The application of mathematical concepts generally covered up to the 12th level is given importance in the CMI admission exam. The main areas of the exam are Calculus, Algebra, and Geometry. However, there are additional questions on Combinatorics, Number theory, and a Variety of other Mathematical Disciplines. Moreover, candidates may encounter problems that test their mathematical thinking skills, such as logic puzzles. Instead of only testing memory and routine application of mathematical principles, the exam tries to measure independent thinking. The CMI admission exam encourages applicants to think critically and creatively in order to efficiently solve mathematical issues by providing difficult scenarios.
For Computer Science
| Syllabus | Important topics |
|---|---|
| Discrete Mathematics: Elementary Probability Theory | Sets and relations, elementary counting techniques, pigeonhole 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 non-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, and 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 |
For Mathematics
| Subject | Topics |
|---|---|
| Algebra Part 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 |
| 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, Rouché’s theorem, Morera’s theorem |
| Calculus and Real Analysis |
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| 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. |
| M.Sc Applications of Mathematics | The entrance test for MSc Applications of Mathematics will consist of Class XII / BSc level questions on the following topics:
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For Computer Science
For Mathematics
| Subject | Best books |
|---|---|
| Algebra |
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| Complex Analysis |
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| Calculus and Real Analysis |
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| Topology | Topology, James Munkres |
| MSc Applications of Mathematics |
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