CMI Entrance Exam BSc Syllabus 2025: Download Subject/Section wise Syllabus PDF

Chennai Mathematics Institute Entrance Exam 2025 ( CMI Entrance Exam )

This exam is conducted for courses given below:
Manisha Kumari
Updated on Sep 17, 2024 15:54 IST

By Manisha Kumari, Associate Senior Executive

CMI Entrance Exam Syllabus 2025 will be 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. 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:

Q:   What is the official website for downloading CMI Entrance Exam 2025 syllabus?

A: 

Candidates preparing for CMI Entrance exam for the academic session 2025-2026 will be able to download the CMI entarnce exam syllabus 2025 byvisiting the official website of Chennai Mathematical Institute exam 2025. 

CMI has not released the CMI entarnce exam 2025 syllabus, therefore aspirants are left with the option of going through the CMI entrance exam 2025 syllabus. It is highly expected that CMI exam syllabus doesn't change year to year, so candidates are suggested to either go to the CMI exam 2024 official website and search for CMI exam syllabus there.

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Q:   When will CMI entrance exam 2025 notification releasing?

A: 

Chennai Mathematical Institute is expected to release the CMI Entrance exam notification for the academic session 2025-2026 in the fourth week of February 2025. Candidates who wish to get admission in the BSc, MSc degree programmes offered by the Chennai Mathematical Institute will be able to fill out the application form in the first week of March 2025, tentatively.

The announcement on the official website contains all important information about the exam, including the eligibility criteria, syllabus, exam pattern, exam dates, and application process. The examination will be conducted for eight degree (BSc, MSc, PhD) programmes.

Candidates are advised to keep checking the CMI website regularly for the latest updates on the CMI Entrance Exam 2025.

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Q:   What are the academic programmes offered by Chennai Mathematical Institute?

A: 

Admission through the CMI Entrance Exam will be made to the following programmes in 2024–25.

  • BSc (Hons.) in Mathematics and Computer Science 
  • BSc (Hons.) in Mathematics and Physics 
  • MSc in Mathematics.
  • MSc in Computer Science.
  • MSc in Data Science.
  • PhD in Mathematics.
  • PhD in Computer Science.
  • PhD in Physics (For PhD in Physics, candidates should write the Joint Entrance Screening Test)
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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

  1. Frank Harary: Graph Theory, Narosa
  2. John Hopcroft and Jeffrey D Ullman: Introduction to Automata, Languages and Computation, Narosa.
  3. Jon Kleinberg and Eva Tardos: Algorithm Design, Pearson.
  4. C. Liu: Elements of Discrete Mathematics, Tata McGraw-Hill
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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:

  • Sets, operations on sets. Prime numbers, factorization of integers and divisibility. Rational and irrational numbers. Permutations and combinations. Binomial theorem. Logarithms. Theory of quadratic equations. Polynomials and remainder theorem. Arithmetic, geometric and harmonic progressions. Complex numbers. Algebraic inequalities.
  • Functions, one-one functions, onto functions. Limits and continuity. Derivatives and applications to maxima and minima. Sequences and series.
  • Matrices, Rank of a Matrix, eigenvalues, the system of linear equations.

Also Read: Previous Years Papers for CMI Entrance Exam 

Best Books to refer for MSc-PhD Maths 

Subject Best books 
Algebra
  • Algebra, M. Artin
  • Topics in Algebra, Herstein
  • Basic Algebra, Jacobson
  • Abstract Algebra, Dummit and Foote
Complex Analysis
  • Functions of one complex variable, John Conway
  • Complex Analysis, L V Ahlfors
  • Complex Analysis, J Bak and D J Newman
Calculus and Real Analysis
  • Principles of mathematical analysis, Rudin
  • Real Analysis, Royden
  • Calculus, Apostol
Topology Topology, James Munkres
MSc Applications of Mathematics
  • Calculus, Volume 1, Tom M. Apostol.
  • Understanding Mathematics, K.B. Sinha et al, Universities Press, Hyderabad.

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