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.
| Syllabus | Important topics |
|---|---|
| Discrete Mathematics | Sets and relations, elementary counting techniques, pigeonhole principle, partial orders, |
| Elementary probability theory | |
| Logic | Boolean logic, truth tables, boolean circuits — and, or, not, and, and 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 |
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