefficients, Fundamental theorem of symmetric polynomial (without proof), Evaluation of symmetric functions of roots. Rational roots of polynomials with integral coefficients.
Unit-5
Descartes rule of sign, Strum’s theorem (statement only) Solution of cubic equation, Cardon’s method and solution of bi-quadratic equation.

Textbook(s)
1. Gallian, J. A. Contemporary Abstract Algebra, Narosa, 1995.
2. Mapa, S. K. Higher Algebra, Asoke Prakashan, Calcutta, 2006.

Reference book(s)
1. Herstein, I. N. Topics in Algebra, 2nd Edition (Wiley Eastern Limited, 1998).
2. Fraleigh, J. B. A First Course in Abstract Algebra, (Narosa, 1995).
3 Barbeau, E. J. Polynomials, (Springer 2003).
MI 206 Integral Equations and Transforms (L3 -T1 -P0 -CH4 -CR 4)
Unit -1
Elementary idea of Improper Integrals, their convergence, Beta and Gamma fnctions, their properties. Integral as a function of parameter (excluding improper integrals). Continuity and derivability of an integral as a function of a parameter.
Unit -2
Linear integral equations of the first and second kind of Fredholm and Volterra type: Definitions of integral equations and their classification. Eigen values and Eigen functions. Integral equations of second kind with separable kernels. Reduction to a system of algebraic equations. Method of successive approximations. Iterative scheme for integral equations of the second kind.
Unit -3
Integral Transform Methods: Fourier Series, Generalized Fourier series, Fourier Cosine series, Fourier Sine series, Fourier integrals. Fourier transform, Laplace transform. Inverse Transform: Inverse Laplace and Fourier Transform, Solution of differential equation by Laplace and Fourier transform methods.
Unit -4
Tensor: Transformation of coordinates, summation convention, kronecker delta. Definition of tensors, covariant, contravarient and mixed tensor, symmetric and antisymmetric tensors, outer and inner product of tensors, contraction, quotient law.

Textbook(s)
1. Parashar, B.P. Differential and Integral Equations, 2nd ed., (CBS Publishers, 2008).
2. Mikhlin, S. G. Linear Integral Equations, (Hindustan Book Agency, 1990).
3. Spain, B. Tensor Calculus, (Radha Publishing House, 2000).

Reference book(s)
1. Kanwal, R. P. Linear Integral Equation. Theory and Techniques, (Academic Press, 1991).
2. Poularikas, D. The Transforms and Applications, (CRC Press, 1996).
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