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CMI Entrance Exam Syllabus 2025: Students who are willing to take admission in the Chennai Mathematical Institute must check the CMI Entrance Exam 2025 syllabus first. Applicants can take the downloaded copy of the CMI 2025 entrance exam syllabus from the official website at cmi.ac.in. The CMI entrance exam syllabus is important to score good marks in the examination. The Chennai Mathematical Institute released the separate entrance syllabus for every subject.
The CMI 2025 entrance exam syllabus contains the basic topics that are mainly related to 12 standards. The conducting body will likely conduct the CMI entrance exam in May 2025. Students are advised to complete their concerned CMI entrance 2025 syllabus a month before the examination and practise it regularly. The CMI applicants must read this article to know about the CMI entrance exam syllabus 2025 and their related things.
Also Read, CMI application form 2025
Candidates can get the CMI entrance syllabus 2025 pdf from the website by following these easy steps.
Go to the link cmi.ac.in.
Search for the ‘Admission’ tab and click over there.
Click on the ‘Entrance Exam Syllabus and Past Papers’ tab present on the right side of the web page.
A page containing links of the exam syllabus and the previous year paper is open to your screen.
Click on the desired link.
The CMI entrance exam syllabus will open to your screen in pdf format.
Download the syllabus and study by using it.
There are different courses offered by the CMI. Interested candidates can check the detailed CMI syllabus below.
Algebra | Geometry |
Calculus | Number Theory |
Relation and Function | Coordinate Geometry |
Vector | Matrices (upto 3 dimension) |
Counting | Probability |
All the NCERT topics for Mathematics from class 9 to 12 |
The Mathematics and Physics syllabus is the same as the syllabus of Mathematics And Computer Science. The entrance examination is a test of aptitude for the subjects featuring both multiple choice questions and problems requiring detailed solutions drawn mostly from the 12th standard. Students are advised to follow the same table and the link given.
Topics | Sub topics |
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, regular languages, non regularity (pumping lemma), context free grammars, basic ideas about computable and uncomputable functions. |
Algorithms | O notation, recurrence relations, time complexity of algorithms, sorting and searching (bubble sort, quick sort, merge sort, heap sort). |
Data structures | Lists, queues, stacks, binary search trees, heaps. |
Graphs | Basic definitions, trees, bipartite graphs, matchings in bipartite graphs, breadth first search, depth first search, minimum spanning trees, shortest paths. |
Algorithmic techniques | Dynamic programming, divide and conquer, greedy. |
Logic | Boolean logic, truth tables, boolean circuits — and, or, not, and, and gates. |
Check Link: Syllabus of MSc and PhD in Computer Science
Topics | Sub topics |
Algebra | (a) 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 (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, zeros 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, |
Check Link: Syllabus of MSc and PhD in Mathematics
Topics | Sub topics |
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 | Sets and relations, combinations and permutations, elementary counting techniques, pigeonhole principle, binomial theorem, mathematical induction, boolean logic and truth tables |
Probability Theory | Elementary probability theory, conditional probability, and Bayes theorem; random variables, density functions, distribution functions; standard distributions (Gaussian etc.); expectation and variance; data interpretation; summary statistics |
Programming | Ability to read and interpret algorithms written in simple pseudocode (variables, conditionals, loops) |
Check Link: Syllabus of MSc Data Science
The CMI exam pattern is different for different courses. The exam pattern has two sections. Part A and Part B. Questions will be asked both in MCQ and descriptive format. There is also negative marking in some questions. For UG candidates the marks are given in points. While for other courses the paper is set for 100 marks. The maximum time duration given is 3.5 hours.
Students who are preparing for the CMI entrance exam must follow some of the preparation tips to boost their preparation.
Go through the CMI entrance syllabus and exam pattern thoroughly.
Complete all the topics as fast as possible and start revising those topics.
It is very important to solve as many questions to score good marks in the examination.
Solve the previous year questions to enhance the preparation.Syllabus of MSc and PhD in Computer Science
Students are able to download the syllabus from the official website of the CMI Chennai at cmi.ac.in.
The entrance is conducted at UG, PG and PhD level.
The Central Mathematical Institute offers mathematics, data science, computer science and physics at different levels.
The major topics of the mathematics exam are algebra, probability, calculus, graphs, complex numbers and many more.
In the entrance exam both MCQ and descriptive questions are there.
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