CMI Entrance Exam Syllabus 2025: Download Latest Syllabus PDF

Discrete Mathematics

Elementary probability theory

Logic

(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.

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.

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.

• Algebra, M. Artin
• Topics in Algebra, Herstein
• Basic Algebra, Jacobson
• Abstract Algebra, Dummit and Foote

• Functions of one complex variable, John Conway
• Complex Analysis, L V Ahlfors
• Complex Analysis, J Bak and D J Newman

• Principles of mathematical analysis, Rudin
• Real Analysis, Royden
• Calculus, Apostol

• Calculus, Volume 1, Tom M. Apostol.
• Understanding Mathematics, K.B. Sinha et al, Universities Press, Hyderabad.