The minor programme in mathematics is meant for the B.Tech. students of all disciplines (except B.Tech. in Mathematics and Computing) who have interest in mathematics and want to learn more than what are already covered in their basic compulsory mathematics courses. Courses like MA2091M and MA2092M will be also directly helpful for those who want to use this programme only for industry internships or industry placements. The other courses will help the students to learn mathematics apart from helping them to learn critical thinking and improve reasoning ability.

MA1092M Modern Algebra [3-0-0-6]

Formal properties of integers, equivalence relations, congruences, Groups, group homomorphisms, subgroups, cosets, Lagrange's theorem , normal subgroups, quotient groups, permutation groups; cyclic groups,  Groups actions, orbits, stabilizers, Cayley's theorem, conjugacy, class equation, Sylow's theorems and applications, Rings, ring homomorphisms, ideals, integral domains, Principal ideal domains, Euclidean domains, unique factorization domains, polynomial rings; Fields, characteristic of a field, field extensions, algebraic extensions, finite fields.

Texts:

1. J. A. Gallian, Contemporary Abstract Algebra, Eighth Edition, Cengage India, 2019.
2. D. S. Dummit & R. M. Foote, Abstract Algebra, Third Edition, Wiley, 2011

References:

1. I. N. Herstein, Topics in Algebra, Wiley, 2004
2. J. B. Fraleigh, A First Course in Abstract Algebra, Seventh Edition, Pearson, 2013

MA2091M Mathematical Statistics  [3-0-0-6]

Probability - probability spaces, random variables and random vectors, functions of random vectors, univariate and multivariate distributions, mathematical expectations, moment generating functions, convergence in probability and in distribution and related results; Sampling distributions; Point estimation - estimators, sufficiency, completeness, minimum variance unbiased estimation, maximum likelihood estimation, method of moments, Cramer-Rao inequality, consistency; Interval estimation; Testing of hypotheses - tests and critical regions, Neymann-Pearson lemma, uniformly most powerful tests, likelihood ratio tests; Correlation and linear regression.

Texts:

1. R. V. Hogg, J. W. McKean and A. T. Craig, Introduction to Mathematical Statistics, Eighth Edition, Pearson, 2020.
2. B. L. S. Prakasa Rao, A First Course in Probability and Statistics, World Scientific/Cambridge University Press India, 2009

References:

1. V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, Third Edition, Wiley, 2015.
2. G. Casella and R. L. Berger, Statistical Inference, Second Edition, Cengage Learning, 2006

MA2092M Scientific Computing  [3-0-0-6]

Errors; Iterative methods for nonlinear equations; Polynomial interpolation, spline interpolations; Numerical integration based on interpolation, quadrature methods, Gaussian quadrature; Initial value problems for ordinary differential equations - Euler method, Runge-Kutta methods, multi-step methods, predictor-corrector method, stability and convergence analysis; Finite difference schemes for partial differential equations - Explicit and implicit schemes; Consistency, stability and convergence; Stability analysis (matrix method and von Neumann method), Lax equivalence theorem; Finite difference schemes for initial and boundary value problems (FTCS, Backward Euler and Crank-Nicolson schemes, ADI methods, Lax Wendroff method, upwind scheme).

Texts:

1. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, Third Edition, American Mathematical Society, 2009 .
2. G. D. Smith, Numerical Solutions of Partial Differential Equations, Third Edition, Clarendon Press, 1986

References:

1. K. E. Atkinson, An Introduction to Numerical Analysis, Second Edition, Wiley, 1989.
2. S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw Hill, 1981.
3. R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, John Wiley, 1980

MA3091M Real Analysis  [3-0-0-6]

Metrics and norms - metric spaces, normed vector spaces, convergence in metric spaces, completeness, pointwise and uniform convergence of sequence of functions; Functions of several variables - differentiability, chain rule, Taylor's theorem, inverse function theorem, implicit function theorem; Introduction to Lebesgue measure and integral - measureable sets, measurable functions, Lebesgue integral, dominated convergence theorem, monotone convergence theorem

Texts:

1. N. L. Carothers, Real Analysis, Cambridge University Press, 2000.
2. J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, Second Edition, W. H. Freeman, 1993.

References:

1. M. Capinski and E. Kopp, Measure, Integral and Probability, Second Edition, Springer, 2007.

MA3092M Differential Geometry  [3-0-0-6]

Local theory of plane and space curves, curvature and torsion formulas, Serret-Frenet formulas, fundamental Theorem of space curves; Regular surfaces, change of parameters, differentiable functions, tangent plane, differential of a map; First and second fundamental form; Orientation, Gauss map and its properties, Euler's theorem on principal curvatures; Isometries, Gauss's Theorema Egregium; Parallel transport, geodesics, Gauss-Bonnet theorem and its applications to surfaces of constant curvature

Texts:

1. J. McCleary, Geometry from a Differentiable Viewpoint, Cambridge University Press, 1994.
2. A. Pressley, Elementary Differential Geometry, Springer, 2002.

References:

1. M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976.