#### Mathematics Syllabus - CMI Entrance Exam

Chennai Mathematical Institute ( CMI ) Ph.D Entrance Examination Mathematics Syllabus -2018

Algebra.

(a) Groups, homeomorphisms, cosets, Lagrange’s Theorem, group actions, Sylow Theorems, symmetric group Sn, conjugacy class, rings, ideals, quotient by ideals, maximal and prime ideals, fields, algebraic extensions, finite fields

(b) Matrices, determinants, vector spaces, linear transformations, span, linear independence, basis, dimension, rank of a matrix, characteristic polynomial, eigenvalues, eigenvectors, upper triangulation, diagonalization, nilpotent matrices, scalar (dot) products, angle, rotations, orthogonal matrices, GLn, SLn, On, SO2, SO3.

Complex Analysis.

Holomorphic functions, Cauchy-Riemann equations, integration, zeroes of analytic functions, Cauchy formulas, maximum modulus theorem, open mapping theorem, Louville’s theorem, poles and singularities, residues and contour integration, conformal maps, Rouche’s theorem, Morera’s theorem

Calculus and Real Analysis.

(a) Real Line: Limits, continuity, differentiability, Reimann integration, sequences, series, limsup, liminf, pointwise and uniform convergence, uniform continuity, Taylor expansions,

(b) Multivariable: Limits, continuity, partial derivatives, chain rule, directional derivatives, total derivative, Jacobian, gradient, line integrals, surface integrals, vector fields, curl, divergence, Stoke’s theorem

(c) General: Metric spaces, Heine Borel theorem, Cauchy sequences, completeness, Weierstrass approximation.

Topology. Topological spaces, base of open sets, product topology, accumulation points, boundary, continuity, connectedness, path connectedness, compactness, Hausdorff spaces, normal spaces, Urysohn’s lemma, Tietze extension, Tychonoff’s theorem.

#### Other Important Details About CMI Entrance Exam

##### Eligibility Criteria

Chennai Mathematical Institute CMI Ph D Entrance Examination Eligibility Criteria- Ph D in Mathematics Students with an M Sc degree in Mathematics or equivalent and students with a bachelor s degree in Engineering or Science with a strong aptitude for

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##### Application Procedure

Chennai Mathematical Institute CMI Ph D Entrance Examination Application Procedure- For Mathematics Computer Science and Physics When admissions are open you may apply online or request a printed application form either by post or in person For all the programmes

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##### Courses Offered

Chennai Mathematical Institute CMI Ph D Entrance Examination Examination Centers Ph D in Mathematics Ph D in Computer Science Ph D in Physics For other details visit https www cmi ac in admissions brochure cmi-brochure- pdf

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##### Examination Centres

Chennai Mathematical Institute CMI Ph D Entrance Examination Test Centers- For Mathematics Computer Science and Physics Selection for all PhD programmes will involve an interview at Chennai Ahmedabad Allahabad Bangalore Bhubaneswar Calicut Chennai Coimbatore Delhi Guwahati Hyderabad Imphal Indore Kolkata

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Chennai Mathematical Institute CMI Ph D Entrance Examination Contact Address- For Mathematics Computer Science and Physics Chennai Mathematical Institute H SIPCOT IT Park Siruseri Kelambakkam India Telephone - - Direct inward dialing details - - hellip - - Fax -

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##### Important Dates

Chennai Mathematical Institute CMI Ph D Entrance Examination Important Dates- middot nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Applications for August will open in March The exact dates will be announced later For other details visit https www cmi

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##### Physics Syllabus

Chennai Mathematical Institute CMI Ph D Entrance Examination Physics Syllabus - I Classical Mechanics Newtonian Mechanics Variational Principles amp Lagrange rsquo s Equations The Central Force Problem Kinematics and Dynamics of Rigid Bodies Small Oscillations Hamilton rsquo s Equations Canonical

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##### Computer Science Syllabus

Chennai Mathematical Institute CMI Ph D Entrance Examination Computer Science Syllabus - Discrete Mathematics Sets and relations elementary counting techniques pigeon hole principle partial orders Elementary probability theory Automata Theory Regular expressions non deterministic and deterministic finite automata subset construction

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