## CHENNAI MATHEMATICAL INSTITUTE

Chennai Mathematical Institute is a teaching and research institute in Mathematical science. It was established in the year 1989 as a part of SPIC foundation. Later in 1991, it was established as a autonomous institute. The research areas of the institution are Mathematics, Physics and Computer Science. The research areas in Mathematics are algebra, analysis, differential equations, geometry and topology. The research areas in Computer Science are formal methods in the specification and verification of software systems, design and analysis of algorithms, computational complexity theory and computer security. The research areas in Physics are quantum field theory and mathematical physics. The campus of the institution is located at Siruseri of five acres in Old Mahabalipuram Road which I the IT hub of Chennai which is been surrounded with a library and auditorium and all the other facilities for the students.

### Courses offered

- B.Sc. (Hons.) in Mathematics and Computer Science (3 year integrated course).
- B.Sc. (Hons.) in Mathematics and Physics (3 year integrated course).
- M.Sc. in Mathematics
- M.Sc. in Applications of Mathematics
- M.Sc. in Computer Science
- Ph.D. in Mathematics
- Ph.D. in Computer Science
- Ph.D. in Physics

**Entrance Examinations**

The Entrance Examination is conducted for B.Sc, M.Sc and Ph D courses.The eligibility Criteria is listed as below;

- B Sc (Hons) Mathematics and Computer Science: 12th standard or equivalent
- B Sc (Hons) Mathematics and Physics: 12th standard or equivalent
- M Sc in Mathematics: B.Sc (Math)/B.Math/B.Stat/B.E./B.Tech
- M Sc in Applications of Mathematics: B.Sc (Math/Physics/Statistics)/B.Math/B.Stat/B.E./B.Tech
- M Sc in Computer Science: B.E/B.Tech/B.Sc (C.S.)/B.C.A. or B.Sc (Math) with a strong background in C.S
- PhD in Mathematics: B.E/B.Tech/B.Sc (Math)/M.Sc (Math)
- PhD in Computer Science: B.E/B.Tech/M.Sc (C.S.)/M.C.A
- PhD in Physics: B.E/B.Tech/B.Sc (Physics)/M.Sc (Physics)

The examination centres where the exams are been conducted are;

- Ahmedabad
- Allahabad
- Bangalore
- Bhubaneswar
- Calicut
- Chennai
- Coimbatore
- Delhi
- Guwahati
- Hyderabad
- Imphal
- Kolkata
- Madurai
- Mumbai
- Nagpur
- Patna
- Pune
- Ranchi
- Shillong
- Silchar
- Srinagar
- Trivandrum

**Selection Procedure**

The selection procedure consists of written test and interview for PhD programmes. The eligible candidates from the written examination are called for the interview process. The interview is been held at Chennai.

**How to Apply**

- Download the online application form
- Fill all the details by the candidate itself
- Attach the photo and all other certificates along with the application
- Make the DD on the payment of Chennai Mathematical Institute
- Send the application form o the address provided in the notification

**Syllabus**

The Syllabus for the written examination for M.Sc and Ph.D is;

**Algebra.**

(a) Groups, homomorphisms, cosets, Lagrange’s Theorem, 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, differentiablity, 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.