Real quadratic forms, Reduction of pair of real symmetric matrices, Extrema of quadratic forms Classification of quadratic forms – Rank and signature Definiteness of matrices – Extrema of quadratic forms [3 Lectures] References:1. D. Credits:11

Syllabus: Pre-requisite: MTH102, None for M. a fantastic read Linear Transformations: Rank Nullity Theorem, isomorphism, matrix representation of linear transformation, change of basis, similar matrices, linear functional and dual space.

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J. Normal forms. Stein and R. Bayes’ risk, and its properties. D.

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Gopalakrishnan: Commutative Algebra, Oxonian Press. Credits:9

Credits3-0-0-0(9)PrerequisitesPrerequisites: Instructor’s consent. Reference materials:Conway: Operator Theory. Practical parallel computing, computational tools for optimization and implementation of least squares. Tree based methods; Classification and Regression Trees. A Pressley: Elementary differential geometry, Springer India.

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Mackie: Proof Theory and Automated Deduction, Kluwer, 1997. Engel’s theorem and Lie’s theorem. Solution of Linear Equations Homogeneous systems – General linear systems Sweep out method for solving linear systems. Standard statistical visualizations.

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(Time permitting: Finitely-generated abelian groups, Free groups, Composition series, Jordan-Hölder theorem, Nilpotent and solvable groups). Topics and concepts to be covered in the course includes: Dimension Reduction and Visualization Techniques; Chernoff faces, principal component analysis. Prodi: A primer of Nonlinear Analysis, Cambridge studies in advanced mathematics. Special focus will be given on rates of convergence of a Markov chain and comparing different MCMC algorithms.

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Lang: Algebra. Bapat, click here to read (Time permitting: Artinian local rings and structure theorem of Artinian rings, Tensor products and multilinear forms, Exterior and Symmetric Algebra, Direct and Inverse system of modules. Rao, H. )Reference materials:J. N.

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Completeness of PC with respect to the class of all Boolean algebras. Statistical Modelling; design, estimation and inferential aspects of multiple regression, Kernel regression techniques. Open problems. Computational Geometry: Line segment properties; Intersection of any pair of segments; Finding the convex hull; Finding the closest pair of points. Legendre polynomials and properties, Bessel functions and properties, Sturm comparison theorem, Sturm-Liouville boundary value problems, orthogonal functions.

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W. Curvature, Bianchi Identity, Sectional curvature. S. Conway: A First Course in Functional AnalysisRon Douglas: Banach Algebra Techniques in Operator Theory Credits:9

Syllabus: Pre-requisite: MTH301 / Instructor’s consent, Riesz Interpolation Theorem, Hilbert Transform, Hardy-Littlewood Maximal function, and BMO, Distributions, Important example have a peek at this site distributions, Calderon-Zygmund Distributions.

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Aims of the courseThe Coxeter groups find applications in many areas of mathematics. A number field is a finite field extension of the field of rational numbers. Lay, D. Computational implementations of drawing samples, density functions, mass functions, summary functions, numerical integration for expectations. Immersions, embeddings, regular value, level sets, submersions. The L-function of a modular form is a central object of study in number theory both from analytic as well as arithmetic point of view.

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 Credits:9

Syllabus: Pre-requisite(s): MTH 301, MTH 404/ Instructor’s ConsentHarmonic analysis on : Fourier Transform, basic properties, inversion formula, Plancherel formula, Paley-Wiener theorem, Young’s inequality. Credits:

Credits: 3-1-0-0 [11]Prerequisites:This is a compulsory course for 2-year M. e. Distribution of functions of random variables including order statistics; Properties of random vectors which are equal in distribution; Exchangeable random variables and their properties. Countable and uncountable sets. are discussed.

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Credits:9

Credits3-0-0-0 (9)PrerequisitesMSO201A: Probability and Statistics, consent of the instructor. 53IntegrationConformal mapping (for linear transformation), Contours and contour integration. Page and E. References:

Credits: 1-0-2-0 (5)Prerequisites:MTH208A: Data Science Lab 1Objectives:To demonstrate concepts being learn’t in concurrent elementary statistics and probability courses. Universal consistency results. Munkres: Topology: A First Course, Prentice-Hall, 1975.

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Classification and Discriminant Analysis Tools; classification based on Fisher’s discriminant functions, Bayes classifier, TPM and ECM minimizing classification rules, logistic discrimination rules, perceptron learning and Support Vector Machines. K. Focus will be on collecting, cleaning, and organizing data, and presenting clean insights via interactive web-based apps. P. Cluster Analysis: hierarchical and non-hierarchical techniques.

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(Time permitting: Simple transcendental extension and Luroth’s theorem. Amarnath, An Elementary Course in Partial Differential Equations, Narosa Publications Credits:11

Syllabus: Pre-requisite: MSO201 / Instructor’s consentBrief review of distribution theory of uni-dimensional random variables. .

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