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Science & ResearchCMI Entrance Exam
Chennai Mathematical Institute
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परीक्षा सारांश
अवलोकन
आयोजक संस्था
Chennai Mathematical Institute
आपको क्या मिलेगा
Admission to B.Sc & M.Sc in Mathematics and Computer Science at CMI
नवीनतम सामग्री चक्र
2026
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Complete exam guide
Eligibility, pattern, syllabus, dates and official resources in one structured view.
EligibilityPending verification
Exam patternPending verification
Qualification pathway
Clear each applicable stage in order
Final selection or admission still depends on the published cutoff or merit list and any applicable counselling, document, medical, preference and vacancy rules.
Selection sequence
- 1
Written entrance examination
RequiredHeld on 2 May 2026 at centres throughout the country.
Entrance Examination Date: 2026-05-02
- 2
Interview
RequiredAn interview in Chennai follows the written test for the M.Sc. Mathematics and all Ph.D. programmes. The brochure does not describe an interview stage for the B.S. programmes.
Paper and stage details
What each stage contains
Written entrance examination
Questions
Not stated
Maximum marks
Not stated
Duration
Not stated
Interview
Questions
Not stated
Maximum marks
Not stated
Duration
Not stated
SyllabusPending verification
सभी 24 विषय और 30 अध्याय शामिल हैं — पूरे 266 टॉपिक यहाँ दिखाए गए हैं।
Mathematics
All topics normally covered up to 12th standard in the NCERT syllabus for mathematics
- relations and functions
- algebra
- calculus
- coordinate geometry
- vectors and matrices (up to 3 dimensions)
- counting
- probability
- all topics covered until 10th standard including in particular Euclidean geometry and basic number theory
You will need to know and be able to reason about standard real valued functions
- analyzing their roots and other quantitative/qualitative aspects of their graphs
- polynomials
- exponential
- logarithmic
- trigonometric
- inverse trigonometric functions
- functions built by combining these basic functions using the four arithmetic operations (e.g., rational functions) and composition
The following topics from number theory
- unique factorization of a natural number as a product of prime numbers
- GCD via Euclid’s long division algorithm and via Bezout’s lemma
- modular arithmetic
Complex numbers
- both in the form z = a + ib and in the form r e^{iθ} = r cos θ + i r sin θ where r = |z| = sqrt(a^2 + b^2) and θ is the appropriate angle (for nonzero z)
- roots of unity on the unit circle in the complex plane
- the statement of the fundamental theorem of algebra
Discrete Mathematics
Discrete Mathematics
- Elementary combinatorics
- principle of induction
- pigeon hole principle
- permutations and combinations
- basic finite set theory
- functions and relations
Logic
Logic
- Boolean logic
- truth tables
- boolean circuits — and, or, not, nand gates
Graphs
Graphs
- Basic definitions
- trees
- bipartite graphs
- matchings in bipartite graphs
- breadth first search
- depth first search
- minimum spanning trees
- shortest paths
Formal Languages and Automata Theory
Formal Languages and Automata Theory
- Regular expressions
- non-deterministic and deterministic finite automata
- subset construction
- regular languages
- non-regularity (pumping lemma)
- context free grammars
- basic ideas about computable and noncomputable functions
Algorithms
Algorithms
- O notation
- recurrence relations
- time complexity of algorithms
- sorting and searching (bubble sort, quick sort, merge sort, heap sort)
Algorithmic Techniques
Algorithmic Techniques
- Dynamic programming
- divide and conquer
- greedy
Data Structures
Data Structures
- Lists
- queues
- stacks
- binary search trees
- heaps
Probability Theory
Probability Theory
- Finite probability spaces
- Bayes theorem
- conditional probability
- elementary distributions
- expectation
- variance
- moments
- Markov and Chebyshev bounds
Calculus
Calculus
- Limits
- continuity
- differentiability
- functions of several variables
- derivatives and partial derivatives
- integral calculus
Linear Algebra
Linear Algebra
- Vector spaces
- linear operators
- eigenvalues and eigenvectors
- linear equations
- determinants
- linear independence
- inner product spaces
- symmetric and Hermitian matrices
Algebra
Algebra
- Groups
- homomorphisms
- 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
- 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
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
Real Line
- Limits
- continuity
- differentiablity
- Reimann integration
- sequences
- series
- limsup
- liminf
- pointwise and uniform convergence
- uniform continuity
- Taylor expansions
Multivariable
- Limits
- continuity
- partial derivatives
- chain rule
- directional derivatives
- total derivative
- Jacobian
- gradient
- line integrals
- surface integrals
- vector fields
- curl
- divergence
- Stoke’s theorem
General
- Metric spaces
- Heine Borel theorem
- Cauchy sequences
- completeness
- Weierstrass approximation
Topology
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
School Level Mathematics
School Level Mathematics
- Arithmetic and geometric progressions
- arithmetic, geometric and harmonic mean
- polynomials
- matrices (basic operations, inverse, transpose)
- determinants
- solving linear equations
- prime numbers and divisibility
- GCD
- LCM
- modular arithmetic
- logarithms
- basic properties of functions (domain, range, injective, bijective, surjective)
- elementary calculus (differentiation, maxima-minima, integration and its applications)
Discrete Mathematics
Discrete Mathematics
- Sets and relations
- combinations and permutations
- elementary counting techniques
- pigeonhole principle
- binomial theorem
- mathematical induction
- boolean logic and truth tables
Probability Theory
Probability Theory
- Elementary probability theory
- conditional probability
- Bayes theorem
- random variables
- density functions
- distribution functions
- standard distributions (Gaussian etc.)
- expectation and variance
- data interpretation
- summary statistics
Programming
Programming
- Ability to read and interpret algorithms written in simple pseudocode (variables, conditionals, loops)
Classical Mechanics
Classical Mechanics
- Newtonian Mechanics
- Variational Principles & Lagrange’s Equations
- The Central Force Problem
- Kinematics and Dynamics of Rigid Bodies
- Small Oscillations
- Hamilton’s Equations
- Canonical Transformations
- Hamilton-Jacobi Theory
- Special Relativity
Quantum Mechanics
Quantum Mechanics
- Physical Basis of Quantum Mechanics
- Schrodinger Equation
- Operators
- Eigenfunctions
- Eigenvalues
- Wavepackets
- One Dimensional Bound State and Scattering Problems
- Harmonic Oscillator
- Angular Momentum
- Hydrogen Atom
- Collisions in Three Dimensions
- Scattering from Spherically Symmetric Potentials
- Matrix Formulation of Quantum Mechanics
- Symmetry in Quantum Mechanics
- Identical Particles and Spin
- Stationary Perturbation Theory (Degenerate and Non-degenerate cases)
- Variational Method
- WKB Approximation
- Time-dependent Perturbation Theory
- Green’s functions
- Scattering Matrix
- Born Approximation and Partial Wave Analysis
Electrodynamics
Electrodynamics
- Electrostatics
- Electric Field in Matter
- Conductors
- Dielectrics
- Magnetostatics
- Magnetic Fields in Matter
- Electrodynamics
- Maxwell’s Equations
- Conservation Laws
- Electromagnetic Waves
- Potentials and Fields
- Radiation
- Special Relativity
Statistical Mechanics
Thermodynamics and Kinetic Theory
- Laws of Thermodynamics and Applications
- Maxwell-Boltzmann Distribution
- Transport Phenomena
- Conservation Laws
- Hydrodynamics
Classical and Quantum Statistical Mechanics
- Microcanonical, Canonical, and Grand Canonical Ensembles
- Density Matrix
- Ideal Gases
- Partition Function
- Ideal Fermi Gas
- Ideal Bose Gas
- Phase Transitions
Mathematical Physics
Mathematical Physics
- Matrices and Linear Algebra
- Ordinary Differential Equations
- Complex Analysis and Partial Differential Equations
- Fourier series and transforms
Important datesPending verification
2026 cycle
Latest confirmed cycle has concluded
Entrance Examination Date: 2026-05-02
Next examination date has not yet been published in StudyBddy's verified official record. The date above is historical—not an upcoming deadline.
Full published timeline1 completed · 0 awaiting dates⌄
Entrance Examination Date
Completed2026-05-02
Job profile & salaryPending verification
Notes
The CMI entrance exam is an admission test, not a recruitment examination.
CutoffsNot loaded
Previous-year papersPending verification
Books & study sourcesNot loaded
Official & trusted free resourcesPending verification
How to applyPending verification
- 1Fill the CMI Application Form in full detail on the official application portal and pay the application fee.
- 2If you qualify for direct admission through an Olympiad category, email admissions@cmi.ac.in with your application details and the qualifying category; you will receive a confirmation if you are exempted from the entrance exam.
- 3Otherwise, sit the written entrance examination at your chosen centre.
- 4Shortlisted candidates for M.Sc. Mathematics and the Ph.D. programmes attend an interview in Chennai.
FAQsPending verification
When is the CMI entrance examination held?
The 2026 examination was held on 2 May 2026 at centres throughout the country. The 2027 date has not yet been announced.
Can I skip the entrance exam?
Yes, in specific cases. B.S. applicants who qualified for IMOTC/EGMOTC, the Physics OCSC, or IOITC — or were shortlisted for EGOI team selection or won an INOI gold or silver medal in Class 11 or 12 — qualify for direct admission. Ph.D. Mathematics applicants with an NBHM PhD Fellowship go straight to interview, and Ph.D. Computer Science also admits through GATE and JEST.
What does CMI cost?
Tuition is Rs 1,25,000 per semester for the B.S. and for M.Sc. Mathematics and Computer Science, and Rs 2,50,000 per semester for M.Sc. Data Science. About 30-35 B.S. scholarships give a full four-year tuition waiver, and CMI offers partial and total waivers on economic grounds.
Is the B.S. three years or four?
From 2026 the programme is a 4-year B.S. (Honours), with an option to exit after 3 years with a B.Sc. degree by completing 112 credits including one Humanities elective.
Final eligibility and dates are always subject to the latest official notification. Content marked “Pending verification” is not presented as verified advice.