CMI Entrance Exam Syllabus 2025 has been shared for each subject by the exam conducting institute on their official website for the academic session 2025-2026. The syllabus provides a common platform for assessing candidates' knowledge and abilities, ensuring fairness and transparency in the admission process.
Candidates should also check the CMI Entrance Exam exam pattern 2025 to know the structure and types of questions that will be asked in the examination and the depth of covering the CMI Entrance Exam 2025 syllabus will then be based on that. Both the syllabus and exam pattern play a pivotal role in the CMI Entrance Exam 2025 preparation strategy.
The CMI entrance exam 2025 will be held in a pen-paper based test mode for all courses on May 24, 2025. The question paper for the CMI entrance exam 2025 will be based on the key topics from each subject as mentioned on this page below:
NOTE: Students with exceptionally good performance in the National Olympiads in Mathematics, Physics and Informatics are exempted from writing the BSc entrance examination.
Latest Updates:
- CMI Entrance Exam 2025 Syllabus for MSc/PhD Computer Science
- CMI Entrance Exam 2025 Syllabus for MSc/PhD Mathematics
CMI Entrance Exam 2025 Syllabus for MSc/PhD Computer Science
The key topics for the question paper for MSc/ PhD CS are as under:
| Syllabus | Important topics |
|---|---|
| Discrete Mathematics Elementary probability theory |
Sets and relations, elementary counting techniques, pigeon hole principle, partial orders, |
| Logic |
Boolean logic, truth tables, boolean circuits — and, or, not, and, nand gates. |
| 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 no computable functions. |
| Algorithms | O notation, recurrence relations, the 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 |
Best Books to refer to for MSc-PhD Computer Sciences
- Frank Harary: Graph Theory, Narosa
- John Hopcroft and Jeffrey D Ullman: Introduction to Automata, Languages and Computation, Narosa.
- Jon Kleinberg and Eva Tardos: Algorithm Design, Pearson.
- C. Liu: Elements of Discrete Mathematics, Tata McGraw-Hill
Commonly asked questions
CMI Entrance Exam 2025 Syllabus for MSc/PhD Mathematics
The question paper will be based on the topics as under:
| Subject | Topics |
|---|---|
| Algebra Part A | Groups, homomorphism’s, 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 |
| Algebra Part B | Matrices, determinants, vector spaces, linear transformations, span, linear independence, basis, dimension, the 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, Liouville'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. |
| MSc Applications of Mathematics | The entrance test for MSc Applications of Mathematics will consist of Class XII / BSc level questions on the following topics:
|
Also Read: Previous Years Papers for CMI Entrance Exam
Best Books to refer for MSc-PhD Maths
| Subject | Best books |
|---|---|
| Algebra |
|
| Complex Analysis |
|
| Calculus and Real Analysis |
|
| Topology | Topology, James Munkres |
| MSc Applications of Mathematics |
|
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